Based on a simple ecosystem model with predators and prey, I argue that fishing may increase total harms to wild animals whereas agriculture may decrease total harms. However, as this is based on a very simplified model (it only includes herbivorous and predatory vertebrate animals), and as there is large uncertainty about the sign of average wild animal welfare (whether it is net positive[i] or net negative[ii]), this conclusion is very tentative. 

The mathematics of the harm cascade

The harm cascade occurs when individuals (humans or animals) harm other individuals (humans or animals) that also harm other individuals that harm other individuals and so on. If you help the first individuals, they cause more harm to the second group of individuals. Hence, helping some individuals can indirectly harm other individuals. But that extra harm to the second group of individuals means those individuals cause less harm to the third group of individuals. That third group is then very indirectly helped by your help offered to the first group of individuals. 

With a harm cascade it becomes very difficult to estimate whether helping individuals is net beneficial or harmful to the total group of all individuals. The harm cascade is a prime example of complex cluelessness in consequentialist ethics.[iii] That is why it is extremely difficult to estimate whether human activities such as fishing and agriculture are harmful to animals overall. To better understand the effects of human activities on wild animal welfare, we can use a generalized Lotka-Volterra ecosystem model given by two dynamic equations that represent the rate of changes of herbivorous animals and predatory animals. 

The rate of change of the herbivorous animals is given by the equation

dH/dt = r.H – m.H – h.H – c.H.H – p.H.P,

with H the population size of all herbivorous animals (as a function of time t), r the reproduction rate (number of offspring per animal per unit of time), m the intrinsic mortality rate (the fraction of herbivorous animals that die per time unit due to ageing, non-infectious diseases, extreme cold and heat and other causes that do not depend on the populations of humans, herbivores or predators), h the human-caused mortality rate (due to fishing, hunting, pollution, environmental degradation, agricultural pest control, ploughing and other human activities), c the competition parameter (the mortality due to competition for scarce resources, starvation, fighting with other herbivores and infectious diseases from other herbivores), p the predation pressure parameter (the mortality due to predation) and P the population size of all predator animals (as a function of time t).

The rate of change of the group of predator animals is given by

dP/dt = r’.P + p’.H.P  – m’.P – h’.P – c’.P.P,

with r’ the intrinsic predator reproduction rate (the number of offspring per predator animal per unit of time due to predators being omnivores eating plant food sources), p’ the predator population growth rate parameter due to predation, m’ the predator intrinsic mortality rate, h’ the human-caused predator mortality rate (from fishing and other human activities) and c’ the predator competition parameter. The predator reproduction rate due to predation is given by p’.H and hence depends on the herbivore population density. If predators are pure carnivores that do not eat plants (i.e. r’=0) and if there are no herbivores (i.e. H=0), then predators cannot eat anything, which means they cannot reproduce, which means their population cannot grow. 

Note that the terms c.H.H, p.H.P and c’.P.P in the equations are negative, which means they represent harms, and that those terms are proportional to the products of population sizes, which means that those harms are caused by other animals. Hence, these terms are the source of the harm cascade. For example the term c.H.H includes the herbivore mortality rate of competition c.H, which is the fraction of herbivores that are killed by other herbivores per unit of time. This mortality rate depends on the number of herbivores, because the other herbivores are the cause of the competition and hence the cause of death. This competition not only includes competition for food or water, but also infectious diseases that herbivores can get from other herbivores. The more herbivores there are, the easier infectious diseases can spread.

In reality, the parameters (r, m, h,…) are stochastic variables, but for simplicity we can assume they are constants. Then the ecosystem model has a steady state or equilibrium given by the equilibrium population sizes

H* = (r-m-h-p.P*)/c,

P* = (r’+p’.H*-m’-h’)/c’.

Note that the competition parameters c and c’ generally cannot be zero, otherwise the equilibrium population sizes could easily explode to infinity. That means there is always some harm cascade: animals are always harmful to other animals. 

The total death rates (fractions of animals dying per unit of time) of the herbivores and predators in the steady state are respectively:

d* = m + h + c.H* + p.P* = r,

d’* = m’ + h’ + c’.P* = r’ + p’.H*.

With these equations, we can study the effects of fishing and agriculture. 

The overall impact of fishing

Fishing increases the parameters h and h’, but humans mainly fish for predator species, so primarily h’ increases and is larger than h. As a result, the steady state predator population P* decreases and the herbivore population H* increases. This is in line with empirical data on fish populations. The biomass of predatory fish decreased over the past century, whereas the biomass of prey fish (herbivorous and planktivorous fish) increased.[iv] As marine food webs usually have a pyramid structure, with more biomass in the lower trophic levels, and as prey fish at the lower trophic levels are usually smaller than predatory fish at higher levels, the total fish population H*+P* increases. This is also in line with empirical data. For example, the unweighted marine Living Planet Index shows an increase, which means that the (unweighted geometric) average marine vertebrate population increased since 1970.[v]

As the number of fish increases due to fishing, the total mortality d*.H*+d’*.P* increases. This does not yet mean that the harm to animals increases, because obviously more animals means more animals dying. To study the harm, we have to look at the average death rate, which is the total mortality divided by the population size H*+P*. Note that the herbivory fish death rate d* equals r and hence does not depend on the fishing rates h and h’. But the predatory fish death rate d* depends on H*, which increases if the fishing rate h’ increases. Hence, fishing increases the average death rate of fish, due to an increased death rate of predatory fish. In that sense, fishing is overall harmful to fish. However, marine invertebrates may also be sentient but are not included in the above model. If more abundant planktivorous fish decrease the population size of sentient zooplankton, fishing could be beneficial by reducing total aquatic animal harms (because of a reduced average death rate of fish and invertebrates combined).

The overall impact of agriculture

Agriculture (even vegan agriculture) increases the human-caused mortality rates h and h’, because animals may be accidentally killed when ploughing and harvesting or they are controlled (intentionally killed) with pesticides and predators. The increased mortality rates due to agriculture is the primary reason of vertebrate land animal populations declining (see the terrestrial Living Planet Index^[vi]). As with fishing, the herbivore death rate d* stays constant, but in contrast with fishing, the predatory death rate d’* decreases due to a decrease in the herbivore population H*. 

This may seem counter-intuitive: agriculture decreases the average death rate of vertebrate animals and hence decreases lethal harm to wild animals. Some meat eaters argue that eating meat is permissible because vegan agriculture is also harmful to animals just like animal agriculture. If vegans may harm animals (either directly or indirectly, by increasing their death rates), then meat eaters are also allowed to harm animals (by eating them), so the argument goes. This argument is fallacious, because vegan agriculture may decrease harm to wild animals (compared to no agriculture), by decreasing the death rates of predatory animals. And as vegan agriculture also decreases the number of predators (compared to no agriculture), the number of animals used as merely a means (killed and eaten) also decreases. However, compared to animal agriculture, it is not clear whether vegan agriculture is less harmful to wild animals, because animal agriculture could result in stronger declines of wild herbivorous and predatory animal populations. After all, animal agriculture has a higher land use than vegan agriculture, and land use is the main driver of wild animal population declines. Furthermore, note that the changes in death rates and population sizes due to vegan and animal agriculture have unknown effects on the total welfare of wild vertebrate animals, because we do not know whether wild animals have a positive or negative welfare on average.

The importance of wildlife fertility control

The steady state death rates d* and d’* are dependent on the reproduction rates r and r’. This means that if we want to decrease wild animal harms by decreasing the death rates of wild animals, we have to decrease the reproduction rates. This explains why the high fertility rates are the root cause of the harm cascade. Animals with an r-selection reproductive strategy have a high reproduction rate r, which means they get many offspring.[vii] Those animals are either more likely to be harmed by other animals such as predators, such that they die prematurely, or they more likely cause harm to other animals, for example through increased competition. As lowering the reproduction rates are crucial to mitigate the harm cascade, wildlife fertility control is of crucial importance. 

[i] Browning, H., & Veit, W. (2023). Positive wild animal welfare. Biology & Philosophy, 38(2), 14.

[ii] Horta, O. (2010). Debunking the Idyllic View of Natural Processes: Population Dynamics and Suffering in the Wild. Télos 17(1), 73–88.

[iii] Greaves, H. (2016, December). Xiv—cluelessness. In Proceedings of the Aristotelian Society (Vol. 116, No. 3, pp. 311-339). Aristotelian Society.

[iv] Christensen, V., Coll, M., Piroddi, C., Steenbeek, J., Buszowski, J., & Pauly, D. (2014). A century of fish biomass decline in the ocean. Marine ecology progress series, 512, 155-166.

[v] Toszogyova, A., Smyčka, J., & Storch, D. (2024). Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline. Nature Communications, 15(1), 5295.

McRae, L., Deinet, S., & Freeman, R. (2017). The diversity-weighted living planet index: controlling for taxonomic bias in a global biodiversity indicator. PloS one, 12(1), e0169156.

[vi] Toszogyova, A., Smyčka, J., & Storch, D. (2024). Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline. Nature Communications, 15(1), 5295.

McRae, L., Deinet, S., & Freeman, R. (2017). The diversity-weighted living planet index: controlling for taxonomic bias in a global biodiversity indicator. PloS one, 12(1), e0169156.

[vii] Johannsen, K. (2017). Animal Rights And The Problem Of R-strategists. Ethical Theory And Moral Practice, 20(2). 333-345.