Is the relationship between population density and body size consistent across independent studies? A meta-analytical approach.

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Abstract
The Energetic Equivalence Rule (EER) is a controversial issue in ecology. This rule states that the amount of energy that each species uses per unit of area is independent of its body size. Here, we perform a meta-analytical procedure to combine and compare the slopes of population density and body size relationships across independent studies of mammals and birds. We then compared a distribution of 50,000 bootstrap combined slopes with the expected slope (b = -0.75) under the EER. The combined slopes obtained for mammals and birds separately were -0.755 and -0.321, respectively. The homogeneity hypothesis (i. e. within studies the slopes differ by no more than would be expected due sampling variation) was rejected in both cases. So, EER cannot be supported since the use of an exponent of -0.75 is, in fact, an oversimplification. Significant heterogeneity of slopes within each group (mammals and birds) is an indicator of inferential problems related with variation in body size, spatial scale, the regression model adopted and phylogenetic relationships among species. So, we consider that questions regarding the estimation and validity of slopes is the next challenge of density-body size relationship studies.