The establishment of hybrids of the Daphnia longispina complex explained by a mathematical model incorporating different overwintering life history strategies.

Interspecific hybridization (i.e. mating between species) occurs frequently in animals. Among cyclical parthenogens, hybrids can proliferate and establish through parthenogenetic reproduction, even if their sexual reproduction is impaired. In water fleas of the Daphnia longispina species complex, interspecific hybrids hatch from sexually produced dormant eggs. However, fewer hybrid genotypes contribute to the dormant egg bank and their hatching rate from dormant eggs is reduced, compared to eggs resulting from intraspecific crosses. Therefore, Daphnia hybrids would benefit from adaptations that increase their survival over winter as parthenogenetic lineages, avoiding the need to re-establish populations after winter from sexually produced dormant eggs. Here, we constructed a mathematical model to examine the conditions that could explain the frequently observed establishment of hybrids in the D. longispina species complex. Specifically, we compared the outcome of hybrid and parental taxa competition given a reduced contribution of hybrids to hatchlings from the sexually produced dormant egg bank, but their increased ability to survive winter as parthenogenetic lineages. In addition, different growth rates of parental species and differences in average annual temperatures were evaluated for their influence on hybrid production and establishment. Our model shows that increased overwinter performance as parthenogenetic females can compensate for reduced success in sexual reproduction, across all tested scenarios for varying relative growth rates of parental species. This pattern holds true for lower annual temperatures, but at higher temperatures hybrids were less successful. Consequently, hybrids might become less abundant as temperatures rise due to climate change, resulting in reduced diversity and faster differentiation of the parental species.

Reversible phenotypic plasticity with continuous adaptation.

We introduce a novel model for continuous reversible phenotypic plasticity. The model includes a one-dimensional environmental gradient, and we describe performance of an organism as a function of the environmental state by a Gaussian tolerance curve. Organisms are assumed to adapt their tolerance curve after a change of the environmental state. We present a general framework for calculating the genotype fitness if such adaptations happen in a continuous manner and apply the model to a periodically changing environment. Significant differences of our model with previous models for plasticity are the continuity of adaptation, the presence of intermediate phenotypes, that the duration of transformations depends on their extent, fewer restrictions on the distribution of the environment, and a higher robustness with respect to assumptions about environmental fluctuations. Further, we show that continuous reversible plasticity is beneficial mainly when environmental changes occur slow enough so that fully developed phenotypes can be exhibited. Finally we discuss how the model framework can be generalized to a wide variety of biological scenarios from areas that include population dynamics, evolution of environmental tolerance and physiology.

Phenotypic plasticity with instantaneous but delayed switches.

Phenotypic plasticity is a widespread phenomenon, allowing organisms to better adapt to changing environments. Most empirical and theoretical studies are restricted to irreversible plasticity where the expression of a specific phenotype is mostly determined during development. However, reversible plasticity is not uncommon; here, organisms are able to switch back and forth between phenotypes. We present two optimization models for the fitness of (i) non-plastic, (ii) irreversibly plastic, and (iii) reversibly plastic genotypes in a fluctuating environment. In one model, the fitness values of an organism during different life phases act together multiplicatively (so as to consider traits that are related to survival). The other model additionally considers additive effects (corresponding to traits related to fecundity). Both models yield qualitatively similar results. If the only costs of reversible plasticity are due to temporal maladaptation while switching between phenotypes, reversibility is virtually always advantageous over irreversibility, especially for slow environmental fluctuations. If reversibility implies an overall decreased fitness, then irreversibility is advantageous if the environment fluctuates quickly or if stress events last relatively short. Our results are supported by observations from different types of organisms and have implications for many basic and applied research questions, e.g., on invasive alien species.

Body condition dependent dispersal in a heterogeneous environment.

We find the evolutionarily stable dispersal behaviour of a population that inhabits a heterogeneous environment where patches differ in safety (the probability that a juvenile individual survives until reproduction) and productivity (the total competitive weight of offspring produced by the local individual), assuming that these characteristics do not change over time. The body condition of clonally produced offspring varies within and between families. Offspring compete for patches in a weighted lottery, and dispersal is driven by kin competition. Survival during dispersal may depend on body condition, and competitive ability increases with increasing body condition. The evolutionarily stable strategy predicts that families abandon patches which are too unsafe or do not produce enough successful dispersers. From families that invest in retaining their natal patches, individuals stay in the patch that are less suitable for dispersal whereas the better dispersers disperse. However, this clear within-family pattern is often not reflected in the population-wide body condition distribution of dispersers or non-dispersers. This may be an explanation why empirical data do not show any general relationship between body condition and dispersal. When all individuals are equally good dispersers, then there exist equivalence classes defined by the competitive weight that remains in a patch. An equivalence class consists of infinitely many dispersal strategies that are selectively neutral. This provides an explanation why very diverse patterns found in body condition dependent dispersal data can all be equally evolutionarily stable.

Variability within families and the evolution of body-condition-dependent dispersal.

In a population where body condition varies between and within families, we investigate the evolution of dispersal as a function of body condition ('strength', e.g. body size). Strong individuals are better competitors in a weighted lottery. If body condition does not influence survival during dispersal, then there is no unique evolutionarily stable strategy. Instead, there are infinitely many dispersal strategies that all lead to the same non-dispersing weight in a patch. These strategies are all selectively neutral but determine wildly different relationships between body condition and disposal probability. This may explain why there is no consistent pattern between body condition and dispersal found in empirical studies. If body condition influences survival during dispersal, then neutrality is removed and individuals with higher survival probability disperse. Dispersal may be the competitively weaker individuals if smaller body size helps to avoid dispersal risks.

Evolution of condition-dependent dispersal under kin competition.

Dispersers often differ in body condition from non-dispersers. The social dominance hypothesis explains dispersal of weak individuals, but it is not yet well understood why strong individuals, which could easily retain their natal site, are sometimes exposed to risky dispersal. Based on the model for dispersal under kin competition by Hamilton and May, we construct a model where dispersal propensity depends on body condition. We consider an annual species that inhabits a patchy environment with varying patch qualities. Offspring body condition corresponds to the quality of the natal patch and competitive ability increases with body condition. Our main general result balances the fitness benefit from not dispersing and retaining the natal patch and the benefit from dispersing and establishing somewhere else. We present four different examples for competition, which all hint that dispersal of strong individuals may be a common outcome under the assumptions of the present model. In three of the examples, the evolutionarily stable dispersal probability is an increasing function of body condition. However, we found an example where, counterintuitively, the evolutionarily stable dispersal probability is a non-monotone function of body condition such that both very weak and very strong individuals disperse with high probability but individuals of intermediate body condition do not disperse at all.

Quasi-local competition in stage-structured metapopulations: a new mechanism of pattern formation.

A central question of ecology is what determines the presence and abundance of species at different locations. In cases of ecological pattern formation, population sizes are largely determined by spatially distributed interactions and may have very little to do with the habitat template. We find pattern formation in a single-species metapopulation model with quasi-local competition, but only if the populations have (at least) two age or stage classes. Quasi-local competition is modeled using an explicit resource competition model with fast resource dynamics, and assuming that adults, but not juveniles, spend a fraction of their foraging time in habitat patches adjacent to their home patch. Pattern formation occurs if one stage class depletes the common resource but the shortage of resource affects mostly the other stage. When the two stages are spatially separated due to quasi-local competition, this results in competitive exclusion between the populations. We find deep similarity between spatial pattern formation and population cycles due to competitive exclusion between cohorts of biennial species, and discuss the differences between the present mechanism and established ways of pattern formation such as diffusive instability and distributed competition with local Allee-effects.

Does quasi-local competition lead to pattern formation in metapopulations? An explicit resource competition model.

In metapopulations, competitive interactions may extend beyond the confines of the local population such that members of neighbouring habitat patches affect each other adversely (quasi-local competition). We derive a model for quasi-local competition from first principles, assuming that individuals compete for shared resources and members of a population spend a certain fraction of their foraging time in the adjacent populations. Contrary to the results of Doebeli and Killingback [2003. Theor. Popul. Biol. 64, 397-416], our model does not produce spatial patterns of population densities in homogeneous environments. Quasi-local competition nevertheless contributes to pattern formation by amplifying the effect of heterogeneities in the external environment, and this amplification can be extremely strong when dispersal is absent. We discuss why apparently similar models lead to contrasting results.