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Aim Although species-occupancy distributions (SODs) and species-area relationships (SARs) arise from the two marginal sums of the same presence/absence matrices, the two biodiversity patterns are usually explored independently. Here, we aim to unify the two patterns for isolate-based data by constraining the SAR to conserve information from the SOD. Location Widespread. Methods Focusing on the power-model SAR, we first developed a constrained form that conserved the total number of occupancies from the SOD. Next, we developed an additive-constrained SAR that conserves the entire shape of the SOD within the power-model SAR function, using a single parameter (the slope of the endemics-area relationship). We then relate this additive-constrained SAR to multiple-sites similarity measures, based on a probabilistic view of Sorensen similarity. We extend the constrained and additive-constrained SAR framework to 23 published SAR functions. We compare the fit of the original and constrained forms of 12 SAR functions using 154 published data sets, covering various spatial scales, taxa and systems. Main conclusions In all 23 SAR functions, the constrained form had one parameter less than the original form. In all 154 data sets the model with the highest weight based on the corrected Akaike's information criteria (wAICc) had a constrained form. The constrained form received higher wAICc than the original form in 98.79% of valid pairwise cases, approaching the wAICc expected under identical log-likelihood. Our work suggests, both theoretically and empirically, that all SAR functions may have one unnecessary parameter, which can be excluded from the function without reduction in goodness-of-fit. The more parsimonious constrained forms are also easier to interpret as they reflect the probability of a randomly chosen occupancy to be found in an isolate. The additive-constrained SARs accounts for two complimentary turn-over components of occupancies: turnover between species and turnover between sites.

AimPatterns that relate species richness with fragment area (the species–area relationship, SAR) and with isolation (the species–isolation relationship, SIR) are well documented. However, those that relate species density – the number of species within a standardized area – with fragment area (D-SAR) or isolation (D-SIR) have not been sufficiently explored, despite the potential for such an analysis to disentangle the underlying mechanisms of SARs and SIRs. Previous spatial theory predicts that a significant D-SAR or D-SIR is unlikely to emerge in taxa with high dispersal limitation, such as plants. Furthermore, a recent model predicts that the detection and the significance of D-SARs or D-SIRs may decrease with grain size. We combined a literature review with grain size-dependent sampling in a fragmented landscape to evaluate the prevalence and grain size-dependent nature of D-SARs and D-SIRs in plants.LocationWorldwide (review) and a semi-arid agro-ecosystem in Israel (case study).MethodsWe combined an extensive literature review of 31 D-SAR studies of plants in fragmented landscapes with an empirical study in which we analysed grain size-dependent D-SARs and D-SIRs using a grain size-dependent hierarchical sampling of species density and species richness in a fragmented, semi-arid agro-ecosystem.ResultsWe found that significantly increasing D-SARs are rare in plant studies. Furthermore, we found that the detection of a significant D-SAR is often possible only after the data have been stratified by species, habitat or landscape characteristics. The results from our case study indicated that the significance and the slopes of both D-SARs and D-SIRs increase as grain size decreases.Main conclusionsThese results call for a careful consideration of scale while analysing and interpreting the responses of species richness and species density to fragmentation. Our results suggest that grain size-dependent analyses of D-SARs and D-SIRs may help to disentangle the mechanisms that generate SARs and SIRs and may enable early detection of the effects of fragmentation on plant biodiversity.

Habitat loss reduces species diversity, but the effect of habitat fragmentation on number of species is less clear because fragmentation generally accompanies loss of habitat. We compared four methods that aim to decouple the effects of fragmentation from the effects of habitat loss. Two methods are based on species-area relations, one on Fisher's alpha index of diversity, and one on plots of cumulative number of species detected against cumulative area sampled. We used these methods to analyze the species diversity of spiders in 2, 3.2 × 4 km agricultural landscapes in Southern Judea Lowlands, Israel. Spider diversity increased as fragmentation increased with all four methods, probably not because of the additive within-patch processes, such as edge effect and heterogeneity. The positive relation between fragmentation and species diversity might reflect that most species can disperse through the fields during the wheat-growing season. We suggest that if a given area was designated for the conservation of spiders in Southern Judea Lowlands, Israel, a set of several small patches may maximize species diversity over time. Resumen: La perdida de habitat reduce la diversidad de especies, pero el efecto de la fragmentacion del habitat sobre muchas especies es menos claro porque la fragmentacion generalmente es acompanada por la perdida de habitat. Comparamos cuatro metodos que tratan de separar los efectos de la fragmentacion sobre los efectos de la perdida de habitat. Dos metodos se basan en las relaciones especies-area, uno en el indice de diversidad alfa de Fisher, y uno en graficos del numero acumulativo de especies detectadas versus el area muestreada acumulada. Utilizamos estos metodos para analizar la diversidad de aranas en 2 paisajes agricolas de 3.2 × 4 km en las Tierras Bajas de Judea del Sur, Israel. La diversidad de aranas incremento a medida que incremento la fragmentacion con los cuatro metodos, probablemente no debido a los procesos aditivos intra-parche, como el efecto de borde y la heterogeneidad. La relacion positiva entre la fragmentacion y la diversidad de especies puede ser reflejo de que la mayoria de las especies se pueden dispersar en los campos durante la epoca de siembra de trigo. Sugerimos que si un area determinada fuera designada para la conservacion de aranas en las Tierras Bajas de Judea del Sur, Israel, un conjunto de parches muy pequenos puede maximizar la diversidad de especies en el tiempo.

Aims: (1) Understanding how the relationship between species richness and its determinants depends on the interaction between scales at which the response and explanatory variables are measured. (2) Quantifying the relative contributions of local, intermediate and large-scale determinants of species richness in a fragmented agro-ecosystem. (3) Testing the hypothesis that the relative contribution of these determinants varies with the grain size at which species richness is measured. Location: A fragmented agro-ecosystem in the Southern Judea Lowland, Israel, within a desert–Mediterranean transition zone. Methods: Plant species richness was estimated using hierarchical nested sampling in 81 plots, positioned in 38 natural vegetation patches within an agricultural matrix (mainly wheat fields) among three land units along a sharp precipitation gradient. Explanatory variables included position along that gradient, patch area, patch isolation, habitat heterogeneity and overall plant density. We used general linear models and hierarchical partitioning of variance to test and quantify the effect of each explanatory variable on species richness at four grain sizes (0.0625, 1, 25 and 225 m2). Results: Species richness was mainly affected by position along a precipitation gradient and overall plant density, and to a lesser extent by habitat heterogeneity. It was also significantly affected by patch area and patch isolation, but only for small grain sizes. The contribution of each explanatory variable to explained variance in species richness varied with grain size, i.e. scale-dependent. The influence of geographic position and habitat heterogeneity on species richness increased with grain size, while the influence of plant density decreased with grain size. Main conclusions: Species richness is determined by the combined effect of several scale-dependent determinants. Ability to detect an effect and effect size of each determinant varies with the scale (grain size) at which it is measured. The combination of a multi-factorial approach and multi-scale sampling reveals that conclusions drawn from studies that ignore these dimensions are restricted and potentially misleading.

Summary 1. We tested the hypothesis that Gerbillus henleyi (de Winton 1903), the smallest species (10 g) of a pssamophilic guild in Israel, is scarce on relatively productive dunes of the Israeli desert, due to negative interactions from the common G. allenby i (Thomas 1918) and G. pyramidum (Geoffroy 1825). 2. The alternative hypothesis was that scarcity on sand resulted from the size of its naked hind feet, that do not allow efficient locomotion on sand. 3. Despite their naked soles the weight-bearing surface of G. henleyi feet carry less mass/area than those of any other species. 4. We measured interaction coefficients with the two common species using fieldmanipulation experiments in two enclosures. 5. Habitat usage of G. henleyi changed from significantly preferring the stabilized sand, when alone, to significantly using the semistabilized dune, when G. allenbyi was also present. 6. We also estimated the interaction coefficients and calculated the G. henleyi ’s isoclines competing with the two common gerbil species using a technique we developed elsewhere. 7. The stability analysis of the isoclines of G. henleyi competing with either G. allenbyi or with G. pyramidum suggests that stable coexistence occurs when G. henleyi is relatively scarce while the competitors are common. 8. Interspecific competition from either G. allenbyi or G. pyramidum accounts for 90·3% reduction in G. henleyi density, relative to when it is alone. 9. We concluded that the negative interactions from congeners was the major cause for the scarcity of G. henleyi on the relatively rich sand dunes of the Israeli desert.

Larger species tend to occupy more habitats, but a theoretical framework for the pattern is lacking. I modified the continuous-time logistic equation of population growth in two ways to allow for such a habitat-based theoretical framework. First, I separated birth rate from death rate. Second, I included two new terms in the equation: (1) an explicit spatial variable for habitat quality that reflects the match between a habitat and a population (species–habitat match), and (2) a demand/supply function that depends on the ratio between the energy used by all populations occurring in a habitat, and energy available in that habitat. Energy was used as a common currency to overcome differences between species of different body sizes as well as to overcome differences caused by disproportional intra- and interspecific effects. Allometric relations were used to characterize parameter values that correlate with body size, such as metabolic rate, birth rate, and death rate. The analytical solution of the equation for carrying capacity shows that, for a population to have a positive carrying capacity, its ratio of death rate to birth rate should be less than its match to the habitat it occupies. Literature-based body-size-dependent birth and death rates of Eutherian mammals show that the death-rate:birth-rate ratio decreases with body size. Combining the analytical solution and the death-rate:birth-rate ratio reveals that habitat generality should positively scale with body size. I used this model to simulate simple spatially explicit landscapes having diverse habitats and combinations of species of various body sizes. Using realistic parameters, the model generates results that are consistent with field observations. Thus, one can focus on specific processes to explore macroecological questions.

Ecologists need not despair ot discovering the mechanisms that lead to large scale patterns. The search for process at higher scales has already led to enhanced confidence in the patterns and to improvements in their description. For example, species-area relationships turn out to form not one. but three patterns. Each is controlled by gain-loss dynamics at its own scale. At the macroscale, origination and global extinction reign. At the archipelagic scale, immigration and island extinction determine the results. At the local scale, metapopulation processes do. The three scales exhibit species-area curves with systematically different slopes in logarithmic space. We use the three scales of species-area to illuminate the relationship between local and regional diversity. Algebra shows that the latter pattern is an echo of species-area curves, and that those echoes ought to be nearly linear. So. we call the relationship of local and regional diversity, the Echo pattern. Ecology has long known that species-area curves within a region reflect the accumulation of habitat variety. Thus, their connection to Echo patterns argues against concluding that local diversity has little or nothing to do with population interactions. To obtain a pure Echo pattern, one should draw data from independent regions rather than separate islands. The independence allows natural selection to adjust the fundamental niches of species to diversity. Theory suggests that higher diversity should shrink niches, allowing the coexistence of more species locally. Hence, independence should tend to produce the straightest Echoes. However, archipelagic species-area curves predict that even when different islands are used as the regions, the Echoes should show only very gentle curvatures. Flouting theory, some archipelagic Echoes approach an asymptote as regional diversity increases. These must have logarithmic slopes that increase with regional pool size. We do not understand why.