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.     

The Genetic Structure of a Tribal Population, the Yanomama Indians. Xv. Patterns Inferred by Autocorrelation Analysis

Fifteen allele frequencies have previously been determined for 50 villages of the Yanomama, an Amerindian tribe from southern Venezuela and northern Brazil. These frequencies were subjected to spatial autocorrelation analysis to investigate their population structure. There are significant spatial patterns for most allele frequencies. Clinical patterns, investigated by one-dimensional and directional spatial correlograms, were relatively few in number and were moderate in strength. Overall, however, there is a marked decline in genetic similarity with geographic distance. The results are compatible with a hierarchic population structure superimposed on the geography, and generated by a stochastic fission-fusion model of village propagation, followed by localized gene flow. Strong temporal autocorrelations of allele frequencies based on linguistic-historical distances representing time since divergence were also found. There appears to be a stronger relation between geography and linguistic-historical hierarchic subdivisions than between either feature and genetic distances. These findings confirm by different approaches the results of earlier analyses concerning the important roles of both stochastic and social factors in determining village allele frequencies and the occurrence within this tribe of some allele frequency clines most likely due to the operation of chance historical processes.     

Isolation by resistance across a complex coral reef seascape

A detailed understanding of the genetic structure of populations and an accurate interpretation of processes driving contemporary patterns of gene flow are fundamental to successful spatial conservation management. The field of seascape genetics seeks to incorporate environmental variables and processes into analyses of population genetic data to improve our understanding of forces driving genetic divergence in the marine environment. Information about barriers to gene flow (such as ocean currents) is used to define a resistance surface to predict the spatial genetic structure of populations and explain deviations from the widely applied isolation-by-distance model. The majority of seascape approaches to date have been applied to linear coastal systems or at large spatial scales (more than 250 km), with very few applied to complex systems at regional spatial scales (less than 100 km). Here, we apply a seascape genetics approach to a peripheral population of the broadcast-spawning coral Acropora spicifera across the Houtman Abrolhos Islands, a high-latitude complex coral reef system off the central coast of Western Australia. We coupled population genetic data from a panel of microsatellite DNA markers with a biophysical dispersal model to test whether oceanographic processes could explain patterns of genetic divergence. We identified significant variation in allele frequencies over distances of less than 10 km, with significant differentiation occurring between adjacent sites but not between the most geographically distant ones. Recruitment probabilities between sites based on simulated larval dispersal were projected into a measure of resistance to connectivity that was significantly correlated with patterns of genetic divergence, demonstrating that patterns of spatial genetic structure are a function of restrictions to gene flow imposed by oceanographic currents. This study advances our understanding of the role of larval dispersal on the fine-scale genetic structure of coral populations across a complex island system and applies a methodological framework that can be tailored to suit a variety of marine organisms with a range of life-history characteristics.     

Genetic diversity and population structure of Eugenia dysenterica DC. (``cagaiteira' – Myrtaceae) in Central Brazil: Spatial analysis and implications for conservation and management

Studies about the organization of the genetic variability and population structure in natural plant populations are used to support conservation and management programs. Among the Cerrado fruit tree species that possess potential economic importance in agriculture, the “Cagaiteira” (Eugenia dysenterica DC. – Myrtaceae), deserves an special position. We obtained information about allele and genotypic frequencies in 10 local populations, situated up to 250 km apart, from six isozymes that furnished a total of 8 loci. The average within-population fixation index (f) was 0.337, and the out crossing rate was 0.835, suggesting a mixed mating system for this species, which seems to be preferably alogamous. Based on genetic diversity and analysis of variance techniques, a high degree of population differentiation (θ_P = 0.154) was found, in comparison with other tropical tree species. Genetic divergence, analyzed by Nei's genetic distances, clustered with UPGMA and ordinated by non-metric multidimensional scaling, showed spatial patterns of clusters of local populations. Explicit spatial analyses, using Mantel tests and boundary tests, basically confirmed these patterns and revealed a complex pattern of genetic variation in geographic space. The intercept of the multivariate spatial correlograms was around 120 km, an indication of the minimum distance between samples needed to conserve genetic diversity among samples. This spatial scale can be used to define population genetics units for conservation programs or to establish sampling strategies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Drivers of the beta diversity of spider assemblages in southern Brazilian temporary wetlands

1. The composition of local assemblages is assembled by an interplay of species sorting, mass effects and dispersal limitation processes. The contributions of assembly processes to metacommunity structure can change with ecosystem type and specificities of the study area. Spider composition is influenced by environmental features such as habitat structure and climate, and also by spatial distances between patches. However, little is known about the roles of assembly processes in spider metacommunity structure in wetlands. 2. The beta diversity patterns of spider assemblages were assessed in 24 temporary wetlands distributed along a latitudinal gradient in southern Brazil. The study also assessed the individual correspondence of beta diversity (and its turnover and richness components) with dissimilarities in habitat structure and climate, as well as with geographic distances, using Mantel and partial Mantel correlation tests and multivariate correlograms. 3. Turnover was the most important component of spider beta diversity. Mantel tests detected significant correlations of spider beta diversity with habitat structure. Partial Mantel tests detected significant relationships only between spider beta diversity (and the richness component) and geographic distances. Additionally, spider composition was more similar than chance on smaller scales. 4. These results evidenced a complex interplay of assembly processes explaining spider metacommunity structure in temporary wetlands. Although species-sorting processes associated with habitat structure were important in structuring local spider composition, mass effects and dispersal limitation across climatic zones played an important role on a broader scale.     

Multiple Mantel tests and isolation-by-distance, taking into account long-term historical divergence

Mantel tests of matrix correspondence have been widely used in population genetics to examine microevolutionary processes, such as isolation-by-distance (IBD). We used partial and multiple Mantel tests to simultaneously test long-term historical effects and current divergence and equilibrium processes, such as IBD. We used these procedures to calculate genetic divergence among Eugenia dysenterica (Myrtaceae) populations in Central Brazil. The Nei's genetic distances between pairs of local populations were strongly correlated with geographic distances, suggesting an IBD process, but field observations and the geographic distribution of the samples suggest that populations may have been subjected to more complex evolutionary processes of genetic divergence. Partial Mantel regression was used to partition the effects of geographic structure and long-term divergence associated with a possible historical barrier. The R(2) of the model with both effects was 73.3%, and after the partition 21.9% of the variation in the genetic distances could be attributed to long-term historical divergence alone, whereas only 1.5% of the variation in genetic distances could be attributed to IBD. As expected, there was a large overlap between these processes when explaining genetic divergence, so it was not possible to entirely partition divergence between historical and contemporary processes.     

Hidden patterns of phylogenetic non‐stationarity overwhelm comparative analyses of niche conservatism and divergence

Aim Despite the importance of the niche concept in ecological and evolutionary theory, there are still many discussions about its definition and operational evaluation, especially when dealing with niche divergence and conservatism in an explicit phylogenetic context. Here we evaluate patterns of niche evolution in 67 New World Carnivora species, measured using Hellinger distances based on MAXENT models of species distribution. We show how inferences on niche conservatism or divergence depend on the way phylogenetic patterns are analysed using matrix comparison techniques. Innovation Initially we used the simplest approach of Mantel tests to compare Hellinger distances ( N ) derived from MAXENT and phylogenetic distances ( P ) among species. Then we extended the Mantel test to generate a multivariate correlogram, in which phylogenetic patterns are analysed at multiple levels in the phylogeny and can reveal nonlinearity in the relationship between divergence and time. Finally, we proposed a new approach to generate ‘local’ (or ‘specific’) leverages of components for Mantel correlation, evaluating the non‐stationarity in the relationship between N and P for each species. This new approach was used to show if some lineages are more prone to niche shift or conservatism than others. Main conclusions Standard Mantel tests indicated a poor correspondence between N and P matrices, discarding the idea of niche conservatism for Carnivora, but the correlogram supports that closely related species tend to be more similar than expected by chance. Moreover, the variance among Hellinger distances between pairs of closely phylogenetically related species is much larger than for the entire clade. Phylogenetic non‐stationarity analysis shows that in some Carnivora families the niche tends to divergence (Mustelidae and Canidae), whereas in others it tends to conservatism (Procyonidae and Mustelidae) at short phylogenetic distances. Our analyses clearly show that misleading results may appear if niche divergence is analysed only by simple matrix correlations not taking into account complex patterns of phylogenetic nonlinearity and non‐stationarity.     

The role of diet and temperature in shaping cranial diversification of South American human populations: an approach based on spatial regression and divergence rate tests

Aim Understanding the importance of ecological factors in the origin and maintenance of patterns of phenotypic variation among populations, in an explicit geographical context, is one of the main goals of human biology, ecology and evolutionary biology. Here we study the ecological factors responsible for craniofacial variation among human populations from South America. Location South America. Methods We studied a dataset of 718 males from 40 South American populations, coming from groups that inhabited different geographical and ecological regions. Cranial size and shape variation were studied using 30 cranial measurements. We first used spatial correlograms and interpolated maps to address spatial patterns. We then regressed the shape (principal component scores) and size variables against ecology (mean annual temperature and diet) using multiple and multivariate spatial regression. Finally, the expected magnitudes of shape and size divergence under the influence of genetic drift and mutations alone were evaluated using neutral expectation for the divergence rate. Results The spatial correlograms showed a cline affecting the entire South American distribution. Interpolated maps showed that size and allometric shape vary from south‐east to north‐west. Multiple and multivariate regression analyses suggested that diet has the largest and most significant effect on this pattern of size and allometric shape variation. Finally, the results of the divergence rate test suggested that random processes alone cannot account for the morphological divergence exhibited by cranial size and allometric shape scores among southernmost populations. Main conclusions Correlograms, spatial regression and divergence rate analyses showed that although local factors (neutral processes or local environmental conditions) are important to explain spatial interpopulation differentiation in cranial characteristics among these populations, there is significant correlation of cranial size and allometric shape variation with diet. Gene flow among human populations, or local environmental conditions, could explain spatial variation mainly at smaller spatial scales, whereas the large‐scale pattern of the South American dataset is mainly related to the high proportion of carbohydrates and low proportion of proteins consumed.     

Will the clinical development of 4th-generation “double mutant active” ALK TKIs (TPX-0131 and NVL-655) change the future treatment paradigm of ALK+ NSCLC?

Our current treatment paradigm of advanced anaplastic lymphoma kinase fusion (ALK+) non-small cell lung cancer (NSCLC) classifies the six currently approved ALK tyrosine kinase inhibitors (TKIs) into three generations. The 2nd-generation (2G) and 3rd-generation (3G) ALK TKIs are all “single mutant active” with varying potencies across a wide spectrum of acquired single ALK resistance mutations. There is a vigorous debate among clinicians which is the best upfront ALK TKI is for the first-line (1L) treatment of ALK+ NSCLC and the subsequent sequencing strategies whether it should be based on the presence of specific on-target ALK resistance mutations or not. Regardless, sequential use of “single mutant active” ALK TKIs will eventually lead to double ALK resistance mutations in cis. This has led to the creation of fourth generation (4G) “double mutant active” ALK TKIs such as TPX-0131 and NVL-655. We discuss the critical properties 4G ALK TKIs must possess to be clinically successful. We proposed conceptual first-line, second-line, and molecularly-based third-line registrational randomized clinical trials designed for these 4G ALK TKIs. How these 4G ALK TKIs would be used in the future will depend on which line of treatment the clinical trial design(s) is adopted provided the trial is positive. If approved, 4G ALK TKIs may usher in a new treatment paradigm for advanced ALK+ NSCLC that is based on classifying ALK TKIs based on the intrinsic functional capabilities (“singe mutant active” versus “double mutant active”) rather than the loosely-defined “generational” (first-, second-,third-,fourth-) classification and avoid the current clinical approaches of seemingly random sequential use of 2G and 3G ALK TKIs.     

Geographical patterns of turnover and nestedness-resultant components of allelic diversity among populations

The analysis of geographical patterns in population divergence has always been a powerful way to infer microevolutionary processes involved in population differentiation, and several approaches have been used to investigate such patterns. Most frequently, multivariate spatial patterns of population differentiation are analyzed by computing pairwise genetic distances or F_ST (or related statistics, such as ?_ST from AMOVA), which are then correlated with geographical distances or landscape features. However, when calculating distances, especially based on presence-absence of alleles in local populations, there would be a confounding effect of allelic richness differences in the population differentiation. Moreover, the relative magnitude of these components and their spatial patterns can help identifying microevolutionary processes driving population differentiation. Here we show how recent methodological advances in ecological community analyses that allows partitioning dissimilarity into turnover (turnover) and richness differences, or nestedness-resultant dissimilarity, can be applied to allelic variation data, using an endemic Cerrado tree (Dipteryx alata) as a case study. Individuals from 15 local populations were genotyped for eight microsatellite loci, and pairwise dissimilarities were computed based on presence-absence of alleles. The turnover of alleles among populations represented 69?% of variation in dissimilarity, but only the richness difference component shows a clear spatial structure, appearing as a westward decrease of allelic richness. We show that decoupling richness difference and turnover components of allelic variation reveals more clearly how similarity among populations reflects geographical patterns in allelic diversity that can be interpreted in respect to historical range expansion in the species.     

Effects of landscape and history on diversification of a montane, stream-breeding amphibian

Aim The aim of this study was to understand the roles of landscape features in shaping patterns of contemporary and historical genetic diversification among populations of the Andean tree frog (Hypsiboas andinus) across spatial scales. Location Andes mountains, north‐western Argentina, South America. Methods Mitochondrial DNA control region sequences were utilized to assess genetic differentiation among populations and calculate population pair‐wise genetic distances. Three models of movement, namely traditional straight‐line distance and two effective distances based on habitat classification, were examined to determine which of these explained the most variation in pair‐wise population genetic differentiation. The two habitat classifications were based on digital vegetation and hydrology layers that were generated from a 90‐m resolution digital elevation model (DEM) and known relationships between elevation and habitat. Mantel tests were conducted to test for correlations between geographic and genetic distance matrices and to estimate the percentage variation explained by each type of geographic distance. To investigate the location of possible barriers to gene flow, we used Monmonier’s maximum difference algorithm as implemented in barrier 2.2. Results At both geographic scales, effective distances explained more variation in genetic differentiation than did straight‐line distance. The least‐cost distances based on the simple classification performed better than the more detailed habitat classification. We controlled for the effects of historical range fragmentation determined from previous nested clade analyses, and therefore evaluated the effect of different distances on the genetic variation attributable to more recent factors. Effective distances identified populations that were highly divergent as a result of isolation in unsuitable habitats. The proposed locations of barriers to gene flow identified using Monmonier’s maximum difference algorithm corresponded well with earlier analyses and supported findings from our partial Mantel tests. Main conclusions Our results indicate that landscape features have been important in both historical and contemporary genetic structuring of populations of H. andinus at both large and small spatial scales. A landscape genetic perspective offers novel insights not provided by traditional phylogeographic studies: (1) effective distances can better explain patterns of differentiation in populations, especially in heterogeneous landscapes where barriers to dispersal may be common; and (2) least‐cost path analysis can help to identify corridors of movement between populations that are biologically more realistic.     

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.     

Genome-wide association to fine-scale ecological heterogeneity within a continuous population of Biscutella laevigata (Brassicaceae)

Gene flow, drift and selection can be detected through different signatures across the genome and the landscape. Genetic discontinuities along with their correlation to environmental features can be used to tease out isolation-by-distance and isolation-by-time from processes related to selection. Using spatial statistics (spatial autocorrelation methods, canonical correspondence analysis and partial Mantel tests) dealing with genome-wide amplified fragment length polymorphism (AFLP) under unlikely Hardy-Weinberg assumptions, this study investigates 124 individuals within a continuous population of the autopolyploid Biscutella laevigata (Brassicaceae). Fine-scale spatial genetic structure was strong and the mosaic-like distribution of AFLP genotypes was consistently associated with habitat factors, even when controlled for geographical distances. The use of multivariate analyses enabled separation of the factors responsible for the repartition of the genetic variance and revealed a composite effect of isolation by distance, phenological divergence and local adaptation to habitats characterised by different solar radiation regimes. These results suggest that the immigrant inviability barrier facilitated the maintenance of adapted subpopulations to distinct environmental conditions at the local scale.     

Geographic variation of flower traits in Narcissus papyraceus (Amaryllidaceae): do pollinators matter?

Aim The geographic clinal variation of traits in organisms can indicate the possible causes of phenotypic evolution. We studied the correlates of flower trait variation in populations of a style‐dimorphic plant, Narcissus papyraceus Ker‐Gawl., within a region of high biogeographical significance, the Strait of Gibraltar. This species shows a geographic gradient in the style‐morph ratio, suggested to be driven by pollinator shifts. We tested whether parallel geographic variation of perianth traits also exists, concomitant with vegetative trait variation or genetic similarity of plant populations. Location The Strait of Gibraltar region (SG hereafter, including both south‐western Iberian Peninsula and north‐western Morocco). Methods We used univariate and multivariate analyses of flower and vegetative traits in 23 populations. We applied Mantel tests and partial Mantel correlations on vegetative and flower traits and geographic locations of populations to test for spatial effects. We used Moran’s autocorrelation analyses to explore the spatial structure within the range, and performed the analyses with and without the Moroccan samples to test for the effects of the SG on spatial patterns. Amplified fragment length polymorphism data were used to estimate the genetic distance between populations and to ascertain its relationship with morphometric distance. Results There was high variation between and within populations in both flower and vegetative traits. Mantel correlations between geographic and morphometric distances were not significant, but the exclusion of Moroccan populations revealed some distance effect. Partial Mantel correlation did not detect a significant correlation between flower and vegetative morphometric distances after controlling for geographic distance. There were opposite trends in spatial autocorrelograms of flower and vegetative traits. The genetic distance between pairs of populations was directly correlated with geographic distance; however, flower morphometric and genetic distances were not significantly correlated. Main conclusions The SG had some influence on phenotypes, although the causes remain to be determined. The opposite trend of variation in flower and vegetative traits, and the lack of correlation between genetic distance and dissimilarity of flower phenotypes favour the hypothesis of pollinator‐mediated selection on flower morphology, although this may affect only particular traits and populations rather than overall phenotypes. Although stochastic population processes may have a small effect, other factors may account for the high flower variation within and between populations.     

Detecting clinal and balanced selection using spatial autocorrelation analysis under kin-structured migration

Recently spatial autocorrelation has been employed to infer microevolutionary processes from patterns of genetic variation. In theory, different processes should show characteristic signature correlograms; e. g., clinal selection should produce correlograms decreasing from positive to negative autocorrelation, whereas uniform balanced selection should lead to no spatial autocorrelation. The ability of a statistical method such as spatial autocorrelation analysis to distinguish between these selective regimes or even to detect departures from neutrality is dependent on the strength of the evolutionary force and the population structure. Weak selection or migration will not be apparent against the expected background of stochastic noise. Moreover, the population structure may generate sufficient stochastic variation such that even strong evolutionary forces may fail to be detected. This study uses computer simulation to examine the effects of kin-structured migration and three different selective regimes on the shape of spatial correlograms to assess the ability of this technique to detect different microevolutionary processes. Genetic variation among 8 loci is simulated in a linear set of 25 artificial populations. Kin-structured stepping-stone migration among adjacent populations is modeled; directional, balanced, and clinal selection, as well as neutral loci are considered. These experiments show that strong selection produces correlograms of the predicted shape. However, with an anthropologically reasonable population structure, considerable stochastic variation among correlograms for different alleles may still exist. This suggests the need for caution in inferring genetic process from spatial patterns. © 1994 Wiley-Liss, Inc.     

From Shelf to Shelf: Assessing Historical and Contemporary Genetic Differentiation and Connectivity across the Gulf of Mexico in Gag,Mycteroperca microlepis

Describing patterns of connectivity among populations of species with widespread distributions is particularly important in understanding the ecology and evolution of marine species. In this study, we examined patterns of population differentiation, migration, and historical population dynamics using microsatellite and mitochondrial loci to test whether populations of the epinephelid fish, Gag, Mycteroperca microlepis, an important fishery species, are genetically connected across the Gulf of Mexico and if so, whether that connectivity is attributable to either contemporary or historical processes. Populations of Gag on the Campeche Bank and the West Florida Shelf show significant, but low magnitude, differentiation. Time since divergence/expansion estimates associated with historical population dynamics indicate that any population or spatial expansions indicated by population genetics would have likely occurred in the late Pleistocene. Using coalescent-based approaches, we find that the best model for explaining observed spatial patterns of contemporary genetic variation is one of asymmetric gene flow, with movement from Campeche Bank to the West Florida Shelf. Both estimated migration rates and ecological data support the hypothesis that Gag populations throughout the Gulf of Mexico are connected via present day larval dispersal. Demonstrating this greatly expanded scale of connectivity for Gag highlights the influence of “ghost” populations (sensu Beerli) on genetic patterns and presents a critical consideration for both fisheries management and conservation of this and other species with similar genetic patterns.     

Spatial Dependency of Vegetation–Environment Linkages in an Anthropogenically Influenced Wetland Ecosystem

Management and restoration of vegetation patterns in ecosystems depends on an understanding of allogenic environmental factors that organize species assemblages and autogenic processes linked to assemblages. However, our ability to make strong inferences about vegetation–environment linkages in field studies is often limited due to correlations among environmental variables, spatial autocorrelation, and scale dependency of observations. This is particularly true in large, heterogeneous ecosystems such as the Everglades. Here, an extensive canal-and-levee system has modified historical fire regimes and hydropatterns while contributing large inputs of surface-water phosphorus (P), nitrogen (N) and cations such as sodium (Na). Some of these anthropogenic influences have been implicated as factors leading to the shift of sawgrass (Cladium jamaicense Crantz) and slough communities to an assemblage of weedy species such as cattail (Typha domingensis Pers.). To untangle the independent effect of multiple variables, we used a spatially explicit, multivariate approach to identify linkages among spatial patterns, environmental factors, and vegetation composition along a 10-km gradient of anthropogenic influence in the Everglades, an area immediately downstream from canal inflow structures. Clusters of plots were stratified among three zones (Impacted, Transition, and Reference), a design that allowed us to contrast vegetation–environment linkages and spatial patterns at multiple scales and degrees of ecosystem alteration. Along the 10-km gradient, partial Mantel tests showed that nutrients (phosphorus, nitrogen, and potassium) and hydropattern (frequency of dryness) were independently linked to patterns in fine-scale vegetation composition, but phosphorus was the only environmental variable linked to patterns of coarse-scale composition. Regardless of scale, the effect of distance from canal inflows accounted for variation in vegetation that could not be explained by other variables. A significant residual effect of spatial proximity among sampling locations also was detected and was highly suggestive of dispersal or other spatial determinants of vegetation pattern. However, this pure spatial effect was significantly stronger in the Transition and Impacted zones than in the Reference zone—fine-scale environmental variables explained all of the spatial structure in vegetation in the Reference zone. A further examination of spatial patterns in vegetation by using Mantel correlograms revealed significant heterogeneity at fine, local scales in the Reference zone, but this pattern progressively degraded toward homogeneity among closely neighboring locations in the Impacted zone. However, the fine-scale vegetation pattern in the Reference zone was hierarchically nested at a broader scale and yielded a similar coarse pattern across the landscape, whereas the coarse pattern in the Transition and Impacted zones was relatively heterogeneous and fragmented. Collectively, these results indicate that allogenic spatial and environmental factors related to the canal system have disrupted the coupling between pattern and process by altering fine-scale vegetation–environment linkages and spatial patterns characteristic of the natural Everglades ecosystem.     

Genetic structure, population size, and seed production of Pulsatilla vulgaris Mill. (Ranunculaceae) in Central Germany

Pulsatilla vulgaris Mill. (Ranunculaceae) is a rare and rapidly declining grassland community species that was once widespread at a time when Central Germany was covered by steppe vegetation. Through the course of this study, the patterns of random-amplified polymorphic DNA (RAPD) variation among 11 populations of varying size were analysed to assess any possible local differentiation, in relation to spatial isolation, resulting from random genetic drift brought on by reduced population size and lack of migration between geographically isolated populations. Following results attained from methods including: multivariate analysis based on asymmetric Soerensen similarity, φ_ST-statistics, and analysis of molecular variance, we were able to conclude that there is a high within-population variability (84.4%) and a weak, but significant, differentiation among populations (φ_ST=0.17). A matrix correlation between genetic and geographical distances revealed that geographical differentiation was reflected in the RAPD profile (Mantel test: r=0.47,p=0.002). Further significant correlations were noted between population size and both percentage of polymorphic loci (p=0.02) and genetic diversity (p=0.03). An additional analysis of seed production showed that mean seed set, seed number, and mean seed mass per population could be attributed to differences in population size, whereas only seed mass was related to genetic variation.     

Periodicity in spatial data and geostatistical models: autocorrelation between patches

Several recent studies in landscape ecology have found periodicity in correlograms or semi-variograms calculated, for instance, from spatial data of soils, forests, or animal populations. Some of the studies interpreted this as an indication of regular or periodic landscape patterns. This interpretation is in disagreement with other studies that doubt whether such analysis is valid. The objective of our study was to explore the relationship between periodicity in landscape patterns and geostatistical models. We were especially interested in the validity of the assumption that periodicity in geostatistical models indicates periodicity in landscape pattern, and whether the former can characterize frequency and magnitude of the latter. We created maps containing various periodic spatial patterns, derived correlograms from these, and examined periodicity in the correlograms. We also created non-regular maps that we suspected would cause periodicity in correlograms. Our results demonstrate that a) various periodic spatial patterns produce periodicity in correlograms derived from them, b) the distance-lags at which correlograms peak correspond to the average distances between patch centers, c) periodicity is strongest when the diameter of patches is equal to the distance between patch edges, d) periodicity in omni-directional correlograms of complex spatial patterns (such as checkerboards) are combinations of several waves because inter-patch distances differ with direction; multiple directional correlograms can decompose such complexity, and e) periodicity in correlograms can also be caused when the number of patches in a study site is small. These results highlight that correlograms can be used to detect and describe regular spatial patterns. However, it is crucial to ensure that the assumption of stationarity is not violated, i.e., that the study area contains a sufficiently large number of patches to avoid incorrect conclusions.