Species abundance distribution results from a spatial analogy of central limit theorem

Abstract

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.log-normal distribution ͉ spatial autocorrelation ͉ spatial turnover

Between Geometry and Biology: The Problem of Universality of the Species-Area Relationship

“…We did not need information on any particular shape of the SAD to build a SAR under this approach. Indeed, if there is a link between SAD and SAR, it may run the opposite direction, as species' spatial turnover has recently been demonstrated to determine the SAD (Šizling et al 2009c;Ků rka et al 2010). Hence, the variation in species' spatial turnover between adjacent plots (alternatively, z for ) p 2 may prove a master pattern simultaneously driving several macroecological and diversity patterns, including the SAR and the SAD.…”

Phytoplankton functional group dynamics explain species abundance distribution in a directionally changing environment

“…This implies that the wellknown excess of rare species of SAD can be very dynamic and prone to variable external forcing, which emphasizes the need for considering transient states in addition to existing equilibrium theories of SAD (Harte 2003, Sugihara et al 2003, Volkov et al 2003, Magurran 2004, Sizling et al 2009). This implies that the wellknown excess of rare species of SAD can be very dynamic and prone to variable external forcing, which emphasizes the need for considering transient states in addition to existing equilibrium theories of SAD (Harte 2003, Sugihara et al 2003, Volkov et al 2003, Magurran 2004, Sizling et al 2009).…”

“…Firstly, the recent resurgence of interest in the ''excess of rare species'' (i.e., many rare species and a few dominant species) of SAD has stimulated debate on the underlying mechanisms of rarity and SAD (Magurran and Henderson 2003, Volkov et al 2003, McGill et al 2007, Sizling et al 2009, Chisholm and Pacala 2010. Firstly, the recent resurgence of interest in the ''excess of rare species'' (i.e., many rare species and a few dominant species) of SAD has stimulated debate on the underlying mechanisms of rarity and SAD (Magurran and Henderson 2003, Volkov et al 2003, McGill et al 2007, Sizling et al 2009, Chisholm and Pacala 2010.…”

Despotic, high‐impact species and the subcontinental scale control of avian assemblage structure

“…Moving beyond the distributional fitting of SADs to develop theoretical understanding has been a recent major enterprise (McGill et al 2007). A series of new directions has been considered, including the influence of sampling scales (Magurran 2007, Sizling et al 2009), the use of measures other than abundance (e.g., biomass) (Morlon et al 2009, Henderson andMagurran 2010), guild or functional groupings (Magurran and Henderson 2003) and, most recently, relating SADs directly to environmental gradients (Foster and Dunstan 2010). To our knowledge, the profundity of the impacts of despotic species on SADs has not been considered.…”