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Altruism in a volatile world


The evolution of altruism—costly self-sacrifice in the service of others—has puzzled biologists1 since The Origin of Species. For half a century, attempts to understand altruism have developed around the concept that altruists may help relatives to have extra offspring in order to spread shared genes2. This theory—known as inclusive fitness—is founded on a simple inequality termed Hamilton’s rule2. However, explanations of altruism have typically not considered the stochasticity of natural environments, which will not necessarily favour genotypes that produce the greatest average reproductive success3,4. Moreover, empirical data across many taxa reveal associations between altruism and environmental stochasticity5,6,7,8, a pattern not predicted by standard interpretations of Hamilton’s rule. Here we derive Hamilton’s rule with explicit stochasticity, leading to new predictions about the evolution of altruism. We show that altruists can increase the long-term success of their genotype by reducing the temporal variability in the number of offspring produced by their relatives. Consequently, costly altruism can evolve even if it has a net negative effect on the average reproductive success of related recipients. The selective pressure on volatility-suppressing altruism is proportional to the coefficient of variation in population fitness, and is therefore diminished by its own success. Our results formalize the hitherto elusive link between bet-hedging and altruism4,9,10,11, and reveal missing fitness effects in the evolution of animal societies.

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Figure 1: Environmental stochasticity has been missing from models of social evolution.
Figure 2: Increased stochasticity can increase the potential for selection of altruistic behaviour.
Figure 3: Empirical studies of Hamilton’s rule may benefit from incorporating stochasticity.
Figure 4: The trade-off between constitutive and inducible altruism in a stochastic world depends on plasticity costs and information reliability.


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We thank A. Gardner for discussions in the early stages of this work, and P.K. thanks the Behaviour Discussion Group at the Smithsonian Tropical Research Institute in Panama for the opportunity to present and discuss these ideas. We thank S. Schindler, S. Okasha, B. Autzen, J. McNamara and M. Bentley for comments on the project. P.K. was supported by the National Geographic Society (GEF-NE 145-15) and a University of Bristol Research Studentship, A.D.H. by the Natural Environment Research Council (NE/L011921/1), A.N.R. by a European Research Council Consolidator Grant (award no. 682253) and S.S. by the Natural Environment Research Council (NE/M012913/2).

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Authors and Affiliations



P.K. conceived the idea, P.K. and A.D.H. performed the modelling, A.N.R. and S.S. supervised the project. All authors discussed the ideas and wrote the manuscript.

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Correspondence to Patrick Kennedy.

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Extended data figures and tables

Extended Data Figure 1 The interaction between the frequency of altruists and the effectiveness of altruism.

a, The stochastic Hamilton’s rule predicts that selection on volatility-suppressing altruism with fixed costs and benefits can generate negative frequency dependence and is sensitive to mild mean-fecundity costs (cμ). Lower values of η denote greater buffering of recipients from the environment. We evaluate a population undergoing synchronous fluctuations to identify the frequency p* at which there is no expected change in allele frequency. We illustrate the result with individual fecundities in good years (z1) of four offspring and in bad years (z2) of one offspring. Relatedness is r = 0.5. b, Simulated population outcomes (frequency after 100,000 generations) match predictions of the stochastic Hamilton’s rule in a. Warmer colours (pink) denote higher polymorphic frequencies of altruists. In this haploid model (Supplementary Information B1-4), 1% of breeding spots are available each year for replacement by offspring that year: with such constraints on the magnitude of the response to selection, radical stochastic shifts in allele frequency over single generations do not occur, allowing the population to settle at equilibria where all alleles have equal expected relative fitness without being continually displaced (Extended Data Fig. 3). c, Competing an altruistic allele against a defector allele reveals the action of frequency-dependent selection. Here, populations experiencing costs of c = 0.2 and η = 0.466 converge to p* = 0.359 from any initial frequency (coloured lines show five starting frequencies from 0.001 to 0.999), as predicted by the stochastic Hamilton’s rule.

Extended Data Figure 2 Stochasticity as a function of bet-hedger frequency.

Stochasticity for the model of altruistic bet-hedging in Supplementary Information B plotted against frequency (p) and cost (c) for three different values of η. a, b, When η is small, representing high levels of volatility suppression, v declines steeply with p across the range of costs. c, When η is large, the sign of the effect of p on v depends on c. Values of other parameters: z1 = 4, z2 = 1, and frequency of good years d = 0.5.

Extended Data Figure 3 Weak selection negates the capacity of temporal autocorrelation to drive the frequency of altruistic bet-hedgers away from the convergence frequency.

Individual-based simulations from five different initial frequencies of an altruistic bet hedging allele (p) competing against a non-cooperator. a, The population has zero temporal autocorrelation (environmental state in each generation is random). b, The population has strong temporal autocorrelation (environmental state in the next generation has a 90% probability of remaining the same as in the current generation). Despite higher amplitude fluctuations, this population converges to the same point (from the five different starting frequencies) as the uncorrelated population (a). c, The same population is simulated with greater gene frequency changes (10% of the resident genotype frequencies are available to change each generation). The population is repeatedly carried to frequencies far from the convergence point. In this case, the utility of the stochastic Hamilton’s rule is both identifying whether a given trait is immune from invasion by competitors, and identifying the expected generational change at each frequency p. Parameters are z1 = 4, z2 = 1, r = 0.5.

Extended Data Table 1 Parameters of the model

Supplementary information

Life Sciences Reporting Summary (PDF 71 kb)

Supplementary Information

This file contains Supplementary Information Appendices A-C. Appendix A contains derivations of the main text equations. Appendix B contains information on obtaining benefits and costs and Appendix C provides illustrative examples. These three appendices are merged into a single .pdf file. (PDF 1089 kb)

Supplementary Data

This file contains Supplementary Appendix D1, the MATLAB code for simulation detailed in Appendix B. (TXT 5 kb)

Supplementary Data

This file contains Supplementary Appendix D2, the MATLAB code for simulation detailed in Appendix C. (TXT 17 kb)

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Kennedy, P., Higginson, A., Radford, A. et al. Altruism in a volatile world. Nature 555, 359–362 (2018).

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