Resource Variation Within and Between Patches: Where Exploitation Competition, Local Adaptation, and Kin Selection Meet.

AbstractIn patch- or habitat-structured populations, different processes can favor adaptive polymorphism at different scales. While spatial heterogeneity can generate spatially disruptive selection favoring variation between patches, local competition can lead to locally disruptive selection promoting variation within patches. So far, almost all theory has studied these two processes in isolation. Here, we use mathematical modeling to investigate how resource variation within and between habitats influences the evolution of variation in a consumer population where individuals compete in finite patches connected by dispersal. We find that locally and spatially disruptive selection typically act in concert, favoring polymorphism under a wider range of conditions than when in isolation. But when patches are small and dispersal between them is low, kin competition inhibits the emergence of polymorphism, especially when the latter is driven by local competition for resources. We further use our model to clarify what comparisons between trait and neutral genetic differentiation (QST/FST comparisons) can tell about the nature of selection. Overall, our results help us understand the interaction between two major drivers of polymorphism: locally and spatially disruptive selection, and how this interaction is modulated by the unavoidable effects of kin selection under limited dispersal.

Complex life cycles drive community assembly through immigration and adaptive diversification.

Most animals undergo ontogenetic niche shifts during their life. Yet, standard ecological theory builds on models that ignore this complexity. Here, we study how complex life cycles, where juvenile and adult individuals each feed on different sets of resources, affect community richness. Two different modes of community assembly are considered: gradual adaptive evolution and immigration of new species with randomly selected phenotypes. We find that under gradual evolution complex life cycles can lead to both higher and lower species richness when compared to a model of species with simple life cycles that lack an ontogenetic niche shift. Thus, complex life cycles do not per se increase the scope for gradual adaptive diversification. However, complex life cycles can lead to significantly higher species richness when communities are assembled trough immigration, as immigrants can occupy isolated peaks of the dynamic fitness landscape that are not accessible via gradual evolution.

How Does Joint Evolution of Consumer Traits Affect Resource Specialization?

Consumers regularly experience trade-offs in their ability to find, handle, and digest different resources. Evolutionary ecologists recognized the significance of this observation for the evolution and maintenance of biological diversity long ago and continue to elaborate on the conditions under which to expect one or several specialists, generalists, or combinations thereof. Existing theory based on a single evolving trait predicts that specialization requires strong trade-offs such that generalists perform relatively poorly, while weak trade-offs favor a single generalist. Here, we show that this simple dichotomy does not hold true under joint evolution of two or more foraging traits. In this case, the boundary between trade-offs resulting in resource specialists and resource generalists is shifted toward weaker trade-off curvatures. In particular, weak trade-offs can result in evolutionary branching, leading to the evolution of two coexisting resource specialists, while the evolution of a single resource generalist requires particularly weak trade-offs. These findings are explained by performance benefits due to epistatic trait interactions enjoyed by phenotypes that are specialized in more than one trait for the same resource.

The components of directional and disruptive selection in heterogeneous group-structured populations.

We derive how directional and disruptive selection operate on scalar traits in a heterogeneous group-structured population for a general class of models. In particular, we assume that each group in the population can be in one of a finite number of states, where states can affect group size and/or other environmental variables, at a given time. Using up to second-order perturbation expansions of the invasion fitness of a mutant allele, we derive expressions for the directional and disruptive selection coefficients, which are sufficient to classify the singular strategies of adaptive dynamics. These expressions include first- and second-order perturbations of individual fitness (expected number of settled offspring produced by an individual, possibly including self through survival); the first-order perturbation of the stationary distribution of mutants (derived here explicitly for the first time); the first-order perturbation of pairwise relatedness; and reproductive values, pairwise and three-way relatedness, and stationary distribution of mutants, each evaluated under neutrality. We introduce the concept of individual k-fitness (defined as the expected number of settled offspring of an individual for which k-1 randomly chosen neighbors are lineage members) and show its usefulness for calculating relatedness and its perturbation. We then demonstrate that the directional and disruptive selection coefficients can be expressed in terms individual k-fitnesses with k=1,2,3 only. This representation has two important benefits. First, it allows for a significant reduction in the dimensions of the system of equations describing the mutant dynamics that needs to be solved to evaluate explicitly the two selection coefficients. Second, it leads to a biologically meaningful interpretation of their components. As an application of our methodology, we analyze directional and disruptive selection in a lottery model with either hard or soft selection and show that many previous results about selection in group-structured populations can be reproduced as special cases of our model.

The efficacy of good genes sexual selection under environmental change.

Sexual selection can promote adaptation if sexually selected traits are reliable indicators of genetic quality. Moreover, models of good genes sexual selection suggest that, by operating more strongly in males than in females, sexual selection may purge deleterious alleles from the population at a low demographic cost, offering an evolutionary benefit to sexually reproducing populations. Here, we investigate the effect of good genes sexual selection on adaptation following environmental change. We show that the strength of sexual selection is often weakened relative to fecundity selection, reducing the suggested benefit of sexual reproduction. This result is a consequence of incorporating a simple and general mechanistic basis for how sexual selection operates under different mating systems, rendering selection on males frequency-dependent and dynamic with respect to the degree of environmental change. Our model illustrates that incorporating the mechanism of selection is necessary to predict evolutionary outcomes and highlights the need to substantiate previous theoretical claims with further work on how sexual selection operates in changing environments.

Mutual invadability near evolutionarily singular strategies for multivariate traits, with special reference to the strongly convergence stable case.

Over the last two decades evolutionary branching has emerged as a possible mathematical paradigm for explaining the origination of phenotypic diversity. Although branching is well understood for one-dimensional trait spaces, a similarly detailed understanding for higher dimensional trait spaces is sadly lacking. This note aims at getting a research program of the ground leading to such an understanding. In particular, we show that, as long as the evolutionary trajectory stays within the reign of the local quadratic approximation of the fitness function, any initial small scale polymorphism around an attracting invadable evolutionarily singular strategy (ess) will evolve towards a dimorphism. That is, provided the trajectory does not pass the boundary of the domain of dimorphic coexistence and falls back to monomorphism (after which it moves again towards the singular strategy and from there on to a small scale polymorphism, etc.). To reach these results we analyze in some detail the behavior of the solutions of the coupled Lande-equations purportedly satisfied by the phenotypic clusters of a quasi-n-morphism, and give a precise characterisation of the local geometry of the set D in trait space squared harbouring protected dimorphisms. Intriguingly, in higher dimensional trait spaces an attracting invadable ess needs not connect to D. However, for the practically important subset of strongly attracting ess-es (i.e., ess-es that robustly locally attract the monomorphic evolutionary dynamics for all possible non-degenerate mutational or genetic covariance matrices) invadability implies that the ess does connect to D, just as in 1-dimensional trait spaces. Another matter is that in principle there exists the possibility that the dimorphic evolutionary trajectory reverts to monomorphism still within the reign of the local quadratic approximation for the invasion fitnesses. Such locally unsustainable branching cannot occur in 1- and 2-dimensional trait spaces, but can do so in higher dimensional ones. For the latter trait spaces we give a condition excluding locally unsustainable branching which is far stricter than the one of strong convergence, yet holds good for a relevant collection of published models. It remains an open problem whether locally unsustainable branching can occur around general strongly attracting invadable ess-es.

A general condition for adaptive genetic polymorphism in temporally and spatially heterogeneous environments.

Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that fluctuates in space and time, and derive an analytical condition for when these fluctuations promote genetic diversification. As ecological scenario we use a generalized island model with soft selection within patches in which we incorporate generation overlap. We allow for arbitrary fluctuations in the environment including spatio-temporal correlations and any functional form of selection on the trait. Using the concepts of invasion fitness and evolutionary branching, we derive a simple and transparent condition for the adaptive evolution and maintenance of genetic diversity. This condition relates the strength of selection within patches to expectations and variances in the environmental conditions across space and time. Our results unify, clarify, and extend a number of previous results on the evolution and maintenance of genetic variation under fluctuating selection. Individual-based simulations show that our results are independent of the details of the genetic architecture and whether reproduction is clonal or sexual. The onset of increased genetic variance is predicted accurately also in small populations in which alleles can go extinct due to environmental stochasticity.

Evolution of functional specialization and division of labor.

Division of labor among functionally specialized modules occurs at all levels of biological organization in both animals and plants. Well-known examples include the evolution of specialized enzymes after gene duplication, the evolution of specialized cell types, limb diversification in arthropods, and the evolution of specialized colony members in many taxa of marine invertebrates and social insects. Here, we identify conditions favoring the evolution of division of labor by means of a general mathematical model. Our starting point is the assumption that modules contribute to two different biological tasks and that the potential of modules to contribute to these tasks is traded off. Our results are phrased in terms of properties of performance functions that map the phenotype of modules to measures of performance. We show that division of labor is favored by three factors: positional effects that predispose modules for one of the tasks, accelerating performance functions, and synergistic interactions between modules. If modules can be lost or damaged, selection for robustness can counteract selection for functional specialization. To illustrate our theory we apply it to the evolution of specialized enzymes coded by duplicated genes.

Necessary and sufficient conditions for R0 to be a sum of contributions of fertility loops.

Recently, de-Camino-Beck and Lewis (Bull Math Biol 69:1341-1354, 2007) have presented a method that under certain restricted conditions allows computing the basic reproduction ratio R0 in a simple manner from life cycle graphs, without, however, giving an explicit indication of these conditions. In this paper, we give various sets of sufficient and generically necessary conditions. To this end, we develop a fully algebraic counterpart of their graph-reduction method which we actually found more useful in concrete applications. Both methods, if they work, give a simple algebraic formula that can be interpreted as the sum of contributions of all fertility loops. This formula can be used in e.g. pest control and conservation biology, where it can complement sensitivity and elasticity analyses. The simplest of the necessary and sufficient conditions is that, for irreducible projection matrices, all paths from birth to reproduction have to pass through a common state. This state may be visible in the state representation for the chosen sampling time, but the passing may also occur in between sampling times, like a seed stage in the case of sampling just before flowering. Note that there may be more than one birth state, like when plants in their first year can already have different sizes at the sampling time. Also the common state may occur only later in life. However, in all cases R0 allows a simple interpretation as the expected number of new individuals that in the next generation enter the common state deriving from a single individual in this state. We end with pointing to some alternative algebraically simple quantities with properties similar to those of R0 that may sometimes be used to good effect in cases where no simple formula for R0 exists.

What life cycle graphs can tell about the evolution of life histories.

We analyze long-term evolutionary dynamics in a large class of life history models. The model family is characterized by discrete-time population dynamics and a finite number of individual states such that the life cycle can be described in terms of a population projection matrix. We allow an arbitrary number of demographic parameters to be subject to density-dependent population regulation and two or more demographic parameters to be subject to evolutionary change. Our aim is to identify structural features of life cycles and modes of population regulation that correspond to specific evolutionary dynamics. Our derivations are based on a fitness proxy that is an algebraically simple function of loops within the life cycle. This allows us to phrase the results in terms of properties of such loops which are readily interpreted biologically. The following results could be obtained. First, we give sufficient conditions for the existence of optimisation principles in models with an arbitrary number of evolving traits. These models are then classified with respect to their appropriate optimisation principle. Second, under the assumption of just two evolving traits we identify structural features of the life cycle that determine whether equilibria of the monomorphic adaptive dynamics (evolutionarily singular points) correspond to fitness minima or maxima. Third, for one class of frequency-dependent models, where optimisation is not possible, we present sufficient conditions that allow classifying singular points in terms of the curvature of the trade-off curve. Throughout the article we illustrate the utility of our framework with a variety of examples.

Invasion and maintenance of meiotic drivers in populations of ascomycete fungi.

Meiotic drivers (MDs) are selfish genetic elements that are able to become overrepresented among the products of meiosis. This transmission advantage makes it possible for them to spread in a population even when they impose fitness costs on their host organisms. Whether an MD can invade a population, and subsequently reach fixation or coexist in a stable polymorphism, depends on the one hand on the biology of the host organism, including its life cycle, mating system, and population structure, and on the other hand on the specific fitness effects of the driving allele on the host. Here, we present a population genetic model for spore killing, a type of drive specific to fungi. We show how ploidy level, rate of selfing, and efficiency of spore killing affect the invasion probability of a driving allele and the conditions for its stable coexistence with a nondriving allele. Our model can be adapted to different fungal life cycles, and is applied here to two well-studied genera of filamentous ascomycetes known to harbor spore-killing elements, Neurospora and Podospora. We discuss our results in the light of recent empirical findings for these two systems.

Coexistence and limiting similarity of consumer species competing for a linear array of resources.

Consumer-resource systems with linear arrays of substitutable resources form the conceptual basis of much of present-day competition theory. However, most analyses of the limiting similarity of competitors have only employed consumer-resource models as a justification for using the Lotka-Volterra competition equations to represent the interaction. Unfortunately, Lotka-Volterra models cannot reflect resource exclusion via apparent competition and are poor approximations of systems with nonlogistic resource growth. We use consumer-resource models to examine the impact of exclusion of biotic resources or depletion of abiotic resources on the ability of three consumer species to coexist along a one-dimensional resource axis. For a wide range of consumer-resource models, coexistence conditions can become more restrictive with increasing niche separation of the two outer species. This occurs when the outer species are highly efficient; in this case they cause extinction or severe depletion of intermediate resources when their own niches have an intermediate level of separation. In many cases coexistence of an intermediate consumer species is prohibited when niche separation of the two outer species is moderately large, but not when it is small. Coexistence may be most likely when the intermediate species is closer to one of the two outer species, contrary to previous theory. These results suggest that competition may lead to uneven spacing of utilization curves. The implications and range of applicability of the models are discussed.

Determinants of the strength of disruptive and/or divergent selection arising from resource competition.

We investigate how the intensity of competition for resources affects the strength of disruptive selection on a resource acquisition trait. This is done by analyzing several consumer-resource models in which consumers use a linear array of resources. We show that disruptive selection can be diminished under both strong and weak competition, making disruptive selection a unimodal function of the strength of competition. Weak selection under strong competition arises when competition causes the extinction (for self-reproducing resources) or depletion (for abiotic resources) of the most rapidly caught resources. Weak selection under weak competition is a consequence of minimal effects of consumers on resources. The precise relationship between intensity of competition and strength of disruptive selection is sensitive to the shape of the consumer's resource utilization curve and the nature of resource growth. The most strongly unimodal competition-selection relationships result from utilization curves with long tails. Our results show that a simple comparison of the width of the resource abundance distribution and the consumer's utilization function is not sufficient to determine whether selection is disruptive. The results may explain some contradictory experimental findings regarding the effect of consumer mortality on the strength of disruptive selection.

Competition-similarity relationships and the nonlinearity of competitive effects in consumer-resource systems.

Much previous ecological and evolutionary theory about exploitative competition for a continuous spectrum of resources has used the Lotka-Volterra model with competition coefficients given by a Gaussian function of niche separation. Using explicit consumer-resource models, we show that the Lotka-Volterra model and the assumption of a Gaussian competition-similarity relationship both fail to reflect the impact of strong resource depletion, which typically reduces the influence of the most heavily used resources on the competitive interaction. Taking proper account of resource depletion reveals that strong exploitative competition between efficient consumers is usually a highly nonlinear interaction, implying that a single measure is no longer sufficient to characterize the process. The nonlinearity usually entails weak coupling of competing species when their abundances are high and equal. Rare invaders are likely to have effects on abundant residents much larger than those of the resident on the invader. Asymmetrical utilization curves often produce asymmetrical competition coefficients. Competition coefficients are typically non-Gaussian and are often nonmonotonic functions of niche separation. Utilization curve shape and resource growth functions can have major effects on competition-similarity relationships. A variety of previous theoretical findings need to be reassessed in light of these results.

The interplay between behavior and morphology in the evolutionary dynamics of resource specialization.

We analyze the consequences of diet choice behavior for the evolutionary dynamics of foraging traits by means of a mathematical model. The model is characterized by the following features. Consumers feed on two different substitutable resources that are distributed in a fine-grained manner. On encounter with a resource item, consumers decide whether to attack it so as to maximize their energy intake. Simultaneously, evolutionary change occurs in morphological traits involved in the foraging process. The assumption here is that evolution is constrained by a trade-off in the consumer's ability to forage on the alternative resources. The model predicts that flexible diet choice behavior can guide the direction of evolutionary change and mediate coexistence of different consumer types. Such polymorphisms can evolve from a monomorphic population at evolutionary branching points and also at points where a small genetic change in a trait can provoke a sharp instantaneous and nongenetic change in choice behavior. In the case of weak trade-offs, the evolutionary dynamics of a dimorphic consumer population can lead to alternative evolutionarily stable communities. The robustness of these predictions is checked with individual-based simulations and by relaxing the assumption of optimally foraging consumers.

Evolutionary predictions should be based on individual-level traits.

Recent theoretical studies have analyzed the evolution of habitat specialization using either the logistic or the Ricker equation. These studies have implemented evolutionary change directly in population-level parameters such as habitat-specific intrinsic growth rates r or carrying capacities K. This approach is a shortcut to a more detailed analysis where evolutionary change is studied in underlying morphological, physiological, or behavioral traits at the level of the individual that contribute to r or K. Here we describe two pitfalls that can occur when such a shortcut is employed. First, population-level parameters that appear as independent variables in a population dynamical model might not be independent when derived from processes at the individual level. Second, patterns of covariation between individual-level traits are usually not conserved when mapped to the level of demographic parameters. Nonlinear mappings constrain the curvature of trade-offs that can sensibly be assumed at the population level. To illustrate these results, we derive a two-habitat version of the logistic and Ricker equations from individual-level processes and compare the evolutionary dynamics of habitat-specific carrying capacities with those of underlying individual-level traits contributing to the carrying capacities. Finally, we sketch how our viewpoint affects the results of earlier studies.

The evolution of resource specialization through frequency-dependent and frequency-independent mechanisms.

Levins's fitness set approach has shaped the intuition of many evolutionary ecologists about resource specialization: if the set of possible phenotypes is convex, a generalist is favored, while either of the two specialists is predicted for concave phenotype sets. An important aspect of Levins's approach is that it explicitly excludes frequency-dependent selection. Frequency dependence emerged in a series of models that studied the degree of character displacement of two consumers coexisting on two resources. Surprisingly, the evolutionary dynamics of a single consumer type under frequency dependence has not been studied in detail. We analyze a model of one evolving consumer feeding on two resources and show that, depending on the trait considered to be subject to evolutionary change, selection is either frequency independent or frequency dependent. This difference is explained by the effects different foraging traits have on the consumer-resource interactions. If selection is frequency dependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Those traits with frequency-independent selection, however, do indeed follow the predictions based on Levins's fitness set approach. This dichotomy in the evolutionary dynamics of traits involved in the same foraging process was not previously recognized.

Organismal complexity and the potential for evolutionary diversification.

We present two theoretical approaches to investigate whether organismal complexity, defined as the number of quantitative traits determining fitness, and the potential for adaptive diversification are correlated. The first approach is independent of any specific ecological model and based on curvature properties of the fitness landscape as a function of the dimension of the trait space. This approach indeed suggests a positive correlation between complexity and diversity. An assumption made in this first approach is that the potential for any pair of traits to interact in their effect on fitness is independent of the dimension of the trait space. In the second approach, we circumvent making this assumption by analyzing the evolutionary dynamics in an explicit consumer-resource model in which the shape of the fitness landscape emerges from the underlying mechanistic ecological model. In this model, consumers are characterized by several quantitative traits and feed on a multidimensional resource distribution. The consumer's feeding efficiency on the resource is determined by the match between consumer phenotype and resource item. This analysis supports a positive correlation between the complexity of the evolving consumer species and its potential to diversify with the additional insight that also increasing resource complexity facilitates diversification.

Comparing environmental and genetic variance as adaptive response to fluctuating selection.

Phenotypic variation within populations has two sources: genetic variation and environmental variation. Here, we investigate the coevolution of these two components under fluctuating selection. Our analysis is based on the lottery model in which genetic polymorphism can be maintained by negative frequency-dependent selection, whereas environmental variation can be favored due to bet-hedging. In our model, phenotypes are characterized by a quantitative trait under stabilizing selection with the optimal phenotype fluctuating in time. Genotypes are characterized by their phenotypic offspring distribution, which is assumed to be Gaussian with heritable variation for its mean and variance. Polymorphism in the mean corresponds to genetic variance while the width of the offspring distribution corresponds to environmental variance. We show that increased environmental variance is favored whenever fluctuations in the selective optima are sufficiently strong. Given the environmental variance has evolved to its optimum, genetic polymorphism can still emerge if the distribution of selective optima is sufficiently asymmetric or leptokurtic. Polymorphism evolves in a diagonal direction in trait space: one type becomes a canalized specialist for the more common ecological conditions and the other type a de-canalized bet-hedger thriving on the less-common conditions. All results are based on analytical approximations, complemented by individual-based simulations.

Disruptive selection and then what?

Disruptive selection occurs when extreme phenotypes have a fitness advantage over more intermediate phenotypes. The phenomenon is particularly interesting when selection keeps a population in a disruptive regime. This can lead to increased phenotypic variation while disruptive selection itself is diminished or eliminated. Here, we review processes that increase phenotypic variation in response to disruptive selection and discuss some of the possible outcomes, such as sympatric species pairs, sexual dimorphisms, phenotypic plasticity and altered community assemblages. We also identify factors influencing the likelihoods of these different outcomes.