Assessment of the rate of species loss, which we also label extinction, is an urgent task. However, the rate depends on spatial grain (average area A) over which it is assessed-local species loss can be, on average, faster or slower than regional or global loss. Ecological mechanisms behind this discrepancy are unclear. We propose that the relationship between extinction rate and A is driven by a classical ecological phenomenon: density-dependent mortality. Specifically, we hypothesize that (i) when per-individual probability of death (P death) decreases with the number of individuals in a region N (i.e., negative density dependence), per-species extinction rate (Px) should be high at regional grains and low locally. (ii) In contrast, when P death increases with N (i.e., positive density dependence), Px should be low regionally but high locally. (iii) Total counts of extinct species (Ex) should follow a more complex relationship with A, as they also depend on drivers of the species-area relationship (SAR) prior to extinctions, such as intraspecific aggregation, species pools, and species-abundance distributions. We tested these hypotheses using simulation experiments, the first based on point patterns and the second on a system of generalized Lotka-Volterra equations. In both experiments, we used a single continuous parameter that moved between the negative, zero, and positive relationship between P death and N. We found support for our hypotheses, but only when regional species-abundance distributions were uneven enough to provide sufficiently rare or common species for density dependence to act on. In all, we have theoretically demonstrated a mechanism behind different rates of biodiversity change at different spatial grains, which has been observed in empirical data.

• Keywords
• Allee, Janzen–Connell, extirpation, scaling, sixth mass extinction, species richness,
• Publication type
• Journal Article MeSH

Despite the broad conceptual and applied relevance of how the number of species or endemics changes with area (the species-area and endemics-area relationships (SAR and EAR)), our understanding of universality and pervasiveness of these patterns across taxa and regions has remained limited. The SAR has traditionally been approximated by a power law, but recent theories predict a triphasic SAR in logarithmic space, characterized by steeper increases in species richness at both small and large spatial scales. Here we uncover such universally upward accelerating SARs for amphibians, birds and mammals across the world’s major landmasses. Although apparently taxon-specific and continent-specific, all curves collapse into one universal function after the area is rescaled by using the mean range sizes of taxa within continents. In addition, all EARs approximately follow a power law with a slope close to 1, indicating that for most spatial scales there is roughly proportional species extinction with area loss. These patterns can be predicted by a simulation model based on the random placement of contiguous ranges within a domain. The universality of SARs and EARs after rescaling implies that both total and endemic species richness within an area, and also their rate of change with area, can be estimated by using only the knowledge of mean geographic range size in the region and mean species richness at one spatial scale.

• MeSH
• Algorithms MeSH
• Biodiversity * MeSH
• Models, Biological * MeSH
• Species Specificity MeSH
• Ecosystem * MeSH
• Extinction, Biological MeSH
• Amphibians physiology   MeSH
• Birds physiology   MeSH
• Mammals physiology   MeSH
• Conservation of Natural Resources MeSH
• Geography * MeSH
• Animals MeSH
• Check Tag
• Animals MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Research Support, U.S. Gov't, Non-P.H.S. MeSH
• Geographicals
• Africa MeSH
• Americas MeSH
• Asia MeSH
• Australia MeSH
• Europe MeSH

The frequency distribution of species abundances [the species abundance distribution (SAD)] is considered to be a fundamental characteristic of community structure. It is almost invariably strongly right-skewed, with most species being rare. There has been much debate as to its exact properties and the processes from which it results. Here, we contend that an SAD for a study plot must be viewed as spliced from the SADs of many smaller nonoverlapping subplots covering that plot. We show that this splicing, if applied repeatedly to produce subplots of progressively larger size, leads to the observed shape of the SAD for the whole plot regardless of that of the SADs of those subplots. The widely reported shape of an SAD is thus likely to be driven by a spatial parallel of the central limit theorem, a statistically convergent process through which the SAD arises from small to large scales. Exact properties of the SAD are driven by species spatial turnover and the spatial autocorrelation of abundances, and can be predicted using this information. The theory therefore provides a direct link between SADs and the spatial correlation structure of species distributions, and thus between several fundamental descriptors of community structure. Moreover, the statistical process described may lie behind similar frequency distributions observed in many other scientific fields.

• MeSH
• Biodiversity * MeSH
• Models, Biological * MeSH
• Computer Simulation MeSH
• Birds MeSH
• Trees MeSH
• Animals MeSH
• Check Tag
• Animals MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Research Support, U.S. Gov't, Non-P.H.S. MeSH