Evolutionary Stable Strategy

The topic of evolution in interacting species was interpreted to focus upon predator-prey coevolution. This would enable a sound theoretical basis to be constructed for the analysis of evolution in larger systems, such as food webs. As a result all the systems explored in the project were predator-prey systems.
The use of analytical, numerical, and simulation models to study predator­ prey coevolution has shown that there occur a variety of consequences for the ecological dynamics of evolving predator-prey systems.  Evolutionary change can result in a wide range of dynamical behaviour, from stable equilibria to chaos.  The consequences of natural selection need not be stability, as some single-species models and experiments have suggested.  However, ecological dynamic stability is not required for evolutionary persistence.
The results obtained support arguments for the misleading nature of local asymptotic stability as a measure of the dynamics of ecological systems. However, it was not found possible to use permanence as an alternative to local asymptotic stability, as had been the original intention.
Results from the simulation models showed that convergence to ecological equilibrium was not necessarily to be expected in systems of evolving interacting species, in contrast to many models of community assembly and evolution.  The size of the potential parameter space of the simulation models meant that not all the dynamical behaviour of these models could be explored in the time scale of the project.
The analytical models I developed enabled an exploration of evolutionary and ecological dynamics more thoroughly than the simulation models, and compensated for the limited understanding of the simulation systems.  A wide range of evolutionary dynamics, such as ESSs and Red Queen coevolution, were seen to be produced from very simple systems, implying that more complex systems, such as food webs, would have much more interesting evolutionary consequences.  The use of "phenotype space" based techniques enabled a more global understanding of the evolutionary and ecological dynamics of predator-prey interactions than had previously been possible.
In general, the results supported the contentions that both ecological and evolutionary dynamics need to be taken into consideration when studying the evolution of interacting species; and that ecological interactions need to be considered in evolutionary models. The techniques I used to address these questions have potential applications in future research.

A Complex Adaptive System is a collection of autonomous, heterogeneous agents, whose behavior is defined with a limited number of rules. A Game Theory is a mathematical construct that assumes a small number of rational players who have a limited number of actions or strategies available to them. The CAS method has the potential to alleviate some of the shortcomings of GT. On the other hand, CAS researchers are always looking for a realistic way to define interactions among agents. GT offers an attractive option for defining the rules of such interactions in a way that is both potentially consistent with observed real-world behavior and subject to mathematical interpretation. This article reports on the results of an effort to build a CAS system that utilizes GT for determining the actions of individual agents.

Within the framework of evolutionary game theory, equilibrium concepts adapted from rational choice game theory are employed to identify the probable outcomes of evolutionary processes. Over the past several decades results have emerged in the literature demonstrating limitations to each of the proposed equilibrium concepts. These results rely on an undefined notion of evolutionary significance. We explicitly define evolutionary significance for evolutionary games. This definition enables an analysis of the success of equilibrium concepts across different models of evolution. We demonstrate that even under favorable assumptions as to the underlying dynamics and stability concept—the replicator dynamics and asymptotic stability—each equilibrium concept makes errors of either omission or comission; often both.

Moral rules allow humans to cooperate by indirect reciprocity. Yet, it is not clear which moral rules best implement indirect reciprocity and are favoured by natural selection. Previous studies either considered only public assessment, where individuals are deemed good or bad by all others, or compared a subset of possible strategies. Here we fill this gap by identifying which rules are evolutionary stable strategies (ESS) among all possible moral rules while considering private assessment. We develop an analytical model describing the frequency of long-term cooperation, determining when a strategy can be invaded by another. We show that there are numerous ESSs in absence of errors, which however cease to exist when errors are present. We identify the underlying properties of cooperative ESSs. Overall, this paper provides a first exhaustive evolutionary invasion analysis of moral rules considering private assessment. Moreover, this model is extendable to incorporate higher-order rules and other processes.

Termites are eusocial insects that evolved from solitary cockroaches. It is not known precisely what factors drove the evolution of termite eusociality, that is, skewed reproduction with distinct winged reproductive and wingless worker phenotypes. In other eu-social insects (bees and wasps), reproductive skew evolved first and phenotype differences evolved second. We propose that the reverse pattern occurred in termites, that is, that the winged-wingless diphenism evolved before eusociality. We discuss existing phylogenetic and pheromonal evidence supporting our hypothesis. We provide new experimental evidence from the most basal termite species (Mastotermes darwiniensis), suggesting that the ancestral state was indeed diphenic but presocial. We propose that the mechanism promoting a winged-wingless diphenism—in the absence of eusociality—was greater predation of aerial than terrestrial dispersers, and we support this with a game theoretic model. We augment our hypothesis with a novel explanation for the evolution of the developmental pathways leading to winged and wingless phenotypes in termites. An added benefit of our hypothesis is that it neatly explains the origin of termite eusociality itself: in the pre-eusocial ancestral species, the poor dispersal ability of the wingless phenotype would have led to clustering of relatives around shared resources—a prerequisite for nonparental care of close relatives.

We review evolutionary explanations for three major puzzles of the human mind: altruism, religiosity, and self-enhancement. Human altruism reaches beyond reciprocity or close-kin care readily explained by game theory and genetic kin selection. Group selection is widely seen as too weak to lead to substantial altruism as it struggles to contain selfishness favored by within-group selection. Yet, reciprocity and punishment leverage the effectiveness of altruism within a group, and genuine altruism is testified to be weak, leaving scope for explanation even by a force as weak as group selection. Moralistic religious culture appears tightly linked to altruism, yet the fitness advantage of a defector within a religious society makes it difficult to conceive religion or related genetic predisposition as an evolutionarily stable strategy. Self-enhancement has direct links to altruism and religiosity, leading to warm-glow altruistic contributions and increased receptiveness to comforting narratives of heavenly justice. Suggested intrapersonal and interpersonal benefits of self-enhancement do not detail how the trait should be competitive against more direct behavioral adjustments that yield similar personal benefits but avoid the fitness costs of misperception. We explain religion and bias as imperfect ad hoc evolutionary adaptations rather than perfect evolutionarily stable strategies (ESS). The scant time available for fine-tuning the mind since the emergence of higher cognitive capabilities means near-perfect traits were unlikely to emerge. Instead, the extraordinary evolutionary pressure induced by the rapidly evolving environment favored a broad range of genetic novelties despite extra costs.

We analyze group contests for public goods by applying the solution concept of an evolutionary stable strategy (ESS). We show that a global ESS cannot exist, because a mutant free-rider can always invade group behavior succesfully. There does exist, however, a unique local ESS, which we identify with evolutionary equilibrium. It coincides with Nash equilibrium, the hitherto dominant solution concept in contest theory, if and only if groups are symmetric. For asymmetric groups it always proposes a different and arguably more sensible solution than Nash equilibrium. We explore the properties of (local) ESS in detail.

A parasite's host range essentially defines its niche breadth, which, as foraging theory predicts, is influenced by resource availability. For parasites, the interaction of infection and transmission characteristics with host population dynamics determines host availability. An epidemiological model, involving two host types and describing competition between a "generalist" parasite strain and a related "specialist" strain, is used to examine the interplay among host range, relative host availabilities, and adaptational compromises engendered by increased host range. Results show that the generalist can predominate even when it cannot maintain itself in either host alone, but that the specialist can persist if its reproductive rate attains some threshold relative to either of the generalist's respective rates in its two hosts. The model is in rough, qualitative agreement with observed dynamics of two Leishmania parasite-host systems, and overall results s...

To address the problem of quick searching for evolutionary stable strategy in replicated dynamic mechanism, a solving algorithm based on parallel particle sub-swarm optimization (PSSO) is proposed. Firstly, evaluating function is introduced to integrate multiple objectives of all strategies. Secondly, multiplier method is used to derivate the fitness function. Finally, the optimal solution of strategy selection scheme is generated. The results show that the proposed algorithm performs better than standard particle swarm optimization in terms of optimal solution.

In evolutionary games, equilibrium concepts adapted from classical game theory—typically, refinements of the Nash equilibrium—are employed to identify the probable outcomes of evolutionary processes. Over the years, various negative results have been produced demonstrating limitations to each proposed refinement. These negative results rely on an undefined notion of evolutionary significance. We propose an explicit and novel definition of the notion of evolutionary significance in line with what is assumed in these results. This definition enables a comprehensive analysis of the limitations of the proposed equilibrium concepts. Taken together, the results show that even under favorable assumptions as to the underlying dynamics and stability concept—the replicator dynamics and asymptotic stability—all equilibrium concept makes errors of either omission or commission; typically both.

In the classical chemostat, the output of the system has no effect on its input. This contrasts with many ecological systems, where the output at the end of a growing season affects nutrient inputs for subsequent seasons. Here, an iterative-continuous modelling framework is introduced that retains the structure of classical ecological models within each iteration but accounts for nutrient feedbacks between iterations. As an example, the framework is applied to the classical chemostat model, where nutrient outputs affect the supply ratio at each iteration. Furthermore, the biotic parameters in the model, including organismal demands for nitrogen (N) and phosphorus (P), are linked to core biogenic processes—protein and rRNA synthesis. This biosynthesis is further deconstructed into 11 biological constants and rates, most of which are deeply shared among all organisms. By linking the fundamental macromolecular machinery to the cycling of nutrients on the ecosystem scale, the framework enables to rigorously formulate qualitative and quantitative questions about the evolution of nutrient ratios and the existence of stoichiometric attractors, such as the puzzling persistence of the Redfield N:P ratio of 16 in the ocean. While the framework presented here is theoretical, it readily permits setting up empirical experiments for testing its predictions.

A replicator equation with explicit space and global regulation is considered. This model provides a natural framework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable strategy are provided. A sufficient condition for a uniform stationary state to be a spatially distributed evolutionary stable state is presented and illustrated with examples.