Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

We present a general framework for modelling adaptive trait dynamics in which we integrate various concepts and techniques from modern ESS-theory. The concept of evolutionarily singular strategies is introduced as a generalization of the ESS-concept. We give a full classification of the singular strategies in terms of ESS-stability, convergence stability, the ability of the singular strategy to invade other populations if initially rare itself, and the possibility of protected dimorphisms occurring within the singular strategy's neighbourhood. Of particular interest is a type of singular strategy that is an evolutionary attractor from a great distance, but once in its neighbourhood a population becomes dimorphic and undergoes disruptive selection leading to evolutionary branching. Modelling the adaptive growth and branching of the evolutionary tree can thus be considered as a major application of the framework. A haploid version of Levene's soft selection model is developed as a specific example to demonstrate evolutionary dynamics and branching in monomorphic and polymorphic populations.     

Hierarchical competition models with the Allee effect II: the case of immigration

ABSTRACT

This is part II of an earlier paper that dealt with hierarchical models with the Allee effect but with no immigration. In this paper, we greatly simplify the proofs in part I and provide a proof of the global dynamics of the non-hyperbolic cases that were previously conjectured. Then, we show how immigration to one of the species or to both would, drastically, change the dynamics of the system. It is shown that if the level of immigration to one or to both species is above a specified level, then there will be no extinction region where both species go to extinction.     

Eco-evolutionary feedbacks,adaptive dynamics and evolutionary rescue theory

Adaptive dynamics theory has been devised to account for feedbacks between ecological and evolutionary processes. Doing so opens new dimensions to and raises new challenges about evolutionary rescue. Adaptive dynamics theory predicts that successive trait substitutions driven by eco-evolutionary feedbacks can gradually erode population size or growth rate, thus potentially raising the extinction risk. Even a single trait substitution can suffice to degrade population viability drastically at once and cause ‘evolutionary suicide’. In a changing environment, a population may track a viable evolutionary attractor that leads to evolutionary suicide, a phenomenon called ‘evolutionary trapping’. Evolutionary trapping and suicide are commonly observed in adaptive dynamics models in which the smooth variation of traits causes catastrophic changes in ecological state. In the face of trapping and suicide, evolutionary rescue requires that the population overcome evolutionary threats generated by the adaptive process itself. Evolutionary repellors play an important role in determining how variation in environmental conditions correlates with the occurrence of evolutionary trapping and suicide, and what evolutionary pathways rescue may follow. In contrast with standard predictions of evolutionary rescue theory, low genetic variation may attenuate the threat of evolutionary suicide and small population sizes may facilitate escape from evolutionary traps.     

Metaphysiological and evolutionary dynamics of populations exploiting constant and interactive resources:R—K selection revisited

Summary I begin by reviewing the derivation of continuous logistic growth and dynamic consumer—resource interaction equations in terms of specific resource extraction and biomass conversion functions that are considered to hold at a population level. Evolutionary stable strategy (ESS) methods are discussed for analysing populations modelled by these equations. The question of selection trade-offs is then considered, particularly in the context of populations being efficient at extracting resources versus converting resources to their own biomass. Questions relating to single populations with high versus low conversion rates and interacting populations with high versus low self-interference rates are also considered. The models discussed here demonstrate conclusively that self-interference is an essential part of any consumption process: without it population growth and interaction processes do not make any sense. The analysis clarifies concepts relating to the somewhat discredited notion ofr—K selection.     

Biological auctions with multiple rewards

The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.     

Evolutionary stability under the replicator and the gradient dynamics

We unite two general models for evolutionary change under the forces of selection, mutation and reproduction, a genetic model (replicator dynamics) and a cultural model (gradient dynamics). Under the assumption of normality, we find that the mean and variance dynamics are essentially identical under the two models and we relate these to the ESS and convergence stability conditions.     

Eco‐evolutionary feedbacks between private and public goods: evidence from toxic algal blooms

The importance of ‘eco‐evolutionary feedbacks’ in natural systems is currently unclear. Here, we advance a general hypothesis for a particular class of eco‐evolutionary feedbacks with potentially large, long‐lasting impacts in complex ecosystems. These eco‐evolutionary feedbacks involve traits that mediate important interactions with abiotic and biotic features of the environment and a self‐driven reversal of selection as the ecological impact of the trait varies between private (small scale) and public (large scale). Toxic algal blooms may involve such eco‐evolutionary feedbacks due to the emergence of public goods. We review evidence that toxin production by microalgae may yield ‘privatised’ benefits for individual cells or colonies under pre‐ and early‐bloom conditions; however, the large‐scale, ecosystem‐level effects of toxicity associated with bloom states yield benefits that are necessarily ‘public’. Theory predicts that the replacement of private with public goods may reverse selection for toxicity in the absence of higher level selection. Indeed, blooms often harbor significant genetic and functional diversity: bloom populations may undergo genetic differentiation over a scale of days, and even genetically similar lineages may vary widely in toxic potential. Intriguingly, these observations find parallels in terrestrial communities, suggesting that toxic blooms may serve as useful models for eco‐evolutionary dynamics in nature. Eco‐evolutionary feedbacks involving the emergence of a public good may shed new light on the potential for interactions between ecology and evolution to influence the structure and function of entire ecosystems.     

Alternative causes for range limits: a metapopulation perspective

All species have limited distributions at broad geographical scales. At local scales, the distribution of many species is influenced by the interplay of the three factors of habitat availability, local extinctions and colonization dynamics. We use the standard Levins metapopulation model to illustrate how gradients in these three factors can generate species' range limits. We suggest that the three routes to range limits have radically different evolutionary implications. Because the Levins model makes simplifying assumptions about the spatial coupling of local populations, we present numerical studies of spatially explicit metapopulation models that complement the analytical model. The three routes to range limits give rise to distinct spatiotemporal patterns. Range limits in one species can also arise because of environmental gradients impinging upon other species. We briefly discuss a predator–prey example, which illustrates indirect routes to range limits in a metacommunity context.     

Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction

It has recently been demonstrated that ecological feedback mechanisms can facilitate the emergence and maintenance of cooperation in public goods interactions: the replicator dynamics of defectors and cooperators can result, for example, in the ecological coexistence of cooperators and defectors. Here we show that these results change dramatically if cooperation strategy is not fixed but instead is a continuously varying trait under natural selection. For low values of the factor with which the value of resources is multiplied before they are shared among all participants, evolution will always favour lower cooperation strategies until the population falls below an Allee threshold and goes extinct, thus evolutionary suicide occurs. For higher values of the factor, there exists a unique evolutionarily singular strategy, which is convergence stable. Because the fitness function is linear with respect to the strategy of the mutant, this singular strategy is neutral against mutant invasions. This neutrality disappears if a nonlinear functional response in receiving benefits is assumed. For strictly concave functional responses, singular strategies become uninvadable. Evolutionary branching, which could result in the evolutionary emergence of cooperators and defectors, can occur only with locally convex functional responses, but we illustrate that it can also result in coevolutionary extinction.     

How fast is fast? Eco‐evolutionary dynamics and rates of change in populations and phenotypes

It is increasingly recognized that evolution may occur in ecological time. It is not clear, however, how fast evolution – or phenotypic change more generally – may be in comparison with the associated ecology, or whether systems with fast ecological dynamics generally have relatively fast rates of phenotypic change. We developed a new dataset on standardized rates of change in population size and phenotypic traits for a wide range of species and taxonomic groups. We show that rates of change in phenotypes are generally no more than 2/3, and on average about 1/4, the concurrent rates of change in population size. There was no relationship between rates of population change and rates of phenotypic change across systems. We also found that the variance of both phenotypic and ecological rates increased with the mean across studies following a power law with an exponent of two, while temporal variation in phenotypic rates was lower than in ecological rates. Our results are consistent with the view that ecology and evolution may occur at similar time scales, but clarify that only rarely do populations change as fast in traits as they do in abundance.     

A prolegomenon to nonlinear empiricism in the human behavioral sciences

We propose a general framework for integrating theory and empiricism in human evolutionary ecology. We specifically emphasize the joint use of stochastic nonlinear dynamics and information theory. To illustrate critical ideas associated with historical contingency and complex dynamics, we review recent research on social preferences and social learning from behavioral economics. We additionally examine recent work on ecological approaches in history, the modeling of chaotic populations, and statistical application of information theory.     

EVOLUTIONARY BIOLOGY IN BIODIVERSITY SCIENCE,CONSERVATION, AND POLICY: A CALL TO ACTION

Evolutionary biologists have long endeavored to document how many species exist on Earth, to understand the processes by which biodiversity waxes and wanes, to document and interpret spatial patterns of biodiversity, and to infer evolutionary relationships. Despite the great potential of this knowledge to improve biodiversity science, conservation, and policy, evolutionary biologists have generally devoted limited attention to these broader implications. Likewise, many workers in biodiversity science have underappreciated the fundamental relevance of evolutionary biology. The aim of this article is to summarize and illustrate some ways in which evolutionary biology is directly relevant. We do so in the context of four broad areas: (1) discovering and documenting biodiversity, (2) understanding the causes of diversification, (3) evaluating evolutionary responses to human disturbances, and (4) implications for ecological communities, ecosystems, and humans. We also introduce bioGENESIS, a new project within DIVERSITAS launched to explore the potential practical contributions of evolutionary biology. In addition to fostering the integration of evolutionary thinking into biodiversity science, bioGENESIS provides practical recommendations to policy makers for incorporating evolutionary perspectives into biodiversity agendas and conservation. We solicit your involvement in developing innovative ways of using evolutionary biology to better comprehend and stem the loss of biodiversity.     

Exploring context dependency in eco‐evolutionary patterns with the stick insect Timema cristinae

Rapid evolution can influence the ecology of populations, communities, and ecosystems, but the importance of evolution for ecological dynamics remains unclear, largely because the contexts in which evolution is powerful are poorly resolved. Here, we carry out a large observational study to test hypotheses about context dependency of eco‐evolutionary patterns previously identified on the stick insect Timema cristinae. Experiments and observations conducted in 2011 and 2012 documented predator‐mediated negative effects of camouflage maladaptation (i.e., evolutionary dynamics) on: (a) T. cristinae abundance and, (b) species richness and abundance of other arthropods. Here we show that camouflage maladaptation does not correlate with T. cristinae abundance and, instead, is associated with increased abundance and species richness of cohabitating arthropods. We furthermore find that plants with high levels of Timema maladaptation tend to have higher foliar nitrogen, that is, higher nutritional value, and more positive mass‐abundance slopes in the coexisting arthropod communities. We propose explanations for the observed contrasting results, such as negative density‐ and frequency‐dependent selection, feedbacks between herbivore abundance and plant nutritional quality, and common effects of predation pressure on selection and prey abundance. Our results demonstrate the utility of observational studies to assess the context dependency of eco‐evolutionary dynamics patterns and provide testable hypotheses for future work.     

Evolutionary dynamics of collective action in N-person stag hunt dilemmas

In the animal world, collective action to shelter, protect and nourish requires the cooperation of group members. Among humans, many situations require the cooperation of more than two individuals simultaneously. Most of the relevant literature has focused on an extreme case, the N-person Prisoner's Dilemma. Here we introduce a model in which a threshold less than the total group is required to produce benefits, with increasing participation leading to increasing productivity. This model constitutes a generalization of the two-person stag hunt game to an N-person game. Both finite and infinite population models are studied. In infinite populations this leads to a rich dynamics that admits multiple equilibria. Scenarios of defector dominance, pure coordination or coexistence may arise simultaneously. On the other hand, whenever one takes into account that populations are finite and when their size is of the same order of magnitude as the group size, the evolutionary dynamics is profoundly affected: it may ultimately invert the direction of natural selection, compared with the infinite population limit.     

Chaos and the (un)predictability of evolution in a changing environment

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency‐dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco‐evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability.     

Recent evolutionary history predicts population but not ecosystem‐level patterns

In the face of rapid anthropogenic environmental change, it is increasingly important to understand how ecological and evolutionary interactions affect the persistence of natural populations. Augmented gene flow has emerged as a potentially effective management strategy to counteract negative consequences of genetic drift and inbreeding depression in small and isolated populations. However, questions remain about the long‐term impacts of augmented gene flow and whether changes in individual and population fitness are reflected in ecosystem structure, potentiating eco‐evolutionary feedbacks. In this study, we used Trinidadian guppies (Poecilia reticulata) in experimental outdoor mesocosms to assess how populations with different recent evolutionary histories responded to a scenario of severe population size reduction followed by expansion in a high‐quality environment. We also investigated how variation in evolutionary history of the focal species affected ecosystem dynamics. We found that evolutionary history (i.e., gene flow vs. no gene flow) consistently predicted variation in individual growth. In addition, gene flow led to faster population growth in populations from one of the two drainages, but did not have measurable impacts on the ecosystem variables we measured: zooplankton density, algal growth, and decomposition rates. Our results suggest that benefits of gene flow may be long‐term and environment‐dependent. Although small in replication and duration, our study highlights the importance of eco‐evolutionary interactions in determining population persistence and sets the stage for future work in this area.     

Protected polymorphism and evolutionary stability in pleiotropic models with trait-specific dominance

When alleles have pleiotropic effects on a number of quantitative traits, the degree of dominance between a pair of alleles can be different for each trait. Such trait-specific dominance has been studied previously in models for the maintenance of genetic variation by antagonistic effects of an allele on two fitness components. By generalizing these models to an arbitrary number of fitness components or other phenotypic traits with different degrees of dominance, I show that genetic polymorphism is generally impossible without antagonistic fitness effects of different traits and without trait-specific dominance. I also investigate dominance and pleiotropy from a more long-term evolutionary perspective, allowing for the study of general ecological scenarios, and I discuss the effects of trait-specific dominance on evolutionary stability criteria. When selection is mainly directional and only trait-specific dominance and antagonism cause the emergence of polymorphism, then these polymorphisms can be overtaken by single mutants again, such that they are probably short-lived on an evolutionary time scale. Near evolutionarily singular points where directional selection is absent, trait-specific dominance and overdominance facilitate the emergence of polymorphism and cause evolutionary divergence in some cases. An important outcome of these models is that trait-specific dominance allows for the emergence of genetic polymorphisms without a selective disadvantage for heterozygotes. This removes the scope for the evolution of assortative mate choice and affects dominance modification. Sympatric speciation by disruptive ecological selection requires this heterozygote disadvantage in order to evolve, and therefore it becomes less plausible if the emergence of genetic polymorphism usually occurs via trait-specific dominance and antagonistic effects.     

Egg banks in freshwater zooplankton: evolutionary and ecological archives in the sediment

Many representatives of freshwater zooplankton produce at some stage in their life cycle resting stages. A variable portion of the eggs of the previous growing period will hatch at the next occasion while the remaining ones are added to a persistent egg bank, where they can remain viable for decades or longer. The importance of the study of resting eggs and egg banks in general for such different disciplines as taxonomy, ecological biogeography, paleolimnology, nature conservation, evolutionary ecology and community and population ecology is generally appreciated. The major current and expected future developments in this rapidly expanding field of research are presented here. The structure and dynamics of the egg bank are determined by the life history characteristics of the species (or local population), the hatching phenology of their resting stages, and the characteristics of the habitat. The horizontal distribution of dormant stages is generally patchy, with a greater density in the deeper and/or windward parts of a pond or lake. In sediment cores, most viable (responsive) eggs occur in the upper centimeters, although vertical variation related to the history of fish predation or water quality occurs. The accumulation of resting stages of different species, generations and genotypes with variable regeneration niches results in a mixed egg bank with greater potential biodiversity than the active community sampled at any one moment. Through the benthic–pelagic coupling, this dormant reservoir may have considerable impact on the evolutionary potential of the organisms, the ecological dynamics of the community and the distribution of species. Egg banks can be considered the archive of the local habitat, since the pattern of changes in species assemblage and genotypes from the past up to the present reflect changes due to natural or anthropogenic impact that can be used to reconstruct evolutionary processes or even to restore the local habitat. Overlooking the egg bank as an important component of zooplankton communities may lead to erroneous interpretations in the analysis of community and population genetic structure. This review integrates technical and scientific information needed in the study of the structure and function of egg banks in zooplankton with special focus on the fascinating latest developments in the field.