The theory of range-size (RS) distributions. American Museum novitates ; no. 2833

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New York, N.Y. : American Museum of Natural History
"If the frequency distribution of sizes of geographic ranges (the range size or RS distribution) of the species comprising the continental fauna for a given taxonomic group of organisms is viewed as a system in dynamic equilibrium and if the observed 'hollow curve' or logarithmic distribution is taken into consideration, it follows that the geographic range of a species, regardless of its size, is more likely to decrease than to increase. Some of the conditions of the system, including the complications of extinction and speciation, are examined by simulating the system with a Markov chain model on a digital computer. Some general attributes of the system are: diversity and the RS distribution are maintained dynamically, any local change in number of species or transition probability (TP) ramifies throughout the system, and the system converges on a theoretical equilibrium (that keeps changing, in the real world). A simple Basic Logarithmic Model that assumes a logarithmic series of TP values accounts for most of the variation in RS distributions of North American vertebrates. The fit of the model is not improved by making TP values a function of border length rather than area. The Basic Logarithmic Model, regarded as a randomly determined Null Hypothesis, is rejectable. There remain residuals or deviations of data from this model that need further explanation. Actual RS distribution curves for groups of North American vertebrates can be closely simulated by specifying six values: minimum and maximum possible ranges, a logarithmic series of TP values, an inflection point (somewhere between 5.0 and 6.3 km²), and TP ratios (of the probability for an increase, I, to that for a decrease, D) between 0.66 and 0.75 above the inflection point and from 0.85 to 0.89 below"--P. [1].
20 p. : ill. ; 26 cm.
Includes bibliographical references (p. 19-20).