Summary 1.In recent years the use of species distribution models by ecologists and conservation managers has increased considerably, along with an awareness of the need to provide accuracy assessment for predictions of such models. The kappa statistic is the most widely used measure for the performance of models generating presence-absence predictions, but several studies have criticized it for being inherently dependent on prevalence, and argued that this dependency introduces statistical artefacts to estimates of predictive accuracy. This criticism has been supported recently by computer simulations showing that kappa responds to the prevalence of the modelled species in a unimodal fashion. 2. In this paper we provide a theoretical explanation for the observed dependence of kappa on prevalence, and introduce into ecology an alternative measure of accuracy, the true skill statistic (TSS), which corrects for this dependence while still keeping all the advantages of kappa. We also compare the responses of kappa and TSS to prevalence using empirical data, by modelling distribution patterns of 128 species of woody plant in Israel.3. The theoretical analysis shows that kappa responds in a unimodal fashion to variation in prevalence and that the level of prevalence that maximizes kappa depends on the ratio between sensitivity (the proportion of correctly predicted presences) and specificity (the proportion of correctly predicted absences). In contrast, TSS is independent of prevalence. 4. When the two measures of accuracy were compared using empirical data, kappa showed a unimodal response to prevalence, in agreement with the theoretical analysis. TSS showed a decreasing linear response to prevalence, a result we interpret as reflecting true ecological phenomena rather than a statistical artefact. This interpretation is supported by the fact that a similar pattern was found for the area under the ROC curve, a measure known to be independent of prevalence. 5. Synthesis and applications . Our results provide theoretical and empirical evidence that kappa, one of the most widely used measures of model performance in ecology, has serious limitations that make it unsuitable for such applications. The alternative we suggest, TSS, compensates for the shortcomings of kappa while keeping all of its advantages. We therefore recommend the TSS as a simple and intuitive measure for the performance of species distribution models when predictions are expressed as presenceabsence maps.

Movement of individual organisms is fundamental to life, quilting our planet in a rich tapestry of phenomena with diverse implications for ecosystems and humans. Movement research is both plentiful and insightful, and recent methodological advances facilitate obtaining a detailed view of individual movement. Yet, we lack a general unifying paradigm, derived from first principles, which can place movement studies within a common context and advance the development of a mature scientific discipline. This introductory article to the Movement Ecology Special Feature proposes a paradigm that integrates conceptual, theoretical, methodological, and empirical frameworks for studying movement of all organisms, from microbes to trees to elephants. We introduce a conceptual framework depicting the interplay among four basic mechanistic components of organismal movement: the internal state (why move?), motion (how to move?), and navigation (when and where to move?) capacities of the individual and the external factors affecting movement. We demonstrate how the proposed framework aids the study of various taxa and movement types; promotes the formulation of hypotheses about movement; and complements existing biomechanical, cognitive, random, and optimality paradigms of movement. The proposed framework integrates eclectic research on movement into a structured paradigm and aims at providing a basis for hypothesis generation and a vehicle facilitating the understanding of the causes, mechanisms, and spatiotemporal patterns of movement and their role in various ecological and evolutionary processes.''Now we must consider in general the common reason for moving with any movement whatever.'' (Aristotle, De Motu Animalium, 4th century B.C.) motion capacity ͉ navigation capacity ͉ migration ͉ dispersal ͉ foraging

Sampling bias is a common phenomenon in records of plant and animal distribution. Yet, models based on such records usually ignore the potential implications of bias in data collection on the accuracy of model predictions. This study was designed to investigate the effect of roadside bias, one of the most common sources of bias in biodiversity databases, on the accuracy of predictive maps produced by bioclimatic models. Using data on the distribution of 129 species of woody plants in Israel, we tested the following hypotheses: (1) that data collected on woody plant distribution in Israel suffer from roadside bias, (2) that such bias affects the accuracy of model predictions, (3) that the road network of Israel is biased with respect to climatic conditions, and (4) that the impact of roadside bias on model predictions depends on the magnitude of climatic bias in the geographic distribution of the road network.As expected, the frequency of plant observations near roads was consistently greater than that expected from a spatially random distribution. This bias was most pronounced at distances of 500-2000 m from roads, but it was statistically significant also at larger scales. Predictive maps based on near-road observations were less accurate than those based on off-road or ''rectified'' observations (observations corrected for roadside bias). However, the magnitude of these differences was extremely low, indicating that even a strong bias in the distribution of species observations does not necessarily deteriorate the accuracy of predictive maps generated by bioclimatic models. Further analysis of the data indicated that the road network of Israel is relatively unbiased in terms of temperature, and only weakly biased in terms of rainfall conditions. The overall results are consistent with the hypothesis that the impact of roadside bias on model predictions depends on the magnitude of climatic bias in the geographic distribution of the road network. We discuss some theoretical and practical considerations of bias correction in biodiversity databases.

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In spite of increasing application of presence-only models in ecology and conservation and the growing number of such models, little is known about the relative performance of different modelling methods, and some of the leading models (e.g. GARP and ENFA) have never been compared with one another. Here we compare the performance of six presence-only models that have been selected to represent an increasing level of model complexity [BIOCLIM, HABITAT, Mahalanobis distance (MD), DOMAIN, ENFA, and GARP] using data on the distribution of 42 species of land snails, nesting birds, and insectivorous bats in Israel. The models were calibrated using data from museum collections and observation databases, and their predictions were evaluated using Cohen's Kappa based on field data collected in a standardized sampling design covering most parts of Israel. Predictive accuracy varied between modelling methods with GARP and MD showing the highest accuracy, BIOCLIM and ENFA showing the lowest accuracy, and HABITAT and DOMAIN showing intermediate accuracy levels. Yet, differences between the various models were relatively small except for GARP and MD that were significantly more accurate than BIOCLIM and ENFA. In spite of large differences among species in prevalence and niche width, neither prevalence nor niche width interacted with the modelling method in determining predictive accuracy. However, species with relatively narrow niches were modelled more accurately than species with wider niches. Differences among species in predictive accuracy were highly consistent over all modelling methods, indicating the need for a better understanding of the ecological and geographical factors that influence the performance of species distribution models.

For more than 50 y ecologists have believed that spatial heterogeneity in habitat conditions promotes species richness by increasing opportunities for niche partitioning. However, a recent stochastic model combining the main elements of niche theory and island biogeography theory suggests that environmental heterogeneity has a general unimodal rather than a positive effect on species richness. This result was explained by an inherent tradeoff between environmental heterogeneity and the amount of suitable area available for individual species: for a given area, as heterogeneity increases, the amount of effective area available for individual species decreases, thereby reducing population sizes and increasing the likelihood of stochastic extinctions. Here we provide a comprehensive evaluation of this hypothesis. First we analyze an extensive database of breeding bird distribution in Catalonia and show that patterns of species richness, species abundance, and extinction rates are consistent with the predictions of the area-heterogeneity tradeoff and its proposed mechanisms. We then perform a metaanalysis of heterogeneity-diversity relationships in 54 published datasets and show that empirical data better fit the unimodal pattern predicted by the area-heterogeneity tradeoff than the positive pattern predicted by classic niche theory. Simulations in which species may have variable niche widths along a continuous environmental gradient are consistent with all empirical findings. The area-heterogeneity tradeoff brings a unique perspective to current theories of species diversity and has important implications for biodiversity conservation.habitat heterogeneity | neutral theory | stochastic model of community dynamics | conservation planning

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Effective application of species distribution models requires some knowledge concerning the accuracy of model predictions. Yet very few studies have attempted to systematically analyze factors affecting the predictive power of distribution models. This study fills this gap for Climatic Envelope Models, which have been applied extensively for a variety of conservation and management purposes. We hypothesized that model predictions are influenced by properties of the data (both quantity and quality) and distribution properties of the modeled species. Hypotheses concerning the effects of both types of factors were tested by analyzing distribution patterns of 192 species of woody plants in Israel. Analyses were based on Monte Carlo simulations and standard statistical tests. The total number of observations had a strong positive effect on model performance; but on average, 50-75 observations were sufficient to obtain the maximal accuracy. Climatic bias (the degree of sampling bias with respect to climatic conditions) had a significant negative effect on predictive accuracy. Climatic completeness (the degree to which the climatic range occupied by the species is covered by the observations) had a negative effect on model performance-a result contradicting our original hypothesis. Among the species properties, commonness had a positive effect while niche width had a negative one. Niche position with respect to rainfall and temperature was also important in determining the accuracy of model predictions. The overall results are discussed with respect to trade-offs between commission and omission errors and the potential implications of scale dependency.