# 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
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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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