The effect of cost surface parameterization on landscape resistance estimates

A cost or resistance surface is a representation of a landscape's permeability to animal movement or gene flow and is a tool for measuring functional connectivity in landscape ecology and genetics studies. Parameterizing cost surfaces by assigning weights to different landscape elements has been challenging however, because true costs are rarely known; thus, expert opinion is often used to derive relative weights. Assigning weights would be made easier if the sensitivity of different landscape resistance estimates to relative costs was known. We carried out a sensitivity analysis of three methods to parameterize a cost surface and two models of landscape permeability: least cost path and effective resistance. We found two qualitatively different responses to varying cost weights: linear and asymptotic changes. The most sensitive models (i.e. those leading to linear change) were accumulated least cost and effective resistance estimates on a surface coded as resistance (i.e. where high-quality elements were held constant at a low-value, and low-quality elements were varied at higher values). All other cost surface scenarios led to asymptotic change. Developing a cost surface that produces a linear response of landscape resistance estimates to cost weight variation will improve the accuracy of functional connectivity estimates, especially when cost weights are selected through statistical model fitting procedures. On the other hand, for studies where cost weights are unknown and model selection is not being used, methods where resistance estimates vary asymptotically with cost weights may be more appropriate, because of their relative insensitivity to parameterization.     

Spatial genetic structure of a small rodent in a heterogeneous landscape

Gene flow in natural populations may be strongly influenced by landscape features. The integration of landscape characteristics in population genetic studies may thus improve our understanding of population functioning. In this study, we investigated the population genetic structure and gene flow pattern for the common vole, Microtus arvalis, in a heterogeneous landscape characterised by strong spatial and temporal variation. The studied area is an intensive agricultural zone of approximately 500 km² crossed by a motorway. We used individual-based Bayesian methods to define the number of population units and their spatial borders without prior delimitation of such units. Unexpectedly, we determined a single genetic unit that covered the entire area studied. In particular, the motorway considered as a likely barrier to dispersal was not associated with any spatial genetic discontinuity. Using computer simulations, we demonstrated that recent anthropogenic barriers to effective dispersal are difficult to detect through analysis of genetic variation for species with large effective population sizes. We observed a slight, but significant, pattern of isolation by distance over the whole study site. Spatial autocorrelation analyses detected genetic structuring on a local scale, most probably due to the social organisation of the study species. Overall, our analysis suggests intense small-scale dispersal associated with a large effective population size. High dispersal rates may be imposed by the strong spatio-temporal heterogeneity of habitat quality, which characterises intensive agroecosystems.     

Current approaches using genetic distances produce poor estimates of landscape resistance to interindividual dispersal

Landscape resistance reflects how difficult it is for genes to move across an area with particular attributes (e.g. land cover, slope). An increasingly popular approach to estimate resistance uses Mantel and partial Mantel tests or causal modelling to relate observed genetic distances to effective distances under alternative sets of resistance parameters. Relatively few alternative sets of resistance parameters are tested, leading to relatively poor coverage of the parameter space. Although this approach does not explicitly model key stochastic processes of gene flow, including mating, dispersal, drift and inheritance, bias and precision of the resulting resistance parameters have not been assessed. We formally describe the most commonly used model as a set of equations and provide a formal approach for estimating resistance parameters. Our optimization finds the maximum Mantel r when an optimum exists and identifies the same resistance values as current approaches when the alternatives evaluated are near the optimum. Unfortunately, even where an optimum existed, estimates from the most commonly used model were imprecise and were typically much smaller than the simulated true resistance to dispersal. Causal modelling using Mantel significance tests also typically failed to support the true resistance to dispersal values. For a large range of scenarios, current approaches using a simple correlational model between genetic and effective distances do not yield accurate estimates of resistance to dispersal. We suggest that analysts consider the processes important to gene flow for their study species, model those processes explicitly and evaluate the quality of estimates resulting from their model.     

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.     

Adaptation with gene flow across the landscape in a dune sunflower

Isolation by adaptation increases divergence at neutral loci when natural selection against immigrants reduces the rate of gene flow between different habitats. This can occur early in the process of adaptive divergence and is a key feature of ecological speciation. Despite the ability of isolation by distance (IBD) and other forms of landscape resistance to produce similar patterns of neutral divergence within species, few studies have used landscape genetics to control for these other forces. We have studied the divergence of Helianthus petiolaris ecotypes living in active sand dunes and adjacent non-dune habitat, using landscape genetics approaches, such as circuit theory and multiple regression of distance matrices, in addition to coalescent modelling. Divergence between habitats was significant, but not strong, and was shaped by IBD. We expected that increased resistance owing to patchy and unfavourable habitat in the dunes would contribute to divergence. Instead, we found that landscape resistance models with lower resistance in the dunes performed well as predictors of genetic distances among subpopulations. Nevertheless, habitat class remained a strong predictor of genetic distance when controlling for isolation by resistance and IBD. We also measured environmental variables at each site and confirmed that specific variables, especially soil nitrogen and vegetation cover, explained a greater proportion of variance in genetic distance than did landscape or the habitat classification alone. Asymmetry in effective population sizes and numbers of migrants per generation was detected using coalescent modelling with Bayesian inference, which is consistent with incipient ecological speciation being driven by the dune habitat.     

Why replication is important in landscape genetics: American black bear in the Rocky Mountains

We investigated how landscape features influence gene flow of black bears by testing the relative support for 36 alternative landscape resistance hypotheses, including isolation by distance (IBD) in each of 12 study areas in the north central U.S. Rocky Mountains. The study areas all contained the same basic elements, but differed in extent of forest fragmentation, altitude, variation in elevation and road coverage. In all but one of the study areas, isolation by landscape resistance was more supported than IBD suggesting gene flow is likely influenced by elevation, forest cover, and roads. However, the landscape features influencing gene flow varied among study areas. Using subsets of loci usually gave models with the very similar landscape features influencing gene flow as with all loci, suggesting the landscape features influencing gene flow were correctly identified. To test if the cause of the variability of supported landscape features in study areas resulted from landscape differences among study areas, we conducted a limiting factor analysis. We found that features were supported in landscape models only when the features were highly variable. This is perhaps not surprising but suggests an important cautionary note - that if landscape features are not found to influence gene flow, researchers should not automatically conclude that the features are unimportant to the species' movement and gene flow. Failure to investigate multiple study areas that have a range of variability in landscape features could cause misleading inferences about which landscape features generally limit gene flow. This could lead to potentially erroneous identification of corridors and barriers if models are transferred between areas with different landscape characteristics.     

A new analytical approach to landscape genetic modelling: least-cost transect analysis and linear mixed models

Landscape genetics aims to assess the effect of the landscape on intraspecific genetic structure. To quantify interdeme landscape structure, landscape genetics primarily uses landscape resistance surfaces (RSs) and least-cost paths or straight-line transects. However, both approaches have drawbacks. Parameterization of RSs is a subjective process, and least-cost paths represent a single migration route. A transect-based approach might oversimplify migration patterns by assuming rectilinear migration. To overcome these limitations, we combined these two methods in a new landscape genetic approach: least-cost transect analysis (LCTA). Habitat-matrix RSs were used to create least-cost paths, which were subsequently buffered to form transects in which the abundance of several landscape elements was quantified. To maintain objectivity, this analysis was repeated so that each landscape element was in turn regarded as migration habitat. The relationship between explanatory variables and genetic distances was then assessed following a mixed modelling approach to account for the nonindependence of values in distance matrices. Subsequently, the best fitting model was selected using the statistic. We applied LCTA and the mixed modelling approach to an empirical genetic dataset on the endangered damselfly, Coenagrion mercuriale. We compared the results to those obtained from traditional least-cost, effective and resistance distance analysis. We showed that LCTA is an objective approach that identifies both the most probable migration habitat and landscape elements that either inhibit or facilitate gene flow. Although we believe the statistical approach to be an improvement for the analysis of distance matrices in landscape genetics, more stringent testing is needed.     

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.     

Habitat barriers limit gene flow and illuminate historical events in a wide-ranging carnivore, the American puma

We examined the effects of habitat discontinuities on gene flow among puma (Puma concolor) populations across the southwestern USA. Using 16 microsatellite loci, we genotyped 540 pumas sampled throughout the states of Utah, Colorado, Arizona, and New Mexico, where a high degree of habitat heterogeneity provides for a wide range of connective habitat configurations between subpopulations. We investigated genetic structuring using complementary individual- and population-based analyses, the latter employing a novel technique to geographically cluster individuals without introducing investigator bias. The analyses revealed genetic structuring at two distinct scales. First, strikingly strong differentiation between northern and southern regions within the study area suggests little migration between them. Second, within each region, gene flow appears to be strongly limited by distance, particularly in the presence of habitat barriers such as open desert and grasslands. Northern pumas showed both reduced genetic diversity and greater divergence from a hypothetical ancestral population based on Bayesian clustering analyses, possibly reflecting a post-Pleistocene range expansion. Bayesian clustering results were sensitive to sampling density, which may complicate inference of numbers of populations when using this method. The results presented here build on those of previous studies, and begin to complete a picture of how different habitat types facilitate or impede gene flow among puma populations.     

Quantifying the lag time to detect barriers in landscape genetics

Understanding how spatial genetic patterns respond to landscape change is crucial for advancing the emerging field of landscape genetics. We quantified the number of generations for new landscape barrier signatures to become detectable and for old signatures to disappear after barrier removal. We used spatially explicit, individual‐based simulations to examine the ability of an individual‐based statistic [Mantel’s r using the proportion of shared alleles’ statistic (Dps)] and population‐based statistic (F_ST) to detect barriers. We simulated a range of movement strategies including nearest neighbour dispersal, long‐distance dispersal and panmixia. The lag time for the signal of a new barrier to become established is short using Mantel’s r (1–15 generations). F_ST required approximately 200 generations to reach 50% of its equilibrium maximum, although G’_ST performed much like Mantel’s r. In strong contrast, F_ST and Mantel’s r perform similarly following the removal of a barrier formerly dividing a population. Also, given neighbour mating and very short‐distance dispersal strategies, historical discontinuities from more than 100 generations ago might still be detectable with either method. This suggests that historical events and landscapes could have long‐term effects that confound inferences about the impacts of current landscape features on gene flow for species with very little long‐distance dispersal. Nonetheless, populations of organisms with relatively large dispersal distances will lose the signal of a former barrier within less than 15 generations, suggesting that individual‐based landscape genetic approaches can improve our ability to measure effects of existing landscape features on genetic structure and connectivity.     

Different landscape effects on the genetic structure of two broadly distributed woody legumes,Acacia salicina and A. stenophylla (Fabaceae)

Restoring degraded landscapes has primarily focused on re‐establishing native plant communities. However, little is known with respect to the diversity and distribution of most key revegetation species or the environmental and anthropogenic factors that may affect their demography and genetic structure. In this study, we investigated the genetic structure of two widespread Australian legume species (Acacia salicina and Acacia stenophylla) in the Murray–Darling Basin (MDB), a large agriculturally utilized region in Australia, and assessed the impact of landscape structure on genetic differentiation. We used AFLP genetic data and sampled a total of 28 A. salicina and 30 A. stenophylla sampling locations across southeastern Australia. We specifically evaluated the importance of four landscape features: forest cover, land cover, water stream cover, and elevation. We found that both species had high genetic diversity (mean percentage of polymorphic loci, 55.1% for A. salicina versus. 64.3% for A. stenophylla) and differentiation among local sampling locations (A. salicina: Φ_PT = 0.301, 30%; A. stenophylla: Φ_PT = 0.235, 23%). Population structure analysis showed that both species had high levels of structure (6 clusters each) and admixture in some sampling locations, particularly A. stenophylla. Although both species have a similar geographic range, the drivers of genetic connectivity for each species were very different. Genetic variation in A. salicina seems to be mainly driven by geographic distance, while for A. stenophylla, land cover appears to be the most important factor. This suggests that for the latter species, gene flow among populations is affected by habitat fragmentation. We conclude that these largely co‐occurring species require different management actions to maintain population connectivity. We recommend active management of A. stenophylla in the MDB to improve gene flow in the adversity of increasing disturbances (e.g., droughts) driven by climate change and anthropogenic factors.     

Differential permeability of rivers to raccoon gene flow corresponds to rabies incidence in Ontario, Canada

The correlation of landscape features with genetic discontinuities reveals barriers to dispersal that can contribute to understanding present and future spread of wildlife diseases. This knowledge can then be used for targeting control efforts. The impact of natural barriers on raccoon dispersal was assessed through genetic analysis of samples from two regions, Niagara ( N  = 666) and St. Lawrence ( N  = 802). These areas are transected by major rivers and are at the northern front of a raccoon rabies epizootic. Genetic clusters were identified in each region using Bayesian clustering algorithms. In the Niagara region, two clusters were identified corresponding to either side of the Niagara River. For the St. Lawrence region, spatially congruent clusters were not identified, despite the presence of the intervening St. Lawrence River. These genetic data are consistent with raccoon rabies incidence data where rabies has been detected across the St. Lawrence River in Ontario while no cases have been detected in Ontario across the Niagara River. This is despite expectations of rabies incidence in Niagara before the St. Lawrence based on the progression of rabies from New York. The results from the two regions suggest different permeabilities to raccoons between New York and Ontario that may be attributed to the rivers. However, other factors have also been explored that could contribute to this difference between these study sites including the shape of the landscape and resource distribution.     

Streams over mountains: influence of riparian connectivity on gene flow in the Pacific jumping mouse (Zapus trinotatus)

In species affiliated with heterogeneous habitat, we expect gene flow to be restricted due to constraints placed on individual movement by habitat boundaries. This is likely to impact both individual dispersal and connectivity between populations. In this study, a GIS-based landscape genetics approach was used, in combination with fine-scale spatial autocorrelation analysis and the estimation of recent intersubpopulation migration rates, to infer patterns of dispersal and migration in the riparian-affiliated Pacific jumping mouse (Zapus trinotatus). A total of 228 individuals were sampled from nine subpopulations across a system of three rivers and genotyped at eight microsatellite loci. Significant spatial autocorrelation among individuals revealed a pattern of fine-scale spatial genetic structure indicative of limited dispersal. Geographical distances between pairwise subpopulations were defined following four criteria: (i) Euclidean distance, and three landscape-specific distances, (ii) river distance (distance travelled along the river only), (iii) overland distance (similar to Euclidean, but includes elevation), and (iv) habitat-path distance (a least-cost path distance that models movement along habitat pathways). Pairwise Mantel tests were used to test for a correlation between genetic distance and each of the geographical distances. Significant correlations were found between genetic distance and both the overland and habitat-path distances; however, the correlation with habitat-path distance was stronger. Lastly, estimates of recent migration rates revealed that migration occurs not only within drainages but also across large topographic barriers. These results suggest that patterns of dispersal and migration in Pacific jumping mice are largely determined by habitat connectivity.     

landgenreport: a new r function to simplify landscape genetic analysis using resistance surface layers

We describe functions recently added to the r package popgenreport that can be used to perform a landscape genetic analysis (LGA) based on landscape resistance surfaces, which aims to detect the effect of landscape features on gene flow. These functions for the first time implement a LGA in a single framework. Although the approach has been shown to be a valuable tool to study gene flow in landscapes, it has not been widely used to date, despite the type of data being widely available. In part, this is likely due to the necessity to use several software packages to perform landscape genetic analyses. To apply LGA functions, two types of data sets are required: a data set with spatially referenced and genotyped individuals, and a resistance layer representing the effect of the landscape. The function outputs three pairwise distance matrices from these data: a genetic distance matrix, a cost distance matrix and a Euclidean distance matrix. Statistical tests are performed to test whether the cost matrix contributes to the understanding of the observed population structure. A full report on the analysis and outputs in the form of plots and tables of all intermediate steps of the LGA is produced. It is possible to customize the LGA to allow for different cost path approaches and measures of genetic distances. The package is written in the r language and is available through the Comprehensive r Archive. Comprehensive tutorials and information on how to install and use the package are provided at the authors’ website ( www.popgenreport.org ).     

Combining the least cost path method with population genetic data and species distribution models to identify landscape connectivity during the late Quaternary in Himalayan hemlock

Himalayan hemlock (Tsuga dumosa) experienced a recolonization event during the Quaternary period; however, the specific dispersal routes are remain unknown. Recently, the least cost path (LCP) calculation coupled with population genetic data and species distribution models has been applied to reveal the landscape connectivity. In this study, we utilized the categorical LCP method, combining species distribution of three periods (the last interglacial, the last glacial maximum, and the current period) and locality with shared chloroplast, mitochondrial, and nuclear haplotypes, to identify the possible dispersal routes of T. dumosa in the late Quaternary. Then, both a coalescent estimate of migration rates among regional groups and establishment of genetic divergence pattern were conducted. After those analyses, we found that the species generally migrated along the southern slope of Himalaya across time periods and genomic makers, and higher degree of dispersal was in the present and mtDNA haplotype. Furthermore, the direction of range shifts and strong level of gene flow also imply the existence of Himalayan dispersal path, and low area of genetic divergence pattern suggests that there are not any obvious barriers against the dispersal pathway. Above all, we inferred that a dispersal route along the Himalaya Mountains could exist, which is an important supplement for the evolutionary history of T. dumosa. Finally, we believed that this integrative genetic and geospatial method would bring new implications for the evolutionary process and conservation priority of species in the Tibetan Plateau.     

Choosing appropriate genetic markers and analytical methods for testing landscape genetic hypotheses

Landscape genetics and phylogeography both examine population‐level microevolutionary processes, such as population structure and gene flow, in the context of environmental and geographic variation. They differ in terms of the spatial and temporal scales they typically investigate, meaning that different genetic markers and analytical methods are better suited for testing the different hypotheses typically posed by each discipline. In a recent comment, Bohonak & Vandergast (2011) argue that I overlooked the value of mtDNA for landscape genetics in an article I published last year in Molecular Ecology (Wang 2010) and that a gap between landscape genetics and phylogeography, which I outlined, does not exist. Here, I clarify several points in my original article and summarize the commonly held viewpoint that different genetic markers are appropriate for drawing inferences at different temporal scales.     

Landscape genetics and hierarchical genetic structure in Atlantic salmon: the interaction of gene flow and local adaptation

Disentangling evolutionary forces that may interact to determine the patterns of genetic differentiation within and among wild populations is a major challenge in evolutionary biology. The objective of this study was to assess the genetic structure and the potential influence of several ecological variables on the extent of genetic differentiation at multiple spatial scales in a widely distributed species, the Atlantic salmon, Salmo salar . A total of 2775 anadromous fish were sampled from 51 rivers along the North American Atlantic coast and were genotyped using 13 microsatellites. A Bayesian analysis clustered these populations into seven genetically and geographically distinct groups, characterized by different environmental and ecological factors, mainly temperature. These groups were also characterized by different extent of genetic differentiation among populations. Dispersal was relatively high and of the same magnitude within compared to among regional groups, which contrasted with the maintenance of a regional genetic structure. However, genetic differentiation was lower among populations exchanging similar rates of local as opposed to inter-regional migrants, over the same geographical scale. This raised the hypothesis that gene flow could be constrained by local adaptation at the regional scale. Both coastal distance and temperature regime were found to influence the observed genetic structure according to landscape genetic analyses. The influence of other factors such as latitude, river length and altitude, migration tactic, and stocking was not significant at any spatial scale. Overall, these results suggested that the interaction between gene flow and thermal regime adaptation mainly explained the hierarchical genetic structure observed among Atlantic salmon populations.     

Evaluating methods to visualize patterns of genetic differentiation on a landscape

With advances in sequencing technology, research in the field of landscape genetics can now be conducted at unprecedented spatial and genomic scales. This has been especially evident when using sequence data to visualize patterns of genetic differentiation across a landscape due to demographic history, including changes in migration. Two recent model‐based visualization methods that can highlight unusual patterns of genetic differentiation across a landscape, SpaceMix and EEMS, are increasingly used. While SpaceMix's model can infer long‐distance migration, EEMS’ model is more sensitive to short‐distance changes in genetic differentiation, and it is unclear how these differences may affect their results in various situations. Here, we compare SpaceMix and EEMS side by side using landscape genetics simulations representing different migration scenarios. While both methods excel when patterns of simulated migration closely match their underlying models, they can produce either un‐intuitive or misleading results when the simulated migration patterns match their models less well, and this may be difficult to assess in empirical data sets. We also introduce unbundled principal components (un‐PC), a fast, model‐free method to visualize patterns of genetic differentiation by combining principal components analysis (PCA), which is already used in many landscape genetics studies, with the locations of sampled individuals. Un‐PC has characteristics of both SpaceMix and EEMS and works well with simulated and empirical data. Finally, we introduce msLandscape, a collection of tools that streamline the creation of customizable landscape‐scale simulations using the popular coalescent simulator ms and conversion of the simulated data for use with un‐PC, SpaceMix and EEMS.     

Using a genetic network to parameterize a landscape resistance surface for fishers, Martes pennanti

Knowledge of dispersal-related gene flow is important for addressing many basic and applied questions in ecology and evolution. We used landscape genetics to understand the recovery of a recently expanded population of fishers (Martes pennanti) in Ontario, Canada. An important focus of landscape genetics is modelling the effects of landscape features on gene flow. Most often resistance surfaces in landscape genetic studies are built a priori based upon nongenetic field data or expert opinion. The resistance surface that best fits genetic data is then selected and interpreted. Given inherent biases in using expert opinion or movement data to model gene flow, we sought an alternative approach. We used estimates of conditional genetic distance derived from a network of genetic connectivity to parameterize landscape resistance and build a final resistance surface based upon information-theoretic model selection and multi-model averaging. We sampled 657 fishers from 31 landscapes, genotyped them at 16 microsatellite loci, and modelled the effects of snow depth, road density, river density, and coniferous forest on gene flow. Our final model suggested that road density, river density, and snow depth impeded gene flow during the fisher population expansion demonstrating that both human impacts and seasonal habitat variation affect gene flow for fishers. Our approach to building landscape genetic resistance surfaces mitigates many of the problems and caveats associated with using either nongenetic field data or expert opinion to derive resistance surfaces.