Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.     

Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics

The measure dynamics approach to modelling single-species coevolution with a one-dimensional trait space is developed and compared to more traditional methods of adaptive dynamics and the Maximum Principle. It is assumed that individual fitness results from pairwise interactions together with a background fitness that depends only on total population size. When fitness functions are quadratic in the real variables parameterizing the one-dimensional traits of interacting individuals, the following results are derived. It is shown that among monomorphisms (i.e. measures supported on a single trait value), the continuously stable strategy (CSS) characterize those that are Lyapunov stable and attract all initial measures supported in an interval containing this trait value. In the cases where adaptive dynamics predicts evolutionary branching, convergence to a dimorphism is established. Extensions of these results to general fitness functions and/or multi-dimensional trait space are discussed.     

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.     

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.     

When do mixotrophs specialize? Adaptive dynamics theory applied to a dynamic energy budget model

In evolutionary history, several events have occurred at which mixotrophs specialized into pure autotrophs and heterotrophs. We studied the conditions under which such events take place, using the Dynamic Energy Budget (DEB) theory for physiological rules of the organisms' metabolism and Adaptive Dynamics (AD) theory for evolutionary behavior of parameter values. We modeled a population of mixotrophs that can take up dissolved inorganic nutrients by autotrophic assimilation and detritus by heterotrophic assimilation. The organisms have a certain affinity for both pathways; mutations that occur in the affinities enable the population to evolve. One of the possible evolutionary outcomes is a branching point which provides an opportunity for the mixotrophic population to split up and specialize into separate autotrophs and heterotrophs. Evolutionary branching is not a common feature of the studied system, but is found to occur only under specific conditions. These conditions depend on intrinsic properties such as the cost function, the level of the costs and the boundaries of the trait space: only at intermediate cost levels and when an explicit advantage exists to pure strategies over mixed ones may evolutionary branching occur. Usually, such an advantage (and hence evolutionary branching) can be induced by interference between the two affinities, but this result changes due to the constraints on the affinities. Now, only some of the more complicated cost functions give rise to a branching point. In contrast to the intrinsic properties, extrinsic properties such as the total nutrient content or light intensity were found to have no effect on the evolutionary outcomes at all.     

Genetic basis of between‐individual and within‐individual variance of docility

Between‐individual variation in phenotypes within a population is the basis of evolution. However, evolutionary and behavioural ecologists have mainly focused on estimating between‐individual variance in mean trait and neglected variation in within‐individual variance, or predictability of a trait. In fact, an important assumption of mixed‐effects models used to estimate between‐individual variance in mean traits is that within‐individual residual variance (predictability) is identical across individuals. Individual heterogeneity in the predictability of behaviours is a potentially important effect but rarely estimated and accounted for. We used 11 389 measures of docility behaviour from 1576 yellow‐bellied marmots (Marmota flaviventris) to estimate between‐individual variation in both mean docility and its predictability. We then implemented a double hierarchical animal model to decompose the variances of both mean trait and predictability into their environmental and genetic components. We found that individuals differed both in their docility and in their predictability of docility with a negative phenotypic covariance. We also found significant genetic variance for both mean docility and its predictability but no genetic covariance between the two. This analysis is one of the first to estimate the genetic basis of both mean trait and within‐individual variance in a wild population. Our results indicate that equal within‐individual variance should not be assumed. We demonstrate the evolutionary importance of the variation in the predictability of docility and illustrate potential bias in models ignoring variation in predictability. We conclude that the variability in the predictability of a trait should not be ignored, and present a coherent approach for its quantification.     

ON THE LOW HERITABILITY OF LIFE-HISTORY TRAITS

Life-history traits such as longevity and fecundity often show low heritability. This is usually interpreted in terms of Fisher's fundamental theorem to mean that populations are near evolutionary equilibrium and genetic variance in total fitness is low. We develop the causal relationship between metric traits and life-history traits to show that a life-history trait is expected to have a low heritability whether or not the population is at equilibrium. This is because it is subject to all the environmental variation in the metric traits that affect it plus additional environmental variation. There is no simple prediction regarding levels of additive genetic variance in life-history traits, which may be high at equilibrium. Several other patterns in the inheritance of life-history traits are readily predicted from the causal model. These include the strength of genetic correlations between life-history traits, levels of nonadditive genetic variance, and the inevitability of genotype-environment interaction.     

Adaptive evolution of foraging-related traits in a predator-prey community

In this paper, with the method of adaptive dynamics and geometric technique, we investigate the adaptive evolution of foraging-related phenotypic traits in a predator-prey community with trade-off structure. Specialization on one prey type is assumed to go at the expense of specialization on another. First, we identify the ecological and evolutionary conditions that allow for evolutionary branching in predator phenotype. Generally, if there is a small switching cost near the singular strategy, then this singular strategy is an evolutionary branching point, in which predator population will change from monomorphism to dimorphism. Second, we find that if the trade-off curve is globally convex, predator population eventually branches into two extreme specialists, each completely specializing on a particular prey species. However, if the trade-off curve is concave-convex-concave, after branching in predator phenotype, the two predator species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist. The analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible under this model.     

Maternal genetic effects set the potential for evolution in a free-living vertebrate population

Heritable maternal effects have important consequences for the evolutionary dynamics of phenotypic traits under selection, but have only rarely been tested for or quantified in evolutionary studies. Here we estimate maternal effects on early-life traits in a feral population of Soay sheep (Ovis aries) from St Kilda, Scotland. We then partition the maternal effects into genetic and environmental components to obtain the first direct estimates of maternal genetic effects in a free-living population, and furthermore test for covariance between direct and maternal genetic effects. Using an animal model approach, direct heritabilities (h2) were low but maternal genetic effects (m2) represented a relatively large proportion of the total phenotypic variance for each trait (birth weight m2=0.119, birth date m2=0.197, natal litter size m2=0.211). A negative correlation between direct and maternal genetic effects was estimated for each trait, but was only statistically significant for natal litter size (ram= -0.714). Total heritabilities (incorporating variance from heritable maternal effects and the direct-maternal genetic covariance) were significant for birth weight and birth date but not for natal litter size. Inadequately specified models greatly overestimated additive genetic variance and hence direct h2 (by a factor of up to 6.45 in the case of birth date). We conclude that failure to model heritable maternal variance can result in over- or under-estimation of the potential for traits to respond to selection, and advocate an increased effort to explicitly measure maternal genetic effects in evolutionary studies.     

Very low additive genetic variance and evolutionary potential in multiple populations of two rainforest Drosophila species

Most quantitative traits are thought to exhibit high levels of genetic variance and evolutionary potential. However, this conclusion may be biased by a lack of studies on nonmodel organisms and may not generalize to restricted species. A recent study on a single, southern population of the rainforest-restricted Drosophila birchii failed to find significant additive genetic variance for the desiccation resistance trait; however, it is unclear whether this pattern extends to other D. birchii populations or to other rainforest species. Here we use an animal model design to show very low levels of additive genetic variance for desiccation resistance in multiple populations of two highly sensitive rainforest species of Drosophila from tropical northeastern Australia. In contrast, relatively high levels of genetic variance were found for morphological traits in all populations of the species tested. This indicates limited evolutionary potential for evolving increased desiccation resistance in these rainforest restricted species.     

Evolutionary dynamics through multispecies competition

Disruptive selection, emerging from frequency-dependent intraspecific competition can have very exciting evolutionary outcomes. One such outcome is the origin of new species through an evolutionary branching event. Literature on theoretical models investigating the emergence of disruptive selection is vast, with some investigating the sensitivity of the models on assumptions of the competition and carrying capacity functions’ shapes. What is seldom modeled is what happens once the population escapes its effect via increase phenotypic or genotypic variance. The expectation is mixed: disruptive selection could diminish and ultimately disappear or it could still exist leading to further speciation events through multiple evolutionary branching events. Here, we derive the conditions under which disruptive selection drives two subpopulations that originated at a branching point to other points in trait space where each subpopulation again experiences disruptive selection. We show that the general pattern for further branchings require that the competition function to be even narrower than what is required for the first evolutionary branching. However, we also show that the existence of disruptive selection in higher dimensional systems is also sensitive to the shapes of the functions used.     

Allelic diversity for neutral markers retains a higher adaptive potential for quantitative traits than expected heterozygosity

The adaptive potential of a population depends on the amount of additive genetic variance for quantitative traits of evolutionary importance. This variance is a direct function of the expected frequency of heterozygotes for the loci which affect the trait (QTL). It has been argued, but not demonstrated experimentally, that long‐term response to selection is more dependent on QTL allelic diversity than on QTL heterozygosity. Conservation programmes, aimed at preserving this variation, usually rely on neutral markers rather than on quantitative traits for making decisions on management. Here, we address, both through simulation analyses and experimental studies with Drosophila melanogaster, the question of whether allelic diversity for neutral markers is a better indicator of a high adaptive potential than expected heterozygosity. In both experimental and simulation studies, we established synthetic populations for which either heterozygosity or allelic diversity was maximized using information from QTL (simulations) or unlinked neutral markers (simulations and experiment). The synthetic populations were selected for the quantitative trait to evaluate the evolutionary potential provided by the two optimization methods. Our results show that maximizing the number of alleles of a low number of markers implies higher responses to selection than maximizing their heterozygosity.     

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.     

Evolutionary stability for large populations

We present a revision of Maynard Smith's evolutionary stability criteria for populations which are very large (though technically finite) and of unknown size. We call this the large population ESS, as distinct from Maynard Smith's infinite population ESS and Schaffer's finite population ESS. Building on Schaffer's finite population model, we define the large population ESS as a strategy which cannot be invaded by any finite number of mutants, as long as the population size is sufficiently large. The large population ESS is not equivalent to the infinite population ESS: we give examples of games in which a large population ESS exists but an infinite population ESS does not, and vice versa. Our main contribution is a simple set of two criteria for a large population ESS, which are similar (but not identical) to those originally proposed by Maynard Smith for infinite populations.     

Quantitative genetics of the use of conspecific and heterospecific social cues for breeding site choice

Social information use for decision-making is common and affects ecological and evolutionary processes, including social aggregation, species coexistence, and cultural evolution. Despite increasing ecological knowledge on social information use, very little is known about its genetic basis and therefore its evolutionary potential. Genetic variation in a trait affecting an individual's social and nonsocial environment may have important implications for population dynamics, interspecific interactions, and, for expression of other, environmentally plastic traits. We estimated repeatability, additive genetic variance, and heritability of the use of conspecific and heterospecific social cues (abundance and breeding success) for breeding site choice in a population of wild collared flycatchers Ficedula albicollis. Repeatability was found for two social cues: previous year conspecific breeding success and previous year heterospecific abundance. Yet, additive genetic variances for these two social cues, and thus heritabilities, were low. This suggests that most of the phenotypic variation in the use of social cues and resulting conspecific and heterospecific social environment experienced by individuals in this population stems from phenotypic plasticity. Given the important role of social information use on ecological and evolutionary processes, more studies on genetic versus environmental determinism of social information use are needed.     

Mutability as an altruistic trait in finite asexual populations

Mutation rate (MR) is a crucial determinant of the evolutionary process. Optimal MR may enable efficient evolutionary searching and therefore increase the fitness of the population over time. Nevertheless, individuals may favor MRs that are far from being optimal for the whole population. Instead, each individual may tend to mutate at rates that selfishly increase its own relative fitness. We show that in some cases, undergoing a mutation is altruistic, i.e., it increases the expected fitness of the population, but decreases the expected fitness of the mutated individual itself. In this case, if the population is uniform (completely mixed, undivided), immutability is evolutionary stable and is probably selected for. However, our examination of a segregated population, which is divided into several groups (or patches), shows that the optimal, altruistic MR may out-compete the selfish MR if the coupling between the groups is neither too strong nor too weak. This demonstrates that the population structure is crucial for the succession of the evolutionary process itself. For example, in a uniform population, the evolutionary process may be stopped before the highest fitness is reached, as demonstrated in a one-pick fitness landscape. In addition, we show that the dichotomy between evolutionary stable and optimal MRs can be seen as a special case of a more general phenomenon in which optimal behaviors may be destabilized in finite populations, since optimal sub-populations may become extinct before the benefit of their behavior is expressed.     

Plastic flies

Individuals within species and populations vary. Such variation arises through environmental and genetic factors and ensures that no two individuals are identical. However, it is clear that not all traits show the same degree of intraspecific variation. Some traits, in particular secondary sexual characteristics used by males to compete for and attract females, are extremely variable among individuals in a population. Other traits, for example brain size in mammals, are not. Recent research has begun to explore the possibility that the extent of phenotypic variation (here referred to as “variability”) may be a character itself and subject to natural selection. While these studies support the concept of variability as an evolvable trait, controversy remains over what precisely the trait is. At the heart of this controversy is the fact that there are very few examples of developmental mechanisms that regulate trait variability in response to any source of variation, be it environmental or genetic. Here, we describe a recent study from our laboratory that identifies such a mechanism. We then place the study in the context of current research on the regulation of trait variability, and discuss the implications for our understanding of the developmental regulation and evolution of phenotypic variation.     

Y-chromosomes can constrain adaptive evolution via epistatic interactions with other chromosomes

Background

Variation in the non-coding regions of Y-chromosomes have been shown to influence gene regulation throughout the genome in some systems; a phenomenon termed Y-linked regulatory variation (YRV). This type of sex-specific genetic variance could have important implications for the evolution of male and female traits. If YRV contributes to the additive genetic variation of an autosomally coded trait shared between the sexes (e.g. body size), then selection could facilitate sexually dimorphic evolution via the Y-chromosome. In contrast, if YRV is entirely non-additive (i.e. interacts epistatically with other chromosomes), then Y-chromosomes could constrain trait evolution in both sexes whenever they are selected for the same trait value. The ability for this phenomenon to influence such fundamental evolutionary dynamics remains unexplored.

Results

Here we address the evolutionary contribution of Y-linked variance by selecting for improved male geotaxis in populations possessing multiple Y-chromosomes (i.e. possessed Y-linked additive and/or epistatic variation) or a single Y-chromosome variant (i.e. possessed no Y-linked variation). We found that males from populations possessing Y-linked variation did not significantly respond to selection; however, males from populations with no Y-linked variation did respond. These patterns suggest the presence of a large quantity of Y-linked epistatic variance in the multi-Y population that dramatically slowed its response.

Conclusions

Our results imply that YRV is unlikely to facilitate the evolution of sexually dimorphic traits (at least for the trait examined here), but can interfere with the rate of trait evolution in both males and females. This result could have real biological implications as it suggests that YRV can affect how quickly a population responds to new selective pressures (e.g. invasive species, novel pathogens, or climate change). Considering that YRV influences hundreds of genes and is likely typical of other independently-evolved hemizygous chromosomes, YRV-like phenomena may represent common and significant costs to hemizygous sex determination.

     

Integrating animal temperament within ecology and evolution

Temperament describes the idea that individual behavioural differences are repeatable over time and across situations. This common phenomenon covers numerous traits, such as aggressiveness, avoidance of novelty, willingness to take risks, exploration, and sociality. The study of temperament is central to animal psychology, behavioural genetics, pharmacology, and animal husbandry, but relatively few studies have examined the ecology and evolution of temperament traits. This situation is surprising, given that temperament is likely to exert an important influence on many aspects of animal ecology and evolution, and that individual variation in temperament appears to be pervasive amongst animal species. Possible explanations for this neglect of temperament include a perceived irrelevance, an insufficient understanding of the link between temperament traits and fitness, and a lack of coherence in terminology with similar traits often given different names, or different traits given the same name. We propose that temperament can and should be studied within an evolutionary ecology framework and provide a terminology that could be used as a working tool for ecological studies of temperament. Our terminology includes five major temperament trait categories: shyness-boldness, exploration-avoidance, activity, sociability and aggressiveness. This terminology does not make inferences regarding underlying dispositions or psychological processes, which may have restrained ecologists and evolutionary biologists from working on these traits. We present extensive literature reviews that demonstrate that temperament traits are heritable, and linked to fitness and to several other traits of importance to ecology and evolution. Furthermore, we describe ecologically relevant measurement methods and point to several ecological and evolutionary topics that would benefit from considering temperament, such as phenotypic plasticity, conservation biology, population sampling, and invasion biology.