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

Altruistic aging: The evolutionary dynamics balancing longevity and evolvability

Minette Herrera , Aaron Miller and  Joel Nishimura ,

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.

Keywords: Senescence, cooperation, agent-based modeling, evolution, structured populations.
Mathematics Subject Classification: Primary: 92D15, 92D25; Secondary: 91A22.
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.  Google Scholar

[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.  Google Scholar

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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.  Google Scholar

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G. Bavestrello, C. Sommer and M. Sarà, Bi-directional conversion in turritopsis nutricula (hydrozoa), Scientia Marina, 56 (1992), 137-140.   Google Scholar

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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.  Google Scholar

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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.  Google Scholar

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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.  Google Scholar

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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.  Google Scholar

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K. Jin, Modern biological theories of aging, Aging and Disease, 1 (2010), p72.   Google Scholar

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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.   Google Scholar

[13]

T. B. Kirkwood, Evolution of ageing, Mechanisms of Ageing and Development, 123 (2002), 737-745.   Google Scholar

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P. Ljubuncic and A. Z. Reznick, The evolutionary theories of aging revisited-a mini-review, Gerontology, 55 (2009), 205-216.  doi: 10.1159/000200772.  Google Scholar

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P. B. Medawar, An Unsolved Problem of Biology, College, 1952. Google Scholar

[16]

M. A. Nowak, Five rules for the evolution of cooperation, Science, 314 (2006), 1560-1563.  doi: 10.1126/science.1133755.  Google Scholar

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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.  Google Scholar

[18]

L. Partridge and N. H. Barton, Optimality, mutation and the evolution of ageing, Nature: International Weekly Journal of Science, 362 (1993), 305-311.   Google Scholar

[19]

G. B. Pollock and A. Cabrales, Suicidal altruism under random assortment, Evolutionary Ecology Research, 10 (2008), 1077-1086.   Google Scholar

[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.  Google Scholar

[21]

J. Van Cleve, Social evolution and genetic interactions in the short and long term, Theoretical Population Biology, 103 (2015), 2-26.   Google Scholar

[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.  Google Scholar

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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.  Google Scholar

[24]

G. C. Williams, Pleiotropy, natural selection, and the evolution of senescence, Evolution, 11 (1957), 398-411.  doi: 10.2307/2406060.  Google Scholar

show all references

References:
[1]

P. A. Abrams, Does increased mortality favor the evolution of more rapid senescence?, Evolution, 47 (1993), 877-887.  doi: 10.2307/2410191.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[4]

G. Bavestrello, C. Sommer and M. Sarà, Bi-directional conversion in turritopsis nutricula (hydrozoa), Scientia Marina, 56 (1992), 137-140.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

K. Jin, Modern biological theories of aging, Aging and Disease, 1 (2010), p72.   Google Scholar

[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.   Google Scholar

[13]

T. B. Kirkwood, Evolution of ageing, Mechanisms of Ageing and Development, 123 (2002), 737-745.   Google Scholar

[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.  Google Scholar

[15]

P. B. Medawar, An Unsolved Problem of Biology, College, 1952. Google Scholar

[16]

M. A. Nowak, Five rules for the evolution of cooperation, Science, 314 (2006), 1560-1563.  doi: 10.1126/science.1133755.  Google Scholar

[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.  Google Scholar

[18]

L. Partridge and N. H. Barton, Optimality, mutation and the evolution of ageing, Nature: International Weekly Journal of Science, 362 (1993), 305-311.   Google Scholar

[19]

G. B. Pollock and A. Cabrales, Suicidal altruism under random assortment, Evolutionary Ecology Research, 10 (2008), 1077-1086.   Google Scholar

[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.  Google Scholar

[21]

J. Van Cleve, Social evolution and genetic interactions in the short and long term, Theoretical Population Biology, 103 (2015), 2-26.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[24]

G. C. Williams, Pleiotropy, natural selection, and the evolution of senescence, Evolution, 11 (1957), 398-411.  doi: 10.2307/2406060.  Google Scholar

Figure 1.  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
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Figure 2.  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 $s_i = 40 \forall i$
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Figure 3.  The population settles into a somewhat reliable relationship between total population and the average phenotype mismatch (initial transience not displayed). Parameters used: $K=10,000$, $s_i = 40 \forall i$
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Figure 4.  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
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Figure 5.  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
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Figure 6.  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
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figure 3">Figure 7.  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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