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.     

Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Background

Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.

Results

We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.

Conclusions

The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.     

Chiral symmetry conservation principle

We show a chiral symmetry conservation principle based on chemical kinetics using stochastic results. Suppose the chiral symmetry conservation is evoked, and our universe can be considered globally asymmetric. In that case, there are at least two mirrored asymmetric universes if all the chiral properties are strongly correlated. However, if the chiral correlations are weak or nonexistent, there are possibly Many-(Chiral-Symmetry)-Worlds. Alternatively, if our universe is only locally asymmetric, there could be a single universe with segregated chiral regions. The possible mechanisms of the primordial chiral symmetry breaking can only be found if the chiral symmetry is not truly conserved by assuming the initial racemic conditions. In that case, our universe is asymmetric and could be alone. On the other hand, if the chiral symmetry is conserved, there is no chance of finding the primordial chiral symmetry breaking. Based on this conservation (or not), it is possible to infer two opposite hypotheses, where two general scenarios about the chiral universes are possible.     

The architecture of river networks can drive the evolutionary dynamics of aquatic populations

It is widely recognized that physical landscapes can shape genetic variation within and between populations. However, it is not well understood how riverscapes, with their complex architectures, affect patterns of neutral genetic diversity. Using a spatially explicit agent‐based modeling (ABM) approach, we evaluate the genetic consequences of dendritic river shapes on local population structure. We disentangle the relative contribution of specific river properties to observed patterns of genetic variation by evaluating how different branching architectures and downstream flow regimes affect the genetic structure of populations situated within river networks. Irrespective of the river length, our results illustrate that the extent of river branching, confluence position, and levels of asymmetric downstream migration dictate patterns of genetic variation in riverine populations. Comparisons between simple and highly branched rivers show a 20‐fold increase in the overall genetic diversity and a sevenfold increase in the genetic differentiation between local populations. Given that most rivers have complex architectures, these results highlight the importance of incorporating riverscape information into evolutionary models of aquatic species and could help explain why riverine fishes represent a disproportionately large amount of global vertebrate diversity per unit of habitable area.     

THE EFFECTS OF GENE FLOW ON REINFORCEMENT

We explore the possibility that differences in the pattern of gene flow between populations may affect the evolution of reinforcement by comparing pairs of populations undergoing one-way migration versus symmetric migration. The case of symmetric migration is modeled by a two-island model, where the two populations exchange equal proportions of migrants each generation. One-way migration is modeled by a continent-island model, where migration is in one direction from a large continental population with a fixed genotype to an island population whose genotype frequencies can vary. Hybrid inviability is assumed to be caused by epistatic interactions between background loci. We examine the spread of an introduced preference allele for a previously unpreferred male trait that characterizes one of the populations. Computer simulations indicate that with a weak introduced preference, reinforcement is possible under a wide range of parameter values in a symmetric migration model but cannot occur in a one-way migration model. Reinforcement with one-way migration can occur only with a very strong introduced preference and very strong selection against hybrids. Our results suggest that the speciation of a peripheral isolate, which undergoes essentially one-way migration, may be difficult to complete if secondary contact occurs before reproductive isolation is fully developed.     

A sampling theory for asymmetric communities

We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community dynamics, while an analogous extension of Hubbell's metacommunity dynamics is deferred to an appendix. We find that mass-effects may facilitate coexistence in asymmetric local communities and generate unimodal species abundance distributions indistinguishable from those of symmetric communities. Multiple modes, however, only arise from asymmetric processes and provide a strong indication of non-neutral dynamics. Although the exact stationary distributions of fully asymmetric communities must be calculated numerically, we derive approximate sampling distributions for the general case and for nearly neutral communities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability. In the latter case, our approximate distributions are fully normalized, and novel asymptotic expansions of the required hypergeometric functions are provided to make evaluations tractable for large communities. Employing these results in a Bayesian analysis may provide a novel statistical test to assess the consistency of species abundance data with the neutral hypothesis.     

Male and female recombination landscapes of diploid Arabidopsis arenosa

The number and placement of meiotic crossover events during meiosis have important implications for the fidelity of chromosome segregation as well as patterns of inheritance. Despite the functional importance of recombination, recombination landscapes vary widely among and within species, and this can have a strong impact on evolutionary processes. A good knowledge of recombination landscapes is important for model systems in evolutionary and ecological genetics, since it can improve interpretation of genomic patterns of differentiation and genome evolution, and provides an important starting point for understanding the causes and consequences of recombination rate variation. Arabidopsis arenosa is a powerful evolutionary genetic model for studying the molecular basis of adaptation and recombination rate evolution. Here, we generate genetic maps for 2 diploid A. arenosa individuals from distinct genetic lineages where we have prior knowledge that meiotic genes show evidence of selection. We complement the genetic maps with cytological approaches to map and quantify recombination rates, and test the idea that these populations might have distinct patterns of recombination. We explore how recombination differs at the level of populations, individuals, sexes and genomic regions. We show that the positioning of crossovers along a chromosome correlates with their number, presumably a consequence of crossover interference, and discuss how this effect can cause differences in recombination landscape among sexes or species. We identify several instances of female segregation distortion. We found that averaged genome-wide recombination rate is lower and sex differences subtler in A. arenosa than in Arabidopsis thaliana.     

The influence of habitat boundaries on evolutionary branching along environmental gradients

It is well known that habitat boundaries affect ecological dynamics, but their influence on evolutionary dynamics is less well understood. Here, we study the effects of different kinds of boundaries on evolutionary branching in clonal populations along environmental gradients by systematically analyzing individual-based stochastic models in small- and large-range systems, as well as their large-population-size limits through deterministic approximations. Specifically, we examine four prototypical kinds of boundaries: impermeable boundaries at which individuals stop (“stopping”), or from which they continue back into the interior as if bouncing back mechanically (“reflecting”), or that let them abort the dispersal attempt, return to their original position and try a different direction (“reprising”), and semipermeable boundaries that can be crossed without hindrance, but do not allow the crossing individual to return (“absorbing”).We find that boundary conditions shape branching patterns only in small-range systems, where stopping boundaries generate disruptive selection for a wide range of parameters, whereas absorbing boundaries always generate stabilizing selection. Reflecting and reprising boundaries generate disruptive selection at low individual mobilities, and stabilizing selection at high mobilities. To further analyze these findings, we introduce a simple approximation of the invasion fitness in a mobile population, which predicts the observed outcome. The effect of stochasticity on evolutionary outcomes is small even in small populations: stochasticity causes random branch extinctions at steeper slopes and higher mobilities. In large-range systems, frequency-dependent interactions alone induce evolutionary branching for almost all parameters and independent of boundary conditions.     

Asymmetric Evolutionary Games

Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner’s Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games.     

On evolution under symmetric and asymmetric competitions

This paper considers the coevolution of phenotypic traits in a community comprising two competitive species subject to strong Allee effects. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy under symmetric competition. Secondly, we find that evolutionary suicide is impossible when the two species undergo symmetric competition, however, evolutionary suicide can occur in an asymmetric competition model with strong Allee effects. Thirdly, it is found that evolutionary bistability is a likely outcome of the process under both symmetric and asymmetric competitions, which depends on the properties of symmetric and asymmetric competitions. Fourthly, under asymmetric competition, we find that evolutionary cycle is a likely outcome of the process, which depends on the properties of both intraspecific and interspecific competition. When interspecific and intraspecific asymmetries vary continuously, we also find that the evolutionary dynamics may admit a stable equilibrium and two limit cycles or two stable equilibria separated by an unstable limit cycle or a stable equilibrium and a stable limit cycle.     

Relatedness and competitive asymmetry – implications for growth and population dynamics

The members of natural populations often differ in size and relatedness to each other, which may affect the division of limited resources and have consequences on reproductive success and population dynamics. We modeled seasonal growth and dynamics in populations composed of different types of relatives (full-sibs, half-sibs and non-related individuals) under the continuum of competitive scenarios between complete symmetry and asymmetry. Growth was assumed logistic in proportion to individual biomass and the size-differences were weighted by the relatedness of individuals. The symmetric component of competition was experienced by all individuals in proportion to their biomass, whereas the asymmetric component was individual-specific, and influenced only by the individuals larger than the focal individual. Relatedness decreased and competitive asymmetry increased the variability of individual biomasses. Mortality of the smallest individuals and the size threshold of reproduction decreased population density. Population dynamics were stable when there was no size threshold for reproduction but the presence of the threshold led to cyclic dynamics under low competitive asymmetry. The effects of the threshold were greater among related than unrelated individuals. The results suggest that individual differences and the asymmetry of competition can greatly affect population dynamics. Full symmetry of competition may be evolutionarily unstable in populations of related individuals as it may increase the probability of extinction due to demographic stochasticity.     

Left–right asymmetries and shape analysis on Ceroglossus chilensis (Coleoptera: Carabidae)

Bilateral symmetry is widespread in animal kingdom, however most animal can deviate from expected symmetry and manifest some kind of asymmetries. Fluctuating asymmetry is considered as a tool for valuating developmental instability, whereas directional asymmetry is inherited and could be used for evaluating evolutionary development. We use the method of geometric morphometrics to analyze left/right asymmetries in the whole body, in two sites and totally six populations of Ceroglossus chilensis with the aim to infer and explain morphological disparities between populations and sexes in this species. In all individuals analyzed we found both fluctuating asymmetry and directional asymmetry for size and shape variation components, and a high sexual dimorphism. Moreover a high morphological variability between the two sites emerged as well. Differences in diet could influence the expression of morphological variation and simultaneously affect body sides, and therefore contribute to the symmetric component of variation. Moreover differences emerged between two sites could be a consequence of isolation and fragmentation, rather than a response to local environmental differences between sampling sites.     

Evolutionary Stability in the Asymmetric Volunteer's Dilemma

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer''s dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten''s (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.     

The role of gene flow asymmetry along an environmental gradient in constraining local adaptation and range expansion

Theoretically, asymmetric gene flow along an environmental gradient can limit species range expansion by keeping peripheral populations from locally adapting. However, few empirical studies have examined this potentially fundamental evolutionary mechanism. We address this possibility in the cricket Allonemobius socius, which exist along a season‐length gradient where the probability of producing a single generation per year (univoltinism) increases with latitude. As the probability of univoltinism increases northwards, populations are expected to hedge their bets by producing a greater proportion of diapause eggs when exposed to a mild diapause cue. However, gene flow from southern populations may disrupt local adaptation in the north by reducing the proportion of diapause eggs (expected to be 100% in pure univoltine environments). This may limit range expansion along the northern periphery where A. socius compete with A. fasciatus, a sister species that exhibits an invariant diapause‐only egg‐laying strategy. To assess the potential for range limitation, we examined diapause incidence (the proportion of diapause eggs produced under diapause conditions), gene flow symmetry and population structure across nine A. socius populations. We found that gene flow was asymmetric and biased northwards towards the periphery. Furthermore, peripheral populations that inhabited pure univoltine environments produced numerous nondiapause eggs (a southern, bivoltine diapause phenotype), which we assume to be a suboptimal phenotype. These patterns suggest that asymmetric gene flow along the gradient constrains adaptation in peripheral populations, potentially constraining species range expansion.     

Does colonization asymmetry matter in metapopulations?

Despite the considerable evidence showing that dispersal between habitat patches is often asymmetric, most of the metapopulation models assume symmetric dispersal. In this paper, we develop a Monte Carlo simulation model to quantify the effect of asymmetric dispersal on metapopulation persistence. Our results suggest that metapopulation extinctions are more likely when dispersal is asymmetric. Metapopulation viability in systems with symmetric dispersal mirrors results from a mean field approximation, where the system persists if the expected per patch colonization probability exceeds the expected per patch local extinction rate. For asymmetric cases, the mean field approximation underestimates the number of patches necessary for maintaining population persistence. If we use a model assuming symmetric dispersal when dispersal is actually asymmetric, the estimation of metapopulation persistence is wrong in more than 50% of the cases. Metapopulation viability depends on patch connectivity in symmetric systems, whereas in the asymmetric case the number of patches is more important. These results have important implications for managing spatially structured populations, when asymmetric dispersal may occur. Future metapopulation models should account for asymmetric dispersal, while empirical work is needed to quantify the patterns and the consequences of asymmetric dispersal in natural metapopulations.     

The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

When are populations not connected like a circuit? Identifying biases in gene flow from coalescent times

Connectivity and movement patterns of populations are influenced by past and present environmental and biotic factors, which are reflected in genetic relatedness among populations. Methods that estimate the “commute time” between populations based on electrical resistance (i.e., isolation‐by‐resistance [IBR]) have been widely applied to either infer movement patterns directly from environmental factors or detect possible barriers to gene flow given empirical genetic relatedness. Yet, the commute time is only equivalent to the coalescence time between populations under symmetric migration with isotropic landscapes. Asymmetric gene flow is relatively common when populations are expanding, retreating, or with source‐sink dynamics. In a From the Cover paper in this issue of Molecular Ecology Resources, Lundgren and Ralph (Molecular Ecology Resources, 19, 2019) describe a Bayesian method to infer bidirectional gene flow rates and population sizes without the assumption of symmetry. The method shows great accuracy in connectivity estimations under symmetric, as well as asymmetric gene flow scenarios where resistance methods fail. However, computational complexity limits the method to a few populations, preventing its application to finescale environmental maps. Also, as a discrete‐deme static model, the inferred differences in gene flow rates are sensitive to population discretization and cannot be directly used to differentiate among processes (e.g., past expansion vs. current barrier). Here, we discuss scenarios where the new method can best be utilized and provide potential directions to identify the underlying processes causing deviations in gene flow patterns.     

Species abundance and asymmetric interaction strength in ecological networks

The strength of interactions among species in a network tends to be highly asymmetric. We evaluate the hypothesis that this asymmetry results from the distribution of abundance among species, so that species interactions occur randomly among individuals. We used a database on mutualistic and antagonistic bipartite quantitative interaction networks. We show that across all types of networks asymmetry was correlated with abundance, so that rare species were asymmetrically affected by their abundant partners, while pairs of interacting abundant species tended to exhibit more symmetric, reciprocally strong effects. A null model shows that abundance provides a sufficient explanation of the asymmetry structure in some networks, but suggests the role of additional factors in others. Although not universal, our hypothesis holds for a substantial fraction of networks analyzed here, and should be considered as a null model in all studies aimed at evaluating the ecological and evolutionary consequences of species interactions.     

EXPERIMENTAL EVIDENCE FOR THE EVOLUTION OF THE MAMMALIAN BACULUM BY SEXUAL SELECTION

Male genitalia exhibit a taxonomically widespread pattern of rapid and divergent evolution. Sexual selection is generally believed to be responsible for these patterns of evolutionary divergence, although empirical support for the sexual selection hypothesis comes mainly from studies of insects. Here we show that sexual selection is responsible for an evolutionary divergence in baculum morphology among populations of house mice Mus domesticus. We sourced mice from three isolated populations known to be subject to differing strengths of postcopulatory sexual selection and bred them under common‐garden conditions. Mice from populations with strong postcopulatory sexual selection had bacula that were relatively thicker compared with mice from populations with weak selection. We used experimental evolution to determine whether these patterns of divergence could be ascribed to postcopulatory sexual selection. After 27 generations of experimental evolution, populations of mice subjected to postcopulatory sexual selection evolved bacula that were relatively thicker than populations subjected to enforced monogamy. Our data thereby provide evidence that postcopulatory sexual selection underlies an evolutionary divergence in the mammalian baculum and supports the hypothesis that sexual selection plays a general role in the evolution of male genital morphology across evolutionary diverse taxonomic groups.     

Remarks on branching-extinction evolutionary cycles

We show in this paper that the evolution of cannibalistic consumer populations can be a never ending story involving alternating levels of polymorphism. More precisely, we show that a monomorphic population can evolve toward high levels of cannibalism until it reaches a so-called branching point, where the population splits into two sub-populations characterized by different, but initially very close, cannibalistic traits. Then, the two traits coevolve until the more cannibalistic sub-population undergoes evolutionary extinction. Finally, the remaining population evolves back to the branching point, thus closing an evolutionary cycle. The model on which the study is based is purely deterministic and derived through the adaptive dynamics approach. Evolutionary dynamics are investigated through numerical bifurcation analysis, applied both to the ecological (resident-mutant) model and to the evolutionary model. The general conclusion emerging from this study is that branching-extinction evolutionary cycles can be present in wide ranges of environmental and demographic parameters, so that their detection is of crucial importance when studying evolutionary dynamics.