Dispersal and the evolution of specialisation in a two-habitat type metapopulation

Metapopulation theory for the evolution of specialisation is virtually absent. In this article, therefore, we study a metapopulation model for consumers with a fitness trade-off between two habitats. We focus on effects of habitat abundance, dispersal rate and trade-off strength on the evolution of specialisation under two types of trade-off. Adaptation affects either the intrinsic growth rates r or the carrying capacities K. Depending on dispersal rate and trade-off strength, evolution can result in one generalist, one specialist or two specialist types. Higher dispersal rate and a weaker trade-off favour the evolution of a generalist, for both trade-off structures. However, we also find differences between the two trade-off structures. Our results are qualitatively similar to analyses of two-patch models, suggesting that insights from such simpler models can be extrapolated to metapopulation models. Additional effects, however, occur because in classical metapopulations patch lifetime depends on extinction rate. Counterintuitively, this favours the evolution of specialisation when the trade-off affects r.     

Contemporary evolution meets conservation biology II: impediments to integration and application

Conservation biology needs to be concerned not just with exogenous threats to populations, but also with the changing nature of populations themselves. In a previous review paper, we highlighted evolution in contemporary time (years to decades) as a largely overlooked aspect of population responses to environmental perturbations. We argued that these responses might affect the fate of natural, managed and exotic populations. In the present review, we discuss issues that may limit the integration of contemporary evolution into conservation biology—with the intent that recognition of these limitations may foster research, discussion and resolution. In particular, we consider (1) alternative perceptions of “evolutionary” and “ecological” time, (2) the role of contemporary evolution as an ecological process, (3) fitness as a bridge between evolution and conservation, and (4) challenges faced by conservation strategies based on gene flow estimation or manipulation. We close by highlighting some situations in which current conservation approaches and contemporary evolution may require reconciliation.     

Decision-making in variable environments-- a case of group selection and inter-generational conflict?

Suppose organisms need to engage in a particular action exactly once during some fixed period of time. Further suppose they can time this action to optimise their fitness based on the expected current payoff and the probability distribution of later payoffs. For an example we consider the timing of the annual nuptial flight in eusocial insects. Using two population genetics models, we ask whether stochasticity leads to evolutionary conflict between the queen and her offspring. We find that the winning phenotype is independent of who controls the timing. The best response to any non-equilibrium population strategy is the same in both control scenarios, a result that carries over to the diploid case. Although inter-generational conflict is therefore ruled out, the models support a previous observation that at equilibrium some of the offspring have a lower expected payoff than others. By measuring fitness in terms of relative reproductive success, we show that all individuals are in fact equally well off making group-selectionist arguments unnecessary. As such, the models should improve our understanding of the difficult conceptual problem of the unit of natural selection in stochastic environments.     

Slight phenotypic variation in predators and prey causes complex predator-prey oscillations

Predator-prey oscillations are expected to show a 1/4-phase lag between predator and prey. However, observed dynamics of natural or experimental predator-prey systems are often more complex. A striking but hardly studied example are sudden interruptions of classic 1/4-lag cycles with periods of antiphase oscillations, or periods without any regular predator-prey oscillations. These interruptions occur for a limited time before the system reverts to regular 1/4-lag oscillations, thus yielding intermittent cycles. Reasons for this behaviour are often difficult to reveal in experimental systems. Here we test the hypothesis that such complex dynamical behaviour may result from minor trait variation and trait adaptation in both the prey and predator, causing recurrent small changes in attack rates that may be hard to capture by empirical measurements. Using a model structure where the degree of trait variation in the predator can be explicitly controlled, we show that a very limited amount of adaptation resulting in 10–15% temporal variation in attack rates is already sufficient to generate these intermittent dynamics. Such minor variation may be present in experimental predator-prey systems, and may explain disruptions in regular 1/4-lag oscillations.     

The analysis of bi-level evolutionary graphs

Evolutionary graphs (EGs), in which evolutionary dynamic is arranged on a graph, were initially proposed by Lieberman et al. [Lieberman, E., Hauert, C., Nowak, M.A., 2005. Evolutionary dynamics on graphs. Nature 433, 312–316] in the biological field and many biological phenomena are successfully explained. EGs on two levels (or bi-level EGs), based on some biological phenomena, are considered in this paper. The bi-level EGs are compared with the one-rooted EGs in two cases. One has the identical numbers of the followers, the other with the same numbers of total individuals. Then, some properties of the bi-level EGs are obtained. It is showed that bi-level EGs are more stable, and the bi-level EGs with just two leaders are the most stable, if they have identical followers respectively. The bi-level EGs theory can successfully explain the phenomena of symbiosis in biology.     

The fastest evolutionary trajectory

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.     

Surprising evolutionary predictions from enhanced ecological realism

A focus on the eco-evolutionary feedback continually operating between a population's evolution and its environment helps to appreciate the generality of ESS theory. Here we illustrate, through a sequence of four examples, how respecting such feedback in the evolutionary dynamics of quantitative traits may result in qualitatively unexpected outcomes. Reviewing existing insights and complementing these with new results, we show (1) that evolutionary matrix games are fundamentally degenerate and allow a natural unfolding, (2) that selection-driven extinction may not be rare in nature, (3) that evolutionary epidemiology should not rely on R0 maximization, and (4) why the occurrence of Hardy-Weinberg proportions generically requires an evolutionary explanation.     

Deciphering the relative weights of demographic transition and vaccination in the decrease of measles incidence in Italy

In Italy, during the course of the past century to the present-day, measles incidence underwent a remarkable decreasing trend that started well before the introduction of the national immunization programme. In this work, we aim at examining to what extent both the demographic transition, characterized by declining mortality and fertility rates over time, and the vaccination programme are responsible for the observed epidemiological pattern. Making use of a non-stationary, age-structured disease transmission model, we show that in the pre-vaccination era, from 1901 to 1982, the decline in birth rates has resulted in a drastic decrease in the effective transmission rate, which in turn has determined a declining trend of measles incidence (from 25.2 to 10.3 infections per 1000 individuals). However, since 1983, vaccination appears to have become the major contributing factor in the decrease of measles incidence, which otherwise would have remained stable as a consequence of the nearly constant birth rates. This led to a remarkable decrease in the effective transmission rate, to a level well below the critical threshold for disease persistence. These findings call for the adoption of epidemiological models, which deviate the age structure from stationary equilibrium solutions, to better understand the biology of infectious diseases and evaluate immunization programmes.     

The evolution of phenotypic traits in a predator-prey system subject to Allee effect

This paper considers the evolution of phenotypic traits in a community comprising the populations of predators and prey subject to Allee effect. The evolutionary model is constructed from a deterministic approximation of the stochastic process of mutation and selection. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy and evolutionary branching. We find that the strong Allee effect of prey facilitates the formation of continuously stable strategy in the case that prey population undergoes evolutionary branching if the Allee effect of prey is not strong enough. Secondly, we show that evolutionary suicide is impossible for prey population when the intraspecific competition of prey is symmetric about the origin. However, evolutionary suicide can occur deterministically on prey population if prey individuals undergo strong asymmetric competition and are subject to Allee effect. Thirdly, we show that the evolutionary model with symmetric interactions admits a stable limit cycle if the Allee effect of prey is weak. Evolutionary cycle is a likely outcome of the process, which depends on the strength of Allee effect and the mutation rates of predators and prey.     

Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations

Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” [Nowak, et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650]. It states that under weak selection, if the fitness of strategy α is greater than that of strategy β when α has a frequency , strategy α fixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.     

Food-web formation with recursive evolutionary branching

A reaction-diffusion model describing the evolutionary dynamics of a food-web was constructed. In this model, predator-prey relationships among organisms were determined by their position in a two-dimensional phenotype space defined by two traits: as prey and as predator. The mutation process is expressed with a diffusion process of biomass in the phenotype space. Numerical simulation of this model showed co-evolutionary dynamics of isolated phenotypic clusters, including various types of evolutionary branching, which were classified into branching as prey, branching as predators, and co-evolutionary branching of both prey and predators. A complex food-web develops with recursive evolutionary branching from a single phenotypic cluster. Biodiversity peaks at the medium strength of the predator-prey interaction, where the food-web is maintained at medium biomass by a balanced frequency between evolutionary branching and extinction.     

Evolution of cooperation under -person snowdrift games

In the animal world, performing a given task which is beneficial to an entire group requires the cooperation of several individuals of that group who often share the workload required to perform the task. The mathematical framework to study the dynamics of collective action is game theory. Here we study the evolutionary dynamics of cooperators and defectors in a population in which groups of individuals engage in N-person, non-excludable public goods games. We explore an N-person generalization of the well-known two-person snowdrift game. We discuss both the case of infinite and finite populations, taking explicitly into consideration the possible existence of a threshold above which collective action is materialized. Whereas in infinite populations, an N-person snowdrift game (NSG) leads to a stable coexistence between cooperators and defectors, the introduction of a threshold leads to the appearance of a new interior fixed point associated with a coordination threshold. The fingerprints of the stable and unstable interior fixed points still affect the evolutionary dynamics in finite populations, despite evolution leading the population inexorably to a monomorphic end-state. However, when the group size and population size become comparable, we find that spite sets in, rendering cooperation unfeasible.     

Evolutionary graph theory: breaking the symmetry between interaction and replacement

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c>hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak-selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g=h=l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix.     

Optimal resource allocation to seeds and vegetative propagules under density-dependent regulation in Syneilesis palmata (Compositae)

Syneilesis palmata reproduces by both seeds and vegetative propagules (short rhizomes). The latter result in the production of new plants that are larger in size and hence have a higher survival probability and a higher growth rate than seeds. A previous study predicted that the optimal reproductive strategy, in terms of maximizing population growth rate (a fitness measure under no density regulations), was pure vegetative reproduction. However, high resource investment to vegetative propagules can cause local crowding resulting in reduced demographic performances of the plants, because the vegetative propagules of Syneilesis are produced close to one another. We examined, in this situation, the impact of allocating a certain proportion of reproductive resource to seeds with relatively greater capacity for dispersal. We simulated dynamics of hypothetical Syneilesis populations with various reproductive resource allocation balances (from pure seed to pure vegetative reproduction), using a density-dependent matrix model. In the model, it was assumed that plants from vegetative propagules experienced density-dependent reduction in their survival probabilities, but this was not the case for plants originating from seeds. Each allocation strategy was evaluated based on an equilibrium population density, a fitness measure under density-dependent regulations. The optimal reproductive strategy predicted was pure vegetative reproduction. Unrealistic conditions were required for seed reproduction to be favoured, such as the production of seeds one hundred times the normal number per unit resource investment. However, the conditions were fairly relaxed compared with those required in the model where no density effects were incorporated. This indicates that escape from local crowding is likely to be one of the roles of seed production in Syneilesis.