Modeling evolutionary games in populations with demographic structure

Li, Xiangyi; Giaimo, Stefano; Baudisch, Annette; Traulsen, Arne

doi:10.1016/j.jtbi.2015.05.036

Cited by 12 publications

(9 citation statements)

References 40 publications

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“…The game theoretic structure can explain the mechanisms shaping those patterns. The first papers combining both approaches are Garay et al (2016) devoted to the particular biological problem of sib cannibalism, Li et al (2015) and Lessard and Soares (2018) containing the approach incorporating age structure into a matrix game. These results show that after introduction of the age structure, matrix notation becomes very complicated and makes analysis difficult even in the case of two competing strategies and few age classes.…”

Section: Introductionmentioning

confidence: 99%

“…However, the game interactions described by demographic payoffs should affect the demographic structures of subpopulations of carriers of different strategies. In addition Li et al (2015) assumes that payoffs are described by a standard payoff matrix, thus the same actions performed in different ages/stages will generate the same payoffs. However, we can expect that outcomes of individual actions may vary for different ages due to different experiences and physical condition of the playing individuals.…”

Section: Introductionmentioning

confidence: 99%

“…Mortality is described as an exponential decay of the population, which implies that the length of an individual's lifetime is potentially unbounded, and there is no aging and no age specific payoffs. The goal of this paper is to fill this gap and develop a mathematical structure combining selection of individual strategies with an age structured population which will allow us to overcome the problems arising from increasing complexity of the models shown in Li et al (2015) and simplifications ignoring the age dependence of payoffs resulting from certain actions and feedbacks driving the interplay between game dynamics and demography (the fixed age structure assumption). For practical reasons we will develop a high dimensional ODE system consisting of relatively simple equations, which can be generated by a simple loop and solved in every popular numerical platform.…”

Section: Introductionmentioning

confidence: 99%

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Towards a replicator dynamics model of age structured populations

Argasinski

Broom

2021

J. Math. Biol.

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We present a new modelling framework combining replicator dynamics, the standard model of frequency dependent selection, with an age-structured population model. The new framework allows for the modelling of populations consisting of competing strategies carried by individuals who change across their life cycle. Firstly the discretization of the McKendrick von Foerster model is derived. We show that the Euler–Lotka equation is satisfied when the new model reaches a steady state (i.e. stable frequencies between the age classes). This discretization consists of unit age classes where the timescale is chosen so that only a fraction of individuals play a single game round. This implies a linear dynamics and individuals not killed during the round are moved to the next age class; linearity means that the system is equivalent to a large Bernadelli–Lewis–Leslie matrix. Then we use the methodology of multipopulation games to derive two, mutually equivalent systems of equations. The first contains equations describing the evolution of the strategy frequencies in the whole population, completed by subsystems of equations describing the evolution of the age structure for each strategy. The second contains equations describing the changes of the general population’s age structure, completed with subsystems of equations describing the selection of the strategies within each age class. We then present the obtained system of replicator dynamics in the form of the mixed ODE-PDE system which is independent of the chosen timescale, and much simpler. The obtained results are illustrated by the example of the sex ratio model which shows that when different mortalities of the sexes are assumed, the sex ratio of 0.5 is obtained but that Fisher’s mechanism, driven by the reproductive value of the different sexes, is not in equilibrium.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards a replicator dynamics model of age structured populations

Argasinski

Broom

2021

J. Math. Biol.

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“…Yet, it seems instructive to study their interplay, as either approach alone may neglect an important factor driving evolutionary change. Recently, a model was proposed to integrate demography into a standard model of evolutionary game theory (Li et al 2015). Here, we integrate game theory into a standard model of evolutionary demography.…”

Section: Introductionmentioning

confidence: 99%

Evolution of fixed demographic heterogeneity from a game of stable coexistence

Giaimo

Traulsen

et al. 2018

DemRes

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“…In addition, life history also modulates the actual effect that an increase in survival or reproduction has on the growth rate of the population, and it accounts for part of the effective size of the population (Charlesworth, 1994;Engen et al, 2005). For the frequency dependent case, it has been shown that life stage dependent strategic interactions can promote diversity and push strategic behaviours away from the equilibrium determined by game theoretic interactions alone (Li et al, 2015a). However, it is not obvious if certain demographic structures of the population would help or hinder the spread and fixation of a beneficial mutant.…”

Section: Introductionmentioning

confidence: 99%

How life history can sway the fixation probability of mutants

Kurokawa

Giaimo

et al. 2016

Preprint

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In this work, we study the effects of demographic structure on evolutionary dynamics when selection acts on reproduction, survival, or both. In contrast to the previously discovered pattern that the fixation probability of a neutral mutant decreases while the population becomes younger, we show that a mutant with a constant selective advantage may have a maximum or a minimum of the fixation probability in populations with an intermediate fraction of young individuals. This highlights the importance of life history and demographic structure in studying evolutionary dynamics. We also illustrate the fundamental differences between selection on reproduction and selection on survival when age structure is present. In addition, we evaluate the relative importance of size and structure of the population in determining the fixation probability of the mutant. Our work lays the foundation for also studying density-and frequency-dependent effects in populations when demographic structures cannot be neglected.

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Modeling evolutionary games in populations with demographic structure

Cited by 12 publications

References 40 publications

Towards a replicator dynamics model of age structured populations

Towards a replicator dynamics model of age structured populations

Evolution of fixed demographic heterogeneity from a game of stable coexistence

How life history can sway the fixation probability of mutants

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