Mass/Length Residuals: Measures of Body Condition or Generators of Spurious Results?

Abstract

In studies of animal ecology, it is fashionable to use the residuals from an ordinary least squares (OLS) linear regression of body mass against a linear measure of size (the body size indicator, BSI) as an index of body condition. These residual indices are used to study the relationship between condition and reproductive investment, survivorship, habitat use, and other parameters. I identify a series of key assumptions underlying the use of this method, each of which is likely to be violated in some or all studies. These assumptions are: (1) that the functional relationship between mass and BSI is linear; (2) that condition is independent of BSI length; (3) that BSI length accurately indicates structural size; (4) that there is no correlation between the size of BSI relative to other structural components (i.e., shape) and the parameter against which the residuals are analyzed; (5) that BSI length is strictly independent of mass; and (6) that BSI length is not subjected to error. Violations of these assumptions place the results of some studies in question and explain the poor relationship observed between OLS residuals and more direct measures of condition.I use avian morphometric data to illustrate how OLS methods can easily lead to Type I and Type II errors through violations of assumptions (5) and (6). Significant relationships reported between OLS residual indices and parameters correlating with body size (e.g., size of sexual ornaments or egg size) are at particular risk of being spurious when the correlation coefficient between mass and BSI is low. Residual indices of condition are often likely to be more reliable when calculated with alternative methods such as nonparametric or model II regression. However, whatever the method used to produce them, residual indices are not suitable for studying the heritability of condition.

Green nesting material has a function in mate attraction in the European starling

“…The average daily amount of green nest material present per nestbox was calculated as the quotient of total mass and number of days between the day of first measurement and the day of laying the first egg in that nestbox. As an estimate of body condition for adults and nestlings we used body mass and not the regression residuals derived from the equation of tarsus versus mass, as this regression was not always significant (see discussion in Green 2001). For data that were not normally distributed, even after transformation, we used nonparametric tests.…”

The effects of neonatal handling on adrenocortical responsiveness, morphological development and corticosterone binding globulin in nestling American kestrels (Falco sparverius)

“…A body condition index (BCI) was developed based on Dawson and Bortolotti [18], Green [27], and Love et al [36]. First, a principal components analysis was performed separately for males and females using the following measurements taken on day 26 post-hatch: wing chord, tarsus length, and culmen length.…”

The High Cost of Motherhood: End-Lactation Syndrome in Southern Sea Otters (Enhydra Lutris Nereis) on the Central California Coast, Usa

“…Evaluating the body mass relative to body length is one of the most common methods of measuring relative body condition (Schulte-Hostedde et al 2005), the most common approach being to estimate residuals from a regression of body mass (or log body mass) against some measure of structural size, such as body length. This type of index may be useful for assessing relative availability of food resources over the near-term, but it is subject to a number of statistical and biological limitations that can sometimes lead to spurious results (Green 2001). Another approach to assessing body condition, one that is less subject to short-term variation in conditions, is to evaluate age-specific length or mass, and/or the rate of body growth in juveniles (Fowler 1990).…”