Adaptation of a quantitative trait to a changing environment: New analytical insights on the asexual and infinitesimal sexual models.

Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimal phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or their interactions. Here, we develop a methodology that provides quantitative measures of population maladaptation and potential of survival directly from the entire profile of the phenotypic distribution, without any a priori on its shape. We investigate two different systems of reproduction (asexual and infinitesimal sexual models of inheritance), with various forms of selection. In particular, we recover that fitness functions such that selection weakens away from the optimum lead to evolutionary tipping points, with an abrupt collapse of the population when the speed of environmental change is too high. Our unified framework allows deciphering the mechanisms that lead to this phenomenon. More generally, it allows discussing similarities and discrepancies between the two systems of reproduction, which are ultimately explained by different constraints on the evolution of the phenotypic variance. We demonstrate that the mean fitness in the population crucially depends on the shape of the selection function in the infinitesimal sexual model, in contrast with the asexual model. In the asexual model, we also investigate the effect of the mutation kernel and we show that kernels with higher kurtosis tend to reduce maladaptation and improve fitness, especially in fast changing environments.

Dispersal distance is influenced by parental and grand-parental density.

Non-genetic transmission of information across generations, so-called parental effects, can have significant impacts on offspring morphology, physiology, behaviour and life-history traits. In previous experimental work using the two-spotted spider mite Tetranychus urticae Koch, we demonstrated that dispersal distances increase with local density and levels of genetic relatedness. We here show that manipulation of parental and grand-parental density has a significant effect on offspring dispersal distance, of the same order of magnitude as manipulation of offspring density. We demonstrate that offspring exposed to the same density disperse further if they were born to parents exposed to higher density compared with parents exposed to low density. Offspring dispersal distance also increases when grand-parents were exposed to higher density, except for offspring exposed to low densities, which disperse at shorter distances whatever the grand-parental density. We also show that offspring from mothers exposed to higher densities were overall larger, which suggests that parents in high densities invest more in individual offspring, enabling them to disperse further. We propose that our findings should be included in models investigating the spread rate of invasive species or when predicting the success of conservation measures of species attempting to track changing climates.

Density and genetic relatedness increase dispersal distance in a subsocial organism.

Although dispersal distance plays a major role in determining whether organisms will reach new habitats, empirical data on the environmental factors that affect dispersal distance are lacking. Population density and kin competition are two factors theorised to increase dispersal distance. Using the two-spotted spider mite as a model species, we altered these two environmental conditions and measured the mean dispersal distance of individuals, as well as other attributes of the dispersal kernel. We find that both density and relatedness in the release patch increase dispersal distance. Relatedness, but not density, changes the shape of the dispersal kernel towards a more skewed and leptokurtic shape including a longer 'fat-tail'. This is the first experimental demonstration that kin competition can shape the whole distribution of dispersal distances in a population, and thus affect the geographical spread of dispersal phenotypes.

Quantifying the effects of migration and mutation on adaptation and demography in spatially heterogeneous environments.

How do mutation and gene flow influence population persistence, niche expansion and local adaptation in spatially heterogeneous environments? In this article, we analyse a demographic and evolutionary model of adaptation to an environment containing two habitats in equal frequencies, and we bridge the gap between different theoretical frameworks. Qualitatively, our model yields four qualitative types of outcomes: (i) global extinction of the population, (ii) adaptation to one habitat only, but also adaptation to both habitats with, (iii) specialized phenotypes or (iv) with generalized phenotypes, and we determine the conditions under which each equilibrium is reached. We derive new analytical approximations for the local densities and the distributions of traits in each habitat under a migration-selection-mutation balance, compute the equilibrium values of the means, variances and asymmetries of the local distributions of phenotypes, and contrast the effects of migration and mutation on the evolutionary outcome. We then check our analytical results by solving our model numerically, and also assess their robustness in the presence of demographic stochasticity. Although increased migration results in a decrease in local adaptation, mutation in our model does not influence the values of the local mean traits. Yet, both migration and mutation can have dramatic effects on population size and even lead to metapopulation extinction when selection is strong. Niche expansion, the ability for the population to adapt to both habitats, can also be prevented by small migration rates and a reduced evolutionary potential characterized by rare mutation events of small effects; however, niche expansion is otherwise the most likely outcome. Although our results are derived under the assumption of clonal reproduction, we finally show and discuss the links between our model and previous quantitative genetics models.

Optimal life-history schedule in a metapopulation with juvenile dispersal.

Previous models have predicted that when mortality increases with age, older individuals should invest more of their resources in reproduction and produce less dispersive offspring, as both their future reproductive value and their prospect of competing with their own sib decline. Those models assumed stable population sizes. We here study for the first time the evolution of age-specific reproductive effort and of age-specific offspring dispersal rate in a metapopulation with extinction-recolonization dynamics and juvenile dispersal. Our model explores the evolutionary consequences of disequilibrium in the age structure of individuals in local populations, generated by disturbances. Life-history decisions are then shaped both by changes with age in individual performances, and by changes in ecological conditions, as young and old individuals do not live on average in the same environments. Lower juvenile dispersal favours the evolution of higher reproductive effort in young adults in a metapopulation with extinction-recolonization compared with a well-mixed population. Contrary to previous predictions for stable structured populations, we find that offspring dispersal should generally increase with maternal age. This is because young individuals, who are overrepresented in recently colonized populations, should allocate more to reproduction and less to dispersal as a strategy to exploit abundant recruitment opportunities in such populations.

Migration load in plants: role of pollen and seed dispersal in heterogeneous landscapes.

Evolution of local adaptation depends critically on the level of gene flow, which, in plants, can be due to either pollen or seed dispersal. Using analytical predictions and individual-centred simulations, we investigate the specific influence of seed and pollen dispersal on local adaptation in plant populations growing in patchy heterogeneous landscapes. We study the evolution of a polygenic trait subject to stabilizing selection within populations, but divergent selection between populations. Deviations from linkage equilibrium and Hardy-Weinberg equilibrium make different contributions to genotypic variance depending on the dispersal mode. Local genotypic variance, differentiation between populations and genetic load vary with the rate of gene flow but are similar for seed and pollen dispersal, unless the landscape is very heterogeneous. In this case, genetic load is higher in the case of pollen dispersal, which appears to be due to differences in the distribution of genotypic values before selection.

When sources become sinks: migrational meltdown in heterogeneous habitats.

We consider the evolution of ecological specialization in a landscape with two discrete habitat types connected by migration, for example, a plant-insect system with two plant hosts. Using a quantitative genetic approach. we study the joint evolution of a quantitative character determining performance in each habitat together with the changes in the population density. We find that specialization on a single habitat evolves with intermediate migration rates, whereas a generalist species evolves with both very low and very large rates of movement between habitats. There is a threshold at which a small increase in the connectivity of the two habitats will result in dramatic decrease in the total population size and the nearly complete loss of use of one of the two habitats through a process of "migrational meltdown." In some situations, equilibria corresponding to a specialist and a generalist species are simultaneously stable. Analysis of our model also shows cases of hysteresis in which small transient changes in the landscape structure or accidental demographic disturbances have irreversible effects on the evolution of specialization.

Geographical patterns of adaptation within a species' range: interactions between drift and gene flow.

We use individual-based stochastic simulations and analytical deterministic predictions to investigate the interaction between drift, natural selection and gene flow on the patterns of local adaptation across a fragmented species' range under clinally varying selection. Migration between populations follows a stepping-stone pattern and density decreases from the centre to the periphery of the range. Increased migration worsens gene swamping in small marginal populations but mitigates the effect of drift by replenishing genetic variance and helping purge deleterious mutations. Contrary to the deterministic prediction that increased connectivity within the range always inhibits local adaptation, simulations show that low intermediate migration rates improve fitness in marginal populations and attenuate fitness heterogeneity across the range. Such migration rates are optimal in that they maximize the total mean fitness at the scale of the range. Optimal migration rates increase with shallower environmental gradients, smaller marginal populations and higher mutation rates affecting fitness.

Evolution of reproductive effort in a metapopulation with local extinctions and ecological succession.

Using a metapopulation model, we study how local extinctions, limited population life span, and local demographic disequilibrium affect the evolution of the reproductive effort in a species with overlapping generations but no senescence. We show that in a metapopulation with saturation of all sites and an infinite deme maximal life span (no succession), local extinctions simply constitute an additional source of extrinsic mortality. When either the hypothesis of an infinite deme maximal life span or the saturation hypothesis is relaxed, nontrivial predictions arise. in particular, we find interactions between the evolutionarily stable reproductive effort strategy and the demographic dynamics in the metapopulation. We predict that larger reproductive effort may be selected for in habitats of poorer productivity, contrary to what would be predicted in a single population. Also, we predict that higher dispersal rates should favor selection for lower reproductive efforts. However, metapopulation parameters that favor high dispersal rates also favor larger reproductive efforts. Conflicting selection pressures in the metapopulation also allow maintaining evolutionarily stable polymorphism between a low and high reproductive effort for particular trade-offs between survival and fecundity.

Kin selection and natal dispersal in an age-structured population.

We examine the effect of iteroparity on the evolution of dispersal for a species living in a stable but fragmented habitat. We use a kin selection model that incorporates the effects of demographic stochasticity on the local age structure and age-specific genetic identities. We consider two cases: when the juvenile dispersal rate is allowed to change with maternal age and when it is not. In the latter case, we find that the unconditional evolutionarily stable dispersal rate increases when the adult survival rate increases. Two antagonistic forces act upon the evolution of age-specific dispersal rates. First, when the local age structure varies between patches of habitat, the intensity of competition between adults and juveniles in the natal patch is, on average, lower for offspring born to older senescent mothers. This selects for decreasing dispersal with maternal age. Second, offspring born to older parents are on average more related to other juveniles in the same patch and they experience a higher intensity of kin competition, which selects for increasing dispersal with maternal age. We show that the evolutionary outcome results from a balance between these two opposing forces, which depends on the amount of variance in age structure among sub-populations.

Natal dispersal and senescence.

The potential existence of natal dispersal strategies depending on parental age has been suggested by Hamilton and May [Hamilton, W. D. & May, R. M. (1977) Nature 269, 578-581] for organisms whose survival rates decline with age. When competition between parent and offspring is strong, any individual should disperse a smaller fraction of its offspring when it ages. Here, we verify their verbal prediction. First, we determine the evolutionarily stable dispersal strategy conditional on parental age, associated with a particular senescence curve. We show that such a conditional dispersal strategy should evolve independently from the genotype controlling the offspring dispersal behavior. Second, studying a population of common lizards, we provide empirical evidence of a relation between dispersal of female offspring and maternal senescence, in agreement with our theoretical predictions.

The maintenance of nucleocytoplasmic polymorphism in a metapopulation: the case of gynodioecy.

In gynodioecious species, gender is generally determined by epistatic interactions between cytoplasmic and nuclear loci. However, theoretical studies suggest that, for a joint polymorphism at both cytoplasmic and nuclear loci to be maintained in a panmictic population, selection must act differently on the various genotypes that determine the same gender. Here we show that, in a metapopulation with local extinction and restricted gene flow, nucleocytoplasmic polymorphism can be maintained without these differences. We use deterministic simulations. We assume that gene flow occurred only at recolonization. Founder effects create genetic variance between populations in the metapopulation, and local population growth is faster when the local frequency of females is high. Group selection phenomena are involved in the maintenance of the joint polymorphism in the metapopulation. The frequency of females in the metapopulation at equilibrium is higher than in a panmictic population with the same genetic system. However, these conclusions hold only if nuclear alleles restoring male fertility are dominant.