Evolutionary stability in Lotka-Volterra systems

Genesis of ectosymbiotic features based on commensalistic syntrophy

The symbiogenetic origin of eukaryotes with mitochondria is considered a major evolutionary transition. The initial interactions and conditions of symbiosis, along with the phylogenetic affinity of the host, are widely debated. Here, we focus on a possible evolutionary path toward an association of individuals of two species based on unidirectional syntrophy. With the backing of a theoretical model, we hypothesize that the first step in the evolution of such symbiosis could be the appearance of a linking structure on the symbiont's membrane, using which it forms an ectocommensalism with its host. We consider a commensalistic model based on the syntrophy hypothesis in the framework of coevolutionary dynamics and mutant invasion into a monomorphic resident system (evolutionary substitution). We investigate the ecological and evolutionary stability of the consortium (or symbiotic merger), with vertical transmissions playing a crucial role. The impact of the 'effectiveness of vertical transmission' on the dynamics is also analyzed. We find that the transmission of symbionts and the additional costs incurred by the mutant determine the conditions of fixation of the consortia. Additionally, we observe that small and highly metabolically active symbionts are likely to form the consortia.

Coevolutionary stability of host-symbiont systems with mixed-mode transmission

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.

From evolutionary ecosystem simulations to computational models of human behavior

We have a wide breadth of computational tools available today that enable a more ethical approach to the study of human cognition and behavior. We argue that the use of computer models to study evolving ecosystems provides a rich source of inspiration, as they enable the study of complex systems that change over time. Often employing a combination of genetic algorithms and agent-based models, these methods span theoretical approaches from games to complexification, nature-inspired methods from studies of self-replication to the evolution of eyes, and evolutionary ecosystems of humans, from entire economies to the effects of personalities in teamwork. The review of works provided here illustrates the power of evolutionary ecosystem simulations and how they enable new insights for researchers. They also demonstrate a novel methodology of hypothesis exploration: building a computational model that encapsulates a hypothesis of human cognition enables it to be tested under different conditions, with its predictions compared to real data to enable corroboration. Such computational models of human behavior provide us with virtual test labs in which unlimited experiments can be performed. This article is categorized under: Computer Science and Robotics > Artificial Intelligence.

Interaction rates, vital rates, background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics

In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk-Dove example.

An evolutionary stability perspective on oncogenesis control in mature T-cell populations

Here we present a mathematical model for the dynamics of oncogenesis control in mature T-cell populations within the blood and lymphatic system. T-cell homeostasis is maintained by clonal competition for trophic niches (survival signals stimulated through interactions with self-antigens bound to major histocompatibility molecules), where a clone is defined as the set of T cells carrying the same antigen specific T-cell receptor (TCR). We analytically derive fitness functions of healthy and leukemic clone variants, respectively, that capture the dependency of the stability of the healthy T-cell pool against leukemic invaders on clonal diversity and kinetic parameters. Similar to the stability of ecosystems with high biodiversity, leukemic mutants are suppressed within polyclonal T-cell populations, i.e., in the presence of a huge number of different TCRs. To the contrary, for a low clonal diversity the leukemic clone variants are able to invade the healthy T-cell pool. The model, therefore, describes the experimentally observed phenomenon that preleukemic clone variants prevail in quasi-monoclonal experimental settings (in mice), whereas in polyclonal settings the healthy TCR variants are able to suppress the outgrowth of tumours. Between the two extremal situations of mono- and polyclonality there exists a range of coexistence of healthy and oncogenic clone variants with moderate fitness (stability) each. A variation of cell cycle times considerably changes the dynamics within this coexistence region. Faster proliferating variants increase their chance to dominate. Finally, a simplified niche variation scheme illustrates a possible mechanism to increase clonal T-cell diversity given a small niche diversity.

A Biomass Flow Approach to Population Models and Food Webs

The dominant differential equation paradigm for modeling the population dynamics of species interacting in the framework of a food web retains at its core the basic prey-predator and competition models formulation by Alfred J. Lotka (1880-1945) and Vito Volterra (1860-1940) nearly nine decades ago. This paradigm lacks a trophic-level-independent formulation of population growth leading to ambiguities in how to treat populations that are simultaneously both prey and predator. Also, this paradigm does not fundamentally include inertial (i.e. change resisting) processes needed to account for the response of populations to fluctuating resource environments. Here I present an approach that corrects both these deficits and provides a unified framework for accounting for biomass transformation in food webs that include both live and dead components of all species in the system. This biomass transformation formulation (BTW) allows for a unified treatment of webs that include consumers of both live and dead material-both carnivores and carcasivores, herbivores and detritivores-and incorporates scavengers, parasites, and other neglected food web consumption categories in a coherent manner. I trace how BTW is an outgrowth of the metaphysiological growth modeling paradigm and I provide a general compact formulation of BTW in terms of a three-variable differential equation formulation for each species in the food web: viz. live biomass, dead biomass, and a food-intake-related measure called deficit-stress. I then illustrate the application of this new paradigm to provide insights into two-species competition in variable environments and discuss application of BTW to food webs that incorporate parasites and pathogens.

Biomass transformation webs provide a unified approach to consumer-resource modelling

An approach to modelling food web biomass flows among live and dead compartments within and among species is formulated using metaphysiological principles that characterise population growth in terms of basal metabolism, feeding, senescence and exploitation. This leads to a unified approach to modelling interactions among plants, herbivores, carnivores, scavengers, parasites and their resources. Also, dichotomising sessile miners from mobile gatherers of resources, with relevance to feeding and starvation time scales, suggests a new classification scheme involving 10 primary categories of consumer types. These types, in various combinations, rigorously distinguish scavenger from parasite, herbivory from phytophagy and detritivore from decomposer. Application of the approach to particular consumer-resource interactions is demonstrated, culminating in the construction of an anthrax-centred food web model, with parameters applicable to Etosha National Park, Namibia, where deaths of elephants and zebra from the bacterial pathogen, Bacillus anthracis, provide significant subsidies to jackals, vultures and other scavengers.

A stochastic model of evolutionary dynamics with deterministic large-population asymptotics

An evolutionary birth-death process is proposed as a model of evolutionary dynamics. Agents residing in a continuous spatial environment X, play a game G, with a continuous strategy set S, against other agents in the environment. The agents' positions and strategies continuously change in response to other agents and to random effects. Agents spawn asexually at rates that depend on their current fitness, and agents die at rates that depend on their local population density. Agents' individual evolutionary trajectories in X and S are governed by a system of stochastic ODEs. When the number of agents is large and distributed in a smooth density on (X,S), the collective dynamics of the entire population is governed by a certain (deterministic) PDE, which we call a fitness-diffusion equation.

Migration Dynamics for the Ideal Free Distribution

This article verifies that the ideal free distribution (IFD) is evolutionarily stable, provided the payoff in each patch decreases with an increasing number of individuals. General frequency-dependent models of migratory dynamics that differ in the degree of animal omniscience are then developed. These models do not exclude migration at the IFD where balanced dispersal emerges. It is shown that the population distribution converges to the IFD even when animals are nonideal (i.e., they do not know the quality of all patches). In particular, the IFD emerges when animals never migrate from patches with a higher payoff to patches with a lower payoff and when some animals always migrate to the best patch. It is shown that some random migration does not necessarily lead to undermatching, provided migration occurs at the IFD. The effect of population dynamics on the IFD (and vice versa) is analyzed. Without any migration, it is shown that population dynamics alone drive the population distribution to the IFD. If animal migration tends (for each fixed population size) to the IFD, then the combined migration-population dynamics evolve to the population IFD independent of the two timescales (i.e., behavioral vs. population).

Uninvadability in -species frequency models for resident–mutant systems with discrete or continuous time

The uninvadability concept, that was originally introduced through static comparisons of individual fitness in resident-mutant systems for a single species, is developed for multi-species models with frequency-dependent fitness by extending its equivalent single-species dynamic characterization. This multi-species definition is then reinterpreted in terms of individual fitness functions based on intra and interspecific interactions. The resultant concept is discussed in relation to that of an N-species ESS (evolutionarily stable strategy) and to dynamic stability of monomorphic and polymorphic evolutionary systems.

Dynamic multipopulation and density dependent evolutionary games related to replicator dynamics. A metasimplex concept

This paper contains the basic extensions of classical evolutionary games (multipopulation and density dependent models). It is shown that classical bimatrix approach is inconsistent with other approaches because it does not depend on proportion between populations. The main conclusion is that interspecific proportion parameter is important and must be considered in multipopulation models. The paper provides a synthesis of both extensions (a metasimplex concept) which solves the problem intrinsic in the bimatrix model. It allows us to model interactions among any number of subpopulations including density dependence effects. We prove that all modern approaches to evolutionary games are closely related. All evolutionary models (except classical bimatrix approaches) can be reduced to a single population general model by a simple change of variables. Differences between classic bimatrix evolutionary games and a new model which is dependent on interspecific proportion are shown by examples.

A game-theoretic model for punctuated equilibrium: Species invasion and stasis through coevolution

A general theory of coevolution is developed that combines the ecological effects of species' densities with the evolutionary effects of changing phenotypes. Our approach also treats the evolutionary changes between coevolving species with discreet traits after the appearance of a new species. We apply this approach to habitat selection models where new species first emerge through competitive selection in an isolated habitat. This successful invasion is quickly followed by evolutionary changes in behavior when this species discovers the other habitat, leading to punctuated equilibrium as the final outcome.

Stability in N-species coevolutionary systems

Stability criteria have recently been developed for coevolutionary Lotka-Volterra systems where individual fitness functions are assumed to be linear in the population state. We extend these criteria as part of a general theory of coevolution (that combines effects of ecology and evolution) based on arbitrary (i.e. nonlinear) fitness functions and a finite number of individual phenotypes. The central role of the stationary density surface where species' densities are at equilibrium is emphasized. In particular, for monomorphic resident systems, it is shown coevolutionary stability is equivalent to ecological stability combined with evolutionary stability on the stationary density surface. Also discussed is how our theory relates to recent treatments of phenotypic coevolution via adaptive dynamics when there is a continuum of individual phenotypes.