Species interactions commonly coevolve as complex geographic mosaics of populations shaped by differences in local selection and gene flow. We use a haploid matching-alleles model for coevolution to evaluate how a pair of species coevolves when fitness interactions are reciprocal in some locations ("hot spots") but not in others ("cold spots"). Our analyses consider mutualistic and antagonistic interspecific interactions and a variety of gene flow patterns between hot and cold spots. We found that hot and cold spots together with gene flow influence coevolutionary dynamics in four important ways. First, hot spots need not be ubiquitous to have a global influence on evolution, although rare hot spots will not have a disproportionate impact unless selection is relatively strong there. Second, asymmetries in gene flow can influence local adaptation, sometimes creating stable equilibria at which species experience minimal fitness in hot spots and maximal fitness in cold spots, or vice versa. Third, asymmetries in gene flow are no more important than asymmetries in population regulation for determining the maintenance of local polymorphisms through coevolution. Fourth, intraspecific allele frequency differences among hot and cold spot populations evolve under some, but not all, conditions. That is, selection mosaics are indeed capable of producing spatially variable coevolutionary outcomes across the landscapes over which species interact. Altogether, our analyses indicate that coevolutionary trajectories can be strongly shaped by the geographic distribution of coevolutionary hot and cold spots, and by the pattern of gene flow among populations.

Using a population model of selection on an obligate symbiont and its host, we evaluate how demographic differences across geographical landscapes can produce selection mosaics in interacting species. The model assumes that the host populations vary geographically from demographic sources to sinks in the absence of effects by the symbionts, and that a virulent and a relatively avirulent form of the symbiont compete with one another across all habitats. Our results indicate that productivity gradients can create selection mosaics across habitats, resulting in complex fitness landscapes over which evolution occurs. We find that relatively virulent symbionts only persist if they have an advantage over avirulent strains or species in terms of interference (i.e. competition, and/or cross‐transmission) interactions. When such a trade‐off exists, we predict that the more virulent symbiont is most likely to be found in habitats where host population growth is highest, whereas the more avirulent symbiont should tend to persist in more marginal habitats or even habitat sinks for symbiont‐free hosts. Demographic sinks may be the habitats most likely to favour the origin of new mutualisms. Very productive mutualisms can be exploited by hyperparasites or cheaters. We discuss our findings in terms of geographical scenarios for the emergence of mutualisms, and the long‐standing debate about geographical patterns in the maintenance of sex.

We examine the impact of temporal variation on adaptive evolution in "sink" environments, where a species encounters conditions outside its niche. Sink populations persist because of recurrent immigration from sources. Prior studies have highlighted the importance of demographic constraints on adaptive evolution in sinks and revealed that adaptation is less likely in harsher sinks. We examine two complementary models of population and evolutionary dynamics in sinks: a continuous-state quantitative-genetics model and an individual-based model. In the former, genetic variance is fixed; in the latter, genetic variance varies because of mutation, drift, and sampling. In both models, a population in a constant harsh sink environment can exist in alternative states: local maladaptation (phenotype comparable to immigrants from the source) or adaptation (phenotype near the local optimum). Temporal variation permits transitions between these states. We show that moderate amounts of temporal variation can facilitate adaptive evolution in sinks, permitting niche evolution, particularly for slow or autocorrelated variation. Such patterns of temporal variation may particularly pertain to sinks caused by biotic interactions (e.g., predation). Our results are relevant to the evolutionary dynamics of species' ranges, the fate of exotic invasive species, and the evolutionary emergence of infectious diseases into novel hosts.

Theoretical models predict that selection on reaction norms should depend on the relative frequency of environmental states experienced by a population. We report a laboratory experimental test of this prediction for thermal performance curves of larval growth rate in Pieris rapae in relation to their thermal environment. We measured short-term relative growth rate (RGR) for each individual at a series of five temperatures, and then we assigned individuals randomly to warm or cool selection treatments, which differ in the frequency distributions of environmental temperatures. Selection gradient analyses of two independent experiments demonstrated significant positive selection for increasing RGR, primarily through its effects on survival to adulthood and on development rate. In both the warm and cool selection treatments, the magnitude of directional selection on RGR was consistently greater at lower (suboptimal) temperatures than at higher temperatures; differences in selection between the treatments did not match model predictions. The temporal order and duration of environmental conditions may affect patterns of selection on thermal performance curves and other continuous reaction norms, complicating the connections between variation in environment, phenotype, and fitness.