dispersal ability or ecological niche) impact the spatial turnover of biological communities (e.g. Therefore, when the same function is used to model distance-decay patterns of different biological groups, these statistical parameters provide a powerful tool to assess how the biological characteristics of different organisms (i.e. For example, the intercept estimates the expected community similarity at short distances and the slope quantifies the rate at which communities change with distance (Nekola & White, 1999 Soininen et al., 2007). negative exponential or power-law models) are usually employed, and their parameters are interpreted in biological terms. Non-linear regressions of community similarity (e.g. The assessment of spatial turnover in community composition and, more precisely, its dependence on spatial/environmental distance relies on adequately modelling the shape of the relationship between community similarity and spatial/environmental distance. Therefore, we predict that species range size is a crucial link between the processes controlling species distributions and the shape of the relationship between community similarity and spatial (or environmental) distance. On the contrary, the distributions of organisms with low vagility and narrow niches are generally smaller and, thus, higher turnover in community composition is expected for these taxa. In turn, larger distributions increase the probability of different sites having the same species, thus leading to higher similarity in community composition. Thus, organisms with high vagility and wide niches would tend to have larger distributions. Moreover, species range size also depends on dispersal and niche processes (Brown et al., 1996 Willis, 1922). However, the links between distance-decay and key macroecological attributes, such as species range size, have received less attention, even though range size determines to which extent a given species can be found in two different sites. The biogeographic characteristics of the study area (such as spatial scale or latitude) also impact the patterns of distance-decay (Nekola & McGill, 2014 Nekola & White, 1999 Soininen et al., 2007). niche requirements or dispersal ability) and their interaction with the environment (Morlon et al., 2008 Steinbauer et al., 2012). At local or regional scales, distance-decay curves are primarily shaped by the organisms’ biological characteristics (e.g. The decrease in community similarity with spatial or environmental distance, that is, distance-decay of similarity, is a general property of biological systems that has been studied for a large range of organisms, for example, archaea (Barreto et al., 2014), bacteria (Barreto et al., 2014 Milici et al., 2016), diatoms (Astorga et al., 2012 Wetzel et al., 2012), fungi (Bahram et al., 2013), plants (König et al., 2017 La Sorte et al., 2008 Nekola & White, 1999 Qian, 2009) and both invertebrate (Saito et al., 2015 Thieltges et al., 2009) and vertebrate animals (Maloney & Munguia, 2011 Qian & Ricklefs, 2012) in different environments, from neotropical forests (Palmer, 2005) to urban environments (La Sorte et al., 2008) and at different spatial scales (Steinbauer et al., 2012). The Gompertz function is the mathematical model that best accommodates different frequency distributions of species range size and, thus, allows cross-taxa comparison of this biogeographical and ecological pattern. This dependence makes it an interesting tool to detect biodiversity threats associated with species range expansion, such as the biotic homogenization of faunas. The functional form of distance-decay patterns depends on a key biogeographical attribute: species range size. Remarkably, the Gompertz function fits the data reasonably well in all scenarios. Similar results have been found in the distance-decay pattern of South American mammals. An increase in range sizes leads to a negative exponential relationship, taking the shape of a sigmoidal (Gompertz) relationship with the largest range size values. Our simulations showed that the power-law is the best supported model when range sizes tend to be small. We also used distribution data of South American mammals to explore the relationship between species range size and the distance-decay form in an empirical dataset. Simulations were performed using different sample sizes and species detection probabilities. negative exponential, power-law or sigmoidal relationships). We computed distance-decay curves from simulated communities to assess how the species range sizes shape the functional form of distance-decay patterns (i.e. (i) To assess the dependence between the form of the decrease in biological similarity with distance (distance-decay) and species range size and (ii) to introduce the use of a sigmoidal model, the Gompertz function, as a flexible alternative able to fit distance-decay models under a wide variety of species range sizes.
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