Populations facing novel environments can persist by adapting. In nature, the ability to adapt and persist will depend on interactions between coexisting individuals. Here we use an adaptive dynamic model to assess how the potential for evolutionary rescue is affected by intra- and interspecific competition. Intraspecific competition (negative density-dependence) lowers abundance, which decreases the supply rate of beneficial mutations, hindering evolutionary rescue. On the other hand, interspecific competition can aid evolutionary rescue when it speeds adaptation by increasing the strength of selection. Our results clarify this point and give an additional requirement: competition must increase selection pressure enough to overcome the negative effect of reduced abundance. We therefore expect evolutionary rescue to be most likely in communities which facilitate rapid niche displacement. Our model, which aligns to previous quantitative and population genetic models in the absence of competition, provides a first analysis of when competitors should help or hinder evolutionary rescue.

Adaptation often proceeds from standing variation, and natural selection acting on pairs of populations is a quantitative continuum ranging from parallel to divergent. Yet, it is unclear how the extent of parallel genetic evolution during adaptation from standing variation is affected by the difference in the direction of selection between populations. Nor is it clear whether the availability of standing variation for adaptation affects progress toward speciation in a manner that depends on the difference in the direction of selection. We conducted a theoretical study investigating these questions and have two primary findings. First, the extent of parallel genetic evolution between two populations rapidly declines as selection changes from fully parallel toward divergent, and this decline is steeper in organisms with more traits (i.e., greater dimensionality). This rapid decline happens because small differences in the direction of selection greatly reduce the fraction of alleles that are beneficial in both populations. For example, populations adapting to optima separated by an angle of 33° might have only 50% of potentially beneficial alleles in common. Second, relative to when adaptation is from only new mutation, adaptation from standing variation improves hybrid fitness under parallel selection and reduces hybrid fitness under divergent selection. Under parallel selection, genetic parallelism from standing variation reduces the phenotypic segregation variance in hybrids, thereby increasing mean fitness in the parental environment. Under divergent selection, larger pleiotropic effects of alleles fixed from standing variation cause maladaptive transgressive phenotypes when combined in hybrids. Adaptation from standing genetic variation therefore slows progress toward speciation under parallel selection and facilitates progress toward speciation under divergent selection.

To persist in a changing world, populations must adapt. The ability to adapt is influenced by interactions with other species, such as predators. Recent experiments and theory suggest that selective pressures arising from predation may help prey adapt phenotypically to changing environments, but how this influences persistence remains unclear. In particular, it has not yet been shown whether predator-induced adaptation can outweigh predator-imposed reductions in population size, allowing prey to persist when they would otherwise go extinct. Here we examine if (and if so, how) predation can enhance the ability of prey to persist in a directionally changing environment. To do so, we extend a single-species quantitative-genetics framework that predicts rates of environmental change beyond which populations go extinct. While we assume predation decreases prey density, we find that predators can indeed help prey persist if they sufficiently increase prey adaptedness (decrease phenotypic lag). We show two ways this can occur: (1) the selective push, in which predators consume maladapted individuals and thus add selection that pushes the mean prey trait toward its optimum; and (2) the evolutionary hydra effect, when predation reduces prey density and thereby increases prey birthrate, allowing more selective events per unit time and effectively reducing generation time. We also discuss how our results apply more broadly to sources of mortality beyond predation.

Biological diversity depends on the interplay between evolutionary diversification and ecological mechanisms allowing species to coexist. Current research increasingly integrates ecology and evolution over a range of timescales, but our common conceptual framework for understanding species coexistence requires better incorporation of evolutionary processes. Here, we focus on the idea of evolutionarily stable communities (ESCs), which are theoretical endpoints of evolution in a community context. We use ESCs as a unifying framework to highlight some important but under‐appreciated theoretical results, and we review empirical research relevant to these theoretical predictions. We explain how, in addition to generating diversity, evolution can also limit diversity by reducing the effectiveness of coexistence mechanisms. The coevolving traits of competing species may either diverge or converge, depending on whether the number of species in the community is low (undersaturated) or high (oversaturated) relative to the ESC. Competition in oversaturated communities can lead to extinction or neutrally coexisting, ecologically equivalent species. It is critical to consider trait evolution when investigating fundamental ecological questions like the strength of different coexistence mechanisms, the feasibility of ecologically equivalent species, and the interpretation of different patterns of trait dispersion.

Both body size and temperature directly influence consumer-resource dynamics. There is also widespread empirical evidence for the temperature-size rule (TSR), which creates a negative relationship between temperature and body size. However, it is not known how the TSR affects community dynamics. Here we integrate temperature- and size-dependent models to include indirect effects of warming, through changes in body size, to answer the question, How does the TSR affect the predicted response of consumer-resource systems to warming? We find that the TSR is expected to maintain consumer-resource biomass ratios and buffer the community from extinctions under warming. While our results are limited to conditions where organisms are below their thermal optimum, they hold under a range of realistic temperature-size responses and are robust to the type of functional response. Our analyses suggest that the widely observed TSR may reduce the impacts of warming on consumer-resource systems.