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Inconstancy of Taylor's b : Simulated sampling with different quadrat sizes and spatial distributions
Author(s) -
Sawyer Alan J.
Publication year - 1989
Publication title -
population ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.819
H-Index - 59
eISSN - 1438-390X
pISSN - 1438-3896
DOI - 10.1007/bf02515802
Subject(s) - quadrat , sample size determination , statistics , sample (material) , population , mathematics , sample variance , spatial ecology , sampling (signal processing) , scale (ratio) , range (aeronautics) , variance (accounting) , spatial distribution , contrast (vision) , ecology , biology , demography , physics , geography , cartography , accounting , materials science , shrub , sociology , detector , optics , business , composite material , thermodynamics
Summary Taylor 's power law, s 2 = am b , provides a precise summary of the relationship between sample variance ( s 2 ) and sample mean ( m ) for many organisms. The coefficient b has been interpreted as an index of aggregation, with a characteristic value for a given species in a particular environment, and has been thought to be independent of the sample unit. Simulation studies were conducted that demonstrate that the value of b may vary with the size of the sample unit in quadrat sampling, and this relationship, in turn, depends on the underlying spatial distribution of the population. For example, simulated populations with hierarchical aggregation on a large scale produced values of b that increased with the size of the sample unit. In contrast, for a simulated population with randomly distributed clusters of individuals, the value of b eventually decreased with increasing quadrat size, as sample counts became more uniform. A single value of Taylor 's b , determined with a particular sample unit, provides neither a fixed index of aggregation nor a complete picture of a species' spatial distribution. Rather, it describes a consistent relationship between sample variance and sample mean over a range of densities, on a spatial scale related to the size of the sample unit. This relationship may reflect, but not uniquely define, density‐dependent population and behavioral processes governing the spatial distribution of the organism. Interpretation of Taylor 's b for a particular organism should be qualified by reference to the sample unit, and comparisons should not be made between cases in which different sample units were used. Whenever possible, a range of sample units should be used to provide information about the pattern of distribution of a population on various spatial scales.