Isolation by distance,resistance and/or clusters? Lessons learned from a forest‐dwelling carnivore inhabiting a heterogeneous landscape

Landscape genetics provides a valuable framework to understand how landscape features influence gene flow and to disentangle the factors that lead to discrete and/or clinal population structure. Here, we attempt to differentiate between these processes in a forest‐dwelling small carnivore [European pine marten (Martes martes)]. Specifically, we used complementary analytical approaches to quantify the spatially explicit genetic structure and diversity and analyse patterns of gene flow for 140 individuals genotyped at 15 microsatellite loci. We first used spatially explicit and nonspatial Bayesian clustering algorithms to partition the sample into discrete clusters and evaluate hypotheses of ‘isolation by barriers’ (IBB). We further characterized the relationships between genetic distance and geographical (‘isolation by distance’, IBD) and ecological distances (‘isolation by resistance’, IBR) obtained from optimized landscape models. Using a reciprocal causal modelling approach, we competed the IBD, IBR and IBB hypotheses with each other to unravel factors driving population genetic structure. Additionally, we further assessed spatially explicit indices of genetic diversity using sGD across potentially overlapping genetic neighbourhoods that matched the inferred population structure. Our results revealed a complex spatial genetic cline that appears to be driven jointly by IBD and partial barriers to gene flow (IBB) associated with poor habitat and interspecific competition. Habitat loss and fragmentation, in synergy with past overharvesting and possible interspecific competition with sympatric stone marten (Martes foina), are likely the main factors responsible for the spatial genetic structure we observed. These results emphasize the need for a more thorough evaluation of discrete and clinal hypotheses governing gene flow in landscape genetic studies, and the potential influence of different limiting factors affecting genetic structure at different spatial scales.     

Limiting similarity and functional diversity along environmental gradients

Recent developments in community models emphasize the importance of incorporating stochastic processes (e.g. ecological drift) in models of niche‐structured community assembly. We constructed a finite, spatially explicit, lottery model to simulate the distribution of species in a one‐dimensional landscape with an underlying gradient in environmental conditions. Our framework combines the potential for ecological drift with environmentally‐mediated competition for space in a heterogeneous environment. We examined the influence of niche breadth, dispersal distances, community size (total number of individuals) and the breadth of the environmental gradient on levels of species and functional trait diversity (i.e. differences in niche optima). Three novel results emerge from this model: (1) niche differences between adjacent species (e.g. limiting similarity) increase in smaller communities, because of the interaction of competitive effects and finite population sizes; (2) immigration from a regional species pool, stochasticity and niche‐assembly generate a bimodal distribution of species residence times (‘transient’ and ‘resident’) under a heterogeneous environment; and (3) the magnitude of environmental heterogeneity has a U‐shaped effect on diversity, because of shifts in species richness of resident vs. transient species. These predictions illustrate the potential importance of stochastic (although not necessarily neutral) processes in community assembly.     

A simulation study of microevolutionary inferences by spatial autocorrelation analysis

To explore the extent to which microevolutionary inference can be made using spatial autocorrelation analysis of gene frequency surfaces, we simulated sets of surfaces for nine evolutionary scenarios, and subjected spatially-based summary statistics of these to linear discriminant analysis. Scenarios varied the amounts of dispersion, selection, migration, and deme sizes, and included: panmixia, drift, intrusion, and stepping-stone models with 0–2 migrations, 0–2 selection gradients, and migration plus selection. To discover how weak evolutionary forces could be and still allow discrimination, each scenario had both a strong and a weak configuration. Discriminant rules were calculated using one collection of data (the training set) consisting of 250 sets of 15 surfaces for each of the nine scenarios. Misclassification rates were verified against a second, entirely new set of data (the test set) equal in size. Test set misclassification rates for the 20 best discriminating variables ranged from 39.3% (weak) to 3.6% (strong), far lower than the expected rate of 88.9% absent any discriminating ability. Misclassification was highest when discriminating the number of migrational events or the presence or number of selection events. Discrimination of drift and panmixia from the other scenarios was perfect. A subsequent subjective analysis of a subset of the data by one of us yielded comparable, although somewhat higher, misclassification rates. Judging by these results, spatial autocorrelation variables describing sets of gene frequency surfaces permit some microevolutionary inferences.     

Using simulations to evaluate Mantel‐based methods for assessing landscape resistance to gene flow

Mantel‐based tests have been the primary analytical methods for understanding how landscape features influence observed spatial genetic structure. Simulation studies examining Mantel‐based approaches have highlighted major challenges associated with the use of such tests and fueled debate on when the Mantel test is appropriate for landscape genetics studies. We aim to provide some clarity in this debate using spatially explicit, individual‐based, genetic simulations to examine the effects of the following on the performance of Mantel‐based methods: (1) landscape configuration, (2) spatial genetic nonequilibrium, (3) nonlinear relationships between genetic and cost distances, and (4) correlation among cost distances derived from competing resistance models. Under most conditions, Mantel‐based methods performed poorly. Causal modeling identified the true model only 22% of the time. Using relative support and simple Mantel r values boosted performance to approximately 50%. Across all methods, performance increased when landscapes were more fragmented, spatial genetic equilibrium was reached, and the relationship between cost distance and genetic distance was linearized. Performance depended on cost distance correlations among resistance models rather than cell‐wise resistance correlations. Given these results, we suggest that the use of Mantel tests with linearized relationships is appropriate for discriminating among resistance models that have cost distance correlations <0.85 with each other for causal modeling, or <0.95 for relative support or simple Mantel r. Because most alternative parameterizations of resistance for the same landscape variable will result in highly correlated cost distances, the use of Mantel test‐based methods to fine‐tune resistance values will often not be effective.     

CLINAL VARIATION AT MICROSATELLITE LOCI REVEALS HISTORICAL SECONDARY INTERGRADATION BETWEEN GLACIAL RACES OF COREGONUS ARTEDI (TELEOSTEI: COREGONINAE)

Abstract Classical models of the spatial structure of population genetics rely on the assumption of migration‐drift equilibrium, which is seldom met in natural populations having only recently colonized their current range (e.g., postglacial). Population structure then depicts historical events, and counfounding effects due to recent secondary contact between recently differentiated lineages can further counfound analyses of association between geographic and genetic distances. Mitochondrial polymorphisms have revealed the existence of two closely related lineages of the lake cisco, Coregonus artedi, whose significantly different but overlaping geographical distributions provided a weak signal of past range fragmentation blurred by putative subsequent extensive secondary contacts. In this study, we analyzed geographical patterns of genetic variation at seven microsatellite loci among 22 populations of lake cisco located along the axis of an area covered by proglacial lakes 12,000–8000 years ago in North America. The results clearly confirmed the existence of two genetically distinct races characterized by different sets of microsatellite alleles whose frequencies varied clinally across some 3000 km. Equilibrium and nonequilibrium analyses of isolation by distance revealed historical signal of gene flow resulting from the nearly complete admixture of these races following neutral secondary contacts in their historical habitat and indicated that the colonization process occurred by a stepwise expansion of an eastern (Atlantic) race into a previously established Mississippian race. This historical signal of equilibrium contrasted with the current migration‐drift disequilibrium within major extant watersheds and was apparently maintained by high effective population sizes and low migration regimes.     

Spatially explicit models of divergence and genome hitchhiking

Strong barriers to genetic exchange can exist at divergently selected loci, whereas alleles at neutral loci flow more readily between populations, thus impeding divergence and speciation in the face of gene flow. However, ‘divergence hitchhiking’ theory posits that divergent selection can generate large regions of differentiation around selected loci. ‘Genome hitchhiking’ theory suggests that selection can also cause reductions in average genome‐wide rates of gene flow, resulting in widespread genomic divergence (rather than divergence only around specific selected loci). Spatial heterogeneity is ubiquitous in nature, yet previous models of genetic barriers to gene flow have explored limited combinations of spatial and selective scenarios. Using simulations of secondary contact of populations, we explore barriers to gene flow in various selective and spatial contexts in continuous, two‐dimensional, spatially explicit environments. In general, the effects of hitchhiking are strongest in environments with regular spatial patterning of starkly divergent habitat types. When divergent selection is very strong, the absence of intermediate habitat types increases the effects of hitchhiking. However, when selection is moderate or weak, regular (vs. random) spatial arrangement of habitat types becomes more important than the presence of intermediate habitats per se. We also document counterintuitive processes arising from the stochastic interplay between selection, gene flow and drift. Our results indicate that generalization of results from two‐deme models requires caution and increase understanding of the genomic and geographic basis of population divergence.     

The spatial structure of the gene pool of a viviparous population of Poa alpina - environmental controls and spatial constraints

Bjømstad, O. N., Iversen, A. & Hansen, M. 1995. The spatial structure of the gene pool of a viviparous population of Poa alpina — environmental controls and spatial constraints. — Nord. J. Bot. 15: 347–354. Copenhagen. ISSN 0107–055X.
Because both the genetic make-up and the environmental conditions of a population are spatially autocorrelated, it is difficult to infer processes of selection or drift for population genetic mappings. We propose a methodology based on partial Mantel techniques and partial autocorrelation techniques to separate the action of these processes. The method is applied to data on Poa alpina to indicate that isolation-by-distance (drift) is the main process inducing positive autocorrelation at the scale of diaspore dispersal (< 100m). The pattern at larger distances is more consistent with selection.     

Dispersal ability and habitat requirements determine landscape‐level genetic patterns in desert aquatic insects

Species occupying the same geographic range can exhibit remarkably different population structures across the landscape, ranging from highly diversified to panmictic. Given limitations on collecting population‐level data for large numbers of species, ecologists seek to identify proximate organismal traits—such as dispersal ability, habitat preference and life history—that are strong predictors of realized population structure. We examined how dispersal ability and habitat structure affect the regional balance of gene flow and genetic drift within three aquatic insects that represent the range of dispersal abilities and habitat requirements observed in desert stream insect communities. For each species, we tested for linear relationships between genetic distances and geographic distances using Euclidean and landscape‐based metrics of resistance. We found that the moderate‐disperser Mesocapnia arizonensis (Plecoptera: Capniidae) has a strong isolation‐by‐distance pattern, suggesting migration–drift equilibrium. By contrast, population structure in the flightless Abedus herberti (Hemiptera: Belostomatidae) is influenced by genetic drift, while gene flow is the dominant force in the strong‐flying Boreonectes aequinoctialis (Coleoptera: Dytiscidae). The best‐fitting landscape model for M. arizonensis was based on Euclidean distance. Analyses also identified a strong spatial scale‐dependence, where landscape genetic methods only performed well for species that were intermediate in dispersal ability. Our results highlight the fact that when either gene flow or genetic drift dominates in shaping population structure, no detectable relationship between genetic and geographic distances is expected at certain spatial scales. This study provides insight into how gene flow and drift interact at the regional scale for these insects as well as the organisms that share similar habitats and dispersal abilities.     

Connectivity in a pond system influences migration and genetic structure in threespine stickleback

Neutral genetic structure of natural populations is primarily influenced by migration (the movement of individuals and, subsequently, their genes) and drift (the statistical chance of losing genetic diversity over time). Migration between populations is influenced by several factors, including individual behavior, physical barriers, and environmental heterogeneity among populations. However, drift is expected to be stronger in populations with low immigration rate and small effective population size. With the technological advancement in geological information systems and spatial analysis tools, landscape genetics now allows the development of realistic migration models and increased insight to important processes influencing diversity of natural populations. In this study, we investigated the relationship between landscape connectivity and genetic distance of threespine stickleback (Gasterosteus aculeatus) inhabiting a pond complex in Belgjarskógur, Northeast Iceland. We used two landscape genetic approaches (i.e., least-cost-path and isolation-by-resistance) and asked whether gene flow, as measured by genetic distance, was more strongly associated with Euclidean distance (isolation-by-distance) or with landscape connectivity provided by areas prone to flooding (as indicated by Carex sp. cover)? We found substantial genetic structure across the study area, with pairwise genetic distances among populations (D_PS) ranging from 0.118 to 0.488. Genetic distances among populations were more strongly correlated with least-cost-path and isolation-by-resistance than with Euclidean distance, whereas the relative contribution of isolation-by-resistance and Euclidian distance could not be disentangled. These results indicate that migration among stickleback populations occurs via periodically flooded areas. Overall, this study highlights the importance of transient landscape elements influencing migration and genetic structure of populations at small spatial scales.     

The spatial scale of population fluctuations and quasi-extinction risk

Using a spatially homogeneous population model with migration (random individual dispersal) and spatially autocorrelated environmental noise, we show how migration and local density regulation affect the spatial scale of fluctuations in the log of population sizes as well as the 1-yr differences in these. The difference between the squares of these two spatial scales of population fluctuations does not depend on the spatial scale of the noise but only on migration rate and strength of local density regulation. We also show how migration, local density regulation, and spatially correlated environmental noise affect the realized population process at a specific location. As the migration increases, the realized local density regulation and the expected population size increase, while the realized environmental noise decreases. This approach also enables us to analyze the dynamics of the total population size within quadrats of different sizes. The risk of local quasi extinction is strongly reduced by increasing quadrat size or migration rate, while an increase in environmental stochasticity or spatial correlation in the environmental noise increases the risk of quasi extinction.     

Species diversity and population density affect genetic structure and gene dispersal in a subtropical understory shrub

Aims The dispersal of pollen and seeds is spatially restricted and may vary among plant populations because of varying biotic interactions, population histories or abiotic conditions. Because gene dispersal is spatially restricted, it will eventually result in the development of spatial genetic structure (SGS), which in turn can allow insights into gene dispersal processes. Here, we assessed the effect of habitat characteristics like population density and community structure on small-scale SGS and estimate historical gene dispersal at different spatial scales.Methods In a set of 12 populations of the subtropical understory shrub Ardisia crenata, we assessed genetic variation at 7 microsatellite loci within and among populations. We investigated small-scale genetic structure with spatial genetic autocorrelation statistics and heterogeneity tests and estimated gene dispersal distances based on population differentiation and on within-population SGS. SGS was related to habitat characteristics by multiple regression.Important findings The populations showed high genetic diversity (H e = 0.64) within populations and rather strong genetic differentiation (F ′ ST = 0.208) among populations, following an isolation-by-distance pattern, which suggests that populations are in gene flow–drift equilibrium. Significant SGS was present within populations (mean Sp = 0.027). Population density and species diversity had a joint effect on SGS with low population density and high species diversity leading to stronger small-scale SGS. Estimates of historical gene dispersal from between-population differentiation and from within-population SGS resulted in similar values between 4.8 and 22.9 m. The results indicate that local-ranged pollen dispersal and inefficient long-distance seed dispersal, both affected by population density and species diversity, contributed to the genetic population structure of the species. We suggest that SGS in shrubs is more similar to that of herbs than to trees and that in communities with high species diversity gene flow is more restricted than at low species diversity. This may represent a process that retards the development of a positive species diversity–genetic diversity relationship.     

Population genetic analysis of microsatellite variation of guppies (Poecilia reticulata) in Trinidad and Tobago: evidence for a dynamic source–sink metapopulation structure,founder events and population bottlenecks

Riverine fish populations are traditionally considered to be highly structured and subject to strong genetic drift. Here, we use microsatellites to analyse the population structure of the guppy (Poecilia reticulata), focussing on the headwater floodplain area of the Caroni drainage in Trinidad. We also analyse the population genetics of guppies in the Northern Drainage in Trinidad, a habitat characterized by rivers flowing directly into the sea, and a small isolated population in Tobago. Upland Caroni populations are highly differentiated and display low levels of genetic diversity. However, we found no evidence to suggest that these upland populations experienced recent population crashes and the populations appear to approach mutation–drift equilibrium. Dominant downstream migration over both short‐ and long‐time frames has a strong impact on the population genetics of lowland Caroni populations. This drainage system could be considered a source–sink metapopulation, with the tributary furthest downstream representing a ‘super sink’, receiving immigrants from rivers upstream in the drainage. Moreover, the effective population size in the lowlands is surprisingly low in comparison with the apparently large census population sizes.     

Effects of sample size,number of markers,and allelic richness on the detection of spatial genetic pattern

The influence of study design on the ability to detect the effects of landscape pattern on gene flow is one of the most pressing methodological gaps in landscape genetic research. To investigate the effect of study design on landscape genetics inference, we used a spatially‐explicit, individual‐based program to simulate gene flow in a spatially continuous population inhabiting a landscape with gradual spatial changes in resistance to movement. We simulated a wide range of combinations of number of loci, number of alleles per locus and number of individuals sampled from the population. We assessed how these three aspects of study design influenced the statistical power to successfully identify the generating process among competing hypotheses of isolation‐by‐distance, isolation‐by‐barrier, and isolation‐by‐landscape resistance using a causal modelling approach with partial Mantel tests. We modelled the statistical power to identify the generating process as a response surface for equilibrium and non‐equilibrium conditions after introduction of isolation‐by‐landscape resistance. All three variables (loci, alleles and sampled individuals) affect the power of causal modelling, but to different degrees. Stronger partial Mantel r correlations between landscape distances and genetic distances were found when more loci were used and when loci were more variable, which makes comparisons of effect size between studies difficult. Number of individuals did not affect the accuracy through mean equilibrium partial Mantel r, but larger samples decreased the uncertainty (increasing the precision) of equilibrium partial Mantel r estimates. We conclude that amplifying more (and more variable) loci is likely to increase the power of landscape genetic inferences more than increasing number of individuals.     

Spatially heterogeneous pressure raises risk of catastrophic shifts

Ecosystems may exhibit catastrophic shifts, i.e. abrupt and irreversible responses of ecosystem functions and services to continuous changes in external conditions. The search for early warning signs of approaching shifts has so far mainly been conducted on theoretical models assuming spatially-homogeneous external pressures (e.g. climatic). Here, we investigate how a spatially explicit pressure may affect ecosystems’ risk of catastrophic shifts and the associated spatial early-warning signs. As a case study, we studied a dryland vegetation model assuming ‘associational resistance’, i.e. the mutual reduction of local grazing impact by neighboring plants sharing the investment in defensive traits. Consequently, grazing pressure depends on the local density of plants and is thus spatially-explicit. We focus on the distribution of vegetation patch sizes, which can be assessed using remote sensing and are candidate early warning signs of catastrophic shifts in drylands. We found that spatially explicit grazing affected both the resilience and the spatial patterns of the landscape. Grazing impact became self-enhancing in more fragmented landscapes, disrupted patch growth and put apparently ‘healthy’ drylands under high risks of catastrophic shifts. Our study highlights that a spatially explicit pressure may affect the nature of the spatial pattern observed and thereby change the interpretation of the early warning signs. This may generalize to other ecosystems exhibiting self-organized spatial patterns, where a spatially-explicit pressure may interfere with pattern formation.     

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature. Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.     

Integrating genetic data and population viability analyses for the identification of harbour seal (Phoca vitulina) populations and management units

Identification of populations and management units is an essential step in the study of natural systems. Still, there is limited consensus regarding how to define populations and management units, and whether genetic methods allow for inference at the relevant spatial and temporal scale. Here, we present a novel approach, integrating genetic, life history and demographic data to identify populations and management units in southern Scandinavian harbour seals. First, 15 microsatellite markers and model‐ and distance‐based genetic clustering methods were used to determine the population genetic structure in harbour seals. Second, we used harbour seal demographic and life history data to conduct population viability analyses (PVAs) in the vortex simulation model in order to determine whether the inferred genetic units could be classified as management units according to Lowe and Allendorf's (Molecular Ecology, 19, 2010, 3038) ‘population viability criterion’ for demographic independence. The genetic analyses revealed fine‐scale population structuring in southern Scandinavian harbour seals and pointed to the existence of several genetic units. The PVAs indicated that the census population size of each of these genetic units was sufficiently large for long‐term population viability, and hence that the units could be classified as demographically independent management units. Our study suggests that population genetic inference can offer the same degree of temporal and spatial resolution as ‘nongenetic’ methods and that the combined use of genetic data and PVAs constitutes a promising approach for delineating populations and management units.     

Population biology of Avena

Summary Pollen and seed dispersal patterns were analyzed in both natural and experimental populations of Avena barbata. Localized estimates of gene flow rates and plant densities gave estimates of neighborhood size in the range of 40 to 400 plants; the estimates of mean rate and distance of gene flow seemed to vary widely due to variable wind direction, rodent activity, microsite heterogeneity, etc. The relative sizes of neighborhoods in several populations were correlated with the patchy distribution of different genotypes (scored for lemma color and leaf sheath hairiness) within short distances, but patch sizes had a wide range among different sites. Highly localized gene flow patterns seemed to account for the observed pattern of highly patchy variation even when the dispersal curves for both pollen and seed were platykurtic in many cases. Measures of the stability of patches in terms of their size, dispersion in space and genetic structure in time are needed in order to sort out the relative roles of founder effects, random drift (due to small neighborhood size), and highly localized selection. However, our observations suggest that many variables and stochastic processes are involved in such studies so as to allow only weak inference about the underlying role of natural selection, drift and factors of population regulatien.     

Differentiation among populations with migration, mutation, and drift: implications for genetic inference

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.     

The effects of migration and drift on local adaptation to a heterogeneous environment

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.     

Relationships between migration rates and landscape resistance assessed using individual-based simulations

Linking landscape effects on gene flow to processes such as dispersal and mating is essential to provide a conceptual foundation for landscape genetics. It is particularly important to determine how classical population genetic models relate to recent individual-based landscape genetic models when assessing individual movement and its influence on population genetic structure. We used classical Wright-Fisher models and spatially explicit, individual-based, landscape genetic models to simulate gene flow via dispersal and mating in a series of landscapes representing two patches of habitat separated by a barrier. We developed a mathematical formula that predicts the relationship between barrier strength (i.e., permeability) and the migration rate (m) across the barrier, thereby linking spatially explicit landscape genetics to classical population genetics theory. We then assessed the reliability of the function by obtaining population genetics parameters (m, F(ST) ) using simulations for both spatially explicit and Wright-Fisher simulation models for a range of gene flow rates. Next, we show that relaxing some of the assumptions of the Wright-Fisher model can substantially change population substructure (i.e., F(ST) ). For example, isolation by distance among individuals on each side of a barrier maintains an F(ST) of ～0.20 regardless of migration rate across the barrier, whereas panmixia on each side of the barrier results in an F(ST) that changes with m as predicted by classical population genetics theory. We suggest that individual-based, spatially explicit modelling provides a general framework to investigate how interactions between movement and landscape resistance drive population genetic patterns and connectivity across complex landscapes.