Helene H. Wagner

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.

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.

Identifying future research needs in landscape genetics: Where to from here?

Landscape genetics is an emerging interdisciplinary field that combines methods and concepts from population genetics, landscape ecology, and spatial statistics. The interest in landscape genetics is steadily increasing, and the field is evolving rapidly. We here outline four major challenges for future landscape genetic research that were identified during an international landscape genetics workshop. These challenges include (1) the identification of appropriate spatial and temporal scales; (2) current analytical limitations; (3) the expansion of the current focus in landscape genetics; and (4) interdisciplinary communication and education. Addressing these research challenges will greatly improve landscape genetic applications, and positively contribute to the future growth of this promising field.

QUANTIFYING DISPERSAL AND ESTABLISHMENT LIMITATION IN A POPULATION OF AN EPIPHYTIC LICHEN

Dispersal is a process critical for the dynamics and persistence of metapopulations, but it is difficult to quantify. It has been suggested that the old-forest lichen Lobaria pulmonaria is limited by insufficient dispersal ability. We analyzed 240 DNA extracts derived from snow samples by a L. pulmonaria-specific real-time PCR (polymerase chain reaction) assay of the ITS (internal transcribed spacer) region allowing for the discrimination among propagules originating from a single, isolated source tree or propagules originating from other locations. Samples that were detected as positives by real-time PCR were additionally genotyped for five L. pulmonaria microsatellite loci. Both molecular approaches demonstrated substantial dispersal from other than local sources. In a landscape approach, we additionally analyzed 240 snow samples with real-time PCR of ITS and detected propagules not only in forests where L. pulmonaria was present, but also in large unforested pasture areas and in forest patches where L. pulmonaria was not found. Monitoring of soredia of L. pulmonaria transplanted to maple bark after two vegetation periods showed high variance in growth among forest stands, but no significant differences among different transplantation treatments. Hence, it is probably not dispersal limitation that hinders colonization in the old-forest lichen L. pulmonaria, but ecological constraints at the stand level that can result in establishment limitation. Our study exemplifies that care has to be taken to adequately separate the effects of dispersal limitation from a limitation of establishment.

SPATIAL COVARIANCE IN PLANT COMMUNITIES: INTEGRATING ORDINATION, GEOSTATISTICS, AND VARIANCE TESTING

Spatial structure in plant communities occurs in the forms of (1) single- species aggregation and dispersion patterns, (2) distance-dependent interactions between species, and (3) the response to the spatial structure of environmental conditions. Different methods deal with these components of spatial variation: geostatistical analysis reveals autocorrelation in a spatial sample; the variance of species richness has been used as an indicator for interspecific interactions due to niche limitation; and ordination techniques describe multispecies responses to environmental factors. Based on the mathematical prop- erties of presence-absence data, it is shown how variogram modeling, the testing of in- terspecific associations, and multiscale ordination can be integrated using the same set of distance-dependent variance-covariance matrices (variogram matrix). The variogram matrix partitions the variance of community data into spatial components at the levels of the individual species, species composition, and species richness. It can be used to factor out the effects of single-species aggregation patterns, interspecific interactions, or environ- mental heterogeneity. The mathematical integration of traditionally unrelated methods in- creases the interpretability of variograms of plant communities, provides a spatial extension and an empirical null model for the variance test of species richness, and extends multiscale ordination to nonsystematic spatial samples. Beyond the individual applications, the var- iogram matrix provides a framework for a mathematical unification of geostatistics, mul- tivariate data analysis, and the analysis of variance that may enable ecologists from a broad range of fields to incorporate spatial effects into their research and to integrate analyses across different levels of biological organization.

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.

Vertical and horizontal photobiont transmission within populations of a lichen symbiosis

Lichens are widespread symbioses and play important roles in many terrestrial ecosystems. The genetic structure of lichens is the result of the association between fungal and algal populations constituting the lichen thallus. Using eight fungus‐ and seven alga‐specific highly variable microsatellite markers on within‐population spatial genetic data from 62 replicate populations across Europe, North America, Asia and Africa, we investigated the contributions of vertical and horizontal transmission of the photobiont to the genetic structure of the epiphytic lichen Lobaria pulmonaria. Based on pairwise comparisons of multilocus genotypes defined separately for the mycobiont and for the photobiont, we inferred the transmission mode of the photobiont and the relative contribution of somatic mutation and recombination. After constraining the analysis of one symbiont to pairs of individuals with genetically identical symbiotic partners, we found that 77% of fungal and 70% of algal pairs were represented by clones. Thus, the predominant dispersal mode was by means of symbiotic vegetative propagules (vertical transmission), which dispersed fungal and algal clones co‐dependently over a short distance, thus shaping the spatial genetic structure up to distances of 20 m. Evidence for somatic mutation generating genetic diversity was found in both symbionts, accounting for 30% of pairwise comparisons in the alga and 15% in the fungus. While the alga did not show statistically significant evidence of recombination, recombination accounted for 7.7% of fungal pairs with identical algae. This implies that, even in a mostly vegetatively reproducing species, horizontal transmission plays a role in shaping the symbiotic association, as shown in many coral and other symbioses in nature.

Effect of disturbances on the genetic diversity of an old-forest associated lichen

Lichens associated with old forest are commonly assumed to be negatively affected by tree logging or natural disturbances. However, in this study performed in a spruce‐dominated sylvopastoral landscape in the Swiss Jura Mountains, we found that genetic diversity of the epiphytic old‐forest lichen Lobaria pulmonaria depends on the type of disturbance. We collected 923 thalli from 41 sampling plots of 1 ha corresponding to the categories stand‐replacing disturbance (burnt), intensive logging (logged) and uneven‐aged forestry (uneven‐aged), and analysed the thalli at six mycobiont‐specific microsatellite loci. We found evidence for multiple independent immigrations into demes located in burnt and logged areas. Using spatial autocorrelation methods, the spatial scale of the genetic structure caused by the clonal and recombinant component of genetic variation was determined. Spatial autocorrelation of genotype diversity was strong at short distances up to 50 m in logged demes, up to 100 m in uneven‐aged demes, with the strongest autocorrelation up to 150 m for burnt demes. The spatial autocorrelation was predominantly attributed to clonal dispersal of vegetative propagules. After accounting for the clonal component, we did not find significant spatial autocorrelation in gene diversity. This pattern may indicate low dispersal ranges of clonal propagules, but random dispersal of sexual ascospores. Genetic diversity was highest in logged demes, and lowest in burnt demes. Our results suggest that genetic diversity of epiphytic lichen demes may not necessarily be impacted by stand‐level disturbances for extended time periods.

Quantifying habitat specificity to assess the contribution of a patch to species richness at a landscape scale

Assessing and predicting the species richness of a complex landscape remains a problem because there is no simple scaling function of species richness in a heterogeneous environment. Furthermore, the potential value of an area for biodiversity conservation may depend on which, rather than how many, species the area contains. This paper shows how we can objectively evaluate the contribution of an area, e.g., a habitat patch, to larger-scale plant species richness, e.g., a landscape composed of patches of several habitat types, and how we can test hypotheses that attempt to explain this contribution. We quantified the concept of habitat specificity to assess the proportion of each observed plant population that is concentrated within a given spatial element. A case study of a biodiversity-monitoring program in the Swiss Canton of Aargau showed that the relative contribution of the three main types of land use to the overall species richness differed strongly between higher taxa (vascular plants and molluscs). However, the type of data, i.e., presence-absence or abundance, was not important. Resampling of the plant data suggested that stratification provided an unbiased estimate of relative specificity, whereas unstratified sampling caused bias even for large samples. In a second case study of vascular plants in an agricultural landscape in central Switzerland, we tested whether the type, size or shape of a landscape element can predict its contribution to the species richness of the landscape. Habitat types that were less frequently disturbed contributed more per m2 to landscape species richness than more frequently disturbed ones. Contrary to expectation, patch size was negatively correlated to specificity per m2 for arable fields, whereas patch shape appeared to be unrelated to the specificity per m2 both for arable fields and for meadows. The specificity approach provides a solution to the problem of scaling species richness and is ideally suited for testing hypotheses on the effect of landscape structure on landscape species richness. Specificity scores can easily be combined with measures of other aspects of rarity to assess the contribution of a spatial element to conservation goals formulated at regional, national or global level.

A conceptual framework for the spatial analysis of landscape genetic data

Understanding how landscape heterogeneity constrains gene flow and the spread of adaptive genetic variation is important for biological conservation given current global change. However, the integration of population genetics, landscape ecology and spatial statistics remains an interdisciplinary challenge at the levels of concepts and methods. We present a conceptual framework to relate the spatial distribution of genetic variation to the processes of gene flow and adaptation as regulated by spatial heterogeneity of the environment, while explicitly considering the spatial and temporal dynamics of landscapes, organisms and their genes. When selecting the appropriate analytical methods, it is necessary to consider the effects of multiple processes and the nature of population genetic data. Our framework relates key landscape genetics questions to four levels of analysis: (i) node-based methods, which model the spatial distribution of alleles at sampling locations (nodes) from local site characteristics; these methods are suitable for modeling adaptive genetic variation while accounting for the presence of spatial autocorrelation. (ii) Link-based methods, which model the probability of gene flow between two patches (link) and relate neutral molecular marker data to landscape heterogeneity; these methods are suitable for modeling neutral genetic variation but are subject to inferential problems, which may be alleviated by reducing links based on a network model of the population. (iii) Neighborhood-based methods, which model the connectivity of a focal patch with all other patches in its local neighborhood; these methods provide a link to metapopulation theory and landscape connectivity modeling and may allow the integration of node- and link-based information, but applications in landscape genetics are still limited. (iv) Boundary-based methods, which delineate genetically homogeneous populations and infer the location of genetic boundaries; these methods are suitable for testing for barrier effects of landscape features in a hypothesis-testing framework. We conclude that the power to detect the effect of landscape heterogeneity on the spatial distribution of genetic variation can be increased by explicit consideration of underlying assumptions and choice of an appropriate analytical approach depending on the research question.