Constancy in the Size Ratios of Sympatric Species

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Abstract
A literature survey reveals many problems with the use of 1.3 as an ecological constant. Much of the empirical support for the existence of a 1.3 rule, or general law of size ratios in sympatric species, risks circular reasoning or involves unwarranted selection or manipulation of data. Many authors subscribe to a rule, yet easily explain the frequent occurrence of larger or smaller figures. Models of competition do not predict specific values of size ratios unless certain rigid requirements or untested assumptions are incorporated. Depending on the model, character displacement can produce an exponential distribution as well as one centered on 1.3 or concentrated at high values of ratios. Before asserting that a biological law exists, one should establish that its empirical basis is statistically significant. Several statistical methods are mentioned here. One which measures rhythmic tendencies is briefly described and applied to a data set chosen because it appears to be distributed according to a constant multiplicative factor. The weights of 8 sympatric species of pigeons approximate a geometric series based on a factor of 1.5 with significance between 0.05 and 0.10; thus there is some evidence of a pattern in 1 carefully selected set of data, but the ratios do not equal 1.3 or 2, as previous work might have predicted. More statistically verified evidence should be produced. In a 2nd example, culmen ratios between sympatric birds form a histogram which resembles an exponential curve, suggesting that divergence in bill size occurs without regard to the actual numerical value of such ratios. Ratios and patterns in data should not be compared indiscriminately, however. Establishing the reality of a pattern in data and providing an explanation for that pattern are separate matters. To be useful, both empirical patterns and theoretical treatments should be interpretable in a biological context.