Skip to main content

Does suffering dominate enjoyment in the animal kingdom? An update to welfare biology


Ng (Biol Philos 10(3):255–285, 1995. models the evolutionary dynamics underlying the existence of suffering and enjoyment and concludes that there is likely to be more suffering than enjoyment in nature. In this paper, we find an error in Ng’s model that, when fixed, negates the original conclusion. Instead, the model offers only ambiguity as to whether suffering or enjoyment predominates in nature. We illustrate the dynamics around suffering and enjoyment with the most plausible parameters. In our illustration, we find surprising results: the rate of failure to reproduce can improve or worsen average welfare depending on other characteristics of a species. Our illustration suggests that for organisms with more intense conscious experiences, the balance of enjoyment and suffering may lean more toward suffering. We offer some suggestions for empirical study of wild animal welfare. We conclude by noting that recent writings on wild animal welfare should be revised based on this correction to have a somewhat less pessimistic view of nature.

This is a preview of subscription content, access via your institution.


  1. 1.

    It may be the case, of course, that the concavity of the square of a function changes over its domain, so while this condition is sufficient, it is not necessary.

  2. 2.

    Evidence of concave utility functions in economics traditionally draws on research into risk aversion, which shows that averaging a concave (Bernoulli) utility function across possible outcomes gives rise to risk-averse behavior (Pratt 1964). Behavioral economics modifies the traditional picture of risk aversion to include the possibility of loss aversion, where both the utility of gains and negative utility of losses are concave (Tversky and Kahneman 1992).

    While Tversky and Kahneman’s finding supports the concavity of suffering and enjoyment, it may seem to undermine the claim of symmetry because people tend to weigh losses more than gains. On further inspection, this result is entirely consistent with symmetric evolutionary cost functions based on the simple fact that apparent losses in the wild more often pose a risk of failure to survive than successes. Weber et al. (2004) note that prospect theory closely represents the energy budget rule for animals’ risk-related behavior (Caraco 1980; Stephens 1981), because apparent losses generally pose a greater risk of starvation than equally-sized apparent gains. This implies that even if the evolutionary costs of suffering and enjoyment are identical, organisms should be more averse to losses than to gains. Hence available evidence is consistent with symmetrical functions for the evolutionary cost of suffering and enjoyment.

  3. 3.

    In the original paper (Ng 1995), n was defined as the number of failing organisms per successful organism, but this leads to a problem in the interpretation of a budget of the form CE + nCS = M. As n increases, two different attributes of the species increase: the failure rate and the total number of organisms whose costs are included by the budget. When n = 5, for example, the constant budget must be divided over six organisms. This is a problem, because we are interested in the optimization for each individual organism. We can think of there being a probability p of an organism succeeding and p − 1 of an organism failing, so that pCE + (p − 1)CS = M. This simplifies to CE + ((p − 1)/p)CS = M, so we can think of n as being equal to (p − 1)/p, or the ratio of the rate of failure to the rate of success, with no loss of generality.

    An alternative way of dealing with this problem would be to include a further parameter, say b, for the number of successful organisms constrained by the budget, as Dawrst (2009) does. This would give us bCE + bnCS = M. This leads to the same conclusions, as the equation simplifies to CE + nCS = M/b. Note that M/b is exactly what we have defined M as above: the evolutionary suffering and enjoyment budget for an individual organism. Hence we can safely define n as the ratio between failure and success, and M as the individual budget constraint.

  4. 4.

    The optimization problem here is to maximize the total extent of affective emotions per organism, that is, E(CE) + S(CS), subject to the posited constraint, CE+nCS=M. Ng (1995) argues that genetic selection maximizes the per-organism difference between enjoyment in the case of success and negative enjoyment in the case of failure, which is equivalent to the sum of enjoyment per reproductive success and suffering per failure.


  1. Berridge KC (2000) Measuring hedonic impact in animals and infants: microstructure of affective taste reactivity patterns. Neurosci Biobehav Rev 24(2):173–198.

    Article  Google Scholar 

  2. Berridge KC, Robinson TE (1998) What is the role of dopamine in reward: hedonic impact, reward learning, or incentive salience? Brain Res Rev 28(3):309–369.

    Article  Google Scholar 

  3. Broom DM (1991) Animal welfare: concepts and measurement. J Anim Sci 69(10):4167–4175.

    Article  Google Scholar 

  4. Caraco T (1980) On foraging time allocation in a stochastic environment. Ecology 61(1):119–128.

    Article  Google Scholar 

  5. Chalmers DJ (1995) Facing up to the problem of consciousness. J Conscious Stud 2(3):200–219.

    Article  Google Scholar 

  6. Clark S (1979) The rights of Wild things. Inquiry 22 (1–4):171–188

    Article  Google Scholar 

  7. Cowen T (2003) Policing nature. Environ Ethics 25(2):169–182.

    Article  Google Scholar 

  8. Cunha LC (2015) If natural entities have intrinsic value, should we then abstain from helping animals who are victims of natural processes. Relat Beyond Anthropocentrism 3:51.

    Article  Google Scholar 

  9. Dawrst A (2009) The predominance of wild-animal suffering over happiness: an open problem. Essays on Reducing Suffering.

  10. Dehaene S (2003) The neural basis of the Weber–Fechner law: a logarithmic mental number line. Trends Cognit Sci 7(4):145–147.

    Article  Google Scholar 

  11. Donaldson S, Will K (2013) A defense of animal citizens and sovereigns. Law Ethics Philos 1:143–160

    Google Scholar 

  12. Duncian I (1992) Measuring preferences and the strength of preferences. Poult Sci 71(4):658–663.

    Article  Google Scholar 

  13. Ebert R, Machan TR (2012) Innocent threats and the moral problem of carnivorous animals. J Appl Philos 29(2):146–159.

    Article  Google Scholar 

  14. Gossen HH (1854/1983) The laws of human relations and the rules of human action derived therefrom. MIT Press, Cambridge, English translation of the 1854 original

  15. Harsanyi JC (1953) Cardinal utility in welfare economics and in the theory of risk-taking. J Polit Econ 61:434–435.

    Article  Google Scholar 

  16. Harsanyi JC (1955) Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J Polit Econ 63(4):309–321.

    Article  Google Scholar 

  17. Horta O (2010a) Debunking the idyllic view of natural processes: population dynamics and suffering in the wild. Télos 17(1):73–88

    Google Scholar 

  18. Horta O (2010b) The ethics of the ecology of fear against the nonspeciesist paradigm: a shift in the aims of intervention in nature. Between Species 13(10):10.

    Article  Google Scholar 

  19. Horta O (2015) The problem of evil in nature: evolutionary bases of the prevalence of disvalue. Relat Beyond Anthropocentrism 3:17.

    Article  Google Scholar 

  20. Kosfeld M et al (2005) Oxytocin increases trust in humans. Nature 435(7042):673.

    Article  Google Scholar 

  21. Krueger LE (1991) Reconciling Fechner and Stevens: toward a unified psychophysical law. Behav Brain Sci 14(1):187.

    Article  Google Scholar 

  22. Kymlicka W, Donaldson S (2011) Zoopolis: a political theory of animal rights. Oxford University Press, Oxford

    Google Scholar 

  23. Lesch K-P et al (1996) Association of anxiety-related traits with a polymorphism in the serotonin transporter gene regulatory region. Science 274(5292):1527–1531.

    Article  Google Scholar 

  24. Luce RD, Eugene G (1963) Psychophysical scaling. Handb Math Psychol 1:245–307

    Google Scholar 

  25. Maina G et al (2004) Weight gain during long-term treatment of obsessive-compulsive disorder: a prospective comparison between serotonin reuptake inhibitors. J Clin Psychiatry 65(10):1365–1371.

    Article  Google Scholar 

  26. Mannino A (2015) Humanitarian intervention in nature: crucial questions and probable answers. Relat Beyond Anthropocentrism 3:109

    Google Scholar 

  27. Matthews D (2015) The world’s most famous utilitarian on whether all carnivorous animals should be killed. Vox.

  28. McMahan J (2010) The meat eaters. The New York Times 19.

  29. National Research Council (2014) Subjective well-being: measuring happiness, suffering, and other dimensions of experience. National Academies Press, Washington DC

    Google Scholar 

  30. Ng Y-K (1995) Towards welfare biology: evolutionary economics of animal consciousness and suffering. Biol Philos 10(3):255–285.

    Article  Google Scholar 

  31. Ng Y-K (2016a) How welfare biology and commonsense may help to reduce animal suffering. Animal Sent 7(1):1–10

    Google Scholar 

  32. Ng Y-K (2016b) Utilitarianism generalized to include animals: response to commentary on Ng on animal suffering. Anim Sent 1:19

    Google Scholar 

  33. Pratt JW (1964) Risk aversion in the small and in the large. Econometrica 32(1/2):122–136.

    Article  Google Scholar 

  34. Rankin CH et al (2009) Habituation revisited: an updated and revised description of the behavioral characteristics of habituation. Neurobiol Learn Mem 92(2):135–138.

    Article  Google Scholar 

  35. Stephens DW (1981) The logic of risk-sensitive foraging preferences. Anim Behav 29(2):628–629.

    Article  Google Scholar 

  36. Stevenson B, Justin W (2008) Economic growth and subjective well-being: reassessing the Easterlin paradox. No. w14282. National Bureau of Economic Research.

  37. Sugita Y, Suzuki Y (2003) Audiovisual perception: implicit estimation of sound-arrival time. Nature 421(6926):911.

    Article  Google Scholar 

  38. Thompson R, Spencer W (1966) Habituation: a model phenomenon for the study of neuronal substrates of behavior. Psychol Rev 1(73):16–43.

    Article  Google Scholar 

  39. Tomasik B (2016) Habitat destruction, not preservation, generally reduces wild animal suffering.

  40. Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297–323.

    Article  Google Scholar 

  41. Waldinger MD et al (1998) Effect of SSRI antidepressants on ejaculation: a double-blind, randomized, placebo-controlled study with fluoxetine, fluvoxamine, paroxetine, and sertraline. J Clin Psychopharmacol 18(4):274–281

    Article  Google Scholar 

  42. Weber EU, Shafir S, Blais A-R (2004) Predicting risk sensitivity in humans and lower animals: risk as variance or coefficient of variation. Psychol Rev 111(2):430.

    Article  Google Scholar 

  43. Wemelsfelder F et al (2000) The spontaneous qualitative assessment of behavioural expressions in pigs: first explorations of a novel methodology for integrative animal welfare measurement. Appl Anim Behav Sci 67(3):193–215.

    Article  Google Scholar 

  44. Wild Animal Welfare Committee (2019) Who are the guardians of wild animla welfare? Conference program. Wild Animal Welfare Committee, Edinburgh

    Google Scholar 

Download references


This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1656518.

Author information



Corresponding author

Correspondence to Zach Groff.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix: Derivation of Eq. (5)

Appendix: Derivation of Eq. (5)

We derive Eq. (5) starting with the following maximization problem:

$$\begin{aligned} & \max_{{\left\{ {C_{E} , C_{S} } \right\}}} \ln (\alpha C_{E} + 1) + \ln (\upalpha{\text{C}}_{\text{S}} + 1) \\ & \quad \quad s.t.\quad M = \frac{1}{n + 1}C_{E} + \frac{n}{n + 1} C_{S} \\ \end{aligned}$$

This yields the Lagrangian:

$$L = \ln (\alpha C_{E} + 1) + \ln (\upalpha{\text{C}}_{\text{S}} + 1) + \mu (M(n + 1) - C_{E} - nC_{S} )$$

Leading to first-order conditions:

$$0 = \frac{\partial L}{{\partial C_{E} }} = \frac{\alpha }{{\alpha C_{E} + 1}} - \mu$$
$$0 = \frac{\partial L}{{\partial C_{S} }} = \frac{\alpha }{{\alpha C_{S} + 1}} - n\mu$$

Combining and rearranging terms gives:

$$C_{E} = nC_{S} + \frac{n - 1}{\alpha }$$

Plugging this into the budget leads to the following:

$$M(n + 1) = n C_{S} + \frac{n - 1}{\alpha } + nC_{S} = 2nC_{S} + \frac{n - 1}{\alpha }$$
$$C_{S} = \frac{M}{2n}(n + 1) - \frac{n - 1}{2n\alpha }$$

Combining this with the equation for \(C_{E}\) in terms of \(C_{S}\), we get:

$$C_{E} = \frac{M}{2}(n + 1) + \frac{n - 1}{2\alpha }$$

Now we can calculate the balance of suffering and enjoyment by taking suffering minus enjoyment per individual:

$$\begin{aligned} \frac{1}{n + 1}(nS(C_{S} ) - E(C_{E} )) & \quad = \frac{1}{n + 1}\left( {n\ln \left[ {\frac{M\alpha }{2n}(n + 1) - \frac{n - 1}{2n} + 1} \right] - \ln \left[ {\frac{M\alpha }{2}(n + 1) + \frac{n - 1}{2} + 1} \right]} \right) \\ & \quad = \frac{1}{n + 1}\left( {n\ln \left[ {\frac{1}{n}\left( {\frac{M\alpha }{2}(n + 1) + \frac{n + 1}{2}} \right)} \right] - \ln \left[ {\frac{M\alpha }{2}(n + 1) + \frac{n + 1}{2}} \right]} \right) \\ & \quad= \frac{1}{n + 1}\left( {\ln \left[ {\frac{1}{{n^{n} }}\left( {\frac{(M\alpha + 1)(n + 1)}{2}} \right)^{n - 1} } \right]} \right) \\ &\quad = \left( {\frac{1}{n + 1}} \right)\ln \left[ {\frac{{(\upalpha{\text{M}} + 1)^{{{\text{n}} - 1}} (n + 1)^{n - 1} }}{{2^{n - 1} n^{n} }}} \right] \\ \end{aligned}$$

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Groff, Z., Ng, YK. Does suffering dominate enjoyment in the animal kingdom? An update to welfare biology. Biol Philos 34, 40 (2019).

Download citation


  • Animal welfare
  • Animal suffering
  • Welfare biology
  • Effective altruism
  • Evolutionary biology