# 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:

show all references

##### References:
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
">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
 [1] Holly Gaff. Preliminary analysis of an agent-based model for a tick-borne disease. Mathematical Biosciences & Engineering, 2011, 8 (2) : 463-473. doi: 10.3934/mbe.2011.8.463 [2] Gianluca D'Antonio, Paul Macklin, Luigi Preziosi. An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix. Mathematical Biosciences & Engineering, 2013, 10 (1) : 75-101. doi: 10.3934/mbe.2013.10.75 [3] Rinaldo M. Colombo, Thomas Lorenz, Nikolay I. Pogodaev. On the modeling of moving populations through set evolution equations. Discrete & Continuous Dynamical Systems, 2015, 35 (1) : 73-98. doi: 10.3934/dcds.2015.35.73 [4] Xi Huo. Modeling of contact tracing in epidemic populations structured by disease age. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1685-1713. doi: 10.3934/dcdsb.2015.20.1685 [5] Dobromir T. Dimitrov, Aaron A. King. Modeling evolution and persistence of neurological viral diseases in wild populations. Mathematical Biosciences & Engineering, 2008, 5 (4) : 729-741. doi: 10.3934/mbe.2008.5.729 [6] Karl Peter Hadeler. Structured populations with diffusion in state space. Mathematical Biosciences & Engineering, 2010, 7 (1) : 37-49. doi: 10.3934/mbe.2010.7.37 [7] Agnieszka Bartłomiejczyk, Henryk Leszczyński. Structured populations with diffusion and Feller conditions. Mathematical Biosciences & Engineering, 2016, 13 (2) : 261-279. doi: 10.3934/mbe.2015002 [8] Karan Pattni, Mark Broom, Jan Rychtář. Evolving multiplayer networks: Modelling the evolution of cooperation in a mobile population. Discrete & Continuous Dynamical Systems - B, 2018, 23 (5) : 1975-2004. doi: 10.3934/dcdsb.2018191 [9] Thomas G. Hallam, Qingping Deng. Simulation of structured populations in chemically stressed environments. Mathematical Biosciences & Engineering, 2006, 3 (1) : 51-65. doi: 10.3934/mbe.2006.3.51 [10] Cédric Wolf. A mathematical model for the propagation of a hantavirus in structured populations. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1065-1089. doi: 10.3934/dcdsb.2004.4.1065 [11] Àngel Calsina, József Z. Farkas. Boundary perturbations and steady states of structured populations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6675-6691. doi: 10.3934/dcdsb.2019162 [12] Sebastian Aniţa, Vincenzo Capasso, Ana-Maria Moşneagu. Global eradication for spatially structured populations by regional control. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2511-2533. doi: 10.3934/dcdsb.2018263 [13] József Z. Farkas, Peter Hinow. Physiologically structured populations with diffusion and dynamic boundary conditions. Mathematical Biosciences & Engineering, 2011, 8 (2) : 503-513. doi: 10.3934/mbe.2011.8.503 [14] Dieter Armbruster, Christian Ringhofer, Andrea Thatcher. A kinetic model for an agent based market simulation. Networks & Heterogeneous Media, 2015, 10 (3) : 527-542. doi: 10.3934/nhm.2015.10.527 [15] Georgy P. Karev. Dynamics of heterogeneous populations and communities and evolution of distributions. Conference Publications, 2005, 2005 (Special) : 487-496. doi: 10.3934/proc.2005.2005.487 [16] H.Thomas Banks, Shuhua Hu. Nonlinear stochastic Markov processes and modeling uncertainty in populations. Mathematical Biosciences & Engineering, 2012, 9 (1) : 1-25. doi: 10.3934/mbe.2012.9.1 [17] H. T. Banks, R. A. Everett, Neha Murad, R. D. White, J. E. Banks, Bodil N. Cass, Jay A. Rosenheim. Optimal design for dynamical modeling of pest populations. Mathematical Biosciences & Engineering, 2018, 15 (4) : 993-1010. doi: 10.3934/mbe.2018044 [18] Cécile Carrère, Grégoire Nadin. Influence of mutations in phenotypically-structured populations in time periodic environment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3609-3630. doi: 10.3934/dcdsb.2020075 [19] Marcello Delitala, Tommaso Lorenzi. Evolutionary branching patterns in predator-prey structured populations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2267-2282. doi: 10.3934/dcdsb.2013.18.2267 [20] Anton Arnold, Laurent Desvillettes, Céline Prévost. Existence of nontrivial steady states for populations structured with respect to space and a continuous trait. Communications on Pure & Applied Analysis, 2012, 11 (1) : 83-96. doi: 10.3934/cpaa.2012.11.83

2018 Impact Factor: 1.313

## Metrics

• HTML views (65)
• Cited by (1)

• on AIMS