Erin L. Landguth

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 (FST) 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). FST required approximately 200 generations to reach 50% of its equilibrium maximum, although G’ST performed much like Mantel’s r. In strong contrast, FST 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.

Spurious correlations and inference in landscape genetics

Reliable interpretation of landscape genetic analyses depends on statistical methods that have high power to identify the correct process driving gene flow while rejecting incorrect alternative hypotheses. Little is known about statistical power and inference in individual‐based landscape genetics. Our objective was to evaluate the power of causal‐modelling with partial Mantel tests in individual‐based landscape genetic analysis. We used a spatially explicit simulation model to generate genetic data across a spatially distributed population as functions of several alternative gene flow processes. This allowed us to stipulate the actual process that is in action, enabling formal evaluation of the strength of spurious correlations with incorrect models. We evaluated the degree to which naïve correlational approaches can lead to incorrect attribution of the driver of observed genetic structure. Second, we evaluated the power of causal modelling with partial Mantel tests on resistance gradients to correctly identify the explanatory model and reject incorrect alternative models. Third, we evaluated how rapidly after the landscape genetic process is initiated that we are able to reliably detect the effect of the correct model and reject the incorrect models. Our analyses suggest that simple correlational analyses between genetic data and proposed explanatory models produce strong spurious correlations, which lead to incorrect inferences. We found that causal modelling was extremely effective at rejecting incorrect explanations and correctly identifying the true causal process. We propose a generalized framework for landscape genetics based on analysis of the spatial genetic relationships among individual organisms relative to alternative hypotheses that define functional relationships between landscape features and spatial population processes.

CDPOP: A spatially explicit cost distance population genetics program

Spatially explicit simulation of gene flow in complex landscapes is essential to explain observed population responses and provide a foundation for landscape genetics. To address this need, we wrote a spatially explicit, individual‐based population genetics model (cdpop). The model implements individual‐based population modelling with Mendelian inheritance and k‐allele mutation on a resistant landscape. The model simulates changes in population and genotypes through time as functions of individual based movement, reproduction, mortality and dispersal on a continuous cost surface. This model will be a valuable tool for the study of landscape genetics by increasing our understanding about the effects of life history, vagility and differential models of landscape resistance on the genetic structure of populations in complex landscapes.

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.

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.

A simulation-based evaluation of methods for inferring linear barriers to gene flow

Different analytical techniques used on the same data set may lead to different conclusions about the existence and strength of genetic structure. Therefore, reliable interpretation of the results from different methods depends on the efficacy and reliability of different statistical methods. In this paper, we evaluated the performance of multiple analytical methods to detect the presence of a linear barrier dividing populations. We were specifically interested in determining if simulation conditions, such as dispersal ability and genetic equilibrium, affect the power of different analytical methods for detecting barriers. We evaluated two boundary detection methods (Monmonier’s algorithm and WOMBLING), two spatial Bayesian clustering methods (TESS and GENELAND), an aspatial clustering approach (STRUCTURE), and two recently developed, non‐Bayesian clustering methods [PSMIX and discriminant analysis of principal components (DAPC)]. We found that clustering methods had higher success rates than boundary detection methods and also detected the barrier more quickly. All methods detected the barrier more quickly when dispersal was long distance in comparison to short‐distance dispersal scenarios. Bayesian clustering methods performed best overall, both in terms of highest success rates and lowest time to barrier detection, with GENELAND showing the highest power. None of the methods suggested a continuous linear barrier when the data were generated under an isolation‐by‐distance (IBD) model. However, the clustering methods had higher potential for leading to incorrect barrier inferences under IBD unless strict criteria for successful barrier detection were implemented. Based on our findings and those of previous simulation studies, we discuss the utility of different methods for detecting linear barriers to gene flow.

Scale dependent inference in landscape genetics

Ecological relationships between patterns and processes are highly scale dependent. This paper reports the first formal exploration of how changing scale of research away from the scale of the processes governing gene flow affects the results of landscape genetic analysis. We used an individual-based, spatially explicit simulation model to generate patterns of genetic similarity among organisms across a complex landscape that would result given a stipulated landscape resistance model. We then evaluated how changes to the grain, extent, and thematic resolution of that landscape model affect the nature and strength of observed landscape genetic pattern–process relationships. We evaluated three attributes of scale including thematic resolution, pixel size, and focal window size. We observed large effects of changing thematic resolution of analysis from the stipulated continuously scaled resistance process to a number of categorical reclassifications. Grain and window size have smaller but statistically significant effects on landscape genetic analyses. Importantly, power in landscape genetics increases as grain of analysis becomes finer. The analysis failed to identify the operative grain governing the process, with the general pattern of stronger apparent relationship with finer grain, even at grains finer than the governing process. The results suggest that correct specification of the thematic resolution of landscape resistance models dominates effects of grain and extent. This emphasizes the importance of evaluating a range of biologically realistic resistance hypotheses in studies to associate landscape patterns to gene flow processes.

Separating the effects of habitat area, fragmentation and matrix resistance on genetic differentiation in complex landscapes

Little is known about how variation in landscape mosaics affects genetic differentiation. The goal of this paper is to quantify the relative importance of habitat area and configuration, as well as the contrast in resistance between habitat and non-habitat, on genetic differentiation. We hypothesized that habitat configuration would be more influential than habitat area in influencing genetic differentiation. Population size is positively related to habitat area, and therefore habitat area should affect genetic drift, but not gene flow. In contrast, differential rates and patterns of gene flow across a landscape should be related to habitat configuration. Using spatially explicit, individual-based simulation modeling, we found that habitat configuration had stronger relationships with genetic differentiation than did habitat area, but there was a high degree of confounding between the effects of habitat area and configuration. We evaluated the predictive ability of six widely used landscape metrics and found that patch cohesion and correlation length of habitat are among the strongest individual predictors of genetic differentiation. Correlation length, patch density and clumpy are the most parsimonious set of variables to predict the magnitude of genetic differentiation in complex landscapes.

Simulating the effects of climate change on population connectivity of American marten (Martes americana) in the northern Rocky Mountains, USA

We utilize empirically derived estimates of landscape resistance to assess current landscape connectivity of American marten (Martes americana) in the northern Rocky Mountains, USA, and project how a warming climate may affect landscape resistance and population connectivity in the future. We evaluate the influences of five potential future temperature scenarios involving different degrees of warming. We use resistant kernel dispersal models to assess population connectivity based on full occupancy of suitable habitat in each of these hypothetical future resistance layers. We use the CDPOP model to simulate gene exchange among individual martens in each of these hypothetical future climates. We evaluate: (1) changes in the extent, connectivity and pattern of marten habitat, (2) changes in allelic richness and expected heterozygosity, and (3) changes in the range of significant positive genetic correlation within the northern Idaho marten population under each future scenario. We found that even moderate warming scenarios resulted in very large reductions in population connectivity. Calculation of genetic correlograms for each scenario indicates that climate driven changes in landscape connectivity results in decreasing range of genetic correlation, indicating more isolated and smaller genetic neighborhoods. These, in turn, resulted in substantial loss of allelic richness and reductions in expected heterozygosity. In the U.S. northern Rocky Mountains, climate change may extensively fragment marten populations to a degree that strongly reduces genetic diversity. Our results demonstrate that for species, such as the American marten, whose population connectivity is highly tied to climatic gradients, expected climate change can result in profound changes in the extent, pattern, connectivity and gene flow of populations.

Sample design effects in landscape genetics

An important research gap in landscape genetics is the impact of different field sampling designs on the ability to detect the effects of landscape pattern on gene flow. We evaluated how five different sampling regimes (random, linear, systematic, cluster, and single study site) affected the probability of correctly identifying the generating landscape process of population structure. Sampling regimes were chosen to represent a suite of designs common in field studies. We used genetic data generated from a spatially-explicit, individual-based program and simulated gene flow in a continuous population across a landscape with gradual spatial changes in resistance to movement. Additionally, we evaluated the sampling regimes using realistic and obtainable number of loci (10 and 20), number of alleles per locus (5 and 10), number of individuals sampled (10–300), and generational time after the landscape was introduced (20 and 400). For a simulated continuously distributed species, we found that random, linear, and systematic sampling regimes performed well with high sample sizes (>200), levels of polymorphism (10 alleles per locus), and number of molecular markers (20). The cluster and single study site sampling regimes were not able to correctly identify the generating process under any conditions and thus, are not advisable strategies for scenarios similar to our simulations. Our research emphasizes the importance of sampling data at ecologically appropriate spatial and temporal scales and suggests careful consideration for sampling near landscape components that are likely to most influence the genetic structure of the species. In addition, simulating sampling designs a priori could help guide filed data collection efforts