by Brian Tomasik
First written: 27 Dec. 2015 to 3 Feb. 2016; last update: 25 Oct. 2016

## Summary

This essay aims to quantify the impact of Brazilian beef production on wild-animal (in particular, wild-insect) suffering. It provides an interactive calculator for estimating a Bayesian probability distribution for the net impact of Brazilian beef, considering new rainforest destruction for cattle pasture, preventing existing land from reverting to its native state, greenhouse-gas (GHG) emissions, and suffering endured by the cattle themselves.

The conclusion is that rainforest-beef production probably reduces wild-insect suffering. In fact, purchasing one kg of Brazilian beef prevents insect-years of suffering as a median estimate and insect-years in expectation. The sign of this conclusion could flip around if you substantially change certain input parameters -- particularly if you think death by burning is many times more painful than predation and other non-burning deaths.

Rainforest beef probably reduces several times more suffering per kilogram than soy or palm oil from rainforest areas, although bigger fractions of soy and palm oil are exported than the fraction of Brazilian beef that's exported.

This piece is only a small input to the broader analysis of the net impact of beef consumption in general, since only a small fraction of the beef consumed in Europe and especially the US comes from rainforest regions. The net impact of beef produced in Europe or the US is less clear, though it's plausibly also positive for wild animals -- especially in the case of grass-fed beef.

Part of my goal with this piece was to challenge ideas that we can't know enough to make statements about our impacts on ecosystems. Obviously my analysis still has huge uncertainty, but it illustrates that we can make progress by actually learning about relevant ecological details rather than priding ourselves on how ignorant we are.

## Introduction

Veg*an advocates sometimes point out that beef production contributes to loss of tropical rainforests. While they intend this as an argument against eating cattle, those who think wild animals experience more suffering than happiness on balance may look on this fact favorably. This piece aims to estimate the net impact of rainforest beef production on wild-animal suffering.

In this piece I focus on Brazil as a prototypical example of a country that produces rainforest beef. This is appropriate because Brazil was also the biggest beef exporter as of 2006a:

However, the analysis should roughly translate to other countries where beef production displaces rainforest. (My calculations will not translate "out of the box" to beef production in temperate grasslands, etc.)

Nearly 20% of world beef production is from South America as a whole. Rainforest degradation due to cattle farming has been severe in other Latin American countries like Costa Rica, where the majority of rainforest has been lost in recent decades. That said, cattle-driven deforestation is not much of an issue in Africa or Asia.

### Land-use changes by country

This paper, published in 2007, compiled the following predictions for land-use changes by 2010:

The total predicted increase in pasture for Brazil is ~17 million hectares, while for all other countries in the table combined, it's ~11 million hectares.

## How much beef sold in rich countries comes from Brazil?

While veg*ans like to highlight that "Cattle ranching is now the biggest cause of deforestation in the Amazon", what they don't as often say is that only a small fraction of beef consumed in rich countries comes from Brazil.

The biggest consumer of Brazilian beef is Brazil itself:

While the above figure shows ~2 million tons of exports by 2005-2006, this page reports a much lower number for 2012: 0.265 million tons of exports. I'm unsure what accounts for this discrepancy; maybe it's just an error in the 2012 figure.

This paper says: "In 2004 Brazil became the world’s leading beef exporter, with 38% of its exports destined for the EU, 12% for the Middle East, and 10% for Russia (MDIC 2005)."

Fresh beef is converted into burgers sold in fast-food restaurants and grocery stores across Brazil, Russia, Venezuela, and a number of other countries. Processed meat finds its way into canned products in Europe and America, while leather goes to China, Italy, Vietnam, and Hong Kong where it is used in shoes and apparel sold worldwide.

The interactive graphic on this page shows the biggest importers of Brazilian beef in 2014:

That said, even if you're in a country that doesn't import much Brazilian beef, some actions you might take will affect Brazilian beef consumption. For example, supporting veg ads in countries that do eat Brazilian beef would (slightly) reduce rainforest loss.

### United States

Most beef consumed in the US is produced at home. In 2014, US beef consumption was 24.1 billion pounds, with only 2.947 billion pounds carcass weight of imports, 0.602 billion pounds of which came from Canada. Significant imports also come from Australia and New Zealand. "U.S. imports from both Argentina and Brazil are restricted to cooked products because of disease restrictions, but these two countries provide a significant portion of the total cooked beef imported into the United States."

Imports from Brazil in particular were 37,000 metric tons in 2014, which is 0.082 billion pounds. Brazil's agriculture ministry claims that by 2020, 100,000 metric tons of fresh beef might be imported to the US from Brazil. Even if future beef imports are somewhat higher than they are now -- say 0.3 billion pounds -- Brazilian beef would constitute only 0.3/24.1 = 1% of US beef consumption. So considerations of rainforest destruction are unlikely to dominate calculations of the net impact of beef consumed by Americans.

That said, Brazilian exports occupy a larger percentage of processed beef in the US, such as "the frozen beef used on pizzas or the stuff used in fast-food hamburger patties."b This study reports that in 2002, the US imported 46,000 metric tons of processed beef, relative to 148,000 metric tons exported from Brazil as a whole -- i.e., 31% of Brazil's processed beef went to the US.

In Dec. 2015, the US Congress repealed the "country-of-origin labeling rule", as a result of which "America could [...] see an influx of imports from Australia, New Zealand, and Brazil."

### European Union

Collectively, the EU imports quite a bit more Brazilian beef than the US:

In this table, CWE means "carcass weight equivalents". I couldn't figure out which EU countries were included here, but the source text mentions EU-25 in other places, so I'll assume that. The population of EU-25 in 2004 was 457 million, and per-capita consumption of beef + veal in 2007 was about 12 kg retail weight. Later in this piece I report an estimate that ~68% of carcass weight ends up as edible beef, so 12 kg edible beef is 18 kg carcass weight. Over 457 million people, that amounts to 8100 million kg of carcass weight consumed, or 8100 thousand metric tons. Given 472 thousand metric tons of Brazilian carcass weight imported in 2007 based on the above table, this suggests that ~(472/8100) = 6% of beef consumed in the EU is from Brazil. And the percentage from all rainforest-rich countries combined is a bit higher.

This report, citing France's National Interprofessional Office for Meat, Livestock and Agriculture, says "Between 1990 and 2001, the percentage of Europe's transformed meat imports that came from Brazil rose from 40% to 74%." That's quite a high percentage (although it's a fraction of imports, not of total "transformed beef" sold in the EU, which might also include domestic production). If something like this is still true today, then at least eating "transformed beef" in the EU seems to contribute nontrivially to Brazilian beef farming.

## Moratoria and declining deforestation rates

Surprisingly, deforestation rates in Brazil have declined by about 5-fold since 2004. This decline is not just due to economic fluctuations: "Deforestation rates have continued to fall both before and after the recession of 2008-2009, and through the recent years of record agricultural prices". Two important drivers of the reduction in deforestation have been recent moratoria in the Brazilian soy and beef industries against buying products from newly deforested land.

The soy moratorium begain in 2006 in response to pressure from environmentalists and other activists. This moratorium is still in effect as of early 2016 and has significantly reduced new deforestation due to soy. One article says:

The recent detailed examination by Macedo et al., of soybean production and deforestation in Mato Grosso, where the industry’s expansion has been concentrated, reinforces these conclusions and provides evidence that the link between soy and deforestation—strong until recently—has now been broken.1,15,16

That said, loss of Cerrado land for soy production remains more of an issue than in the Amazon -- see the figure at the top of this page.

In 2009, activist pressure led four major cattle producers to declare a similar moratorium (the "G4 cattle agreement") on beef from newly deforested land. A 2015 study reported that the moratorium had been very effective. For example: "Before the agreement, 40% of JBS-Friboi’s direct suppliers were linked to recent deforestation. By 2013, the number had fallen to less than 4%." That said:

The G4 Agreement only extends to three meatpacking companies, which leaves about half of the documented slaughter in the Brazilian Amazon exposed to relatively minimal (if any) monitoring for deforestation and illegal activities. In addition, direct suppliers are the only segment of the supply chain that is current covered by these monitoring efforts. Cattle can move from calving ranches and fattening farms through middlemen and other indirect suppliers without being monitored. Preliminary evidence indicates that the majority of deforestation is now likely occurring on these indirect supplying ranches.

As far as I know, this moratorium doesn't apply to other countries. For example, as of 2011, Colombia didn't have a similar moratorium. But beef exports are also less important for Colombia than for Brazil. This post shows that the rate of deforestation has remained about constant or maybe increased slightly in non-Brazilian countries between the first half and the second half of the decade 2000-2010.

Since 2011, Indonesia has had a moratorium on new "concessions" of land for palm oil. The moratorium was renewed in 2015. By 2014, 96% of palm oil worldwide was covered by policies of no new deforestation, although it remains to be seen how effective the implementation will be.

The website Supply Change reports on how well different companies are performing in terms of reducing deforestation. If you think deforestation is good for wild animals on balance, you might take these deforestation-reduction achievements as negative rather than positive.

## Suffering units

This page calls rainforests "the last unspoiled bits of paradise on our planet." But for many animals in rainforests, life is difficult, and death is agonizingly painful. Given that many species give birth to large numbers of offspring, most of which die before maturity, I think many people would consider the lives of most wild animals, especially most wild insects, to be not worth living. Regardless, in this piece, I focus exclusively on reducing suffering rather than on the moments of happiness that many wild animals also experience.

I measure suffering in the unit of "insect-years". One insect-year is the average suffering that a population of one wild insect experiences over one year. This doesn't mean I assume a single insect lives for a whole year. Rather, I mean this: Picture a constant population size of N insects, with some being born and some dying all the time. The total suffering in this population over one year, including from the painful deaths of insects, constitutes N insect-years. For example, if in that population, there's an average of 10 * N insect deaths per year (including infant mortality), then an insect-year of suffering would include 10 insect deaths as part of what it encompasses. And if we think death is a particularly severe form of suffering, these deaths might comprise a majority of the insect-year's suffering.

We can describe suffering by larger animals in terms of insect-years by trade ratios between species. For example, if you think a frog counts 5000 times more than an insect, then a frog-year of suffering would, very roughly, be about 5000 insect-years (ignoring differences in how painful the per-year lives of insects vs. frogs are).

Note that when I talk about "insects", I mean "bugs" more generally -- insects, arachnids, worms, and other creepy crawlies. I use "insect" and "bug" interchangeably.

## Framework for how rainforest beef affects wild-animal suffering

Consider the Brazilian beef industry as a prototypical case of rainforest-grown beef. Some parts of Brazil are established pasture, while other parts are being newly deforested to create more pasture for cattle.

### Reducing rainforest

The most salient impact of rainforest-grown beef is clearing of pristine rainforest land to make way for cattle pasture. Often this is done by burning. Cattle pasture supports lower wild-animal populations than native rainforest, and even if the pasture is abandoned and allowed to regrow as forest, it will be less productive than before. This has the effect of reducing the populations, and hence the suffering, of rainforest animals for many years to come.

In particular, suppose virgin rainforest supports a density D of insects per hectare. Once cleared, even if the land is allowed to regrow secondary forest, it will support only s * D insects per hectare for the next Y years (after which it becomes mature forest again). Then clearing the forest once now reduces suffering from D * Y insect-years per hectare to s * D * Y insect-years per hectare.

Of course, in practice, the land will not just immediately be allowed to revert to secondary forest but will be used for grazing or crop cultivation. However, I'll consider that effect in the next section. Since grazing produces new meat every year, the impact of grazing in any given year should be attributed to the specific meat produced in that year. Hence, the impact of clearing virgin forest should only be measured as what it by itself accomplishes -- namely, turning old-growth forest into less productive secondary forest for some decades. The additional effects of sustained grazing should be attributed to later meat production.

Of course, in reality, initial deforestation may reduce the costs of later grazing, just like road construction in the rainforest reduces the costc of slashing and burning it:

The construction of roads to access logging, oil, and mining sites in the rainforest opens vast stretches of forest to exploitation by landless peasants who are responsible for the majority of rainforest destruction today.

There's a complex web of causation among activities. But as a first approximation, I try to attribute a given impact only to the activity that immediately causes it, and doing this avoids double-counting.

#### The pain of burning

One additional consideration is that burning the rainforest causes immense pain to the animals in the fire's path. It's unclear to me how many animals die in flames vs. how many die of suffocation (vs. how many fly or run away), but the number that die in flames might be nontrivial, especially for invertebrates that have lower metabolic requirements and so aren't as quickly suffocated. Death by fire seems like it might be several times worse than a typical death, and insects display aversion to heat, so this judgment may not be mere anthropomorphism.

To account for this fact, suppose that death by burning is b times worse than the average non-burning death, and suppose that an insect-year of suffering is equivalent to the suffering entailed by diy non-burning deaths. Then burning causes an additional b/diy insect-years of suffering per insect burned.d

However, for every insect burned, the population of insects is reduced by one, at least for some time period of tb years until the insect population recovers. (For example, if it takes 2 months for insects to return to a burned field, tb = 2/12.) Hence, burning prevents tb insect-years of suffering per burned insect.

All told, the insect-years of suffering resulting from burning one bug is (b/diy - tb), and the impact of burning D bugs per hectare is then D * (b/diy - tb) insect-years per hectare. This calculation implicitly assumes that burning kills all bugs, which is not true, especially since some bugs may live underground. However, this inaccuracy doesn't matter much because burning is a one-time impact, so this term is small compared with other parts of the analysis.

Since the first instance of burning a forest is a one-time suffering impact, it isn't multiplied by Y. Hence, the total reduction in suffering is (1 - s) * D * Y - b * D = D * [(1 - s) * Y - (b/diy - tb)].

#### Multiply by number of hectares and animal populations

Let C be the number of hectares that the Brazilian beef industry as a whole clears per year. Total suffering reduced per year from this component of the calculation is then C * D * [(1 - s) * Y - (b/diy - tb)] insect-years per year.

Let N be the world population of (sentience-weighted) wild animals as measured in insect units. For example, if we think insects dominate in importance, N is approximately the world population of insects: ≈1018. I'll rewrite D to be a function of N. The reason to do this is that I'll later draw random values for parameters from their Bayesian probability distributions, and if I drew D separately from N, then the two values wouldn't be correlated, whereas in fact, they should be pretty closely related. Let A be the total area of land on Earth. Then N/A is the average insect density on Earth's land. Presumably the insect density D in rainforests is several times bigger than that -- say D = u * N/A for some u.

### Changes on land not newly cleared

In addition to creating pressure to clear new rainforest, grazing occupied already cleared land. In this section, I divide grazing land into two very general types:

1. former rainforest
2. Cerrado, which is tropical savanna (i.e., grassland with some trees).

Let the total amount of grazed land be H hectares, and let frf be the fraction of this that's former rainforest. I assume this fraction would return to secondary forest if it were to stop being grazed. The fraction 1-frf I assume would return to savanna if left ungrazed.

#### Rainforest

Grazing not only clears new rainforest land but also keeps existing deforested land in a grazed state rather than letting it revert back to secondary forest.e In particular, I assume that for every year that land is grazed, its opportunity to revert back to secondary forest is delayed by a year, and hence its eventual return to old-growth forest is delayed by a year.f

Let insect densities per hectare on grazed land be g * D. By preventing development of secondary forest, grazing changes insect abundances per hectare from s * D to g * D, and by delaying return to old-growth forest, grazing delays a change from s * D to D by one year. Hence, the total impact is effectively to allow g * D rather than D insects per hectare. Over all frf * H hectares of grazed land, the suffering prevented or created by grazing is (1 - g) * D * frf * H insect-years per year.

Maintaining land in a grazed state may require reburning it every few years. Regular burning matters more to the overall calculations than the one-time burning impact when clearing new rainforest, so I'll be a bit more careful with this calculation. The suffering impact per burned bug from before was (b/diy - tb). However, now I'm going to add an extra component to the calculation to account for the fact that fire destroys biomass that would have been decomposed organically, in part by detritivorous bugs.g Let bb be (the bug-years of suffering that would have been created by decomposition of the biomass that was instead burned away insentiently by fire) divided by (the number of bugs burned). Thus, now the suffering impact per burned bug is (b/diy - tb - bb).

There are some additional factors to consider. The population of bugs at the time of burning may differ from the average population of bugs throughout the whole year. The average population of bugs per hectare throughout the year is g * D, and suppose that the population at the time of burning is mb * g * D. Also, only some fraction fb of the bug population actually gets burned, since some bugs may be underground or otherwise escape the flames. Finally, suppose that burning one hectare of pasture leads fires to spill over into additional, non-pasture fields. Let the ratio of total area burned to pasture burned be rb. Suppose burning happens once every B years. Then the total insect-years of suffering per grazed hectare per year is g * D * rb * fb * mb * (b/diy - tb - bb) / B. For shorthand, let's denote this expression by g * D * Pb (where "Pb" stands for "pain of burning").

Over frf * H hectares of grazed land, suffering from burning is frf * H * g * D * Pb per year. Thus, total suffering reduced per year by pasturing on former rainforest land is (1 - g) * D * frf * H - frf * H * g * D * Pb = D * frf * H * [(1 - g) - g * Pb].

The following figure illustrates the variables discussed so far, ignoring painfulness of burning:

Let the insect density of Cerrado be Dc, where Dc = uc * N/A for some uc. Grazing keeps the insect densities of the Cerrado at gc * Dc rather than Dc. And as with rainforest, Cerrado may be burned every few years. I'll assume that all parameters in the expression for Pb are the same as above. Then total suffering reduced by Cerrado grazing is Dc * (1-frf) * H * [(1 - gc) - gc * Pb].

### Climate change

Clearing rainforest also has the effect of emitting GHGs, due to burning or decomposing of the forest biomass. In addition, the cattle raised also emit methane and require other energy-intensive inputs. These contribute to climate change, which will affect global populations of insects and other wild animals.

Let N * pcl ("cl" stands for "carbon, long-term") be the increase in insect-years of suffering over a very long time period resulting from an extra metric ton of CO2 emissions, and let N * pml be the same for methane. N * pcs ("s" stands for "short-term") is the increase in insect-years of suffering from CO2 only over the next ~100 or so years, and N * pms is the analogous quantity for methane. Because CO2 emissions from burning or decaying rainforest vegetation should in principle be re-sequestered in the further future, we should only count the short-term wild-animal impacts of that CO2.h

First, let's examine CO2. When old-growth rainforest is destroyed, CO2 is released into the atmosphere for some time, until that CO2 is re-sequestered once the forest returns to an old-growth state. If the old-growth forest were merely burned and then allowed to recover, without any grazing, there would be secondary forest for Y years and then old-growth forest thereafter. Let cog be the metric tons of CO2 sequestered by an old-growth forest per hectare and cs be the same for a secondary forest. N * pcs represents the insect-years of suffering created by the effects of a metric ton of CO2 over ~100 years. Assuming a constant impact per year, the impact over just Y years would be roughly N * pcs * (Y/100) * (cog - cs) insect-years per hectare, and this should be multiplied by C newly destroyed hectares per year.

Next, let's consider the effect of grazing on land that's already pasture. As we saw previously, such grazing has the effects both of delaying regrowth of secondary forest and of creating pasture rather than secondary forest. Let cg be the metric tons of CO2 per hectare sequestered by a grazing pasture. An extra year of failing to re-sequester this CO2 has roughly 1/100 of the total impact of climate change over 100 years. So the suffering due to climate change here is N * pcs * (1/100) * (cog - cg) insect-years per hectare per year, and this is multiplied by frf * H hectares grazed on land that used to be rainforest. For grazing land that used to be native Cerrado, the corresponding expression is (1-frf) * H * N * pcs * (1/100) * (cc - cg), where cc is carbon stored by native Cerrado grassland.

Now we can do methane. Let the metric tons of methane released per hectare of newly burned rainforest be rm. The global-warming impact of methane itself is concentrated in the first few decades, because methane has a short lifespan. Methane eventually degrades into CO2, which would be resequestered when the rainforest returns after Y years. Since the impact of methane is clearly not evenly distributed over the next ~100 years, I won't multiply by Y/100 like I did before. Rather, I'll assume methane released for Y years has the same impact as methane released for 100 years. So the methane impact from new deforestation is C * N * pms * rm insect-years per year.

Finally, we consider emissions due to factors other than land-use change. Let T be the carcass weight in kg of beef produced per year. Let tc be the metric tons of CO2 released due to causes other than land-use change per kg of beef carcass weight, and tm is the analogous number for methane. Then the impact from these emissions is N * pcl * tc * T + N * pml * tm * T = N * T * (pcl * tc + pml * tm). Here I use long-term climate-change impacts for both CO2 and methane because these emissions won't be re-sequestered by default.

### Suffering of cattle raised and slaughtered

The total weight of cattle killed in Brazil is T kg per year. Let W be the average weight of a mature cow in kg. (In this piece, I use "cow" in its colloquial, gender-neutral sense to refer to any bovine, although technically a cow is defined specifically as an adult female.) The number of cattle killed per year would then be T/W. Suppose each cow is killed when it's K years old. A stationary population of cows would thus be K * T/W, implying that many cow-years of suffering per year. Let Q be the number of times more that a cow-year counts than an insect-year, i.e., Q is the number of insect-years of suffering per cow-year of suffering. Then the total suffering of cattle would be Q * K * T/W insect-years per year.

### Putting it all together

Adding together the four factors described above (with negative signs applied to climate change and cattle suffering) gives an overall amount of suffering reduced per year. If the result is a positive number, that means suffering decreases on balance.

To make the output of this calculation more meaningful, let's divide it by the number of kg of edible beef produced per year. The number T is carcass weight of beef, which is somewhat more than the weight of the edible end product. Let x be the fraction of the carcass weight that's edible, and pretend for simplicity that other parts of the carcass have no economic value. Then the total edible weight produced is x * T, and the quantity (total insect-years of suffering per year) / (x * T) shows the suffering created or prevented by producing 1 kg of edible rainforest beef.

Then, to convert this into the impact of increasing demand for rainforest beef by 1 kg, we can multiply it by what Animal Charity Evaluators calls the "cumulative elasticity factor", which I'll denote by ec.

The final result is the expected amount of suffering created or prevented per 1 kg of rainforest-grown beef bought.

## Limitations of my analysis

### Ignoring non-insect wild animals

In this piece, I ignore suffering by wild animals bigger than insects. One reason is that insects probably dominate in total sentience, unless you care drastically more about bigger animals. This piece says:

in tropical rain forest near Manaus, in the Brazilian Amazon, each hectare (or 2.5 acres) contains a few dozen birds and mammals but well over one billion invertebrates, of which the vast majority are not beetles this time but mites and springtails. There are about 200 kilograms dry weight of animal tissue in a hectare, of which 93 percent consists of invertebrates. The ants and termites alone compose one-third of this biomass.

This piece cites even higher invertebrate biomass:

In terms of biomass, insects in tropical forests constitute several tons per hectare compared to a few kilograms per hectare for birds and mammals (reviewed in Dajoz 2000).

Termites, half-blind distant cousins of cockroaches. There are so many millions living in this grassland that their combined weight is far greater than that of all the mammals living here put together.

Assuming there are ~1013 reptiles and amphibians in the world compared with ~1018 insects, and assuming these proportions hold true in rainforest specifically, we would need to consider a salamander or snake about 100,000 times as important as an insect before vertebrate animals would become relevant to the calculations.

Moreover, the factors that I discuss below probably tend to affect populations of bigger animals in similar ways as they affect insects, so the overall sign of Brazilian beef's impact probably wouldn't change even if only vertebrates were considered.

### Ignoring water pollution

This piece doesn't count some impacts of cattle production, like eutrophication and other forms of water pollution. Including those factors would probably suggest a bigger reduction in long-term wild-animal suffering, though the sign of net impact of eutrophication isn't obvious.

### Ignoring cattle feed

Most Brazilian beef is basically entirely pasture-fed. This paper (p. 21, Table 3.4) reports that only 5% of Brazilian beef farms are intensive ones that use mostly feed-lots. Another 15% of farms are semi-intensive; some of them may use creep feeding but still mostly feed native or planted grasses. I don't know if the fraction of cows in feed-lots is higher than 5% if intensive farms tend to be bigger than non-intensive farms? But even if so, I would guess that most Brazilian cows are still grass-fed. This is consistent with what I've seen in pictures and videos of Brazilian beef production.

The current piece ignores the wild-animal impacts of growing crops to feed non-grass-fed cows. That said, a section at the end of this piece begins to explore a wild-animal evaluation of feed-lot beef production (in rich countries, not in Brazil), and it concludes that even if crop cultivation is net bad in rich countries (which is unclear), that fact is relatively unlikely to render as overall bad the process of cattle production that also includes pasturing. Moreover, crop cultivation in rainforest countries like Brazil seems quite likely to be positive because the land that would have existed absent crop farms would probably have been much richer and more insect-dense. This point makes it even less likely that consideration of the feed given to a minority of Brazilian cows would overturn the apparently positive sign of expected net impact of Brazilian beef.

### Not fully considering beef substitution on world market

If you specifically aimed to buy beef from Brazil, you might slightly increase its price and lead international consumers to substitute away to some degree. In that case, the analysis in this piece would somewhat overstate the impact of buying Brazilian beef. However, I suspect that few people are able to explicitly buy beef from Brazil. Rather, in most cases, the conclusions in this piece will serve as one component of an evaluation of the total impact of buying beef in general, which means buying beef from the suite of all countries that produce it.

Substitution on the world market might be somewhat captured by the cumulative elasticity factor, but I think the cumulative elasticity factor doesn't tell the whole story. Simple supply and demand curves assume a single price for the product. But if Brazilian beef becomes more expensive relative to beef in other countries, then we don't have a single price for the product; instead, we have something more analogous to several markets for slightly different products (Brazilian beef, American beef, EU beef, etc.) that are substitutes. I don't know enough economics to model this appropriately, but I assume that considerations of substitution in international markets wouldn't change the result by more than a factor of ~2 or something, and they seem unlikely to change the sign of the result.

### Ignoring substitution away from other meats

In some cases, people who eat more beef will eat less of other farm animals, like pigs and chickens. Insofar as beef generally seems more likely to be positive for wild animals than pork/poultry and is less bad per kg for the farmed animals themselves, this seems probably to be a net win.

Other actions that affect consumption of Brazilian beef (such as veg outreach) don't necessarily cause substitution toward or away from eating other kinds of animal flesh.

### Total vs. marginal impacts

Because it's difficult to determine whether a given Brazilian beef product came from existing or newly deforested pasture, and because demand for one type of beef probably creates demand for the other type due to substitution by other consumers, I consider the aggregate impact of Brazil's whole beef industry.

That said, one could also argue that marginal beef consumption would have more deforestation impact than Brazil's average, since new land needs to be cleared to increase total production (assuming that cattle-grazing efficiency gainsi alone don't suffice to increase output). For example:

The domestic consumption of beef in Brazil has been relative stable during the past decade. In 1997, almost the total beef production (97 %) was consumed within Brazil, while in 2006, ~75 % of production was consumed internally. The overall production increase over the past decade (approximately 2.16 MT CWE) is driven by increased demands on the export market, not by domestic demands.

If we assume that a stable domestic supply of beef could be produced without expanding into new rainforest land (which is probably not totally true, especially since pasture land may become degraded after a few years, combined with the fact that it may be cheaper to expand than continue farming existing pasture for various other random reasons), then these numbers suggest that much of new deforestation would be attributable to exports.

This report likewise says that in the 1990s-2000s, "the growth in Brazilian livestock production - 80% of which was in the Amazon - was largely export driven".

About half of the growth in production between 1997 and 2006 came from expanding into the rainforest-rich Legal Amazon Region:

there has been a strong increase in beef production in Brazil, from 6.44 to 8.6 million tonnes (MT) carcass weight equivalents (CWE) between 1997 and 2006. [...] Approximately half of the production increase during the last decade has occurred in the nine states of the Legal Amazon and half in the rest of Brazil.

So the impact of a marginal increase in beef consumption might be higher than the average impact of all current beef consumption. On the other hand, given the beef moratorium in recent years, this trend may not be as true today.

In addition, in certain countries, it's possible that marginal increases in beef consumption entail a higher-than-average percentage of imports. For example: "In Sweden, there has been a significant increase of meat consumption between 1990 and 2005 (from 60 kg to 82 kg meat per person and year), and [...] this consumption increase is almost solely based on imported meat". So even if X% of Sweden's overall beef is imported, maybe an additional purchase of 1 kg of beef in Sweden would be like 3X% imported or something?

Fortunately, the distinction between marginal vs. total impacts is unlikely to change the sign of the overall calculations, though it might change the magnitude by a few times. In certain cases it could change the sign of the analysis if a higher proportion of new rainforest clearing vs. existing pasture would lead to different overall results, but at least with my default parameters, this doesn't seem to be the case.

### Ignoring interactions among land uses

This piece treats land-use change from cattle grazing as resulting purely from the cattle industry. But in fact, different land uses can impact one another. For example, Brazilian soy may contribute indirectly to deforestation by cattle because increased soy production makes crop land more expensive, so some ranchers are driven toward cheaper land in the Amazon.

### Ignoring leather and other non-beef byproducts

Besides beef, leather, tallow, and other meat byproducts are also made from cows. According to this page, 74% of leather from Brazilian cattle is exported, compared with 20% of beef itself and 1% of tallow. That said, leather "is not as important as beef as an economic driver of pasture expansion—the hides are relatively low in quality and only worth selling as a by-product of beef—but it does provide some additional income to ranches."

Here are some rough estimates of the contribution of leather to cattle production overall:

• This page reporst that "Leather is worth 10 percent of the total value of the cow".
• This book reports that a steer's hide is only 7.5% of its value, and this represents 59-68% (average = 64%) of the value of all cattle byproducts. So that suggests that all byproducts are only worth ~7.5%/0.64 = 11.7% of a steer's value. This suggests that omitting byproducts shouldn't change the numbers in this piece dramatically.
• This article (written in 1922) reports that leather constitutes 6.5% of the value of cattle. It adds: "Animals are not produced for their hides alone and the variations in the price of the hide has little influence on the rate of cattle production."

In the particular case of Brazilian exports, the interactive graphic on this page shows that US imports of Brazilian beef were worth US$231 million in 2014, while imports of leather were worth US$35 million. So Americans' consumption of beef was ~6.6 times more important than their consumption of leather as far as the impact on Brazilian cattle. And no US imports of tallow were listed at all.

This study, like mine, ignores non-beef cattle products when calculating impacts of Brazilian beef production per kilogram.

### Ignoring memetic and far-future impacts

My calculations concern only the direct impact of rainforest beef on cows and wild animals. I don't consider the impacts of climate change or rainforest loss on humanity's long-term future, such as development of artificial general intelligence, in part because I have high uncertainty about the sign of net impact of these factors for humanity's trajectory. I think their expected value may hover around 0.

This piece also doesn't consider the social or ideological spill-over effects of beef consumption.

## Parameters and results

This section presents my parameter estimates and their justifications. You can change the estimates and see how the results adjust in response.

### Explanation of uncertainty measures

Each parameter estimate is associated with a Bayesian probability distribution representing your subjective beliefs about what values the parameter might take. It turns out that for this calculation, most of the parameters are well described by a lognormal distribution, because typically the uncertainty is about what order of magnitude of the parameter has. Also, all the parameters except pcs, pms, pcl, and pml must be positive, and a lognormal distribution enforces that constraint.

In particular, I use log base 10. If a parameter has, say, a median of 5 * 102 and a standard deviation on the log scale of 1, this means that I model the log10 of the values of the parameter as following a normal distribution centered around log10(5 * 102) with a standard deviation of 1.

The exceptions to this are the parameters g, s, and gc, which I model as merely normal rather than lognormal. I found that if I modeled these as lognormal, then the results tended to be overly negative in value because, for example, 1 - g can get quite negative for the extreme-tail cases where g is very big. I set g to 0 if its randomly sampled value is negative, and likewise for s and gc.

Another exception is the parameters pcs, pms, pcl, and pml, which can be positive or negative. For each of these parameters, I model it as lognormal, and then with the specified probability, I multiply it by -1 to make it negative. I make all four parameters either positive or negative together because they're correlated.

These uncertain inputs are combined to create a result distribution for the final overall number using Monte Carlo sampling. That is, I randomly draw a number of samples from the probability distributions of each variable, combine those inputs using the equations discussed above, and get a distribution of output values. This Monte Carlo approach assumes that the error in each input is independent of the error in every other input, which unfortunately is probably not true in practice.

### Results

Here's a histogram showing suffering reduced per kg edible beef purchased based on draws from the probability distributions of the parameters.

The following table reports distributional statistics about the results of the calculation, including the distributions of each of the four components of the overall total.

 Components of the model th percentile th percentile th percentile Mean of the middle % of values onlyj Reducing rainforest Impact on pasture not newly cleared Climate change Cattle themselves Total

### Parameter settings

 Parameter Units Point estimate, i.e., median of the distribution Standard deviationk 95% confidence interval N insect population = insect-years per year * 10 A hectares 1.5 * 1010 0 u (insects per hectare in rainforest) / (average insects per hectare worldwide); max allowed value: uc (insects per hectare in Cerrado) / (average insects per hectare worldwide); max allowed value: b (insect-years per burning death) / (insect-years per non-burning death) diy non-burning deaths per insect-year tb insect-years per burning death bb insect-years per burning death g (insects per hectare on grazed former rainforest) / (insects per hectare in old-growth rainforest); min allowed value: 0 s (insects per hectare in secondary rainforest) / (insects per hectare in old-growth rainforest); min allowed value: 0 Y years C hectares per year * 10 H hectares * 10 B years frf (hectares of grazed land that's former rainforest) / (hectares of total grazed land); max allowed value: 1 gc (insects per hectare on grazed Cerrado pasture) / (insects per hectare in untouched Cerrado); min allowed value: 0 mb (insects per hectare at burning time) / (average insects per hectare throughout the year) fb (insects burned) / (total insects at time of burning); max allowed value: 1 rb (total hectares burned) / (hectares of pasture burned); min allowed value: 1 pcs years/(metric tons CO2); probability pcs, pms, pcl, and pml are negative: * 10 pms years/(metric tons methane) * 10 pcl years/(metric tons CO2) * 10 pml years/(metric tons methane) * 10 cog metric tons of CO2 per hectare cs metric tons of CO2 per hectare cg metric tons of CO2 per hectare cc metric tons of CO2 per hectare rm metric tons of methane per hectare tc metric tons CO2 directly emitted per kg carcass weight produced tm metric tons methane directly emitted per kg carcass weight produced T kg carcass weight produced per year * 10 Q insect-years per cow-year * 10 0 K cow-years per slaughtered cow W kg carcass weight per slaughtered cow x kg edible beef per kg carcass weight ec (change in kg beef produced)/(change in kg beef demanded)

#### Turn off uncertainty

This button let's you turn off all uncertainty except regarding the sign of climate change in the above table:
This allows you to see how the calculations in this piece would turn out if only point estimates were used. The point-estimate median is different from -- and in fact, several times higher than -- the median of the Monte Carlo distribution. In general, the median of a product of numbers is not the product of the medians.

### Why is the distribution almost symmetric?

The results probability distribution has a lot of mass on net-negative impacts. There are a few main reasons for this, although readers can play with the parameters to do a more complete analysis:

• The "Reducing rainforest" component is variable mainly because the parameter s has large variance, including a reasonable probability for s > 1. While it's clear that secondary forests have less standing biomass than old-growth forests, it's less clear that they have less productivity than old-growth forests. Moreover, population dynamics of forest consumers can change in unexpected ways. For example, this article found that "total invertebrate biomass was doubled [...], in logged relative to primary forest." Of course, logging is a less dramatic ecological change than completely burning a forest, but the point remains that the impacts of environmental destruction on insect abundance can sometimes be counterintuitive.
• The "Impact on pasture not newly cleared" component is variable because of variance in g and gc and because of the relatively high value of b. gc is reasonably close to 1 because it's not obvious that grazed land has lower productivity than native grassland, and in well managed pastures, grazing might sometimes actually increase total productivity.
• The "Climate change" component has high variance because it's randomly made negative or positive with 50% probability, due to my very high uncertainty about the net impact of climate change on wild-animal suffering.

### Why is the model so complex?

I generally favor simple models because I think adding complexity tends to make errors more likely. The calculations in this piece involve lots of parameters that could have been omitted. So why add them?

When I started out this piece, I had a relatively simple model, one that didn't consider the effects of burning and less precisely separated out individual climate-change components. The calculation results were pretty similar to what you see in the current, more complex model: The effect of preventing forest regrowth was biggest, followed by the effect of new deforestation, followed by the effect of climate change. As I went along, I decided to add a few extra parameters here and there to make sure my calculations would be robust against modifications. By and large, these changes preserved the basic trends in the results.

While it's quite possible there are logical errors in my equations or software errors in my JavaScript implementation of them, the fact that the basic end results remained pretty stable gives me some confidence that whatever errors may be present don't invalidate the overall results. You can check this out yourself by tweaking or settting to zero some parameters and noting that the results are generally pretty stable.

The relative stability of the results during complexification of the model gives me a tiny amount of confidence that my results are not highly sensitive to the particular model used.

### Sources for parameter values

This paper is an important source for some parameters below. In this spreadsheet, I attempted to reconstruct the numbers calculated in that paper to verify my understanding of it.

#### N

The number of insects is ~1018 to ~1019, although this may depend on whether one counts springtails and such as insects or not.

#### A

The total area of land on Earth is about 150,000,000 km2 = 1.5 * 1010 hectares. This value is precise enough that error bars aren't needed.

#### u

u should presumably be greater than 1, since rainforests are some of the more insect-rich regions of the world. One reason rainforests have more insect-years of suffering per year than temperate forests is that "In the tropics, the period of insect activity is on average longer, the percentage of species active throughout the year is greater and the peaks of abundance are less well defined than in temperate areas."

We can get a bound on u based on the observation that if a fraction f of the world is tropical rainforest, then u can't exceed 1/f, since if it did, then the world population of insects would be more than (1/f) * N/A insects per hectare of rainforest times f * A total hectares of rainforest, i.e., more than the world population of insects, N.

So what is f? Sources seem to differ:

• "Rainforests once covered 14% of the earth's land surface; now they cover a mere 6%" (source)
• "Rainforests cover only a small part of the earth's surface - about 6%" (source)
• "Rainforests only cover around 2 percent the total surface area of the Earth" (source)
• This page includes a pie chart showing tropical rainforests as constituting 13% of Earth.
• This page says rainforests occupy 17 million km2, and in the discussion of the A parameter just above, we saw that the Earth's total land area is 150 million km2 So f = 17/150 = 11%.

I'll go with 6% as a middling number. In that case, 1/f = 17. And probably u is less than ~10 or something, given that other biomes also have insects. In my calculator, if I ever randomly sample a value for u bigger than 10, I change it to equal 10.

Following are some further numbers for estimating u, though they're pretty noisy.

Assuming 1018 insects on Earth, we have a global average of 1018 / (1.5 * 1010) = 7 * 107 per hectare.

Eight million ants and one million termites per hectare make up more than one-third the animal biomass in Amazonian terra firma [i.e., non-floodplain] rainforest (Holldobler and Wilson 1990).

If we naively multiplied (8 million + 1 million) insects by ~3 given that these insects make up more than ~1/3 of biomass, we'd get only 27 million insects, which is lower than the world average of 7 * 107 per hectare. Probably the total comes out higher when considering smaller, less massive insects, but still, these numbers are surprisingly low. Maybe they suggest that the global estimate of 1018 insects is too high?

That same article says "insects in tropical forests constitute several tons per hectare". Say it's 3 metric tons = 3 * 106 g. Assume that the average insect weighs ~3 mg. Then rainforests would contain 109 insects per hectare, which implies u = 109 / (7 * 107) = 14.

This piece also says there are at least 109 bugs per hectare in the Brazilian rainforest.

This book notes (p. 73) that there may be 390 to 2270 termites per m2 in Malaysian rainforests, and termites can eat up to 16% of dead plant matter in some regions. If we approximate this as 103 termites per m2, that's 107 per hectare. Dead plant matter is eaten not just by termites but also by millipedes, woodlice, and beetles -- as well as by non-bugs like fungi and bacteria (p. 73). Termites are plausibly bigger than other, more numerous bugs. So probably there is at least the world-average number (7 * 107) of bugs per hectare, but how many more than that isn't clear.

This textbook reports: "The highest biomass reported for termites, 50-100 g/m2 in southern Cameroon forest (Eggleton et al. 1996), is greater than any other component of the invertebrate (or vertebrate) biota and may constitute as much as 95% of all soil insect biomass (Bignell et al. 1997)." This paper gives estimates for termite biomass in tropical forests of around a somewhat more modest ~10 g/m2. Assuming a termite weighs 1-3 mg, ~10 g/m2 implies ~3,000 to ~10,000 termites per m2 or 3 * 107 to 108 per hectare.

Basset et al. (2012) found 6144 arthropod species in 0.48 hectares. Unfortunately I don't know how many individuals per species were present. One page claims "It is estimated that one acre of Amazon rainforest contains more than 70,000 species of insects." But this figure doesn't have a citation, and it seems like a much more dramatic result than was reported by the rigorous Basset et al. (2012) study, which estimated only ~25,000 species even when extrapolating to the entire 6000-hectare forest.

This section estimates that rainforest net primary productivity may be ~3 times the global average on land. If insect densities are proportional to net primary productivity, then we'd have u ≈ 3.

This section argues for u ≈ 2 based on global termite densities.

#### uc

Savannas occupy "nearly 20 percent" of the Earth's land area. Since it's also clear that the ~6% of land occupied by tropical forests is insect-rich, an upper bound on uc is 1/(.2 + .06) = 3.8. And given that other regions of Earth also have bugs, I'll set the bound at 3.

In the Cerrado, one giant anteater may consume 35,000 termites daily! There may be up to 40,000 termite mounds per km2 in the Cerrado, which is 400 per hectare. In South Africa, one termite mound has roughly 55,000 individuals. In Nigeria, there may be "between 14158.00 and 24777.67" individuals per mound, ignoring "reproductives". Let's assume 40,000 termites per mound. Over 400 mounds, that's 16 million termites. It's several times lower than the global average of 70 million bugs per hectare, but perhaps termites comprise a small percentage of all Cerrado bugs by numerosity.

This page notes that "Grasslands are an important part of life on Earth in terms of primary productivity. They cover about 14% of the Earth’s surface and account for 2% of global phytomass and 17% of global productivity (Esser, 1992)." 14% of land area producing 17% of productivity suggests that grasslands probably have insect abundances somewhat above the global average, and tropical grasslands probably have higher densities than temperate ones.

This section estimates that savanna net primary productivity may be ~1.2 times the global average on land. If insect densities are proportional to net primary productivity, then we'd have uc ≈ 1.2.

#### b

The sign of the results is reasonably sensitive to this parameter, and you can flip the sign around if you increase it to like 8 or more.

As a human, I'd probably rather experience being eaten alive 2-3 times to avoid dying by burning once. Moreover, insects sometimes don't show much aversive reaction to bodily injury, but they do show aversive reactions to heat, so maybe the ratio of (badness of burning)/(badness of being eaten, etc.) is even higher for insects?

YouTube has a number of disturbing videos of burning insects. I hesitate to link to them to avoid giving the authors of the videos more publicity (and in some cases, ad revenue), but they do offer some useful information. Following are my observations from some videos.

 Title and link How long bug took to die Bug reacted aversively? "Cockroach On Fire!" ~10-30 seconds of partial burning with a lighter. The roach was already half crushed when the burning started. Yes. The cockroach clearly found the flames aversive and struggled with its legs to make them stop. "Burned alive cockroaches" at least ~20 seconds of flames, though the cockroach may not have been dead by the end of the video yes "big spider on fire" 45-60 seconds (burning starts at 0:47, spider last moves around 1:28). Spider is completely immersed in flames the whole time. yes scorpion vs. centipede at least 1 minute, probably several. The centipede struggled during the first ~1 minute of the video, and then the action was cut until later. yes -- centipede struggled violently for the first ~15 seconds in particular beetle kills scorpion The bugs battle for several minutes. The video cuts out a lot, but probably it took several minutes for the scorpion to die. yes leech swallows worm The worm is swallowed within a minute, but I don't know how long it continued to survive inside the leech. Yes. At first it seemed like the worm didn't know what was going on, but it did struggle once it was partly eaten. "Cockroach firecracker - How to kill a Cockroach with fire" 10-30 seconds? (begins burning around 1:13, seems to stop moving around 1:30, but it's hard to tell) yes "Bug On Fire" 10-15 seconds (starts burning at 0:53, stops moving around 1:07; fully engulfed in flames) yes "Burning a Roach alive" ~30 seconds: burns at 0:15-0:23, then again 0:41-1:04, at which point it mostly stops moving yes

In contrast, following are some videos of bugs dying by means other than burning. Not all of them are of rainforest insects, but the general idea probably translates across biomes.

 How eaten (plus video link) How long bug took to die Bug reacted aversively? caterpillar eaten by turtle a few minutes (starts at 0:11, caterpillar stops squirming around 1:41?, but then it continues showing some movements even after that) Yes -- caterpillar squirmed to get free. The caterpillar was stationary between bites by the turtle. One interpretation of this is that the squirms are only reflexes that don't get triggered when the caterpillar isn't being bitten. Other interpretations are that the caterpillar is conserving effort or pretending to be dead or something else. wheelbug killing caterpillar hard to tell: bites at 1:50, caterpillar seems to have less response within a few seconds, though it keeps moving at the end of the video at 2:13 yes beetle eaten by ants many minutes :( The video is only 53 seconds long, but it looked like the beetle had been eaten for at least many minutes so far. yes -- legs struggled to move away the whole time bullfrogs eating scorpions, spiders, etc. A frog swallows prey almost instantly, but probably it takes some time for the prey to die in its stomach. probably (can't tell from the video, since the squirming would be inside the frog) grasshopper eats katydid a few minutes: katydid begins struggling around 0:07, becomes less able to resist around 1:00, but continues moving its legs until at least the end of the video at 3:31 yes wasp larvae hatch inside aphids Probably a long time, but the video doesn't show how long. not clear from the video mantis eats cockroach ~7 seconds (caught at 0:08, stops moving at 0:15) Yes, but short-lived. I'm unsure why the cockroach died so quickly here.

Of course, not all wild insects are eaten. Plausibly other ways of dying are much less intensely painful.

#### diy

If we ignore suffering during life and only count the painfulness of death, then 1 insect-year of suffering would correspond to the average number of bug deaths endured by an average population of one insect. For example, consider an insect where adults live 160 days on average, and non-surviving offspring live 5 days on average. (I'm just making up these numbers for illustration.) Suppose the ratio of surviving adults to non-surviving kids is 2 to 9. Then, in the 365 days of one year, there'd be 2 adults (160 days * 2 = 320 days) and 9 kids (5 days * 9 = 45 days), all of which would die during the year. So one insect-year would entail 11 deaths.

However, we should probably weigh the badness of these 11 deaths by the sentience of the animals involved. Assuming child bugs are less sentient than adults, the total sentience-weighted number of deaths would be less than 11.

For a more precise calculation of the number of sentience-weighted deaths per insect-year, I went to this piece and changed the default parameters to set L = 0 and D = -1. This means suffering during life is ignored, and suffering while dying is counted as -1 for a mature organism. The result, using the other default parameters as of 20 Jan. 2016, is PWSPY/Pmeas = -8.1 for the southern green stink bug. That means there are 8.1 sentience-weighted deaths in an insect-year for that species.

Of course, the southern green stink bug, while found in Brazil, is not representative of all Brazilian insects. But I assume that the diy number for other bugs would be within a factor of like 2 or 3 of this number.

When I divide b/diy, shouldn't the b parameter also be weighted by sentience? If a child bug dies, it's presumably less painful than if an adult bug dies. This is true, but I ignore it for simplicity. Since adults live longer and are thus around longer to be potentially killed by fire, the fraction of burned bugs who are adults is bigger than the non-sentience-weighted fraction of all dying bugs who are adults. Moreover, "in the cerrados, the burning season does not coincide with the breeding season of most wildlife".

#### tb

This paper says "burn scars in tropical savannas ecosystems can disappear within a few weeks [14]." If burn scars roughly correlate with plant and thus bug absence, tb might be something like a few weeks.

This book says vegetation sprouts "a few days or weeks after a burn-off". Of course, recovery of plant biomass is gradual:

That said, I typically assume that primary productivity (the first derivative of the curves in the above figure, ignoring plant consumption, death, etc.) is a more relevant determinant of insect productivity than is the static biomass of plants available.

Say it takes 3 weeks for bugs to return. Then tb = 3/52.

While burning prevents bugs for a short while, a later section discusses the possibility that burning can increase plant growth afterward. In principle, I could have introduced another parameter to the model to capture this point, but I can also capture it implicitly by slightly increasing the gc parameter. Since I take the frequency of burning as given rather than as something that we as decision-makers are optimizing, I could in principle roll all the "effects of burning" parameters into the g and gc values, but I separated out some of them just to make them more explicit.

#### g

When we look at pictures of pasture compared with rainforest, such as those in this report, the difference seems very stark -- rainforests have many times more biomass than pastures. But biomass is a limited stock of potential insect food, and what matters more in the long run is primary productivity (rate of creation of new biomass). Presumably primary productivity doesn't differ between rainforest vs. grassland as starkly as biomass does.

Here are some videos showing cattle ranching in rainforest regions, combined with my observations.

I didn't see any non-cow vertebrates in these videos, suggesting that cattle grazing considerably reduces populations of animals bigger than insects (except for the cattle themselves).

This page has pictures showing the contrast between Brazilian rainforest vs. pasture and how dry some of the pasture land can be.

Given that pasture land may contain nontrivial portions of tree cover, it seems that g shouldn't be too low.

One other consideration is that slashing and burning can lead to soil erosion, which may deplete land productivity in the future.

This report says a lot of Brazilian pasture on former rainforest land is degraded:

In the Brazilian Amazon, 95 percent of the deforested area is converted into pasture, 50 percent of which is considered degraded due to mismanagement, phytosanitary problems, poor soil fertility and soil structural modification (linked to soil macro-invertebrate activity). When the forest is converted to pasture, the use of heavy machinery and, later, cattle trampling lead to severe soil compaction, particularly in the 5–10 cm layer, impeding root development.

That source further explains that on degraded pasture

An opportunistic invading earthworm [...] benefits from anthropic disturbances and occupies the empty niche left by native earthworms and soil macrofauna, increasing its biomass to more than 450 kg/ha, equivalent to nearly 90 percent of total soil macro-invertebrate biomass.

So total invertebrate biomass on such pasture is slightly more than 450/0.9 = 500 kg/ha. A previously mentioned source claims that insects in rainforests "constitute several tons per hectare". I'm nervous about comparing these estimates because they're from completely different sources with different methodologies, but this comparison at least weakly suggests that rainforests may have a few times more invertebrates.

Leaf area index (LAI) is one predictor of primary productivity. For example:

This document reports mean LAI of "Tropical pasture" as 2.85, while that of "Tropical deciduous forest" is 4.67 and for "Tropical evergreen rain forest", 5.23.l Of course, this comparison could show mere correlation rather than causation -- maybe regions with better growing conditions are more likely to have rainforest and also produce more leaf cover.

All told, I set g relatively close to 1, in part to be cautious and in part because I would guess that primary production doesn't differ by more than a few times between rainforest and pasture.

This piece examines further the question of how grazing affects insect densities in general (especially in temperate regions, rather than tropical rainforests).

#### s

In the long run, secondary forest can become reasonably productive, even if the trees are shorter and smaller than in virgin forest. Abundances of certain insects, such as perhaps mosquitoes, might even be higher in secondary forest. This article reports that "In the Amazon, for example, one study showed an increase in deforestation by some 4 percent increased the incidence of malaria by nearly 50 percent, because mosquitoes, which transmit the disease, thrive in the right mix of sunlight and water in recently deforested areas."

However, one other important consideration is that burning of primary forest releases years' worth of stored plant energy via the non-sentient process of combustion. I could have counted this consideration separately, but instead I incorporate it into the s parameter. Why? Because the effect of burning stored biomass now is to avoid decomposition of those old trees in the future.

A primary forest has old trees dying all the time. Structural features of old-growth forests include:

• Presence of standing dead and dying trees in various stages of decay
• Fallen, coarse woody debris
• Natural regeneration of dominant tree species within canopy gaps or on decaying logs

Fallen leaves, dead plants and animals will decay (rot) very quickly. [...] Termites, giant earthworms, millipedes, and beetles eat rotting plants and animals.

In contrast, a forest that has been burned has mainly new growth, with less old wood to decompose. This is one reason a secondary forest recovering from fire may support fewer insects.

How big is this effect? Following are two estimates.

##### Quick estimate of impact of not having decomposing old trees

Consider a brand new forest growing from scratch, without any dead vegetation currently on the ground. Suppose it starts growing at t = 0 years and reaches maturity at t = tm years. Let its net primary productivity be NPP metric tons per hectare per year. Suppose that a fraction fl of this is eaten while the plant is alive -- e.g., by bugs eating leaves -- and 1-fl goes into forest growth, i.e., increasing standing biomass. Assume there are no dying trees until t = tm.

Now, at t = tm, the forest has reached its maximal size, so further productivity has to be balanced by decomposition of existing biomass. Since the net growth of the forest biomass is now zero, new growth in the amount of (1-fl) * NPP must be offset by decomposition of old growth at the same rate. Hence, the total amount of production available for consumption (either on live trees or in dead organic matter) is fl * NPP + (1-fl) * NPP = NPP. This contrasts with only fl * NPP of production that fed herbivores during the period t = 0 to t = tm. If we assume that the fraction of live biomass eaten by bugs equals the fraction of dead biomass eaten by bugs, then the old-growth forest has NPP / (fl * NPP) = 1/fl times more bug production than the forest did during the period t = 0 to t = tm. Thus, just based on this argument, we should set s at most as big as fl.

My intuition is that fl is probably less than 0.5. But setting s lower than 0.5 seems a bit extreme? Anyway, this was a very handwavy calculation with lots of made-up numbers, so I don't put too much stock in the conclusion.

Moreover, this calculation should be adjusted to account for the fact that some rainforest biomass is underground and hence isn't burned away (although this book says "rainforest trees do not maintain a large portion of their biomass underground"), as well as the possibility that not all trees or shrubs are burned when clearing pasture.

##### More convoluted estimate of impact of not having decomposing old trees

This document reports that old-growth rainforest has about 154 metric tons of carbon per hectare above ground. I ignore below-ground and soil biomass on the assumption that these don't burn. Suppose that 100 of these metric tons actually get burned when a forest is cleared, while the other 54 metric tons remain as isolated trees or other vegetation that decompose organically later.

This page says "The carbon content of vegetation is surprisingly constant across a wide variety of tissue types and species. Schlesinger (1991) noted that C content of biomass is almost always found to be between 45 and 50% (by oven-dry mass)." The page recommends using the average of those two estimates: 47.5%. So 100 metric tons of carbon implies about 100/0.475 = 211 metric tons of dry weight of plant biomass.

As noted above, this book says (p. 73) that termites can eat up to 16% of dead plant matter in some rainforests. Presumably the typical fraction is lower, but there are other decomposing bugs besides termites. So let's split the difference and assume that 16% of all decomposing vegatation is eaten by bugs. Then we have 211 * 0.16 = 34 metric tons per hectare of dry vegetation to feed bugs.

Following this calculation, I'll assume an ECI of 10%, so that 34 metric tons of dry biomass translate to 3.4 metric tons of dry insect mass per hectare. Assuming about ~half of a bug is water, that implies about 7 metric tons of wet insect mass.

In this section, I estimated that a typical insect has a wet mass of ~3 mg. So the decomposing vegetation, had it not burned, would have supported (7 metric tons per hectare) * (109 mg per metric ton) / (3 mg per insect) = ~2 * 109 insects per hectare. This decomposition would have been spread out over the full ~40 years of secondary-rainforest regeneration, so the per-year reduction in populations by not having decomposing vegetation is (~2 * 109) / (~40) = 5.6 * 107 insects per hectare.

Assuming the insect density of an old-growth forest is u * N / A = 3 * 108 insects per hectare, loss of decomposing vegetation implies that we should reduce s by (5.6 * 107) / (3 * 108) = 0.19 more than what we naively would have thought. For example, if we were only considering absence of decomposing dead trees when deciding on the value of s, we would set s = 1 - 0.19 = 0.81.

This estimate is obviously extremely noisy and probably has several orders of magnitude of uncertainty, but it's interesting that the final number came out to be so reasonable without any gerrymandering of the inputs on my part.

##### Conclusion

I'm nervous about taking the above estimates too seriously, so I pulled s closer to 1 based on a gut feeling that old-growth vs. secondary forests probably don't differ that much in insect densities.

#### gc

It appears that grazing reduces primary productivity in the Cerrado:

 Land type Above-ground grass productivity (dry Mg per hectare per year) regular Cerrado ("new but unfertilizedm Brazilian Brachiaria decumbensn pastures") 5.5 to 12 "regularly fertilized productive pasture" 4.1 ± 1.6 "degraded pasture fertilized 13 yr previously" 2.1 ± 0.4

Interestingly, the same paper found that pasture didn't necessarily have lower soil fertility: "topsoil fertility in both pastures is increased compared with [Cerrado], and little leaching occurs."

This document reports mean LAI of "Tropical pasture" as 2.85, while that of "Tropical savanna" is 1.81. I don't know if these categories apply specifically to the comparison between native Cerrado vs. pasture, but at least they raise doubt about a general principle that pasture is less productive. Moreover, the "grazing optimization hypothesis" suggests that it may be possible in principle that grazing increases primary production. But in practice, lowered primary production due to overgrazing is probably more common and more important?

Another reason pasture might increase primary production is if it's fertilized. Does this have the potential to make pasture more productive than native savanna?

Even if pasturing land increases primary production, cows may eat some plant material that would otherwise have been consumed by bugs. Figure 3 in this paper shows that cows in São Paulo, Brazil ate something like 30-60% of plant-leaf biomass in most cases. On the other hand, cow poop that's produced from eating this primary production may increase bug populations on pasture land.

This paper says (p. 57):

Today most of the cultivated pastures in the Cerrado region experience some degree of degradation, which means that they have lost some of their capacity to produce biomass (da Silva et al., 2004). It is noteworthy that the deterioration of the pastureland as a resource has become large-scale, after only a few decades of man’s activity and that overgrazing is the predominant cause of this.

##### How burning affects soil fertility

Burning may also have long-term impacts on fertility. This article notes (p. 1) that burning Cerrado can cause "soil degradation, overall biodiversity loss and an increased greenhouse gas emissions [1,2,7,12,13]."

This page says that burning "leads to a gradual reduction in the height and girth of the vegetation components making any recuperation of the Cerrado, which has already lost half of its original vegetation, very difficult to achieve." Fewer plants presumably means fewer bugs. That page also notes that fires can lead to wind erosion that blows away plants and nutrients.

On the other hand, this book notes that the resurgence of plant growth following fire may actually boost "nectarivorous, pollinivorous, frugivorous, and granivorous fauna represented principally by the insects" (p. 101).

This paper notes that "Several environmental benefits may be brought by fire in savannas, especially the stimulus to nutrient recycling and to sprouting, fruiting, and seeding of several plant species; it also increases the vigor and palatability of a number of herbaceous species." However, huge dry-season fires seem to cause "damage to native flora and fauna".

##### Not all "pasture" is grazed

This paper notes (p. 53) that not all land classified as "pasture" is actively grazed:

It could be argued that of the pasture area reported, there is a significant share of land that is idle; native pasture (rangeland) with very low animal density and/or pastures in various degraded conditions. However, the official statistics [...] report all of the 172 Mha pasturelands as agricultural land, and as such, it is correct to include all of it since in some respect it is needed for the grazing animals.

Insofar as some of the so-called pasture land not actively grazed corresponds to native vegetation, gc should be moved somewhat closer to 1. On the other hand, for land not grazed because it's degraded and has few plants, gc should be moved somewhat closer to 0.

#### Y

Y represents an average time required for secondary rainforest to become more like old-growth rainforest. This page explains:

When you consider how long it takes for most big rainforest trees to reach maturity (studies indicate it takes trees typically 60 years just to make the canopy), you begin to appreciate why untouched lowland rainforests are so valuable today; man cannot regrow what takes nature many hundreds or even thousands of years.

This paper found that in secondary forests throughout the Neotropics, "Aboveground biomass stocks took a median time of 66 years to recover to 90% of old-growth values."

This paper includes the following figure (p. 17):

This suggests that forests are mostly recovered at least in terms of biomass by ~40 years, which I'll take as my point estimate of Y.

#### C

This paper found that between 1985 and 2006, 13.5 million hectares of Brazilian land in the Legal Amazon Region were cleared for cattle, ~90% of which was for beef production (p. 1176). That is, ~12 million hectares were cleared for beef. Assuming a constant rate of land clearing, that implies (12 million hectares)/(20 years) = 0.6 million hectares per year. I assume that all new clearing of rainforest was in the Legal Amazon Region. This is probably not exactly true, but I think it's mostly true because I think it's what this paper assumed.

A previous section on land-use changes by country in Latin America predicted an increase of ~17 million hectares of pasture in Brazil over 10 years. This suggests an increase of 1.7 million hectares per year. Perhaps this estimate is higher than 0.6 million hectares per year because it covers a more recent time period.

However, because of the beef moratorium since 2009, deforestation rates have declined considerably. Figure 2 on this page shows that in 2006, deforestation in 2005-06 Brazil was (based on my eyeballing of the graph) around ~1.7 million hectares per year -- the same as the estimate in the previous paragraph. Even though that figure appears to represent all Brazilian deforestation, not just due to cattle, it seems to match the cattle figure quite well, so I'll take it as a measure of deforestation by cattle. By the 2010s, the figure shows (again based on my eyeballing of the graph) that deforestation had declined to about 0.7 million hectares per year once more. I use this as my estimate for C.

I'm not sure if some or much of this was deforestation of secondary rather than old-growth forest. This paper reports that for the Lower Mekong Basin, "The deforestation rates for secondary forests are 3 times higher than the rates for other forest categories and account for two-thirds of the total deforestation." Maybe this is less true in Brazil? Insofar as forests cleared are secondary rather than old-growth, the modeled impact of beef grazing would be less severe. But given that this paper seemed to assume that the newly destroyed rainforest was old-growth, I'll continue doing the same.

The Internet is full of claims that a 1/4-pound hamburger made from rainforest beef causes 55 ft2 of rainforest destruction. Is this claim true? Later I'll estimate the total mass of edible beef produced per year from Brazil as x * T = 0.65 * (8.6 * 109) kg = 1.2 * 1010 pounds = 4.9 * 1010 quarter-pound hamburgers. Since this claim was typically made in the 1990s and 2000s, it probably doesn't take account of the recent cattle moratorium. So let's assume a round value of 1 million hectares of cleared rainforest per year due to beef production. That's 1010 m2 = 1.1 * 1011 ft2. So the actual figure seems to be ~2.2 ft2 destroyed per quarter-pound burger -- quite a bit lower than 55 ft2. Maybe the 55 ft2 figure is supposed to be for only that portion of beef production that destroys new rainforest. This paper reports that for Brazilian beef, "close to 6% was produced on the recently deforested land in the LAR" (p. 1776). So the rainforest loss for that beef specifically is 2.2 / 0.06 = 37 ft2, which is closer to 55 ft2 per quarter-pound burger. So the number seems kind of accurate, though it's a bit misleading to only count beef that newly destroys rainforest when most Brazilian beef is not of that type.

#### H

This paper reports (p. 1775) that 144 million hectares were used for beef production in Brazil in 2006.

This article reports a slightly lower number of 100 million hectares, but this is only for cultivated pastures (not pastures with native vegetation), and it's for all kinds of cattle (not just beef cattle).

#### frf

I couldn't find an explicit statement of how much pasture was on former rainforest land and how much was on savanna. I did find that, as of ~2003, 35-40 million hectares of cattle pasture were in the Cerrado, but given that there were, in 2006, 172 million hectares of total pasture, I suspected that the total amount of savanna-like pasture was higher than 35-40 million.

This paper reports that in 2006, the Cerrado contributed 41.96% of Brazilian beef. But since there are other regions besides Cerrado vs. rainforest, this 1-frf is probably bigger than 0.4196.

To get a more precise picture, I used Table 5.3 of this source, which lists pasture areas by region of Brazil. It shows total pasture, including dairy cows and non-cow livestock, but I'll assume that beef cows vs. non-beef animals have equal proportions in all regions, so that the relative areas of the different regions also represent relative areas of beef grazing specifically.

For each Brazilian state, I classified it as having a biomass density more like rainforest, more like savanna, or about halfway between the two. Several of these states are neither in the Amazon rainforest nor the Cerrado but are instead in the Caatinga, a dry forest. Its level of plant growth looks similar to or perhaps lower than that of savanna, so I count it as "more like savanna" in my classification.

A rough map of different ecoregions of Brazil is the following figure from this paper:

In order to verify these general trends, I looked at Google Earth. The following snapshot from Google Earth shows that it's quite easy to distinguish rainforest from non-rainforest regions of Brazil. I marked on the screenshot the areas I classified as more savanna-like vs. more rainforest-like.

For each state in the following table, I looked it up on Google Earth and then eyeballed, based on the amount of green-ness, its classification. Then I aggregated these classifications over all the states in a given region by a simple average (rather than weighting by the area of each state for simplicity; usually the states were similar enough in area that this simplification shouldn't drastically affect the results).

 Region 2006 pasture (Mha) State Brian's eyeballing of whether lushenss is more like rainforest or savanna North 32.6 Acre rainforest Amapá rainforest Amazonas rainforest Pará rainforest Rondônia rainforest Roraima rainforest Tocantins savanna simple average of the states 6/7 rainforest Northeasto 32.6 Alagoas half of each Bahia savanna Ceará savanna Maranhão savanna Paraíba savanna Piauí savanna Pernambuco savanna Sergipe half of each Rio Grande do Norte savanna simple average of the states 1/9 rainforest Central West 56.8 Mato Grosso half of each Mato Grosso do Sul savanna Goiás and Distrito Federal (merging these two because the latter is tiny) savanna simple average of the states 1/6 rainforest Southeast 32 São Paulo savanna Minas Gerais savanna Rio de Janeiro half of each Espírito Santo half of each simple average of the states 1/4 rainforest South 18.1 Paraná half of each Santa Catarina half of each Rio Grande do Sul savanna simple average of the states 1/3 rainforest

Then, I calculate the average of the fractions of rainforest weighted by a region's area:

frf = [ 32.6 * (6/7) + 32.6 * (1/9) + 56.8 * (1/6) + 32 * (1/4) + 18.1 * (1/3) ] / (32.6 + 32.6 + 56.8 + 32 + 18.1) = 0.32.

Here's another approach to calculating frf. By 2006, 702,186 km2 = ~70 million hectares of Brazil's Amazon rainforest had been lost, and 91% of this was supposedly due to livestock pasture. This paper gives a total area devoted to pasture in 2006 of 168.9 million hectares.p (This includes dairy and non-cow animals, but I assume the statistic about 91% of deforestation being due to livestock does also.) So frf = (0.91 * 70) / 168.9 = 0.38. This is reassuringly close to the 0.32 estimate.

Here's one last sanity check: "Today the Cerrado region contributes more than 70% of the beef cattle production in the country ('Pecuária de Corte no Brasil Central'; Beef Cattle Production in Central Brazil, Corrêa, 1989)". This leaves 30% to occur elsewhere, including in the Amazon. Land use might be more than 30% in non-Cerrado regions assuming cattle production per hectare is less efficient in the rainforest. So an amount of non-Cerrado land use for beef above 30% seems reasonable. (That said, some of this might be in the Caatinga or elsewhere?)

I split the difference and take frf = 0.35.

#### B

This report explains that following initial deforestation:

burning continues in subsequent years, since fires are an effective way to stimulate continued pasture growth during the dry season. Normally the productivity of pasture grasses slows greatly as the rains diminish, but burning helps them re-sprout from the roots and thus produce a new supply of tender shoots at a critical time. It also helps maintain the pasture by killing weeds, as well as the saplings of trees and shrubs that would otherwise colonize and eventually shade out the grass.

Here are some generic estimates of burning frequency:

• "Ranchers and handcrafters use biennial fires" (source, p. 2).
• "cattle ranchers use fire every couple of years to stimulate grass regrowth" (source, p. 5).
• Pasture burn-offs are done every ~3 years, and with more ambitious farming, fires may be done every 2 years or even every year (source, pp. 87-88).
• "In the extensive beef-cattle production, annual or biennial fires are commonly applied to stimulate grass regrowth in the dry season when forage is in short supply." (source, p. 31).
• "Cerrado species do have some limited protection against fires of the type that occurred in the past but not against the increasingly intense annual fires they are being subjected to today, he stated. [...] the annual burning increases the fragmentation of the biome thereby jeopardising the lives of species that need large land areas for their survival, like the big cats." (source)

This study modeled the frequency of fires in the Cerrado but only within a "continuous preserved area", so fire frequency was probably lower than in pure pasture. That said, the area included some farmers who had lived on the land prior to its protected status and who engage in burning. The study found (Table 1, p. 7) that on Shift Cultivation lands, the "Fire rotation period" (i.e., average time between fires) was 3.71 years. Shifting cultivation is not the same as cattle grazing, but it gives a hint about what burning intervals might look like for pasture.

Given all the above estimates, something like B = 1.5 or B = 2 seem like reasonable estimates. Of course, all the above data points are for the Cerrado, while the B parameter also applies to pasture in former rainforest. Unfortunately I don't have data on burning frequencies in the latter kind of land, but perhaps it's not that different from burning frequencies in Cerrado?

##### Natural fires

We should also consider fires that would have happened naturally. This book notes that inhabitants of the Cerrado report natural fires caused by lightning, although "There is absolutely no doubt that man has been the principal cause of fire in the cerrado from the earliest times."

The proper comparison is between the frequency of fires given pasture land vs. the frequency of fires given what the land would be used for otherwise. If the land would otherwise be left idle or preserved, then we should compare frequency of burning by cattle farmers vs. frequency of burning in a mostly natural state. If the land would counterfactually have some other human use, then the baseline frequency of fires might be a bit higher. For example, "the Xavante use controlled burnings in their traditional hunting practices". Still probably the frequency and extent of burning for hunting are probably lower than for cattle farming.

One other consideration is that natural fires typically happened more during the rainy season, when lightning was present. Fires during the rainy season "were patchy and extinguished primarily by rain", although they were also "very frequent". Rainy-season fires might reduce dry-season ones by creating natural firebreaks.

Natural fires are more common in the Cerrado but also happen in rainforest: "Throughout their existence, tropical rainforests have been affected by natural forces like fire, drought, and storms." We can incorporate this consideration into B as follows. Suppose -- to make up numbers -- that an area would naturally burn once every 7 years, but because humans use it for pasture, it's burned every 1.5 years instead. Then the net impact of cattle grazing is to burn at an average rate of 2/3 times per year rather than 1/7. The net increase is 2/3 - 1/7 = 0.52. So if we set B = 1/0.52 ≈ 2, then 1/B will give the appropriate multiplier.

#### mb

This paper notes (p. 1) that Cerrado burning on crop and pasture land is done "most often during the middle and latter months of the 6-month dry season (April to September), under severe fire weather conditions [1,2,6,7,12–14]." This book says cattle ranchers burn during the second half of the dry season (August to September).

This paper studied insect abundances in the Cerrado by month in the following region, which seems to have a mix of trees and grassland:

The following figure from that paper shows abundances of all insects, with the dark area showing the transition from the end of the dry season to the rainy season.

The paper says "Regarding abundance (sum of all the specimens collected), the Insecta class displayed the highest abundance between September and November". Moreover:

In areas with well-defined rainfall cycles, insects tend to be less abundant in the dry season (Wolda 1978). [...] there is evidence that in the tropics the first rains at the end of the dry season act as a trigger for resumption of insect activity (Wolda 1988). Therefore, the increase in temperature, which showed a significant positive relation with abundance (R2 = 0.70 and P = 0.0041), and the increased availability of water, provided by the first rains in September (50 mm), appear to be the factors favoring the increase in insect populations in the "Cerrado". [...]

The changes in climate variables (increased temperature and precipitation) that occur gradually in the transition from the end of the dry season (September) to the start of the rainy one (October) coincide with the peak production of leaves and flowers in the "Cerrado" (Morais & Diniz 2004; Oliveira 2008). Newer leaves contain lower toxin levels, are softer and have higher nutrient content (Feeny 1970). This availability of resources plays an important role in the seasonable patterns of insects (Wolda 1978, 1988). Therefore, the insect populations in the "Cerrado", mainly of herbivores, appear to be synchronized with the increased availability of food resources in this period.

Assuming burning happens before this resurgence of insects, insect abundance at the time of burning is probably lower than average insect abundance, i.e., mb is probably less than 1.

The paper seems to say (though I'm not sure) that "68.4% of the specimens were collected" between Sep. and Nov. (Or is it only Oct. to Nov.?) If we simplistically assume that the insect abundance during Sep. to Nov. is a constant t times higher than during the other 9 months, then if 68.4% of insects are found during those three months, then 3t / (3t + 9) = 0.684, which implies t = 6.49. The average insect population during the year would be (9*1 + 3*t)/12 = 2.37 times the population during a dry month. If fire always occurred prior to Sep., then we'd have mb = 1/2.37 = 0.421. However, I set mb somewhat higher than this because maybe fire sometimes happens after Sep., when bug populations are high? For example, suppose there's a 1/6 chance that burning happens during September when populations are 6.49 times as high as usual. Then mb = [(1/6) * 6.49 + (5/6) * 1] / 2.37 = 0.81.

The paper cautioned that other researchers had found a more even distribution of bugs across months of the year:

In a similar study to that presented here, in a "Cerrado" region but using other types of traps (malaise, pitfall and window), lower measures of concentration [i.e., how sharp a population spike was] were found; the Diptera, Homoptera, Lepidoptera and Orthoptera orders were considered random (dispersed); only Coleoptera presented a relationship with the climate variables; and the abundance peak of the orders with clustered distribution occurred in the rainy season (Pinheiro et al. 2002).

This is a further argument for setting mb close to 1, although since the other study also found a bigger population spike during the rainy season, it still seems sensible to keep mb less than 1.

Another issue is that the paper I'm using here sampled bugs with a light trap 2 meters above the ground, so it presumably sampled mostly for winged bugs. But winged bugs are unlikely to be the kind that burn in Cerrado fires. What we really want to know is the seasonal distribution of those bug taxa that can't fly away or hide underground during fires. By using the results of this study, I'm assuming that flying and non-flying bug populations are correlated, so that statements about the seasonal distribution of flying bugs roughly translate to statements about the seasonal distribution of non-flying bugs.

mb may be closer to 1 in former rainforest areas, assuming seasonality due to dryness is less pronounced there?

#### fb

According to geographer Mara Moscoso, Cerrado fires harm small or slow mammals, nesting birds, giant anteaters with lots of fur, etc.

This book reports that "To escape fire, smaller nonflying animals take shelter in holes and burrows in the soil made by armadillos, ants, etc."

This article reports that "As much as 90 percent of the grass biomass that is decomposed in some savannas can be attributed to termites." This page says "Along with termites, leaf cutter ants are the primary herbivores of the Cerrado and play an important role in consuming and decomposing organic matter, as well as constituting an important food source to many other animal species.[15]" Termites and ants have underground burrows, so I'd assume that a reasonable proportion of them can escape fires?

This book reports (p. 39) that

termites appear to be resilient to fire. [...] Abensperg-Traum et al. (1996, for Australia) suggested that during fire some termites could migrate temporarily to the less susceptible nearby nests.

Some termites are more affected than others, and one study found that intense fire led to more abandoned mounds and fewer termites in non-abandoned mounds (p. 39).

This paper reports that 49.6% of insects sampled in the dry season of the Cerrado (when most fires happen) belonged to Lepidoptera. "Lepidoptera adults [...] were observed in large numbers in the dry season". Of insects in the Lepidoptera order, "Almost all species have some form of membranous wings, except for a few that have reduced wings or are wingless." So maybe most Lepidoptera adults could fly away from fire? However, larvae (caterpillars) would not be able to fly away, and they may also be abundant during dry months: "some studies have also shown that in the 'Cerrado' the immature forms of Lepidoptera show abundance peaks in May and July, in the middle of the dry season (Morais et al. 1999)." Some Lepidopdera get through the dry season "in larval diapause and some as pupae, with both types becoming adults in the rainy season (Janzen 1987; Aiello 1992)." So there might be reasonable numbers of non-flying Lepidoptera during burning events.

By eyeballing Fig. 1 in the same paper, I see that perhaps the next most abundant insect order during dry months after Lepidoptera was flies (Diptera). Members of this order usually have "a single pair of wings", although "some true flies have become secondarily wingless" (i.e., lost their wings from evolutionary ancestors that had them).

One big caveat about this study is that it sampled using a light trap 2 meters above the ground. The authors caution that

Light traps provide reliable information on changes in the real size of populations of many species of night-flying insects (Wolda 1978), but do not reflect the relative abundance of all species in a determined area. Therefore, this type of trap should not be used to estimate the size or density of insect populations in general[.]

This argues against setting fb too low, since this study may have found a bigger fraction of winged insects than are actually present.

#### rb

This paper notes (p. 6) that some savanna/forest types can burn more often because of more frequent burns in neighboring types: "the absence of fire breaks leads to fire spreading." Elsewhere it says (p. 2): "Ranchers and handcrafters use biennial fires, but the absence of firebreaks allows fires to spread over larger areas than required by those land use practices [42]."

This paper says (p. 31) "Most cattle ranchers do not make firebreaks and the fire spreads to large areas."

I don't have any specific data for this parameter, so I made up the estimate.

#### bb

This parameter is tough to estimate, but here's an attempt. Consider an annual or biennial grass species that's burned when it's ~1 year old. Thus, burning prevents decomposition of 1 year's worth of biomass. Suppose the plant produced P units of biomass from primary production during that year.

This textbook says of (temperate, not tropical) grasslands:

The percentage of annual above-ground primary production utilized by herbivores varies greatly, but estimates generally range between 20 and 50% (Scott et al. 1979, Detling 1988). Although much higher levels of utilization can occur, in excess of 90%, they are generally restricted to specific regions or years. Insects and small mammals may consume as much as 10 - 15% of the annual above-ground production.

For concreteness, suppose that cows eat 35% of grass production, bugs eat 15%, and the remaining 50% goes toward growth. So 0.15 * P of biomass went to feed insects. Had the plant decomposed, another 0.5 * P of its grown biomass would have been available for decomposition. Only a fraction of that would have been eaten by bugs (rather than by bacteria or fungi). Say the amount of the grown biomass eventually eaten by detritivorous bugs would have been 0.15 * P. So the plant would have provided as much bug food in death as it did in life.

Suppose there are ng bug generations per year. Then, unrealistically assuming a uniform population of bugs throughout the year, the above-ground bug population at the time of burning when the grass was 1 year old would have been an amount supportable by 0.15 * P / ng of biomass. This is because there are ng generations of bugs, and only one of them would be around at burning time. For simplicitly, I assume that all and only above-ground bugs get burned by fire. The biomass that would have decomposed had it not been burned could have supported a number of bugs that could eat 0.15 * P of biomass. So for every bug burned, the number of future adult detritivorous bugs prevented is (0.15 * P) / (0.15 * P / ng) = ng. Assuming the detritivores also have ng generations per year, adults each live 1/ng years, so the insect-years prevented by burning the biomass is (ng insects per burned bug) * (1/ng years) = 1 insect-year per burned bug.

Actually, this calculation should be amended to include mb, which tells us how many bugs are around at the time of burning relative to the average bug population. In that case, the bugs burned would be proportional to mb * 0.15 * P / ng, so the final result would be 1/mb insect-years per burned bug rather than just 1. Taking mb = 0.81 gives 1/0.81 = 1.2 insect-years per burned bug as our estimate of bb.

This seems too high to me. I don't have good intuitions about what bb should be, but I feel like this number may overestimate the insects supported by decomposition. So instead I choose a much tamer value as the median of my probability distribution for this parameter.

#### pcs, pms, pcl, and pml

These estimates are taken from the default parameters here as of 15 Jan. 2016. (I may have changed those parameters since then.) Since the low-ish and high-ish estimates in that piece are nearly equal in magnitude with opposite signs, I set the following parameters at the absolute value of the estimates, and then I let the parameters be negative with probability 0.5.

 GHG ballpark impact per Gton counting short term only ballpark impact per Gton counting short term and long term CO2 ± 3 * 10-4 ± 6 * 10-3 methane ± 6 * 10-3 ± 2 * 10-2

To convert these into the values entered into the parameters table, I divide by 109 metric tons per Gton.

#### cog, cs, and cg

This document reports the following numbers for total carbon in different types of land. To convert them from mass of carbon to mass of CO2, I multiplied the second column of the below table by (2 * 16 + 12)/12 to get the third column.

 Land type Total carbon (above ground, below ground, and soil) in metric tons per hectare Total CO2 sequestered in metric tons per hectare Old-growth forest 154 + 30 + 44 = 228 cog = 836 Productive pasture 5.35 + 66 = 71.35 262 Degraded pasture 4 + 44 = 48 176 Secondary forest 23.4 + 44 = 67.4 cs = 247

Long-run proportions for productive vs. degraded pasture are 46% vs. 5%, so I take cg = (46 * 262 + 5 * 176) / (46 + 5) = 254.

Here's a quick check of these numbers. Deforesting to a pasture state should release about 836 - 254 = 582 metric tons of CO2 per hectare. Harris et al., 2012 shows Brazilian deforestation of 3.292 million hectares per year from 2000-2005.q That suggests 582 * (3.292 million) = 1.9 billion metric tons of CO2 per year. In contrast, Harris et al., 2012 reports Brazilian emissions from deforestation of 340 million metric tons of carbon per year, which is 1.2 billion metric tons of CO2 per year. Other studies have found similar estimates or higher estimates, so the 1.9 billion estimate based on the numbers I'm using in this piece seems reasonable.

My estimate that clearing rainforest releases 582 metric tons of CO2 per hectare is somewhat higher than the figure of 367 metric tons of CO2 per hectare used in Norway's payments for Brazil's reductions in deforestation.

#### cc

As you can see here soil carbon is the most important carbon sink for pasture, and I assume the same is true for native Cerrado. So in this section, I'll estimate an amount by which soil carbon in native Cerrado differs from that in pasture, and then I'll use this to compute cc based on cg.

There's controversy over whether livestock grazing increases or decreases soil carbon sequestration, and obviously this depends on the particulars of the ecosystem and how cattle are managed. Given the uncertainty about the sign of the impact of grazing on soil carbon, cc shouldn't be dramatically different from cg in expectation.

This paper reviewed several studies of land-use change and reported the following numbers for conversion of native Cerrado to pasture in Brazil:

 Study Original soil organic carbon (Mg/ha) Change in soil organic carbon by converting to pasture (Mg/ha) % change Lilienfein et al., 2003 29.04 3.96 13.6 Lilienfein et al., 2003 29.04 9.84 33.9 Maquere et al., 2008 29.9 4.70 15.7 Maquere et al., 2008 29.9 7.30 24.4 Marcha˜o et al., 2009 39.5 5.50 13.9 D’andre´a et al., 2004 37.9 2.80 7.39 Batlle-Bayer et al., 2010 44.5 5.60 12.6 Batlle-Bayer et al., 2010 68.7 -2.90 -4.22 Batlle-Bayer et al., 2010 68.7 -1.70 -2.47 Batlle-Bayer et al., 2010 54 -0.50 -0.926

So on average, pasture seems to sequester more carbon.

On the other hand, this study found that converting native vegetation to pasture reduced soil carbon stocks, by 26% in the first 10 cm of soil (p. 6148, Table 2) and by 16% in the first 30 cm of soil (p. 6149, Table 3). That said, "native vegetation" here wasn't always Cerrado (pp. 6144-46, Table 1).

All told, I'll assume for simplicity that cc = cg. Even if cc is, say, 20% higher or 20% lower than cg, this won't make as much difference to the results as the loss of carbon sequestration by tropical forests does.

#### rm

This document reports 21 metric tons of CO2-equivalent emissions from methane and nitrous oxide per hectare of newly destroyed rainforest. These were converted (see p. 11, table footnote a) to CO2 using the 2007 IPCC AR4 global-warming potential (GWP) conversion factors over a 100-year timeline: 1 metric ton of methane is 25 metric tons of CO2 and 1 metric ton of nitrous oxide is 298 metric tons of CO2. I'm factoring out methane separately because it has a different impact on warming over very long timescales compared with CO2. I don't have enough data to explicitly factor out nitrous oxide as well, so I'll lump it in with methane, because like methane and unlike CO2, it has a more well-defined lifespan.r Thus, to convert 21 metric tons of CO2-equivalent emissions to tons of methane, I just divide by 25 (rm = 21/25 = 0.84). This process of merely changing the scale of the methane-plus-nitrous-oxide emissions amount preserves the observation that nitrous oxide matters more per ton than methane (at least over ~100 years) due to its longer lifespan.

#### tc and tm

This paper cites an estimate of the direct GHG emissions of cattle themselves at 28 kg of CO2-equivalent GHGs per kg of beef carcass weight (p. 1776). However, this number is a combination of CO2, methane, and nitrous oxide. Since I'm counting CO2 separate from the other GHGs, I went to the original paper to disaggregate these components.

The original paper reports (p. 51, Fig. 9.1) emission amounts for each GHG both

• "at the farm-gate" in terms of carcass-weight equivalents, and
• in terms of bone-free beef exported to Europe,

where the latter includes energy costs from slaughter and shipping. Since this essay is mainly focused on consumption choices by Western consumers, the latter figures are more relevant. However, my parameter T is in units of carcass weight rather than bone-free weight, so I convert the bone-free numbers to carcass numbers. The paper says (p. 13) that "1 kg carcass weight (meat with bone) = 0.70 kg bone-free meat". Using this ratio, the GHG impacts per kg of carcass weight in Fig. 9.1 of the source report become

 GHG kg CO2-equivalent per kg carcass weight CO2 1 * 0.7 = 0.7 methane 30.8 * 0.7 = 21.6 nitrous oxide 9 * 0.7 = 6

Then, as I did with rm above, I'll combine methane and nitrous oxide and express them in terms of kg of methane, which the source paper for these numbers also takes to have 25 times the GWP of CO2.

Finally, note that tc and tm are expressed as metric tons CO2 (or methane) per kg carcass weight, so we need to divide the "kg CO2 (or methane) per kg carcass weight" figures by 1000 kg per metric ton.

In the end, we have tc = 0.0007 and tm = (1/1000) * (21.6 + 6)/25 = 0.0011.

However, the paper on which these numbers are based was, in my opinion, somewhat conservative in its calculations. For example, it omitted certain forms of energy expenditure that were assumed negligible, and it probably underestimated ammonia volatilisation (see p. 46). Therefore, I set tc and tm slightly higher than what's calculated in the previous paragraph.

#### T

This paper reports (p. 1775) that Brazil's annual beef production is 8.6 million metric tons of carcass weight, or 8.6 billion kg. This article reports a similar figure: 8.0 Tg = 8.0 billion kg.

#### Q

A cow's brain is 425 to 458 g (average = 442 g), while a human brain is 1300 to 1400 g (average = 1350 g). Humans have 86 billion neurons. So a crude approximation of a cow's number of neurons is (86 billion) * (442/1350) = 28 billion. [EDIT, 25 Oct. 2016: A revision at the end of this post reports on an estimate that cows may have only ~3 billion neurons. I haven't updated the rest of the present article accordingly, but the fact that I'm using what's plausibly too high of an estimate for cow neurons makes the calculations more conservative in the sense of giving too much weight to farmed-animal suffering relative to wild-animal suffering.]

A prototypical insect is the fruit fly, which has 250,000 neurons. Maybe the average neuron count for insects is a bit lower than this if most insects are really small.

Strictly comparing cow vs. insect neurons, we get something on the order of 105 cow-years of suffering per insect-year of suffering. This estimate may be too low if the median insect has a smaller brain than a fruit fly. On the other hand, the estimate may be too high inasmuch as

• I think suffering should probably scale less than linearly in brain size
• cows die less often than bugs, meaning less organism-relative suffering per year per individual.

Given these considerations, the exchange rate between cow and bug suffering should probably be a bit lower -- say 3 * 104 as a point estimate.

As a hack to avoid two-envelopes issues with moral uncertainty, I artifically require that this point estimate have no uncertainty.

#### K

This document reports that in Brazil as a whole, the average age of slaughter is 4 years.

This report says:

Zylberstein & Filho (2000) give information that the average slaughter age has been reduced from 42 – 48 months to 32 – 40 months. It has not been possible to get verified data on what the average slaughter age is today but different experts and researchers interviewed estimate it at 36 – 42 months.

#### W

This document reports that in Brazil as a whole, the average carcass weight is 200 kg. This report (p. 25, Fig. 3.5) shows mean slaughter weights hovering at just under 200 kg carcass weight.

K * T/W is an approximation of Brazil's total beef-cattle population. Using my point estimates, we get (4 cow-years per cow slaughtered) * (8.6 billion kg per year) / (200 kg per cow slaughtered) = 172 million cow-years per year, i.e., a stationary population of 172 million beef cows. This is close to the actual number, which was probably in the ballpark of 158.5 million in 2005.

#### x

This article reports that 55% to 75% (average = 65%) of carcass meat ends up as edible beef in the supermarket. This paper says 70% (p. 13). This paper assumes 66.7%. I use a compromise value of 68%.

#### ec

Animal Charity Evaluators uses a "best estimate" of 0.5 for ec in the case of beef consumed in the US. This may not translate perfectly to Brazil. But 0.5 is the most basic guess for ec, since it results whenever supply elasticity equals the negative of demand elasticity. So it seems like a reasonable median estimate.

## Impact per dollar

Suppose you buy rainforest beef directly as a bulk commodity. (Perhaps you could burn it to make sure animals don't eat the unused meat. You could also give it away, although that would reduce meat consumption by other people.) Assume that rainforest beef costs the same as domestic US beef. US beef prices are ~$210.29 per cwt dressed weight, which is$4.64 per kg, and assuming that ~68% of a carcass is edible beef, that's 4.64/0.68 = $6.82 per kg edible beef. Here's a sanity check of that number. A McDonald’s Quarter Pounder with Cheese costs$3.79 as of Feb. 2016. If we assume that the cost of the input ingredients is, say, ~half the total price and that the cost of the beef is ~half of the price of the ingredients, that would imply $0.95 for a quarter pound of beef (actually, slightly more than a quarter of a pound), which implies$7.86 per kg of beef.

Say the price is about $7 per kg. Then we have ()/($ per kg edible beef) = insect-years per $. ### How about covering over rainforest land directly? Buying rainforest beef amounts to paying other people to keep rainforest as grazed pasture and, in some cases, to burn new rainforest for pasture. But grazing doesn't completely eliminate insects from the land. It would be more clearly positive if we could cover rainforest land with gravel, or apply salt, or do something else to prevent plant growth. That would remove all but the climate-change uncertainty from the above calculations, since a gravel-covered patch of land can't support many insects. And it would avoid causing suffering to cattle, as well as avoid their methane and nitrous oxide emissions. Here I cite one estimate that 75 acres in Belize can be bought for$28,307, which is $930 per hectare. Suppose you could cover it for, say, ~50 years into the future. Assume taxes would cost several times the purchase price over that time. And you'd also have to hire someone to protect your land. Lastly, buying the covering material would be quite expensive. Gravel costs$1-$3 per square foot in the US. Suppose it's only$1 in a South American country. That's still $108,000 per hectare! Maybe there's some other material that costs substantially less -- say$30,000 per hectare?

Say the total cost of covering a hectare of rainforest for 50 years is, optimistically, $45,000. Assuming you eliminate all of the u * N / A = 3 * 108 insects on the land (including those below ground, which would probably eventually taper off once existing soil food in the form of roots and detritus was eaten up), that would prevent (3 * 108 insect-years per year) * (50 years) /$45,000 = 3 * 105 insect-years per \$.

That's at least in a similar ballpark as buying Brazilian beef, and the uncertainty is high, so it might even be more efficient. But it remains interesting that beef production, which isn't intended to remove insects, may be more cost-effective than directly covering land. I guess this reflects the fact that fires and cows are some of the most efficient ways to remove vegetation from an area.

## Other rainforest agricultural products

This report explains about new deforestation in the Amazon:

Although soy became an important driver for a certain number of years [...], pasture was by far the predominant new land use in the deforested region, occupying over 85 percent of the agricultural land in the “legal” Amazon (Kaimowitz et al. 2004).

According to this report (p. 10):

available data strongly suggest that, in terms of the growth and spread of deforestation, cattle ranching is definitely the main economic activity associated with deforestation and that agriculture per se appears to have very little impact on deforestation. This last observation raises the issue about the possible role of soybean as a cause of deforestation in the Amazon (Costa 2000, Becker 1999, Fearnside 2001). The bulk of converted land in the cerrado has been used for cattle ranching and not soybean production. The latter occupies a relatively small area of the anthropic cerrado, and the prospects for expanding into forest areas are limited (Costa, 2000; see also chapter 4). [...] the area of planted pasture in the cerrado tripled between 1975 and 1995, while the crop areas increased by only 9 percent. Soybean, the most widely-grown crop in the cerrado, accounted for 6.3 million hectares in 2000, and represented only 10 percent of the converted area and 5 percent of the area in agricultural establishments.

Of course, it still remains an important question to examine the per kg impact of soybeans and other rainforest-grown crops. The following subsections attempt quick-and-dirty estimates of the impacts of soy and palm oil that are much less thorough than the calculation for beef in this piece.

### Soy

Brazil's soy is "mainly for export and production of biodiesel and animal feed;[20]", rather than for direct production of tofu or soy milk. So pigs and chickens that are given soy-based feed contribute to Brazilian soy production. Holly Gibbs said: "Without the [soy] moratorium, chicken nuggets would once again contribute to rainforest destruction."

According to a 2007 article: "Dr. Daniel Nepstad of the Woods Hole Research Center said the growing demand for corn ethanol means that more corn and less soy is being planted in the United States. Brazil, the world’s largest producer of soybeans, is more than making up for shortfall, by clearing new land for soy cultivation."

A lot of Brazilian soy was exported to the EU and China. One reason for EU demand was its refusal to import GM soy from the US.

This report includes the following helpful figure:

Eyeballing the graph, we can see that in 2010, about 24 million hectares were used to produce about 68 million metric tons of soybeans. That's 3.5 * 10-4 hectare-years per kg. Suppose each hectare of old-growth rainforest has u * N / A = 3 * 108 insects, and suppose that soybean production reduces insect abundance by ~1/3s, a reduction of ~108 insect-years per year. Then each kg of soybeans reduces (3.5 * 10-4 hectare-years per kg) * (108 insect-years per hectare-year) = 3.5 * 104 insect-years per kg.

This calculation didn't consider the time required for newly destroyed rainforest to restore its old-growth state, but as we saw with the beef calculations, that shouldn't change the results by more than a few times, and given the soy moratorium, it's plausible that preventing regrowth of secondary forest is a bigger part of soy's current impact than is directly causing new deforestation. This calculation also didn't consider climate-change impacts, but as we saw with beef, these are unlikely to dominate the total impact. I also didn't consider whether there's a difference between the mass of raw production of soy vs. the mass of finished, edible soy that's bought by pig/chicken farmers and other consumers.

This per-kg impact for soy is close to but somewhat lower than the median estimate (and lower still than the point estimate, which is the proper comparison) for the per-kg impact of rainforest beef, as we would expect given that beef is generally less efficient than plant foods. On the other hand, the above graph shows that almost half of Brazil's soy is exported, compared with only ~1/4 of beef as shown previously, so it may be that Westerners contribute somewhat more to Brazilian soy cultivation per kg purchased than to Brazilian beef per kg purchased (although this depends on how much of each kind of food your particular country buys).

### Palm oil

Palm oil is somewhat different from both beef and soy in that most palm oil is produced in developing, rainforest-rich nations.

This report from 2006 says palm oil plantations occupy 11 million hectares worldwide. This report from 2011 says:

Tropical land occupied by palm oil plantations increased from about 1.55 million hectares in 1980 to about 12.2 million hectares in 2009 (IFC 2011). Much of this land was unsuitable for other food crops, and all of it was formerly covered by lowland tropical forests. Most of the deforestation is recent and driven directly by conversion for palm oil plantations. During the period 1990 to 2005, at least 55 percent of plantation expansion in Indonesia and Malaysia entailed deliberate forest clearing (Koh and Wilcove 2008). [...]

Conversion of primary forests to palm oil plantations accounted for more than 10 percent of deforestation in Indonesia and Malaysia between 1990 and 2010 (Koh et al. 2011).

The report also includes a table showing that global production of palm oil in 2010-11 was 48.0 million metric tons, with 37.3 million metric tons being exported.

So we have about (12.2 million hectare-years per year) / (48.0 million metric tons palm oil per year) = 0.25 hectare-years per metric ton palm oilt = 2.5 * 10-4 hectare-years per kg palm oil. This is reassuringly close to the soy figure of 3.5 * 10-4 hectare-years per kg soy.

Using the same calculation as for soy, we have (2.5 * 10-4 hectare-years per kg) * (108 insect-years per hectare-year) = 2.5 * 104 insect-years per kg. The same caveats as with soy about what's not counted by this calculation apply.u v I also haven't considered impacts like river pollution by Palm Oil Mill Effluent.

Based on the numbers mentioned above, it seems that a bigger fraction of palm oil is produced on newly deforested land than for beef and (especially now with the moratorium) soy. Therefore, insofar as new deforestation contributes an appreciable fraction of the total impact (rather than merely keeping land from reverting to secondary forest), the impact of palm oil should be somewhat higher than the above calculation suggests.

This report includes several pictures of rainforest cleared for palm production, and it's clear that palm farms have much less biomass (although the ratio of primary production between these forests vs. rainforests is probably more similar, and this is a better proxy for suffering). If palm farms are planeted on previously degraded land, they can be net carbon sinks, and in such cases, they might increase insect suffering, but hopefully this applies in only a minority of cases.

Given that 37.3/48.0 = 77.7% of palm oil is exported, we would expect that the fraction of palm oil that you buy that comes from rainforest regions is even higher than for soy, which is higher than for beef. This consideration somewhat (but probably not completely) counteracts the plausibly lower per-kg impacts of palm oil and soy relative to beef. (Keep in mind that these products also have wild-animal impacts when they aren't imported from rainforest countries, which is why I would guess beef still has considerably higher total per-kg impact.)

One other consideration is that it's possible to produce much more palm oil per hectare than for other oil types. So even if palm oil reduces more suffering per hectare than other oils, it's less clear how it's per kg impact compares.

This page describes the uses of palm and palm kernel oil, noting that "Palm oil and palm kernel oil based ingredients are found in approximately 50% of products on supermarket shelves, including food and non food items." This page says:

The EU is the fourth largest consumer of palm oil, using 5.67 million tonnes in 2013, of which around 2.5 million tonnes was for food production. Approximately 5-10% of the palm oil produced worldwide is used as biofuel, with the remaining 40% in cosmetics, detergents, candles, and as industrial lubricants.

How many kg of palm oil does a typical person purchase per year? This page reports that "Germany's consumption of palm oil is around 1.3 million tonnes per year", and Germany's population was ~81 million in 2013, which implies 16 kg per person per year, or about 0.04 kg per day. For comparison, Germany's annual beef consumption per capita is ~8.6 kg per year, or 0.02 kg per day. (Given that a quarter-pound hamburger is 0.11 kg, that's like eating a quarter-pound hamburger only once every 5 days.)

The US imports only 2% of the world's palm oil. Given that worldwide production is 58.094 million metric tons, Americans consume 1.2 million metric tons, which is 3.6 kg per person per year, or 0.01 kg per day. However, this page shows (Fig. 5) that the US imports about 1 million metric tons of palm oil from just Malaysia, so maybe the above estimate is a bit too low.

#### Does palm oil reduce net suffering?

Does buying palm oil reduce wild-animal suffering? Plausibly, but I have a few concerns.

1. Palm-oil trees have high yields of oil, so maybe they displace less native vegetation than other oils would? And do the crops themselves have high net primary productivity, thereby creating lots of plant food, some of which will be eaten by bugs? These questions could be answered by further research.
2. There's research suggesting that older forests might actually have lower productivity than younger ones. If applicable to rainforest destruction, this would be worrying. Of course, this worry also applies to rainforest beef. But in addition to causing deforestation, cattle farming also reduces available productivity insofar as the cattle eat lots of vegetation, which is a consideration that's absent in the case of farming palm oil (except for the palm products that humans consume from palm plantations).

## How about cattle raised in rich countries?

### Comparison with rainforest beef

Given that ~90-99% of beef consumed in the US and Europe is not grown in rainforest regions, evaluating the net impact of beef relies most heavily on an analysis of US and European cattle production. I hope eventually to write a comprehensive analysis of the wild-animal suffering impacts of US and European beef, but for now, we can make some guesses based on the numbers in this piece. In particular, following are some ways in which the rainforest-beef calculations should be adjusted:

 Difference category Difference Suggests that rich-country beef is (better/less good) than rainforest beef Deforestation In general, my impression is that temperate beef grazing involves less deforestation than what happens in Latin America. less good Insect densities Probably insect densities in temperate US and European climates are lower (maybe a few times lower) than in the rainforest, so the suffering reduced by new deforestation and by sustained grazing of grassland would be lower. less good Land used Intensive beef production in rich countries usually requires less land than in Brazil, and cows mature almost twice as quickly. So the hectare-years of grazing per kg of beef might be several times lower in rich countries. less good Burning My impression is that deliberate burning of grasslands is less common in rich countries than in Brazil, but I could be wrong about this. Fire is occasionally used in temperate climates with the aim of increasing plant diversity. The net impact of grazing on unintentional fires is also disputed. unclear given the unclear sign of fires Climate change Assuming temperate forests and grasslands sequester less carbon per hectare than tropical ones, GHG emissions from land-use change would be correspondingly lower in rich countries than in Brazil. However, direct GHG emissions from cows themselves might be roughly the same as in Brazil, or maybe a bit lowerw given that US and European cows live ~1.5-2 years compared with ~4 years for Brazilian cows. There's debate about whether grass-fed cows produce more or fewer GHGs per kg of beef than grain-fed cows. unclear given unclear sign of climate change Crop cultivation Growing crops to feed livestock is more common in the case of intensive US and European beef. The sign of net impact for crop cultivation is unclear, and my best current guess is that the expected value is about zero or maybe slightly bad for the most productive crops like corn. unclear, perhaps less good

Even though temperate beef production looks less good overall, I find it more likely than not that it still reduces net wild-animal suffering. This topic is explored further in an upcoming piece on this site.

## Acknowledgments

Ozzie Gooen's Guesstimate inspired me to try Monte Carlo sampling for this piece. Doing it makes calculations a bit more complex, but I thought it would be nice to try at least once to get intuition for the amount of uncertainty involved in these kinds of calculations.

## Footnotes

1. By 2015, India was actually the world's biggest beef exporter.  (back)
2. This page says "Brazil exports only canned and frozen cooked meats to the U.S. which are not used in the fast-food hamburger industries." But that report seems to be from the early 1990s, so maybe its information is pretty stale?  (back)
3. That said, according to this report (p. XIX):

The study suggests that the high private profitability of ranching arising from the favorable geo-ecological conditions induces both deforestation and the building of roads. As long as the geo-ecological conditions remain favorable, there will be endogenous pressure to open more roads which will be privately built by cattle ranchers in the absence of government. If ranching were not profitable, the existence of roads per se or of a road network built with more geo-political aims in mind (“exogenous” roads) would not be the cause of the present level of deforestation or forest conversion. It is evident, however, that trunk roads constructed for geo-political purposes make ranching viable and therefore increase deforestation.

4. Actually, since all those bugs would have died anyway, the additional suffering is arguably (b-1)/diy, since every insect burned prevents 1/diy insect-years of suffering from whatever death the insect would have had instead?

However, because the bugs burned are killed before they would have died naturally, burning increases deaths per unit time. If the burned bugs were on average halfway through their lives, then one could argue that the additional suffering from burning should be (b-0.5)/diy.

To see this, imagine that each bug has a lifespan of L years, so in a population with only one insect living at a time, there are floor(1/L) deaths within a year. (Taking the floor accounts for the fact that the last insect may not have died yet by the year's end.) If you kill a bug at age L/2 and it's instantly replaced, then over n future years, there will be one death that you caused and an additional floor[(n-L/2) * 1/L] deaths, because in the remaining (n-L/2) years, there's a death rate of 1/L bugs per year. So that's 1 + floor(n/L - 1/2) deaths over n years. If you hadn't killed the bug, there would have been only floor(n/L) deaths over the next n years. So you created the following number of extra deaths:

1 + floor(n/L - 1/2) - floor(n/L)

If some variable X is uniformly distributed over an interval with integers as its lower and upper bounds, then the expected value of floor(X - 1/2) - floor(X) will be -1/2 (since half the time this difference is 0 and half the time it's 1). Let X = n/L. Then, in expectation, your killing the bug created 1 - 1/2 = 1/2 of an extra death.

Then, ignoring the 1 death you caused, the death you inflicted prevented a net 1/2 of a death later. Hence, burning bugs prevents 0.5 deaths that would have happened anyway. However, assuming b is several times bigger than 0.5, it doesn't seem crucial to worry about the difference between b and b-0.5.  (back)

5. This page says: "Livestock grazing does very little damage to mature forests, although it can interfere with natural reforestation."  (back)
6. It's possible that if land that has already been deforested is no longer needed for grazing, it will sometimes be used for another human purpose rather than reverting purely back to rainforest? If this is true, then the impact of delaying regrowth of forest as calculated in this section may be something of an overestimate, since not all grazed land would counterfactually begin regrowing as forest.  (back)
7. Why didn't I include this term for burning of old-growth rainforest? I decided to instead count the impact of burning away potential decomposition biomass inside of the s parameter itself, as is discussed later. The reason I explicitly separated out elimination of biomass here is because burning to maintain pasture occurs every few years rather than just once, and therefore it would have been more confusing to try to incorporate this consideration directly into the g and gc parameters.  (back)
8. My model for the impact of rainforest beef assumes that without continued human intervention, the rainforest would eventually return to an old-growth state, after some number of years of grazing and then Y more years of being a secondary forest. Once an old-growth state returned, the CO2 emitted by burning the forest would be sequestered and hence wouldn't remain in the atmosphere for thousands of years. Of course, there's a chance that technologically stagnant humans would continue ranching on the land indefinitely, in which case that land wouldn't re-sequester the released carbon. But responsibility for that further delay of reforesting should be attributed to future cattle production, not to present-day cattle production. It's also possible that rainforests will dramatically shrink and be unable to recover due to climate change later this century, but if so, that would have happened even without cattle grazing, so it shouldn't be counted as a marginal impact of pasturing livestock.  (back)
9. For data on intensification of Brazilian cattle production, see p. 14 of this report.  (back)
10. Despite the large number of Monte Carlo samples, the raw means of the resulting distribution are somewhat unstable over multiple re-loadings of this page. This seems to be because I'm using lognormal distributions, where a few freak values can be very big, throwing off the means. To mitigate this, I'm only taking the mean of the middle 90% of values, which eliminates the extreme tail samples.  (back)
11. If the parameter is lognormally distributed, this input is the standard deviation of log10 of parameter. If the parameter is normally distributed, this is just the standard deviation of the parameter itself.  (back)
12. I'm uncertain which of the latter two labels better applies to the majority of tropical rainforests.  (back)
13. Strangely, the source paper elsewhere gives a productivity of 5.5 to 11 Mg/hectare-year for "fertilized" Brachiaria decumbens. So is the "5.5 to 12" number for fertilized or unfertilized? If the paper meant to say "fertilized", then these numbers are less useful for my purpose here because native savanna wouldn't be fertilized.  (back)
14. This type of grass does support insects, though perhaps fewer than are supported by rainforst?  (back)
15. Most of these states are part of the rather than the Cerrado, but I'd guess that primary productivity is closer to that in the Cerrado or maybe even lower.  (back)
16. This source reports a similar 170 million hectares.  (back)
17. That's somewhat higher than the ~2.3 million hectares per year that I see by eyeballing Fig. 2 in this article.  (back)
18. Of course, unlike methane, nitrous oxide doesn't decay into CO2, which means its long-term climate change impact may be considerably smaller than for methane. But methane played a larger role in the estimate of 21 metric tons of CO2-equivalent. As this document says, "The resulting emissions of methane (CH4) and nitrous oxide (N2O) from the initial burning are 16±8 tCO2e ha-1 and 5±2.5 tCO2e ha-1, respectively." Therefore, imprecision about nitrous oxide should affect the calculations of the effect of non-CO2 emissions from land-use changes by less ~25% or something.  (back)
19. Clearing for farming actually requires more complete elimination of forest material than with clearing for pasture: "Clearing had to be quite complete in order to use machinery; while cattle can graze around recently-felled trees, leaving stumps or woody debris in crop fields would risk damaging combines and planters." However, the crops that are grown add primary production to the fields, while cows remove primary production. So the amount of primary production left over to feed insects seems plausibly lower on pasture than crop fields, but this isn't obvious and should be explored further.  (back)
20. This is 4 metric tons per hectare-year. That number agrees with a typical yield of 3.69 metric tons per hectare as reported by this page. And it largely concurs with the statement on this page about palm oil that "The most efficient producers may achieve yields as high as eight tonnes of oil per hectare."

Here are some other estimates for this parameter:

• "In 2012, Malaysia, the world's second largest producer of palm oil,[39] produced 18.79 million tonnes of crude palm oil on roughly 5,000,000 hectares (19,000 sq mi) of land.[40][41]" (source) That implies (5 million hectare-years per year)/(18.79 million metric tons per year) = 0.27 hectare-years per metric ton.
• Malaysia's national average crude palm oil yield in metric tons per hectare in 2011 was about ~4, which implies ~0.25 hectare-years per metric ton.(source)
• "In 2013, Thailand produced 2.0 million tonnes of crude palm oil on roughly 626 thousand hectares.{{FAOStat}}" (source) That implies (0.626 million hectare-years per year)/(2.0 million metric tons per year) = 0.31 hectare-years per metric ton.

This page agrees with the figure of 4 metric tons per hectare-year: "The oil palm planted currently is the tenera hybrid which yields about 4.0 t of palm oil per hectare, together with 0.5 t palm kernel oil and 0.6 t palm kernel cake." As that quote mentions, more than just palm oil is produced on a hectare-year of palm-oil plantations. So my naive calculation of how many hectare-years of palm-oil plantations are caused by consumption of a given amount of palm oil is a slight overestimate, since that calculation assumes that palm oil is the only product sold from plantations, ignoring palm kernel oil and palm kernel cake. On the other hand, my estimate of hectare-years per kg of palm oil may also be slightly too low because it ignores the 30 months of palm-oil farming during which no product is produced: "Oil palm has an economic life of about 25 years. The harvesting of the palm could begin 30 months after field planting." Plus, as the second figure on this page shows, yields are fairly low during the first ~5 years after planting.  (back)

21. Climate change can be a bigger deal for palm oil than for soy because palm plantations on newly cleared peatland release lots of stored carbon as CO2 and methane. Plantations replacing primary forest on mineral soil release between -47 and 225 metric tons of carbon per hectare (where the "-" sign means net sequestration of carbon), while over a 25-year period, plantations replacing peat soil can release 169 to 723 metric tons of carbon per hectare -- which is possibly several times more than in the case of mineral soil. Even so, given that the reduction in insect populations from clearing rainforest typically was bigger than the potential increase in insects from climate change in the case of beef, I doubt this higher climate impact for the 11+% of palm plantations on peat soil outweighs the benefits of reduced primary production by the palm-oil industry as a whole.

As far as direct emissions from processing palm oil, these seem much lower than direct emissions from beef per metric ton. In particular, this paper cites a figure (p. 1776) of 28 kg of CO2-equivalent directly emitted per kg carcass weight, or 28 metric tons of CO2-equivalent directly emitted per metric ton carcass weight. In contrast:

A complete life-cycle carbon model, based on palms grown in established plantations, estimates that growing and refining each metric ton of crude palm oil (CPO) produces the equivalent of 0.86 metric ton of carbon dioxide (Chase and Henson 2010).

Maybe the palm-oil emissions have more CO2 rather than methane and so have more long-term impact (since CO2 lasts millennia, while methane lasts only decades), but beef still seems to dominate palm oil when it comes to the impact of direct emissions during production.  (back)

22. One interesting question is whether palm oil used specifically as biofuel contributes to climate change on balance. This page says "According to Greenpeace, clearing peatland to plant oil palms releases large amounts of greenhouse gasses, and that biodiesel produced from oil palms grown on this land may not result in a net reduction of greenhouse gas emissions.[54]" It's probably true that destroying peatland releases more GHGs than the avoided GHG emissions from one year of grown palm oil. After all, the reason biofuels reduce GHG emissions is that they avoid letting plants decompose naturally and instead burn those plants for energy. But the GHGs that would have been released by one year of decomposition of vegetation that's instead burned as fuel is probably small compared with all the stored carbon in peatlands.

On the other hand, release of peatland GHGs are a one-time cost, while palm-oil biofuel could continue averting fossil-fuel use year after year into the future. So at least in principle, those averted fossil-fuel emissions would seem to outweigh the initial GHG loss in peatlands. Of course, this point doesn't apply to palm oil grown for uses other than biofuel.  (back)

23. This piece reports (p. 6):

The GHG emissions in the primary production of Brazilian beef production (not including land-use changes) are at least 30-40 % higher than current European production. High emissions of methane is the main cause and explained by high slaughter ages and long calving intervals, and also that the majority of beef is produced in cow-calf systems, not as by-products from milk production.

Table 10.4 (p. 58) of the piece shows that EU beef has higher direct (non-land-use-change) CO2 emissions but lower methane emissions than Brazilian beef.  (back)