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The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduced a conceptual model to study the stable coexistence and coevolution of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. Using an age-structured Leslie model for the host, we demonstrated how the obligate symbiont could modify the host's life history traits (survival and fecundity) and the long-term growth rate of the infected lineage. When the symbiont is vertically transmitted, we found that the host and its symbiont could maximize the infected lineage's evolutionary success (multi-level selection). Our model showed that symbionts' effect on host longevity and reproduction might differ, even be opposing, and their net effect might often be counterintuitive. The evolutionary stability of the ecologically stable coexistence was analyzed in the framework of coevolutionary dynamics. Moreover, we found conditions for the ecological and evolutionary stability of the resident host-symbiont pair, which does not allow invasion by rare mutants (each mutant dies out by ecological selection). We concluded that, within the context of our simplified model conditions, a host-symbiont system with mixed-mode transmission is evolutionarily stable unconditionally only if the host can maximize the Malthusian parameters of the infected and non-infected lineages using the same strategy. Finally, we performed a game-theoretical analysis of our selection situation and compared two stability definitions., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The moral rule "Risk your life to save your family members" is, at the same time, a biological phenomenon. The prominent population geneticist, J.B.S. Haldane told his friends that he would risk his life to save two drowning brothers, but not one - so the story goes. In biological terms, Haldane's arithmetic claims that sib altruism is evolutionarily rational, whenever by "self-sacrifice" an altruistic gene "rescues", on average, more than one copy of itself in its lineage. Here, we derive conditions for evolutionary stability of sib altruism, using population genetic models for three mating systems (monogamy, promiscuity and polygyny) with linear and non-linear group effect on the siblings' survival rate. We show that for all considered selection situations, the condition of evolutionary stability is equivalent to Haldane's arithmetic. The condition for evolutionary stability is formulated in terms of genetic relatedness and the group effect on the survival probability, similarly to the classical Hamilton's rule. We can set up a "scale of mating systems", since in pairwise interactions the chance of evolutionary stability of sib altruism decreases in this order: monogamy, polygyny and promiscuity. Practice of marrying and siblings' solidarity are moral rules in a secular world and in various religious traditions. These moral rules are not evolutionarily independent, in the sense that the subsistence of sib altruism is more likely in a monogamous population., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Kleptoparasitism can be considered as a game theoretical problem and a foraging tactic at the same time, so the aim of this paper is to combine the basic ideas of two research lines: evolutionary game theory and optimal foraging theory. To unify these theories, firstly, we take into account the fact that kleptoparasitism between foragers has two consequences: the interaction takes time and affects the net energy intake of both contestants. This phenomenon is modeled by a matrix game under time constraints. Secondly, we also give freedom to each forager to avoid interactions, since in optimal foraging theory foragers can ignore each food type (we have two prey types: either a prey item in possession of another predator or a free prey individual is discovered). The main question of the present paper is whether the zero-one rule of optimal foraging theory (always or never select a prey type) is valid or not, in the case where foragers interact with each other? In our foraging game we consider predators who engage in contests (contestants) and those who never do (avoiders), and in general those who play a mixture of the two strategies. Here the classical zero-one rule does not hold. Firstly, the pure avoider phenotype is never an ESS. Secondly, the pure contestant can be a strict ESS, but we show this is not necessarily so. Thirdly, we give an example when there is mixed ESS., (Copyright © 2020 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Consider and infinitely large asexual population without mutations and direct interactions. The activities of an individual determine the fecundity and the survival probability of individuals, moreover each activity takes time. We view this population model as a simple combination of life history and optimal foraging models. The phenotypes are given by probability distributions on these activities. We concentrate on the following phenotypes defined by optimization of different objective functions: selfish individual (maximizes the average offspring number during life span), survival phenotype (maximizes the probability of non-extinction of descendants) and Darwinian phenotype (maximizes the phenotypic growth rate). We find that the objective functions above can achieve their maximum at different activity distributions, in general. We find that the objective functions above can achieve their maximum at different activity distributions, in general. The novelty of our work is that we let natural selection act on the different objective functions. Using the classical Darwinian reasoning, we show that in our selection model the Darwinian phenotype outperforms all other phenotypes., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Game theory focuses on payoffs and typically ignores time constraints that play an important role in evolutionary processes where the repetition of games can depend on the strategies, too. We introduce a matrix game under time constraints, where each pairwise interaction has two consequences: both players receive a payoff and they cannot play the next game for a specified time duration. Thus our model is defined by two matrices: a payoff matrix and an average time duration matrix. Maynard Smith's concept of evolutionary stability is extended to this class of games. We illustrate the effect of time constraints by the well-known prisoner's dilemma game, where additional time constraints can ensure the existence of unique evolutionary stable strategies (ESS), both pure and mixed, or the coexistence of two pure ESS. Our general results may be useful in several fields of biology where evolutionary game theory is applied, principally in ecological games, where time constraints play an inevitable role., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

The classical Holling type II functional response, describing the per capita predation as a function of prey density, was modified by Beddington and de Angelis to include interference of predators that increases with predator density and decreases the number of killed prey. In the present paper we further generalize the Beddington-de Angelis functional response, considering that all predator activities (searching and handling prey, fight and recovery) have time duration, the probabilities of predator activities depend on the encounter probabilities, and hence on the prey and predator abundance, too. Under these conditions, the aim of the study is to introduce a functional response for fighting the predator and to analyse the corresponding dynamics, when predator-predator-prey encounters also occur. From this general approach, the Holling type functional responses can also be obtained as particular cases. In terms of the activity distribution, we give biologically interpretable sufficient conditions for stable coexistence. We consider two-individual (predator-prey) and three-individual (predator-predator-prey) encounters. In the three-individual encounter model there is a relatively higher fighting rate and a lower killing rate. Using numerical simulation, we surprisingly found that when the intrinsic prey growth rate and the conversion rate are small enough, the equilibrium predator abundance is higher in the three-individual encounter case. The above means that, when the equilibrium abundance of the predator is small, coexistence appears first in the three-individual encounter model., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

In this paper, we study the egalitarianism-game in multilevel selection situation. The individuals form reproductive groups. In each group, an egalitarianism-game determines the number of juveniles of different phenotypes (spiteful, envious, neutral and donator). Before the juveniles form the next reproductive group, they have to survive either predators' attacks or a fight between two groups. We adopt the ESS definition of Maynard Smith to multilevel selection. Based on the "group size advantage" assumption (which claims that each juvenile's survival rate depends on the size of his own group, supposing that either the survival rate under predators' attacks is higher in larger groups, or in inter-group aggression usually the larger group wins) we found that when the survival probability has a massive effect on the average fitness, then "group fitness maximizing behavior" (in our case, either neutral or donator) has evolutionary advantage over "competitive behavior" (in our case, either spiteful or envious)., (© 2013 Elsevier Ltd. All rights reserved.)

The paper is aimed at a theoretical explanation of the following phenomenon. In biological pest control in greenhouses, if an omnivore agent is released before the arrival of the pest, the agent may be able to colonize, feeding only on plant and then control its arriving prey to a low density. If the pest arrives before the release of the agent, then it tends to reach a high density, in spite of the action of the agent. This means that according to the initial state, the system displays different stable equilibria, i.e. bistable coexistence is observed. Based on the biological situation, the explaining theoretical model must take into account the stoichiometry of different nutrients and the optimal foraging of the omnivore agent. We introduce an optimal numerical response which depends on the optimal functional responses and on the 'mixed diet-fitness' correspondence determined by 'egg stoichiometry', in our case by Liebig's Law; moreover we also study the dynamical consequences of the latter when the plant is "inexhaustible". In our model, we found that under Holling type II functional response, the omnivore-prey system has a unique equilibrium, while for Holling type III, we obtained bistable coexistence. The latter fact also explains the above phenomenon that an omnivore agent may control the pest to different levels, according to the timing of the release of the agent., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

The origin and the evolutionary stability of cooperation between unrelated individuals is one of the key problems of evolutionary biology. In this paper, a cooperative defence game against a predator is introduced which is based on Hamilton's selfish herd theory and Eshel's survival game models. Cooperation is altruistic in the sense that the individual, which is not the target of the predator, helps the members of the group attacked by the predator and during defensive action the helper individual may also die in any attack. In order to decrease the long term predation risk, this individual has to carry out a high risk action. Here I show that this kind of cooperative behaviour can evolve in small groups. The reason for the emergence of cooperation is that if the predator does not kill a mate of a cooperative individual, then the survival probability of the cooperative individual will increase in two cases. If the mate is non-cooperative, then-according to the dilution effect, the predator confusion effect and the higher predator vigilance-the survival probability of the cooperative individual increases. The second case is when the mate is cooperative, because a cooperative individual has a further gain, the active help in defence during further predator attacks. Thus, if an individual can increase the survival rate of its mates (no matter whether the mate is cooperative or not), then its own predation risk will decrease.

The paper deals with the following question: when do the phenotypic evolutionarily stable state (ESS) and the evolutionarily stable allele distribution (ESAD) coincide? It is supposed that for a sexual population, in dominant-recessive inheritance system, n allele at one autosomal locus determine n possible pure individual phenotypes and each pure phenotype is obtained as the phenotype of a homozygote. Under these conditions, earlier results of the authors imply that, if a phenotype distribution is an ESS then the allele distribution generating it is an ESAD. In this paper, apart from a certain degenerate pay-off matrices, the inverse statement is also proved: if a distribution is an ESAD then the corresponding phenotypic distribution is an ESS.

The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem.

The classical static concept of an evolutionarily stable strategy (ESS) for a single species gives rise to two new notions when there are more than two species (called an N-species ESS and RL-stability). The paper relates these to the dynamic stability of monomorphic and polymorphic evolutionary systems. It is shown that RL-stability implies the global asymptotic stability of either system with or without mutations. However, the N-species ESS only implies stability of the monomorphic system., (Copyright 2001 Academic Press.)