# American Institute of Mathematical Sciences

April  2017, 14(2): 455-465. doi: 10.3934/mbe.2017028

## Altruistic aging: The evolutionary dynamics balancing longevity and evolvability

 School of Mathematical and Natural Sciences, Arizona State University, Glendale, AZ 85306-4908, USA

*Corresponding author

Received  March 09, 2015 Revised  May 31, 2016 Published  October 2016

Altruism is typically associated with traits or behaviors that benefit the population as a whole, but are costly to the individual. We propose that, when the environment is rapidly changing, senescence (age-related deterioration) can be altruistic. According to numerical simulations of an agent-based model, while long-lived individuals can outcompete their short lived peers, populations composed of long-lived individuals are more likely to go extinct during periods of rapid environmental change. Moreover, as in many situations where other cooperative behavior arises, senescence can be stabilized in a structured population.

Citation: Minette Herrera, Aaron Miller, Joel Nishimura. Altruistic aging: The evolutionary dynamics balancing longevity and evolvability. Mathematical Biosciences & Engineering, 2017, 14 (2) : 455-465. doi: 10.3934/mbe.2017028
##### References:
 [1] P. A. Abrams, Does increased mortality favor the evolution of more rapid senescence?, Evolution, 47 (1993), 877-887.  doi: 10.2307/2410191. [2] P. Bak and K. Sneppen, Punctuated equilibrium and criticality in a simple model of evolution, Physical Review Letters, 71 (1993), 4083.  doi: 10.1103/PhysRevLett.71.4083. [3] S. Balshine-Earn, F. C. Neat, H. Reid and M. Taborsky, Paying to stay or paying to breed? field evidence for direct benefits of helping behavior in a cooperatively breeding fish, Behavioral Ecology, 9 (1998), 432-438.  doi: 10.1093/beheco/9.5.432. [4] G. Bavestrello, C. Sommer and M. Sarà, Bi-directional conversion in turritopsis nutricula (hydrozoa), Scientia Marina, 56 (1992), 137-140. [5] J. Bendor and P. Swistak, Types of evolutionary stability and the problem of cooperation, Proceedings of the National Academy of Sciences, 92 (1995), 3596-3600.  doi: 10.1073/pnas.92.8.3596. [6] J. D. Congdon, R. D. Nagle, O. M. Kinney, R. C. van Loben Sels, T. Quinter and D. W. Tinkle, Testing hypotheses of aging in long-lived painted turtles (chrysemys picta), Experimental Gerontology, 38 (2003), 765-772.  doi: 10.1016/S0531-5565(03)00106-2. [7] F. Fu and M. A. Nowak, Global migration can lead to stronger spatial selection than local migration, Journal of Statistical Physics, 151 (2013), 637-653.  doi: 10.1007/s10955-012-0631-6. [8] L. Hadany, T. Beker, I. Eshel and M. W. Feldman, Why is stress so deadly? an evolutionary perspective, Proceedings of the Royal Society of London B: Biological Sciences, 273 (2006), 881-885.  doi: 10.1098/rspb.2005.3384. [9] W. Hamilton, The genetical evolution of social behaviour. Ⅰ, Journal of Theoretical Biology, 7 (1964), 1-16.  doi: 10.1016/0022-5193(64)90038-4. [10] G. Ichinose, M. Saito, H. Sayama and D.S. Wilson, Adaptive long-range migration promotes cooperation under tempting conditions, Scientific Reports, 3 (2013), p2509.  doi: 10.1038/srep02509. [11] K. Jin, Modern biological theories of aging, Aging and Disease, 1 (2010), p72. [12] M. Kimura and G.H. Weiss, The stepping stone model of population structure and the decrease of genetic correlation with distance, Genetics, 49 (1964), p561. [13] T. B. Kirkwood, Evolution of ageing, Mechanisms of Ageing and Development, 123 (2002), 737-745. [14] P. Ljubuncic and A. Z. Reznick, The evolutionary theories of aging revisited-a mini-review, Gerontology, 55 (2009), 205-216.  doi: 10.1159/000200772. [15] P. B. Medawar, An Unsolved Problem of Biology, College, 1952. [16] M. A. Nowak, Five rules for the evolution of cooperation, Science, 314 (2006), 1560-1563.  doi: 10.1126/science.1133755. [17] H. Ohtsuki, P. Bordalo and M. A. Nowak, The one-third law of evolutionary dynamics, Journal of Theoretical Biology, 249 (2007), 289-295.  doi: 10.1016/j.jtbi.2007.07.005. [18] L. Partridge and N. H. Barton, Optimality, mutation and the evolution of ageing, Nature: International Weekly Journal of Science, 362 (1993), 305-311. [19] G. B. Pollock and A. Cabrales, Suicidal altruism under random assortment, Evolutionary Ecology Research, 10 (2008), 1077-1086. [20] A. Traulsen and M. A. Nowak, Evolution of cooperation by multilevel selection, Proceedings of the National Academy of Sciences, 103 (2006), 10952-10955.  doi: 10.1073/pnas.0602530103. [21] J. Van Cleve, Social evolution and genetic interactions in the short and long term, Theoretical Population Biology, 103 (2015), 2-26. [22] J. W. Vaupel, A. Baudisch, M. Dölling, D. A. Roach and J. Gampe, The case for negative senescence, Theoretical Population Biology, 65 (2004), 339-351, http://www.sciencedirect.com/science/article/pii/S004058090400022X, Demography in the 21st Century. doi: 10.1016/j.tpb.2003.12.003. [23] A. Weismann, E. B. Poulton, S. Schönland and A. E. Shipley, Essays Upon Heredity and Kindred Biological Problems, vol. 1, Clarendon press, 1891. doi: 10.5962/bhl.title.101564. [24] G. C. Williams, Pleiotropy, natural selection, and the evolution of senescence, Evolution, 11 (1957), 398-411.  doi: 10.2307/2406060.

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##### References:
 [1] P. A. Abrams, Does increased mortality favor the evolution of more rapid senescence?, Evolution, 47 (1993), 877-887.  doi: 10.2307/2410191. [2] P. Bak and K. Sneppen, Punctuated equilibrium and criticality in a simple model of evolution, Physical Review Letters, 71 (1993), 4083.  doi: 10.1103/PhysRevLett.71.4083. [3] S. Balshine-Earn, F. C. Neat, H. Reid and M. Taborsky, Paying to stay or paying to breed? field evidence for direct benefits of helping behavior in a cooperatively breeding fish, Behavioral Ecology, 9 (1998), 432-438.  doi: 10.1093/beheco/9.5.432. [4] G. Bavestrello, C. Sommer and M. Sarà, Bi-directional conversion in turritopsis nutricula (hydrozoa), Scientia Marina, 56 (1992), 137-140. [5] J. Bendor and P. Swistak, Types of evolutionary stability and the problem of cooperation, Proceedings of the National Academy of Sciences, 92 (1995), 3596-3600.  doi: 10.1073/pnas.92.8.3596. [6] J. D. Congdon, R. D. Nagle, O. M. Kinney, R. C. van Loben Sels, T. Quinter and D. W. Tinkle, Testing hypotheses of aging in long-lived painted turtles (chrysemys picta), Experimental Gerontology, 38 (2003), 765-772.  doi: 10.1016/S0531-5565(03)00106-2. [7] F. Fu and M. A. Nowak, Global migration can lead to stronger spatial selection than local migration, Journal of Statistical Physics, 151 (2013), 637-653.  doi: 10.1007/s10955-012-0631-6. [8] L. Hadany, T. Beker, I. Eshel and M. W. Feldman, Why is stress so deadly? an evolutionary perspective, Proceedings of the Royal Society of London B: Biological Sciences, 273 (2006), 881-885.  doi: 10.1098/rspb.2005.3384. [9] W. Hamilton, The genetical evolution of social behaviour. Ⅰ, Journal of Theoretical Biology, 7 (1964), 1-16.  doi: 10.1016/0022-5193(64)90038-4. [10] G. Ichinose, M. Saito, H. Sayama and D.S. Wilson, Adaptive long-range migration promotes cooperation under tempting conditions, Scientific Reports, 3 (2013), p2509.  doi: 10.1038/srep02509. [11] K. Jin, Modern biological theories of aging, Aging and Disease, 1 (2010), p72. [12] M. Kimura and G.H. Weiss, The stepping stone model of population structure and the decrease of genetic correlation with distance, Genetics, 49 (1964), p561. [13] T. B. Kirkwood, Evolution of ageing, Mechanisms of Ageing and Development, 123 (2002), 737-745. [14] P. Ljubuncic and A. Z. Reznick, The evolutionary theories of aging revisited-a mini-review, Gerontology, 55 (2009), 205-216.  doi: 10.1159/000200772. [15] P. B. Medawar, An Unsolved Problem of Biology, College, 1952. [16] M. A. Nowak, Five rules for the evolution of cooperation, Science, 314 (2006), 1560-1563.  doi: 10.1126/science.1133755. [17] H. Ohtsuki, P. Bordalo and M. A. Nowak, The one-third law of evolutionary dynamics, Journal of Theoretical Biology, 249 (2007), 289-295.  doi: 10.1016/j.jtbi.2007.07.005. [18] L. Partridge and N. H. Barton, Optimality, mutation and the evolution of ageing, Nature: International Weekly Journal of Science, 362 (1993), 305-311. [19] G. B. Pollock and A. Cabrales, Suicidal altruism under random assortment, Evolutionary Ecology Research, 10 (2008), 1077-1086. [20] A. Traulsen and M. A. Nowak, Evolution of cooperation by multilevel selection, Proceedings of the National Academy of Sciences, 103 (2006), 10952-10955.  doi: 10.1073/pnas.0602530103. [21] J. Van Cleve, Social evolution and genetic interactions in the short and long term, Theoretical Population Biology, 103 (2015), 2-26. [22] J. W. Vaupel, A. Baudisch, M. Dölling, D. A. Roach and J. Gampe, The case for negative senescence, Theoretical Population Biology, 65 (2004), 339-351, http://www.sciencedirect.com/science/article/pii/S004058090400022X, Demography in the 21st Century. doi: 10.1016/j.tpb.2003.12.003. [23] A. Weismann, E. B. Poulton, S. Schönland and A. E. Shipley, Essays Upon Heredity and Kindred Biological Problems, vol. 1, Clarendon press, 1891. doi: 10.5962/bhl.title.101564. [24] G. C. Williams, Pleiotropy, natural selection, and the evolution of senescence, Evolution, 11 (1957), 398-411.  doi: 10.2307/2406060.
For an agent with no environment/phenotype mismatch, the probability an agent survives until a given age decreases during youth and then holds steady until they reach their terminal age (top). Agents with a phenotype $x_i\ne X(t)$ have a probability less than one of surviving each time step
The critical parameter regime is characterized by occasional population crashes, which may or may not result in extinction (primary axis top) and coincide with changes in the environment $X(t)$ (secondary axis). When $\eta>0$ (here $\eta=0.25$) the maximum terminal age can mutate, where larger maximum ages are typical selected for (bottom). $K=4,000$ and $s_i = 40 \forall i$
The population settles into a somewhat reliable relationship between total population and the average phenotype mismatch (initial transience not displayed). Parameters used: $K=10,000$, $s_i = 40 \forall i$
After $7,000$ time steps, populations with a large fixed terminal age are more likely to go extinct than those with a small terminal age. Allowing an agent's terminal age to mutate tends to increase the average terminal age and thus also the probability of extinction. $K = 1,000$ and the standard error of mean is displayed
Out of $500$ trials with an initial population split between $\frac{1}{2}$ with terminal age $1,000$ and $\frac{1}{2}$ with terminal age $20$, the subpopulation with terminal age $20$ was regularly out competed. The mean of the runs is highlighted
Sampled over many trials, populations with uniform, lower terminal ages are more likely to have the ideal phenotype $X(t)$ and even the potential future phenotype $X(t)+1$ than populations with larger phenotypes. $K=1,000$ and results drawn across $500$ runs, at each of $7,000$ different times
As the migration rate decreases, the populations with a lower terminal age begins to outcompete those with a longer terminal age. This was produced using $100$ islands each with $K=400$, and one third initially having populations with $s=20$, another third with $s=1000$ and the final third were initially barren. Otherwise this utilized the same parameters as figure 3
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