by Brian Tomasik
First written: 2016; last update: 9 Nov. 2017

## Summary

This page presents a simple but plausible argument why it's always better to have lower crop yields from the perspective of reducing invertebrate populations.

Note: The claim is that lower crop productivity often reduces invertebrate populations when planting on a given piece of land. It's not always the case that lower-productivity crops are better across all contexts. For example, using irrigation to plant low-productivity vegetables in a desert would probably increase invertebrate populations, while planting crops with somewhat higher productivity than those vegetables but still fairly low productivity in former prairie or forest might reduce invertebrate populations.

## Assumptions and notation

Let pc be the average net primary productivity of cropland plants and pn be the average net primary productivity of native (non-crop) vegetation.

Assume a constant conversion factor f from pc to edible food yields. For instance, pc can be measured as total kJ of energy produced per hectare per year, while f * pc is total kJ of edible food produced per hectare per year. This factor is similar to the harvest index, although rather than being (dry mass of food)/(all aboveground dry mass), I intend f to be (kJ of food produced per year)/(kJ of all aboveground and belowground crop and weed vegetation on the field produced per year).

Assume that humans will always produce some constant amount E of edible food per year, regardless of the cost of food production (which is obviously not true in practice).

Assume that when native land is appropriated for agriculture, the average productivity of the remaining native land remains the same as before. (This isn't quite true in practice, because humans may appropriate more fertile lands for agriculture first. However, relaxing this assumption would suggest that crop cultivation reduces invertebrate populations even more than my argument shows.)

Finally, assume that invertebrate populations are proportional to net primary productivity, except for the fraction of productivity eaten by humans or livestock or used as biofuel.

## Proving the claim

Humans will farm some number of hectares of land Hc such that Hc * f * pc = E. Let H be the total number of hectares of land on Earth. H - Hc hectares on Earth contain native vegetation.

The total net primary productivity not fed to humans or livestock or converted to biofuel on Earth is Hc * pc * (1-f) + (H - Hc) * pn. Because Hc * f * pc = E, Hc = E / (f * pc). So Earth's total net primary productivity left over to potentially feed invertebrates is

[E / (f * pc)] * pc * (1-f) + [H - E / (f * pc)] * pn
= E * (1-f)/ f + H * pn - E * pn / (f * pc).

A smaller value of pc means a smaller value of the above expression. QED.

## A visual demonstration

Conceptually, what's going on here is that if crop productivity is lower, then more land is needed to produce the same amount of crop production, which implies less land left over for native vegetation.

The following picture shows how I think about the situation. (This figure is exaggerated to illustrate the point.) The y axis represents net primary productivity (NPP) per hectare. The x axis shows how many hectares of Earth's land are used up for crops vs. are left over for native vegetation. The area of the orange quadrilateral is constant, to produce a constant total food harvest.

## Practical implications

The argument in this piece suggests that producing the same amount of food energy with lower-yielding crops generally reduces invertebrate suffering (ignoring climate change, far-future effects, etc.). For example, eating foods that yield fewer calories per hectare is generally better. Conversely, fertilizer and irrigation are generally bad. Lower yields are better regardless of whether the crop initially has very high or very low net primary productivity.

In contrast, if we're considering an action that changes not crop yields but the amount of crop consumed (i.e., changes E), then it matters whether the crop has very high or very low net primary productivity compared with native vegetation. If the crop has such high yields that, even after extracting the food eaten by humans/livestock, the remaining net primary productivity per hectare is greater than what would have grown on wild land, then consuming more of this kind of crop increases invertebrate suffering (given the assumptions of my framework). Meanwhile, consuming more of a food that has very low net primary productivity compared with native vegetation reduces invertebrate suffering.

Finally, lowering crop yields by means of greater insect pest damage to crops is probably bad, because the main purpose of lowering yields is to reduce the number of invertebrates fed by plants. To illustrate, here's an example with made-up numbers. Imagine a plant with biomass of B. Suppose that 10% of B is eventually eaten by invertebrate detritivores, with the rest eaten by bacteria, fungi, etc. So invertebrates eat 0.1 * B of biomass. Now suppose that if invertebrate herbivores eat 5% of the plant, they further reduce its growth by 5% in addition to the biomass they eat themselves. So the plant eventually only grows to 0.9 * B of biomass, and 0.05 * B was eaten by invertebrate herbivores along the way. 10% of 0.9 * B = 0.09 * B is eaten by invertebrate detritivores. So the total amount eaten by invertebrates is now 0.05 * B + 0.09 * B = 0.14 * B instead of 0.1 * B before. Thus, there are probably more invertebrates in the scenario of invertebrate herbivory.

There might be a few exceptions to the previous point if the plant damage is very severe due to infestation by only a small number of invertebrates. An unrealistic example to illustrate the point: If a single aphid magically halved the productivity of an entire field of corn, then that insect pest's damage would prevent lots of invertebrates from being born on balance.