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.     

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.     

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.     

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.     

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.     

Perspectives and challenges in landscape genetics

A recent workshop held at the University of Grenoble gathered the leading experts in the field of landscape genetics and spatial statistics. Landscape genetics was only recently defined as an independent research field. It aims to understand the processes of gene flow and local adaptation by studying the interactions between genetic and spatial or environmental variation. This workshop discussed the perspectives and challenges of combining emerging molecular, spatial and statistical tools to unravel how landscape and environmental variables affect genetic variation.