On the Distribution of Proportions and Ratios as Indicators of Ungulate Body Condition

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.