TY - JOUR
T1 - Species abundance distribution results from a spatial analogy of central limit theorem
AU - Šizling, Arnošt L.
AU - Storch, David
AU - Šizlingová, Eva
AU - Reif, Jiří
AU - Gaston, Kevin J.
PY - 2009/4/21
Y1 - 2009/4/21
N2 - 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 nonoverlap-ping 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.
AB - 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 nonoverlap-ping 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.
KW - Log-normal distribution
KW - Spatial autocorrelation
KW - Spatial turnover
UR - http://www.scopus.com/inward/record.url?scp=66149145322&partnerID=8YFLogxK
U2 - 10.1073/pnas.0810096106
DO - 10.1073/pnas.0810096106
M3 - Article
C2 - 19346488
AN - SCOPUS:66149145322
VL - 106
SP - 6691
EP - 6695
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
SN - 0027-8424
IS - 16
ER -