Can environmental constraints determine random patterns of plant species co-occurrence?

Plant community ecologists use the null model approach to infer assembly processes from observed patterns of species co‐occurrence. In about a third of published studies, the null hypothesis of random assembly cannot be rejected. When this occurs, plant ecologists interpret that the observed random pattern is not environmentally constrained – but probably generated by stochastic processes. The null model approach (using the C‐score and the discrepancy index) was used to test for random assembly under two simulation algorithms. Logistic regression, distance‐based redundancy analysis, and constrained ordination were used to test for environmental determinism (species segregation along environmental gradients or turnover and species aggregation). This article introduces an environmentally determined community of alpine hydrophytes that presents itself as randomly assembled. The pathway through which the random pattern arises in this community is suggested to be as follows: Two simultaneous environmental processes, one leading to species aggregation and the other leading to species segregation, concurrently generate the observed pattern, which results to be neither aggregated nor segregated – but random. A simulation study supports this suggestion. Although apparently simple, the null model approach seems to assume that a single ecological factor prevails or that if several factors decisively influence the community, then they all exert their influence in the same direction, generating either aggregation or segregation. As these assumptions are unlikely to hold in most cases and assembly processes cannot be inferred from random patterns, we would like to propose plant ecologists to investigate specifically the ecological processes responsible for observed random patterns, instead of trying to infer processes from patterns.     

Allometry of the baculum and sexual size dimorphism in American martens and fishers (Mammalia: Mustelidae)

Genitalia are among the most variable of morphological traits, and recent research suggests that this variability may be the result of sexual selection. For example, large bacula may undergo post‐copulatory selection by females as a signal of male size and age. This should lead to positive allometry in baculum size. In addition to hyperallometry, sexually selected traits that undergo strong directional selection should exhibit high phenotypic variation. Nonetheless, in species in which pre‐copulatory selection predominates over post‐copulatory selection (such as those with male‐biased sexual size dimorphism), baculum allometry may be isometric or exhibit negative allometry. We tested this hypothesis using data collected from two highly dimorphic species of the Mustelidae, the American marten (Martes americana) and the fisher (Martes pennanti). Allometric relationships were weak, with only 4.5–10.1% of the variation in baculum length explained by body length. Because of this weak relationship, there was a large discrepancy in slope estimates derived from ordinary least squares and reduced major axis regression models. We conclude that stabilizing selection rather than sexual selection is the evolutionary force shaping variation in baculum length because allometric slopes were less than one (using the ordinary least squares regression model), a very low proportion of variance in baculum length was explained by body length, and there was low phenotypic variability in baculum length relative to other traits. We hypothesize that this pattern occurs because post‐copulatory selection plays a smaller role than pre‐copulatory selection (manifested as male‐biased sexual size dimorphism). We suggest a broader analysis of baculum allometry and sexual size dimorphism in the Mustelidae, and other taxonomic groups, coupled with a comparative analysis and with phylogenetic contrasts to test our hypothesis. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 104 , 955–963.     

Comment on ‘Island biogeography: patterns of marine shallow‐water organisms’ by Hachich et al., Journal of Biogeography (2015)

In a recent article, Hachich et al. (2015, Journal of Biogeography, 42 , 1871–1882) studied the large‐scale biogeographical patterns of the species–area, species–island age and species–isolation relationships associated with marine shallow‐water groups (reef fish, gastropods and seaweeds) from 11 Atlantic archipelagos. We here express our concerns regarding the data accuracy used to compute the different models that tested the null hypothesis of species richness being independent of the selected variables. In our commentary, we focus mainly on the use of out‐of‐date checklists of gastropod and seaweed species from different archipelagos, but we also point out inaccuracies in some island age estimates and explain our disagreement with the use of the 200 m depth limit for the shallow‐water gastropods and seaweeds.     

Complexin2 null mutation requires a ‘second hit’ for induction of phenotypic changes relevant to schizophrenia

Schizophrenia is a devastating disease that affects approximately 1% of the population across cultures. Its neurobiological underpinnings are still unknown. Accordingly, animal models of schizophrenia often lack construct validity. As concordance rate in monozygotic twins amounts to only 50%, environmental risk factors (e.g. neurotrauma, drug abuse, psychotrauma) likely act as necessary ‘second hit' to trigger/drive the disease process in a genetically predisposed individual. Valid animal models would have to consider this genetic–environmental interaction. Based on this concept, we designed an experimental approach for modeling a schizophrenia‐like phenotype in mice. As dysfunction in synaptic transmission plays a key role in schizophrenia, and complexin2 (CPLX2) gene expression is reduced in hippocampus of schizophrenic patients, we developed a mouse model with Cplx2 null mutation as genetic risk factor and a mild parietal neurotrauma, applied during puberty, as environmental ‘second hit'. Several months after lesion, Cplx2 null mutants showed reduced pre‐pulse inhibition, deficit of spatial learning and loss of inhibition after MK‐801 challenge. These abnormalities were largely absent in lesioned wild‐type mice and non‐lesioned Cplx2 null mutants. Forced alternation in T‐maze, object recognition, social interaction and elevated plus maze tests were unaltered in all groups. The previously reported mild motor phenotype of Cplx2 null mutants was accentuated upon lesion. MRI volumetrical analysis showed a decrease of hippocampal volume exclusively in lesioned Cplx2 null mutants. These findings provide suggestive evidence for the ‘second hit' hypothesis of schizophrenia and may offer new tools for the development of advanced treatment strategies.     

Bayesian inferences on umbrella orderings

In regression applications with categorical predictors, interest often focuses on comparing the null hypothesis of homogeneity to an ordered alternative. This article proposes a Bayesian approach for addressing this problem in the setting of normal linear and probit regression models. The regression coefficients are assigned a conditionally conjugate prior density consisting of mixtures of point masses at 0 and truncated normal densities, with a (possibly unknown) changepoint parameter included to accommodate umbrella ordering. Two strategies of prior elicitation are considered: (1) a Bayesian Bonferroni approach in which the probability of the global null hypothesis is specified and local hypotheses are considered independent; and (2) an approach which treats these probabilities as random. A single Gibbs sampling chain can be used to obtain posterior probabilities for the different hypotheses and to estimate regression coefficients and predictive quantities either by model averaging or under the preferred hypothesis. The methods are applied to data from a carcinogenesis study.     

Using generalized autoregressive error models to understand fire–vegetation–soil feedbacks in a mulga–spinifex landscape mosaic

Aim To develop a new modelling approach for spatially autocorrelated non‐normal data, and apply it to a case study of the role that fire–vegetation–soil feedbacks play in maintaining boundaries between fire‐sensitive and fire‐promoted plant communities. Location A mulga (Acacia aneura) shrubland–spinifex (Triodia spp.) grassland mosaic, central Australia. Methods Autoregressive error models were extended to non‐normal data by incorporating neighbourhood values of the response and predictor variables into generalized nonlinear models. These models were used to examine the environmental correlates of three response variables: mulga cover; fire frequency in areas free of mulga; and the presence of mulga banding. Mulga cover and mulga banding were assessed visually by overlaying 4477 × 1 km² grid cells on both Landsat 7 ETM+ and very high resolution imagery. Fire frequency was estimated from an existing fire history for central Australia, based on remotely sensed fire scars. Results The autoregressive error models explained 27%, 47% and 57% of the null deviance of mulga cover, fire frequency and mulga banding, respectively, with 12%, 15% and 24% of the null deviance being explained by environmental variables alone. These models accounted for virtually all residual spatial autocorrelation. While there was a clear negative relationship between mulga cover and fire frequency, there was little evidence that mulga was being restricted to parts of the landscape with inherently low fire frequencies. Mulga was most abundant at very low slope angles and on red earths, both of which are likely to reflect high site productivity, while fire frequency was not clearly affected by slope angle and was also relatively high on red earths. Main conclusions The modelling approach we have developed provides a much needed way of analysing spatially autocorrelated non‐normal data and can be easily incorporated into an information‐theoretic modelling framework. Using this approach, we provide evidence that mulga and spinifex have a highly antagonistic relationship. In more productive parts of the landscape, mulga suppresses spinifex and fire, while in less productive parts of the landscape, fire and spinifex suppress mulga, leading to the remarkable abruptness of mulga–spinifex boundaries that are maintained via fire–vegetation–soil feedbacks.     

Overgrowth of a mouse model of Simpson– Golabi–Behmel syndrome is partly mediated by Indian Hedgehog

Loss‐of‐function mutations of Glypican 3 (Gpc3) cause the Simpson–Golabi–Behmel overgrowth syndrome (SGBS), and developmental overgrowth is observed in Gpc3‐null mice, a mouse model for SGBS. We recently reported that GPC3 inhibits Hedgehog (Hh) signalling by inducing its endocytosis and degradation. Here, we show that the developmental overgrowth observed in Gpc3‐null mice is, at least in part, a consequence of the hyperactivation of the Hh pathway. We bred Gpc3‐null mice with mice that are Hh signalling‐deficient owing to the lack of Indian Hh (Ihh), one of the three mammalian Hhs. We found that the Gpc3‐null mice showed a 29.9% overgrowth in an Ihh wild‐type background, whereas an Ihh‐null background partly rescues the overgrowth caused by the lack of Gpc3 as the double mutants were 19.8% bigger than the Ihh‐null mice. Consistent with the role of GPC3 in Hh endocytosis and degradation, the Gpc3‐null mice show increased levels of Ihh protein and signalling, but similar levels of Ihh messenger RNA.     

The Wald Statistic in Proportional Hazards Hypothesis Testing

In survivorship modelling using the proportional hazards model of Cox (1972, Journal of the Royal Statistical Society, Series B, 34, 187–220), it is often desired to test a subset of the vector of unknown regression parameters β in the expression for the hazard rate at time t. The likelihood ratio test statistic is well behaved in most situations but may be expensive to calculate. The Wald (1943, Transactions of the American Mathematical Society 54, 426–482) test statistic is easier to calculate, but has some drawbacks. In testing a single parameter in a binomial logit model, Hauck and Donner (1977, Journal of the American Statistical Association 72, 851–853) show that the Wald statistic decreases to zero the further the parameter estimate is from the null and that the asymptotic power of the test decreases to the significance level. The Wald statistic is extensively used in statistical software packages for survivorship modelling and it is therefore important to understand its behavior. The present work examines empirically the behavior of the Wald statistic under various departures from the null hypothesis and under the presence of Type I censoring and covariates in the model. It is shown via examples that the Wald statistic's behavior is not as aberrant as found for the logistic model. For the single parameter case, the asymptotic non-null distribution of the Wald statistic is examined.     

Robust methods for detecting a small island effect

Aim The small island effect (SIE), i.e. the hypothesis that species richness below a certain threshold area varies independently of island size, has become a widely accepted part of the theory of island biogeography. However, there are doubts whether the findings of SIEs were based on appropriate methods. The aim of this study was thus to provide a statistically sound methodology for the detection of SIEs and to show this by re‐analysing data in which an SIE has recently been claimed ( Sfenthourakis & Triantis, 2009 , Diversity and Distributions, 15 , 131–140). Location Ninety islands of the Aegean Sea (Greece). Methods First, I reviewed publications on SIEs and evaluated their methodology. Then, I fitted different species–area models to the published data of area (A) and species richness (S) of terrestrial isopods (Oniscidea), with log A as predictor and both S (logarithm function) and log S (power function) as response variables: (i) linear; (ii) quadratic; (iii) cubic; (iv) breakpoint with zero slope to the left (SIE model); (v) breakpoint with zero slope to the right; (vi) two‐slope model. I used non‐linear regression with R²_adj., AIC_c and BIC as goodness‐of‐fit measures. Results Many different methods have been applied for detecting SIEs, all of them with serious shortcomings. Contrary to the claim of the original study, no SIE occurs in this particular dataset as the two‐slope variants performed better than the SIE variants for both the logarithm and power functions. Main conclusions For the unambiguous detection of SIEs, one needs to (i) include islands with no species; (ii) compare all relevant models; and (iii) account for different model complexities. As none of the reviewed SIE studies met all these criteria, their findings are dubious and SIEs may be less common than reported. Thus, conservation‐related predictions based on the assumption of SIEs may be unreliable.     

Exact Multiple Comparisons of Three or More Regression Lines: Pairwise Comparisons and Comparisons with a Control

The problem of finding exact simultaneous confidence bounds for differences in regression models for k groups via the union‐intersection method is considered. The error terms are taken to be iid normal random variables. Under an assumption slightly more general than having identical design matrices for each of the k groups, it is shown that an existing probability point for the multivariate studentized range can be used to find the necessary probability point for pairwise comparisons of regression models. The resulting methods can be used with simple or multiple regression. Under a weaker assumption on the k design matrices that allows more observations to be taken from the control group than from the k‐1 treatment groups, a method is developed for computing exact probability points for comparing the simple linear regression models of the k‐1 groups to that of the control. Within a class of designs, the optimal design for comparisons with a control takes the square root of (k‐1) times as many observations from the control than from each treatment group. The simultaneous confidence bounds for all pairwise differences and for comparisons with a control are much narrower than Spurrier's intervals for all contrasts of k regression lines.     

Generation of conditional null alleles for APP and APLP2

Proteolytical cleavage of the β‐amyloid precursor protein (APP) generates β‐amyloid, which is deposited in the brains of patients suffering from Alzheimer's disease (AD). Despite the well‐established key role of APP for AD pathogenesis, the physiological function of APP and its close homologues APLP1 and APLP2 remains poorly understood. Previously, we generated APP^–/– mice that proved viable, whereas APP^–/–APLP2^–/– mice and triple knockouts died shortly after birth, likely due to deficits of neuromuscular synaptic transmission. Here, we generated conditional knockout alleles for both APP and APLP2 in which the promoter and exon1 were flanked by loxP sites. No differences in expression were detectable between wt and floxed alleles, whereas null alleles were obtained upon crossing with Cre‐transgenic deleter mice. These mice will now allow for tissue and time‐point controlled knockout of both genes. genesis 48:200–206, 2010. © 2010 Wiley‐Liss, Inc.     

Multiple Imputation Approaches for the Analysis of Dichotomized Responses in Longitudinal Studies with Missing Data

Summary Often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific time point according to a prespecified threshold value. In the event that the underlying continuous measurements are from a longitudinal study, one can use the repeated‐measures model to impute missing data on responder status as a result of subject dropout and apply the logistic regression model on the observed or otherwise imputed responder status. Standard Bayesian multiple imputation techniques ( Rubin, 1987 , in Multiple Imputation for Nonresponse in Surveys) that draw the parameters for the imputation model from the posterior distribution and construct the variance of parameter estimates for the analysis model as a combination of within‐ and between‐imputation variances are found to be conservative. The frequentist multiple imputation approach that fixes the parameters for the imputation model at the maximum likelihood estimates and construct the variance of parameter estimates for the analysis model using the results of Robins and Wang (2000, Biometrika 87, 113–124) is shown to be more efficient. We propose to apply ( Kenward and Roger, 1997 , Biometrics 53, 983–997) degrees of freedom to account for the uncertainty associated with variance–covariance parameter estimates for the repeated measures model.     

Fire disturbance disrupts co‐occurrence patterns of terrestrial vertebrates in Mediterranean woodlands

Aim This paper uses null model analysis to explore the pattern of species co‐occurrence of terrestrial vertebrate fauna in fire‐prone, mixed evergreen oak woodlands. Location The Erico–Quercion ilicis of the Mediterranean belt (50–800 m a.s.l.) in the Madonie mountain range, a regional park in northern Sicily (37°50′ N, 14°05′ E), Italy. Methods The stratified sampling of vertebrates in a secondary succession of recent burned areas (BA, 1–2 years old), intermediate burned areas (INT, 4–10 years old) and ancient burned areas (CNB, > 50 years old), plus forest fragments left within burned areas (FF, 1–2 years old) permitted the comparison of patterns of species co‐occurrence using a set of separate presence/absence matrices. First, the breeding avifauna derived from standardized point counts was analysed using Stone & Roberts’C‐score, and by a null model algorithm (fixed/equiprobable). Secondly, the analysis was repeated using all vertebrate species recorded in the succession. Results Sixty‐five species were recorded in the 2‐year study period in the four sample treatments. Birds were found to make up the largest component (63%) of the recorded assemblage. The BA treatment had the lowest species richness, followed in order by the small, medium and large FFs, and then by the CNBs. For both analyses (birds and total vertebrates), the C‐scores were quite small and not significantly different from those that could be expected by chance in the BA and INT burned areas; this indicates a random co‐occurrence among vertebrates of those assemblages. Contrariwise, for both analyses in the CNBs, the C‐scores were large and significantly different from the simulated indices, thereby indicating a non‐random co‐occurrence pattern (segregation) of vertebrates in the undisturbed woodlands. In addition, C‐score values for the surviving FFs show a significant aggregation of species. Main conclusions The null model analyses highlighted a new aspect of fire disturbance in Mediterranean woodland ecosystems: the disruption in patterns of co‐occurrence in the terrestrial vertebrate community. Wildfire alters community organization, inducing, for at least 10 years, a random aggregate of species. Communities re‐assemble themselves, showing the occurrence of species segregation at least 50 years after fire.     

Testimation in Regression Parameter Estimation

Testimation is considered in the problem of estimation of regression parameters. The first stage sample is used to test a (null) hypothesis that specifies initial (preassumed) values for some of the regression parameters. Linear combination of the preassumed values and the ordinary least square (OLS) estimates is considered as the estimate if the data agree with the hypothesis. Otherwise, a second sample is taken and parameters are estimated only by using OLS, based on the combined sample. The procedure protects against type II error and against taking larger samples when inference can be made from a smaller sample.     

The Impact of Exposure Misclassification on Associations Between Prepregnancy BMI and Adverse Pregnancy Outcomes

Prepregnancy BMI is a widely used marker of maternal nutritional status that relies on maternal self‐report of prepregnancy weight and height. Pregravid BMI has been associated with adverse health outcomes for the mother and infant, but the impact of BMI misclassification on measures of effect has not been quantified. The authors applied published probabilistic bias analysis methods to quantify the impact of exposure misclassification bias on well‐established associations between self‐reported prepregnancy BMI category and five pregnancy outcomes (small for gestational age (SGA) and large for gestational age (LGA) birth, spontaneous preterm birth (sPTB), gestational diabetes mellitus (GDM), and preeclampsia) derived from a hospital‐based delivery database in Pittsburgh, PA (2003–2005; n = 18,362). The bias analysis method recreates the data that would have been observed had BMI been correctly classified, assuming given classification parameters. The point estimates derived from the bias analysis account for random error as well as systematic error caused by exposure misclassification bias and additional uncertainty contributed by classification errors. In conventional multivariable logistic regression models, underweight women were at increased risk of SGA and sPTB, and reduced risk of LGA, whereas overweight, obese, and severely obese women had elevated risks of LGA, GDM, and preeclampsia compared with normal‐weight women. After applying the probabilistic bias analysis method, adjusted point estimates were attenuated, indicating the conventional estimates were biased away from the null. However, the majority of relations remained readily apparent. This analysis suggests that in this population, associations between self‐reported prepregnancy BMI and pregnancy outcomes are slightly overestimated.     

Long‐distance call evolution in the Felidae: effects of body weight,habitat, and phylogeny

Long‐distance calls used for mate attraction and territorial spacing are distinctive signals in the felid vocal repertoire. Their evolution is subject to natural and sexual selection, as well as various constraints. Body size is an important morphological constraint, with the scaling of the spectral characteristics of a species' vocalizations with its body size being established for several vertebrate groups. Alternatively, the structure of long‐distance calls may have been optimized for transmission in species' habitats (acoustic adaptation hypothesis). The present study assessed whether the mean dominant frequency of long‐distance calls in the Felidae (approximately 70% of all species incorporated) is influenced by the species' body size and/or conforms to the acoustic adaptation hypothesis. After controlling for phylogenetic relationships, we found a significant correlation between mean dominant frequency of a taxon's long‐distance calls and conditions for sound transmission in its habitat type (‘open/heterogeneous’ versus ‘dense’), although no significant influence of body size. Taxa living in more open habitat types have long‐distance calls with significantly lower mean dominant frequencies than those living in dense habitats. The result obtained in the present analysis is fairly robust against random removal of single or few taxa from the data, and also against the use of different branch‐length transformation models in phylogenetic regression. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 487–500.     

Exploring the information in p-values for the analysis and planning of multiple-test experiments

Summary A new methodology is proposed for estimating the proportion of true null hypotheses in a large collection of tests. Each test concerns a single parameter δ whose value is specified by the null hypothesis. We combine a parametric model for the conditional cumulative distribution function (CDF) of the p‐value given δ with a nonparametric spline model for the density g(δ) of δ under the alternative hypothesis. The proportion of true null hypotheses and the coefficients in the spline model are estimated by penalized least squares subject to constraints that guarantee that the spline is a density. The estimator is computed efficiently using quadratic programming. Our methodology produces an estimate of the density of δ when the null is false and can address such questions as “when the null is false, is the parameter usually close to the null or far away?” This leads us to define a falsely interesting discovery rate (FIDR), a generalization of the false discovery rate. We contrast the FIDR approach to Efron's (2004, Journal of the American Statistical Association 99, 96–104) empirical null hypothesis technique. We discuss the use of in sample size calculations based on the expected discovery rate (EDR). Our recommended estimator of the proportion of true nulls has less bias compared to estimators based upon the marginal density of the p‐values at 1. In a simulation study, we compare our estimators to the convex, decreasing estimator of Langaas, Lindqvist, and Ferkingstad (2005, Journal of the Royal Statistical Society, Series B 67, 555–572). The most biased of our estimators is very similar in performance to the convex, decreasing estimator. As an illustration, we analyze differences in gene expression between resistant and susceptible strains of barley.     

The immediate and long‐term effects of water drawdown on macrophyte assemblages in a large subtropical reservoir

1. Disturbances play a central role in determining the spatial and temporal dynamics of many plant communities. In our study of macrophyte assemblages at 150 sites in five arms of a large subtropical reservoir (Itaipu Reservoir, Brazil–Paraguay border), we used co‐occurrence null models and spatiotemporal analyses to describe the patterns in the assemblages during a historically large water drawdown in 2000, in comparison with the previous year (1999) and subsequent years (2001–07). A C‐Score co‐occurrence index tested the null hypothesis of random structure during the drawdown period. A detrended correspondence analysis and multiresponse permutation procedure were used to verify whether species composition differed before, during and after the disturbance. 2. In contrast to our expectations, the null models showed that the macrophyte assemblages were spatially structured during the drawdown (2000), although species composition was significantly different from the previous year (1999) and also changed in the following years (2001–07). Significant species co‐occurrence patterns were generated by the drawdown disturbance, with species extinctions and colonisation by new species from propagules and seed bank germination. 3. The randomness we expected in 2000 actually occurred in 2001, probably because the reestablishment of normal water level enabled both submersed and free‐floating species to recolonise the shore that emergent species had inhabited since the drawdown. Biotic interactions appeared to increase during the years after the disturbance and the habitat preferences of the aquatic macrophytes were re‐established, resulting in higher similarities in aquatic macrophyte species composition in the years after the drawdown.     

A Test for Homogeneity of Odds Ratios in Ordered 2 × 2 Tables

Consider K ordered 2 × 2 contingency tables. A new test of the null hypothesis that the odds ratios of these tables are equal vs the alternative hypothesis that the odds ratios are nondecreasing, is recommended. The test is exact (non‐asymptotic), is easily carried out (software is available), and has other favorable properties. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using between-model comparisons to fine-tune linear models of species ranges

Aim To offer an objective approach to some of the problems associated with the development of logistic regression models: how to compare different models, determination of sample size adequacy, the influence of the ratio of positive to negative cells on model accuracy, and the appropriate scale at which the hypothesis of a non‐random distribution should be tested. Location Test data were taken from Southern Africa. Methods The approach relies mainly on the use of the AUC (Area under the Curve) statistic, based on ROC (threshold Receiver Operating Characteristic) plots, for between‐model comparisons. Data for the distribution of the bont tick Amblyomma hebraeum Koch (Acari: Ixodidae) are used to illustrate the methods. Results Methods for the estimation of minimum sample sizes and more accurate hypothesis‐testing are outlined. Logistic regression is robust to the assumption that uncollected cells can be scored as negative, provided that the sample size of cells scored as positive is adequate. The variation in temperature and rainfall at localities where A. hebraeum has been collected is significantly lower than expected from a random sample of points across the data set, suggesting that within‐site variation may be an important determinant of its distribution. Main conclusions Between‐model comparisons relying on AUCs can be used to enhance objectivity in the development and refinement of logistic regression models. Both between‐site and within‐site variability should be considered as potentially important factors determining species distributions.