A comparison of individual‐based genetic distance metrics for landscape genetics

A major aim of landscape genetics is to understand how landscapes resist gene flow and thereby influence population genetic structure. An empirical understanding of this process provides a wealth of information that can be used to guide conservation and management of species in fragmented landscapes and also to predict how landscape change may affect population viability. Statistical approaches to infer the true model among competing alternatives are based on the strength of the relationship between pairwise genetic distances and landscape distances among sampled individuals in a population. A variety of methods have been devised to quantify individual genetic distances, but no study has yet compared their relative performance when used for model selection in landscape genetics. In this study, we used population genetic simulations to assess the accuracy of 16 individual‐based genetic distance metrics under varying sample sizes and degree of population genetic structure. We found most metrics performed well when sample size and genetic structure was high. However, it was much more challenging to infer the true model when sample size and genetic structure was low. Under these conditions, we found genetic distance metrics based on principal components analysis were the most accurate (although several other metrics performed similarly), but only when they were derived from multiple principal components axes (the optimal number varied depending on the degree of population genetic structure). Our results provide guidance for which genetic distance metrics maximize model selection accuracy and thereby better inform conservation and management decisions based upon landscape genetic analysis.     

The use and misuse of regression models in landscape genetic analyses

The field of landscape genetics has been rapidly evolving, adopting and adapting analytical frameworks to address research questions. Current studies are increasingly using regression‐based frameworks to infer the individual contributions of landscape and habitat variables on genetic differentiation. This paper outlines appropriate and inappropriate uses of multiple regression for these purposes, and demonstrates through simulation the limitations of different analytical frameworks for making correct inference. Of particular concern are recent studies seeking to explain genetic differences by fitting regression models with effective distance variables calculated independently on separate landscape resistance surfaces. When moving across the landscape, organisms cannot respond independently and uniquely to habitat and landscape features. Analyses seeking to understand how landscape features affect gene flow should model a single conductance or resistance surface as a parameterized function of relevant spatial covariates, and estimate the values of these parameters by linking a single set of resistance distances to observed genetic dissimilarity via a loss function. While this loss function may involve a regression‐like step, the associated nuisance parameters are not interpretable in terms of organismal movement and should not be conflated with what is actually of interest: the mapping between spatial covariates and conductance/resistance. The growth and evolution of landscape genetics as a field has been rapid and exciting. It is the goal of this paper to highlight past missteps and demonstrate limitations of current approaches to ensure that future use of regression models will appropriately consider the process being modeled, which will provide clarity to model interpretation.     

Performance of partial statistics in individual‐based landscape genetics

Individual‐based landscape genetic methods have become increasingly popular for quantifying fine‐scale landscape influences on gene flow. One complication for individual‐based methods is that gene flow and landscape variables are often correlated with geography. Partial statistics, particularly Mantel tests, are often employed to control for these inherent correlations by removing the effects of geography while simultaneously correlating measures of genetic differentiation and landscape variables of interest. Concerns about the reliability of Mantel tests prompted this study, in which we use simulated landscapes to evaluate the performance of partial Mantel tests and two ordination methods, distance‐based redundancy analysis (dbRDA) and redundancy analysis (RDA), for detecting isolation by distance (IBD) and isolation by landscape resistance (IBR). Specifically, we described the effects of suitable habitat amount, fragmentation and resistance strength on metrics of accuracy (frequency of correct results, type I/II errors and strength of IBR according to underlying landscape and resistance strength) for each test using realistic individual‐based gene flow simulations. Mantel tests were very effective for detecting IBD, but exhibited higher error rates when detecting IBR. Ordination methods were overall more accurate in detecting IBR, but had high type I errors compared to partial Mantel tests. Thus, no one test outperformed another completely. A combination of statistical tests, for example partial Mantel tests to detect IBD paired with appropriate ordination techniques for IBR detection, provides the best characterization of fine‐scale landscape genetic structure. Realistic simulations of empirical data sets will further increase power to distinguish among putative mechanisms of differentiation.     

Modelling multilocus selection in an individual‐based,spatially‐explicit landscape genetics framework

We implemented multilocus selection in a spatially‐explicit, individual‐based framework that enables multivariate environmental gradients to drive selection in many loci as a new module for the landscape genetics programs, CDPOP and CDMetaPOP. Our module simulates multilocus selection using a linear additive model, providing a flexible platform to evaluate a wide range of genotype‐environment associations. Importantly, the module allows simulation of selection in any number of loci under the influence of any number of environmental variables. We validated the module with individual‐based selection simulations under Wright‐Fisher assumptions. We then evaluated results for simulations under a simple landscape selection model. Next, we simulated individual‐based multilocus selection across a complex selection landscape with three loci linked to three different environmental variables. Finally, we demonstrated how the program can be used to simulate multilocus selection under varying selection strengths across different levels of gene flow in a landscape genetics framework. This new module provides a valuable addition to the study of landscape genetics, allowing for explicit evaluation of the contributions and interactions between gene flow and selection‐driven processes across complex, multivariate environmental and landscape conditions.     

Consequences of population topology for studying gene flow using link‐based landscape genetic methods

Many landscape genetic studies aim to determine the effect of landscape on gene flow between populations. These studies frequently employ link‐based methods that relate pairwise measures of historical gene flow to measures of the landscape and the geographical distance between populations. However, apart from landscape and distance, there is a third important factor that can influence historical gene flow, that is, population topology (i.e., the arrangement of populations throughout a landscape). As the population topology is determined in part by the landscape configuration, I argue that it should play a more prominent role in landscape genetics. Making use of existing literature and theoretical examples, I discuss how population topology can influence results in landscape genetic studies and how it can be taken into account to improve the accuracy of these results. In support of my arguments, I have performed a literature review of landscape genetic studies published during the first half of 2015 as well as several computer simulations of gene flow between populations. First, I argue why one should carefully consider which population pairs should be included in link‐based analyses. Second, I discuss several ways in which the population topology can be incorporated in response and explanatory variables. Third, I outline why it is important to sample populations in such a way that a good representation of the population topology is obtained. Fourth, I discuss how statistical testing for link‐based approaches could be influenced by the population topology. I conclude the article with six recommendations geared toward better incorporating population topology in link‐based landscape genetic studies.     

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.     

A new mixed‐effects regression model for the analysis of zero‐modified hierarchical count data

Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero‐modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)–(b) and (b)–(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed‐effects regression model based on the hurdle version of the Poisson–Lindley distribution. In this framework, the zero‐modification is incorporated by assuming that a binary probability model determines which outcomes are zero‐valued, and a zero‐truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well‐established mixed‐effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian ‐value and the randomized quantile residuals were considered for model diagnostics.     

From mixed effects modeling to spike and slab variable selection: A Bayesian regression model for group testing data

Due to reductions in both time and cost, group testing is a popular alternative to individual-level testing for disease screening. These reductions are obtained by testing pooled biospecimens (eg, blood, urine, swabs, etc.) for the presence of an infectious agent. However, these reductions come at the expense of data complexity, making the task of conducting disease surveillance more tenuous when compared to using individual-level data. This is because an individual's disease status may be obscured by a group testing protocol and the effect of imperfect testing. Furthermore, unlike individual-level testing, a given participant could be involved in multiple testing outcomes and/or may never be tested individually. To circumvent these complexities and to incorporate all available information, we propose a Bayesian generalized linear mixed model that accommodates data arising from any group testing protocol, estimates unknown assay accuracy probabilities and accounts for potential heterogeneity in the covariate effects across population subgroups (eg, clinic sites, etc.); this latter feature is of key interest to practitioners tasked with conducting disease surveillance. To achieve model selection, our proposal uses spike and slab priors for both fixed and random effects. The methodology is illustrated through numerical studies and is applied to chlamydia surveillance data collected in Iowa.     

Thirty‐five years of spatial autocorrelation analysis in population genetics: an essay in honour of Robert Sokal (1926–2012)

We could not start this review, literally from the beginning, without expressing our sadness over the passing of Professor Robert R. Sokal. We are sure, nevertheless, that the importance of his scientific achievements will ensure he is long remembered. In this modest tribute to Professor Sokal, we highlight his contributions to the field of population genetics and spatial statistical methods. Specifically, we discuss how two papers, co‐authored with Professor N. L. Oden and published in the pages of the Biological Journal of the Linnean Society in 1978, revolutionized the field of analytical population genetics. In these papers, Sokal and Oden created an elegant framework for inferring evolutionary processes (e.g. isolation‐by‐distance, demic diffusion, selection gradients, genetic drift) from the spatial autocorrelation analysis of genetic variation patterns. We also highlight the pivotal importance of Sokal's work to the development of emerging fields (e.g. landscape and conservation genetics). We hope this virtual issue containing the papers that Professor Sokal published in BJLS, and later, related papers by other researchers, will help to remember his work and maintain his legacy of spatial analysis in genetics, ecology, and evolutionary biology. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ??, ??–??.     

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.     

Optimizing the trade‐off between spatial and genetic sampling efforts in patchy populations: towards a better assessment of functional connectivity using an individual‐based sampling scheme

Genetic data are increasingly used in landscape ecology for the indirect assessment of functional connectivity, that is, the permeability of landscape to movements of organisms. Among available tools, matrix correlation analyses (e.g. Mantel tests or mixed models) are commonly used to test for the relationship between pairwise genetic distances and movement costs incurred by dispersing individuals. When organisms are spatially clustered, a population‐based sampling scheme (PSS) is usually performed, so that a large number of genotypes can be used to compute pairwise genetic distances on the basis of allelic frequencies. Because of financial constraints, this kind of sampling scheme implies a drastic reduction in the number of sampled aggregates, thereby reducing sampling coverage at the landscape level. We used matrix correlation analyses on simulated and empirical genetic data sets to investigate the efficiency of an individual‐based sampling scheme (ISS) in detecting isolation‐by‐distance and isolation‐by‐barrier patterns. Provided that pseudo‐replication issues are taken into account (e.g. through restricted permutations in Mantel tests), we showed that the use of interindividual measures of genotypic dissimilarity may efficiently replace interpopulation measures of genetic differentiation: the sampling of only three or four individuals per aggregate may be sufficient to efficiently detect specific genetic patterns in most situations. The ISS proved to be a promising methodological alternative to the more conventional PSS, offering much flexibility in the spatial design of sampling schemes and ensuring an optimal representativeness of landscape heterogeneity in data, with few aggregates left unsampled. Each strategy offering specific advantages, a combined use of both sampling schemes is discussed.     

Categorical variables with many categories are preferentially selected in bootstrap‐based model selection procedures for multivariable regression models

Automated variable selection procedures, such as backward elimination, are commonly employed to perform model selection in the context of multivariable regression. The stability of such procedures can be investigated using a bootstrap‐based approach. The idea is to apply the variable selection procedure on a large number of bootstrap samples successively and to examine the obtained models, for instance, in terms of the inclusion of specific predictor variables. In this paper, we aim to investigate a particular important problem affecting this method in the case of categorical predictor variables with different numbers of categories and to give recommendations on how to avoid it. For this purpose, we systematically assess the behavior of automated variable selection based on the likelihood ratio test using either bootstrap samples drawn with replacement or subsamples drawn without replacement from the original dataset. Our study consists of extensive simulations and a real data example from the NHANES study. Our main result is that if automated variable selection is conducted on bootstrap samples, variables with more categories are substantially favored over variables with fewer categories and over metric variables even if none of them have any effect. Importantly, variables with no effect and many categories may be (wrongly) preferred to variables with an effect but few categories. We suggest the use of subsamples instead of bootstrap samples to bypass these drawbacks.     

Inferring past demographic changes from contemporary genetic data: A simulation‐based evaluation of the ABC methods implemented in diyabc

Inferring the demographic history of species and their populations is crucial to understand their contemporary distribution, abundance and adaptations. The high computational overhead of likelihood‐based inference approaches severely restricts their applicability to large data sets or complex models. In response to these restrictions, approximate Bayesian computation (ABC) methods have been developed to infer the demographic past of populations and species. Here, we present the results of an evaluation of the ABC‐based approach implemented in the popular software package diyabc using simulated data sets (mitochondrial DNA sequences, microsatellite genotypes and single nucleotide polymorphisms). We simulated population genetic data under five different simple, single‐population models to assess the model recovery rates as well as the bias and error of the parameter estimates. The ability of diyabc to recover the correct model was relatively low (0.49): 0.6 for the simplest models and 0.3 for the more complex models. The recovery rate improved significantly when reducing the number of candidate models from five to three (from 0.57 to 0.71). Among the parameters of interest, the effective population size was estimated at a higher accuracy compared to the timing of events. Increased amounts of genetic data did not significantly improve the accuracy of the parameter estimates. Some gains in accuracy and decreases in error were observed for scaled parameters (e.g., N_eμ) compared to unscaled parameters (e.g., N_e and μ). We concluded that diyabc ‐based assessments are not suited to capture a detailed demographic history, but might be efficient at capturing simple, major demographic changes.     

Logistic regression when covariates are random effects from a non‐linear mixed model

In many studies, the association of longitudinal measurements of a continuous response and a binary outcome are often of interest. A convenient framework for this type of problems is the joint model, which is formulated to investigate the association between a binary outcome and features of longitudinal measurements through a common set of latent random effects. The joint model, which is the focus of this article, is a logistic regression model with covariates defined as the individual‐specific random effects in a non‐linear mixed‐effects model (NLMEM) for the longitudinal measurements. We discuss different estimation procedures, which include two‐stage, best linear unbiased predictors, and various numerical integration techniques. The proposed methods are illustrated using a real data set where the objective is to study the association between longitudinal hormone levels and the pregnancy outcome in a group of young women. The numerical performance of the estimating methods is also evaluated by means of simulation.     

A comparison of methods for adaptive treatment selection

Traditionally drug development is generally divided into three phases which have different aims and objectives. Recently so-called adaptive seamless designs that allow combination of the objectives of different development phases into a single trial have gained much interest. Adaptive trials combining treatment selection typical for Phase II and confirmation of efficacy as in Phase III are referred to as adaptive seamless Phase II/III designs and are considered in this paper. We compared four methods for adaptive treatment selection, namely the classical Dunnett test, an adaptive version of the Dunnett test based on the conditional error approach, the combination test approach, and an approach within the classical group-sequential framework. The latter two approaches have only recently been published. In a simulation study we found that no one method dominates the others in terms of power apart from the adaptive Dunnett test that dominates the classical Dunnett by construction. Furthermore, scenarios under which one approach outperforms others are described.