Patterns of local adaptation are expected to emerge when selection is spatially heterogeneous and sufficiently strong relative to the action of other evolutionary forces. The observation of local adaptation thus provides important insight into evolutionary processes and the adaptive divergence of populations. The detection of local adaptation, however, suffers from several conceptual, statistical and methodological issues. Here, we provide practical recommendations regarding (1) the definition of local adaptation, (2) the analysis of transplant experiments and (3) the optimisation of the experimental design of local adaptation studies. Together, these recommendations provide a unified approach for measuring local adaptation and understanding the adaptive divergence of populations in a wide range of biological systems.

In host‐parasite coevolutionary arms races, parasites probably have an evolutionary advantage. Parasite populations should be locally adapted, having higher mean fitness on sympatric than allopatric hosts. Here we assess evidence for local parasite advantage. Further we investigate how adaptation and counter‐adaptation of parasites and hosts, necessarily occurring in sympatry, can generate a pattern of local adaptation. Already simple frequency‐dependent selection models generate complex patterns of parasite performance on sympatric and allopatric populations. In metapopulations, with extinction, recolonization, and gene flow, variable selection pressure and stochasticity may obscure local processes or change the level at which local adaptation occurs. Alternatively, gene flow may introduce adaptive variation, so differential migration rates can modify the asymmetry of host and parasite evolutionary rates. We conclude that local adaptation is an average phenomenon. Its detection requires adequate replication at the appropriate level, that at which the local processes occur.

Evolutionary rescue occurs when a population genetically adapts to a new stressful environment that would otherwise cause its extinction. Forecasting the probability of persistence under stress, including emergence of drug resistance as a special case of interest, requires experimentally validated quantitative predictions. Here, we propose general analytical predictions, based on diffusion approximations, for the probability of evolutionary rescue. We assume a narrow genetic basis for adaptation to stress, as is often the case for drug resistance. First, we extend the rescue model of Orr & Unckless ( Am. Nat. 2008 172 , 160–169) to a broader demographic and genetic context, allowing the model to apply to empirical systems with variation among mutation effects on demography, overlapping generations and bottlenecks, all common features of microbial populations. Second, we confront our predictions of rescue probability with two datasets from experiments with Saccharomyces cerevisiae (yeast) and Pseudomonas fluorescens (bacterium). The tests show the qualitative agreement between the model and observed patterns, and illustrate how biologically relevant quantities, such as the per capita rate of rescue, can be estimated from fits of empirical data. Finally, we use the results of the model to suggest further, more quantitative, tests of evolutionary rescue theory.