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.

Understanding how changes in antibiotic consumption affect the prevalence of antibiotic resistance in bacterial pathogens is important for public health. In a number of bacterial species, including Streptococcus pneumoniae, the prevalence of resistance has remained relatively stable despite prolonged selection pressure from antibiotics. The evolutionary processes allowing the robust coexistence of antibiotic sensitive and resistant strains are not fully understood. While allelic diversity can be maintained at a locus by direct balancing selection, there is no evidence for such selection acting in the case of resistance. In this work, we propose a mechanism for maintaining coexistence at the resistance locus: linkage to a second locus that is under balancing selection and that modulates the fitness effect of resistance. We show that duration of carriage plays such a role, with long duration of carriage increasing the fitness advantage gained from resistance. We therefore predict that resistance will be more common in strains with a long duration of carriage and that mechanisms maintaining diversity in duration of carriage will also maintain diversity in antibiotic resistance. We test these predictions in S. pneumoniae and find that the duration of carriage of a serotype is indeed positively correlated with the prevalence of resistance in that serotype. These findings suggest heterogeneity in duration of carriage is a partial explanation for the coexistence of sensitive and resistant strains and that factors determining bacterial duration of carriage will also affect the prevalence of resistance.A ntibacterial resistance is a serious threat to public health, with resistant strains emerging in numerous pathogens. Although estimates of resistance levels vary by region, pathogen, and antibiotic type, a common feature is that fixation of resistance is rarely observed: sensitive and resistant strains tend to coexist robustly. For example, according to the European Antimicrobial Resistance Surveillance Network (EARS-Net; available at ecdc.europa.eu) (1), the prevalence of penicillin and macrolide nonsensitivity in Streptococcus pneumoniae has been stable at around 10 and 15% respectively for the past 15 years in Europe. Similarly, EARS-Net estimates of multidrug resistance in Klebsiella pneumoniae have varied around 20% since 2009 and those for methicillin resistance in Staphylococcus aureus have ranged between 15 and 25% from 1999 onwards, with no persisting directional trend.The stable coexistence of sensitive and resistant strains is unexpected: because these strains compete for the same hosts, simple ecological models predict that the fitter strain would dominate and the weaker strain become extinct ("competitive exclusion"). Understanding how coexistence is maintained is therefore important for predicting the prevalence of resistant strains and for explaining the approximately linear relationship between regional antibiotic consumption and resistance (2). Predicting the prevalence of resistance is, in turn, crucial...

Local adaptation experiments are widely used to quantify the levels of adaptation within a heterogeneous environment. However, theoretical studies generally focus on the probability of fixation of alleles or the mean fitness of populations, rather than local adaptation as it is commonly measured experimentally or in field studies. Here, we develop mathematical models and use them to generate analytical predictions for the level of local adaptation as a function of selection, migration and genetic drift. First, we contrast mean fitness and local adaptation measures and show that the latter can be expressed in a simple and general way as a function of the spatial covariance between population mean phenotype and local environmental conditions. Second, we develop several approximations of a population genetics model to show that the system exhibits different behaviours depending on the rate of migration. The main insights are the following: with intermediate migration, both genetic drift and migration decrease local adaptation; with low migration, drift decreases local adaptation but migration speeds up adaptation; with high migration, genetic drift has no effect on local adaptation. Third, we extend this analysis to cases where the trait under selection is continuous using classical quantitative genetics theory. Finally, we discuss these results in the light of recent experimental work on local adaptation.

Sewall Wright (1932) introduced the metaphor of "fitness landscapes" to think about evolutionary processes. A fitness landscape is defined by a set of genotypes, the mutational distance between them, and their associated fitness. Populations are abstracted into groups of particles that navigate on this landscape (Orr 2005). In this regard, the process of adaptation by natural selection depends on the structure of the fitness landscape. Many fundamental features of adaptation depend on whether the landscape is smooth or rugged, and on the level of epistasis between genotypes on the landscape (note that these two properties are related, Weinreich et al. 2005;Poelwijk et al. 2011). For examples, levels and type of epistasis determine the probability of speciation (Gavrilets 2004;Chevin et al. 2014) and the benefits of sexual reproduction (Kondrashov and Kondrashov 2001;de Visser et al. 2009;Otto 2009;Watson et al. 2011). The ruggedness of the landscape determines the repeatability and predictability of adaptation (Kauffman 1993;Colegrave and Buckling 2005;Chevin et al. 2010;Salverda et al. 2011).It is now possible to explore the fitness landscapes of microbial species using several experimental methods. A common type of experiment consists in isolating a number of mutants and measuring the fitness of genotypes with either a single mutation or various combinations of mutations. The most fascinating of these experiments are perhaps those considering a small number (L) of mutations and reconstructing all possible genotypes (2 L genotypes) from the wild type to the evolved (reviewed in de Visser et al. 1997;Lee et al. 1997;Whitlock and Bourguet 2000;Lunzer et al. 2005;Weinreich et al. 2006;O'Maille et al. 2008;Lozovsky et al. 2009;da Silva et al. 2010;Chou et al. 2011;Khan et al. 2011;Weinreich et al. 2013). The properties of these reconstructed fitness landscapes determine whether adaptation was constrained to follow the particular sequence of mutations that indeed evolved in the experiment, or whether mutations could have evolved in any order with similar probabilities.3The experimental data can be interpreted in the light of various theoretical fitness landscape models. Many models directly define the mapping between individual genotypes and fitness ("discrete" fitness landscape models). The simplest is the additive model, whereby the log-fitness is the sum of additive contributions by individual loci. This model results in no epistasis and a very smooth landscape. At the opposite extreme, the "House of Cards" model (Kingman 1978) assumes that the fitness of each genotype is drawn independently of other genotypes in some distribution. This model results in a highly epistatic and rugged landscape. In between these two extremes, two models where the roughness is a tunable parameter have been designed. The "Rough Mount Fuji" model assumes that log-fitness of a genotype is the sum of additive contributions from mutations and a House of Cards random component (Franke et al. 2011;Szendro et al. 2013). Kauffman's NK model ...