On the distribution of proportions and ratios as indicators of ungulate body condition

Abstract

In the wildlife literature various studies have shown that the amount of fat around the kidneys is often a good indicator of body condition and health of ungulate species ([1],[2]). Wildlife biologies often measure the weights of fat around the kidneys and the kidneys themselves (without fat), comparing these two quantities and transforming them into a ratio or a proportion as surrogates of body condition of dead animals. Later, they use these indices as response variables to model the e®ect of covariates or treatments, such as age group and season of the year, on body condition. The more commonly used models are ANOVA-type. Most debate has been concentrated on whether or not to use a simple ANOVA model of ratios or proportions with ¯xed e®ects, or an ANCOVA model using fat weight as response variable, and the kidneys weight as a covariate ([3]). Results have taken by surprise some biologists because using one or another model with both response variables could lead to very di®erent results for what it considered the most important e®ects. In this manuscript we attempt to highlight the main di®erences and the distributional properties of these response variables, ratio and proportion