The predator-dependent replicator dynamics
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Universidade Federal de Minas Gerais
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Artigo de periódico
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Resumo
Ecological interactions are central to understanding evolution. For example,
Darwin noticed that the beautiful colours of the male peacock increase the
chance of successful mating. However, the colours can be a threat because of the
increased probability of being caught by predators. Eco-evolutionary dynamics
takes into account environmental interactions to model the process of evolu-
tion. The selection of prey types in the presence of predators may be subjected
to pressure on both reproduction and survival. Here, we analyze the evolution-
ary game dynamics of two types of prey in the presence of predators. We call
this model the predator-dependent replicator dynamics. If the evolutionary time
scales are different, the number of predators can be assumed constant, and the
traditional replicator dynamics is recovered. However, if the time scales are
the same, we end up with sixteen possible dynamics: the combinations of four
reproduction’s games with four predation’s games. We analyze the dynamics
and calculate conditions for the coexistence of prey and predator. The main
result is that predators can change the equilibrium of the traditional replicator
dynamics. For example, the presence of predators can induce polymorphism in
prey if one type of prey is more attractive than the other, with the prey ending
with a lower capture rate in this new equilibrium. Lastly, we provide two illus-
trations of the dynamics, which can be seen as rapid feedback responses in a
predator–prey evolutionary arm’s race.
Abstract
Assunto
Teoria dos jogos, Evolução (Biologia), Ecologia, Dinâmica populacional
Palavras-chave
Eco evolutionary dynamics, Evolutionary game theory, Replicator equation, Two-prey one-predator model
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Endereço externo
https://iopscience.iop.org/article/10.1088/1751-8121/ac40e4