Marie-Josée Fortin

Spatial pattern and ecological analysis

The spatial heterogeneity of populations and communities plays a central role in many ecological theories, for instance the theories of succession, adaptation, maintenance of species diversity, community stability, competition, predator-prey interactions, parasitism, epidemics and other natural catastrophes, ergoclines, and so on. This paper will review how the spatial structure of biological populations and communities can be studied. We first demonstrate that many of the basic statistical methods used in ecological studies are impaired by autocorrelated data. Most if not all environmental data fall in this category. We will look briefly at ways of performing valid statistical tests in the presence of spatial autocorrelation. Methods now available for analysing the spatial structure of biological populations are described, and illustrated by vegetation data. These include various methods to test for the presence of spatial autocorrelation in the data: univariate methods (all-directional and two-dimensional spatial correlograms, and two-dimensional spectral analysis), and the multivariate Mantel test and Mantel correlogram; other descriptive methods of spatial structure: the univariate variogram, and the multivariate methods of clustering with spatial contiguity constraint; the partial Mantel test, presented here as a way of studying causal models that include space as an explanatory variable; and finally, various methods for mapping ecological variables and producing either univariate maps (interpolation, trend surface analysis, kriging) or maps of truly multivariate data (produced by constrained clustering). A table shows the methods classified in terms of the ecological questions they allow to resolve. Reference is made to available computer programs.

Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data.

The Mantel test is widely used to test the linear or monotonic independence of the elements in two distance matrices. It is one of the few appropriate tests when the hypothesis under study can only be formulated in terms of distances; this is often the case with genetic data. In particular, the Mantel test has been widely used to test for spatial relationship between genetic data and spatial layout of the sampling locations. We describe the domain of application of the Mantel test and derived forms. Formula development demonstrates that the sum‐of‐squares (SS) partitioned in Mantel tests and regression on distance matrices differs from the SS partitioned in linear correlation, regression and canonical analysis. Numerical simulations show that in tests of significance of the relationship between simple variables and multivariate data tables, the power of linear correlation, regression and canonical analysis is far greater than that of the Mantel test and derived forms, meaning that the former methods are much more likely than the latter to detect a relationship when one is present in the data. Examples of difference in power are given for the detection of spatial gradients. Furthermore, the Mantel test does not correctly estimate the proportion of the original data variation explained by spatial structures. The Mantel test should not be used as a general method for the investigation of linear relationships or spatial structures in univariate or multivariate data. Its use should be restricted to tests of hypotheses that can only be formulated in terms of distances.

Use of resistance surfaces for landscape genetic studies: considerations for parameterization and analysis

Measures of genetic structure among individuals or populations collected at different spatial locations across a landscape are commonly used as surrogate measures of functional (i.e. demographic or genetic) connectivity. In order to understand how landscape characteristics influence functional connectivity, resistance surfaces are typically created in a raster GIS environment. These resistance surfaces represent hypothesized relationships between landscape features and gene flow, and are based on underlying biological functions such as relative abundance or movement probabilities in different land cover types. The biggest challenge for calculating resistance surfaces is assignment of resistance values to different landscape features. Here, we first identify study objectives that are consistent with the use of resistance surfaces and critically review the various approaches that have been used to parameterize resistance surfaces and select optimal models in landscape genetics. We then discuss the biological assumptions and considerations that influence analyses using resistance surfaces, such as the relationship between gene flow and dispersal, how habitat suitability may influence animal movement, and how resistance surfaces can be translated into estimates of functional landscape connectivity. Finally, we outline novel approaches for creating optimal resistance surfaces using either simulation or computational methods, as well as alternatives to resistance surfaces (e.g. network and buffered paths). These approaches have the potential to improve landscape genetic analyses, but they also create new challenges. We conclude that no single way of using resistance surfaces is appropriate for every situation. We suggest that researchers carefully consider objectives, important biological assumptions and available parameterization and validation techniques when planning landscape genetic studies.

SPATIAL ANALYSIS OF LANDSCAPES: CONCEPTS AND STATISTICS

Species patchiness implies that nearby observations of species abundance tend to be similar or that individual conspecific organisms are more closely spaced than by random chance. This can be caused either by the positive spatial autocorrelation among the locations of individual organisms due to ecological spatial processes (e.g., species dispersal, competition for space and resources) or by spatial dependence due to (positive or negative) species responses to underlying environmental conditions. Both forms of spatial structure pose problems for statistical analysis, as spatial autocorrelation in the residuals violates the assumption of independent observations, while environmental heterogeneity restricts the comparability of replicates. In this paper, we discuss how spatial structure due to ecological spatial processes and spatial dependence affects spatial statistics, landscape metrics, and statistical modeling of the species-environment correlation. For instance, while spatial statistics can quantify spatial pattern due to an endogeneous spatial process, these methods are severely affected by landscape environmental heterogeneity. Therefore, sta- tistical models of species response to the environment not only need to accommodate spatial structure, but need to distinguish between components due to exogeneous and endogeneous processes rather than discarding all spatial variance. To discriminate between different components of spatial structure, we suggest using (multivariate) spatial analysis of residuals or delineating the spatial realms of a stationary spatial process using boundary detection algorithms. We end by identifying conceptual and statistical challenges that need to be addressed for adequate spatial analysis of landscapes.

Considering spatial and temporal scale in landscape-genetic studies of gene flow

Landscape features exist at multiple spatial and temporal scales, and these naturally affect spatial genetic structure and our ability to make inferences about gene flow. This article discusses how decisions about sampling of genotypes (including choices about analytical methods and genetic markers) should be driven by the scale of spatial genetic structure, the time frame that landscape features have existed in their current state, and all aspects of a species’ life history. Researchers should use caution when making inferences about gene flow, especially when the spatial extent of the study area is limited. The scale of sampling of the landscape introduces different features that may affect gene flow. Sampling grain should be smaller than the average home‐range size or dispersal distance of the study organism and, for raster data, existing research suggests that simplifying the thematic resolution into discrete classes may result in low power to detect effects on gene flow. Therefore, the methods used to characterize the landscape between sampling sites may be a primary determinant for the spatial scale at which analytical results are applicable, and the use of only one sampling scale for a particular statistical method may lead researchers to overlook important factors affecting gene flow. The particular analytical technique used to correlate landscape data and genetic data may also influence results; common landscape‐genetic methods may not be suitable for all study systems, particularly when the rate of landscape change is faster than can be resolved by common molecular markers.

Spatial autocorrelation and sampling design in plant ecology

Using spatial analysis methods such as spatial autocorrelation coefficients (Morans I and Gearys c) and kriging, we compare the capacity of different sampling designs and sample sizes to detect the spatial structure of a sugar-maple (Acer saccharum L.) tree density data set gathered from a secondary growth forest of southwestern Québec. Three different types of subsampling designs (random, systematic and systematic-cluster) with small sample sizes (50 and 64 points), obtained from this larger data set (200 points), are evaluated. The sensitivity of the spatial methods in the detection and the reconstruction of spatial patterns following the application of the various subsampling designs is discussed. We find that the type of sampling design plays an important role in the capacity of autocorrelation coefficients to detect significant spatial autocorrelation, and in the ability to accurately reconstruct spatial patterns by kriging. Sampling designs that contain varying sampling steps, like random and systematic-cluster designs, seem more capable of detecting spatial structures than a systematic design.

Applications of landscape genetics in conservation biology: concepts and challenges

Landscape genetics plays an increasingly important role in the management and conservation of species. Here, we highlight some of the opportunities and challenges in using landscape genetic approaches in conservation biology. We first discuss challenges related to sampling design and introduce several recent methodological developments in landscape genetics (analyses based on pairwise relatedness, the application of Bayesian methods, inference from landscape resistance and a shift from population-based to individual-based analyses). We then show how simulations can foster the field of landscape genetics and, finally, elaborate on technical developments in sequencing techniques that will dramatically improve our ability to study genetic variation in wild species, opening up new and unprecedented avenues for genetic analysis in conservation biology.

Community ecology in the age of multivariate multiscale spatial analysis

Species spatial distributions are the result of population demography, behavioral traits, and species interactions in spatially heterogeneous environmental conditions. Hence the composition of species assemblages is an integrative response variable, and its variability can be explained by the complex interplay among several structuring factors. The thorough analysis of spatial variation in species assemblages may help infer processes shaping ecological communities. We suggest that ecological studies would benefit from the combined use of the classical statistical models of community composition data, such as constrained or unconstrained multivariate analyses of site-by-species abundance tables, with rapidly emerging and diversifying methods of spatial pattern analysis. Doing so allows one to deal with spatially explicit ecological models of beta diversity in a biogeographic context through the multiscale analysis of spatial patterns in original species data tables, including spatial characterization of fitted or residual variation from environmental models. We summarize here the recent progress for specifying spatial features through spatial weighting matrices and spatial eigenfunctions in order to define spatially constrained or scale-explicit multivariate analyses. Through a worked example on tropical tree communities, we also show the potential of the overall approach to identify significant residual spatial patterns that could arise from the omission of important unmeasured explanatory variables or processes.

INFLUENCE OF FOREST COVER ON THE MOVEMENTS OF FOREST BIRDS: A HOMING EXPERIMENT

Habitat loss and fragmentation affect forest birds through direct loss of breeding habitats, detrimental edge effects such as increased nest predation and brood parasitism, and possibly by limiting movements among remaining forest patches. Despite indirect evidence suggesting that landscape-scale bird movements are constrained by open areas, skepticism remains because birds routinely cross inhospitable terrain during migration. Here, we report evidence from 201 independent homing trials showing that landscape composition and configuration influence the movements (1–4 km) of two neotropical migrant (Black-throated Blue Warbler, Dendroica caerulescens and the Ovenbird, Seiurus aurocapillus) and one resident (Black-capped Chickadee, Poecile atricapillus) forest bird species in Quebec, Canada. Trials consisted of translocating territorial, mated males and measuring the time they needed to return to their territories (homing time), as well as the probability with which they returned to their territories within...

Perspectives on the use of landscape genetics to detect genetic adaptive variation in the field

Understanding the genetic basis of species adaptation in the context of global change poses one of the greatest challenges of this century. Although we have begun to understand the molecular basis of adaptation in those species for which whole genome sequences are available, the molecular basis of adaptation is still poorly understood for most non‐model species. In this paper, we outline major challenges and future research directions for correlating environmental factors with molecular markers to identify adaptive genetic variation, and point to research gaps in the application of landscape genetics to real‐world problems arising from global change, such as the ability of organisms to adapt over rapid time scales. High throughput sequencing generates vast quantities of molecular data to address the challenge of studying adaptive genetic variation in non‐model species. Here, we suggest that improvements in the sampling design should consider spatial dependence among sampled individuals. Then, we describe available statistical approaches for integrating spatial dependence into landscape analyses of adaptive genetic variation.