Abstract
Numerous investigators have used al- lometric regression to characterize the relationship between proportional egg composition and egg size, which is a potentially important characterization for assessing maternal investment in reproduction. Here- in, we document two important shortcomings of this approach. First, regressing log component mass against log egg mass involves regressing Y on itself, since each component (Y) is necessarily a part of the whole egg (X). This creates correlated errors, which leads to biased estimates of the regression slope. To circumvent this problem, we recommend regressing egg component masses on a relatively inert compo- nent like total water mass. Secondly, investigators routinely use ordinary least squares regression to estimate the slope of allometric relationships, which assumes that all error resides in Y. We demonstrate that this assumption is false, but so are the un- derlying error assumptions of commonly used alter- natives such as reduced major axis and major axis regression. Because each egg is unique and de- termining composition involves destructive sampling, there is no obvious way to assess measurement error in Y versus X. As a solution, we recommend that investigators analyze multiple eggs per clutch when- ever possible and fit a reduced major axis based on the among-female component of variability.
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