## Introduction

Body condition is intimately related to an animal’s health, quality or vigour (Peig & Green 2009), and has been widely claimed to be an important determinant of fitness. A wide range of morphological, biochemical or physiological metrics have been proposed as condition indices (CIs) (Stevenson & Woods 2006). Here, we are only concerned with CIs based on the relationship between body mass (*M*) and length measurements (*L*), whose ultimate goal is to interpret variations of body mass for a given body size as an attribute of the individual’s well-being (most typically, variation in the size of energy reserves).

A variety of formulas and statistical methods have been proposed to standardize body size, and there is much debate about which ones are most suitable as CIs (Stevenson & Woods 2006). Among conventional methods, simple ratios (or ratio indices) between *M* and *L* or *L* raised to a specific power (e.g. *M*/*L*, *M*/*L*^{2}, *M*/*L*^{3}) have been in use the longest. Examples include Fulton’s index ‘*K*’ (where *K *= *M*/*L*^{3}) still used in some ecological studies, or Quételet’s index or the body mass index (BMI = *M*/*L*^{2}) universally applied in health sciences. In fisheries, a popular CI is the so-called Relative condition ‘*K*_{n}’, computed as the observed individual mass (*M*_{i}) divided by the predicted mass (*M*_{i}*, where *M*_{i}* = *a L*_{i}^{b}). The estimates *a* and *b* are empirically determined by ordinary least squares (OLS) regression of *M* against *L* (both log-transformed) for the whole study population (LeCren 1951). Even more popular in fisheries is a variant of the *K*_{n} index, called Relative mass ‘*W*_{r}’, where *a* and *b* are determined from a reference population instead of the population under study (Murphy, Willis & Springer 1991).

In recent years, the most widely accepted CI in terrestrial ecology has been the Residual index ‘*R*_{i}’, which uses the residuals from an OLS regression of *M* against one or more length measurements, usually after log transformation (Jakob, Marshall & Uetz 1996; Schulte-Hostedde, Millar & Hickling 2001; Ardia 2005; Schulte-Hostedde *et al.* 2005). Another popular approach is to conduct an analysis of covariance (ancova), which combines features of linear regression and anova to estimate directly the treatment effect on *M* while controlling for a concomitant variable of influence, denoted by *L* (García-Berthou 2001; Velando & Alonso-Alvarez 2003; Serrano *et al.* 2008).

Currently, no consensus exists about the best CI or criteria which allow selection of the most appropriate method in a particular study, and few authors provide a detailed justification of their choice of method. Ecologists and epidemiologists follow traditions within their discipline. Hence, the continuing use of ratios in fisheries and health sciences or the widespread use of *R*_{i} in terrestrial ecology, despite criticisms of these approaches (Albrecht, Gelvin & Hartman 1993; Packard & Boardman 1999; García-Berthou 2001; Green 2001; Freckleton 2002). As we will demonstrate, results may differ dramatically depending on the method of choice, causing concern about the reliability of studies based on less appropriate methods.

Peig & Green (2009) presented a novel CI method called the Scaled mass index ‘‘, which standardizes body mass at a fixed value of a linear body measurement based on the scaling relationship between mass and length, according to equation 1:

Scaled mass index ( ):

where *M*_{i} and *L*_{i} are the body mass and linear body measurement of individual *i* respectively; *b*_{SMA} is the scaling exponent estimated by the standardized major axis (SMA) regression of ln*M* on ln*L*; *L*_{0} is an arbitrary value of *L* (e.g. the arithmetic mean value for the study population); and is the predicted body mass for individual *i* when the linear body measure is standardized to *L*_{0}. Making a comparison of *M*_{i} values between different populations or studies simply requires use of the same *L*_{0} value in eqn. 1. In a variety of vertebrate species (five small mammals, one bird and one snake), the Scaled mass index performed better than the Residual index ‘*R*_{i}’ as a predictor of variations in fat and protein reserves as well as other body components (Peig & Green 2009).

The overall objective of this paper is to critically reappraise current CI methods and compare their performance with that of the Scaled mass index ‘‘. Using field data from small mammals, we compare the performance of , Residual index ‘*R*_{i}’, ancova, Body mass index ‘BMI’, Fulton’s index ‘*K*’, Relative condition ‘*K*_{n}’, and Relative mass ‘*W*_{r}’. We demonstrate empirically that conventional CIs can be inherently biased with regard to animal size, and tend to change condition scores in larger animals owing to violations of statistical assumptions and failure to account for growth and scaling relationships.

We included ratio methods in our study, because they are still widely in use and have not previously been compared with . Although ratio methods have been widely criticized, many of their problems are shared by *R*_{i} and ancova. Exploring the performance of ancova was also important because, like , it has been advocated as a more reliable method than ‘*R*_{i}’ (García-Berthou 2001). The ancova is not strictly a CI but rather an inferential test where individual scores are absent, making validation via correlations with body components such as fat reserves impossible.

First, to help explain why CIs can be unreliable, we consider basic principles underlying the construction of condition indices based on mass and length data.

### First principles for a condition index

As pointed out by Kotiaho (1999), if CIs are assumed to reflect, or be validated by, either the ‘absolute’ or ‘percentage’ amount of energetic tissue, they should not be used for comparisons of condition among individuals of different size. This is because, at each stage of growth and development, there is both an optimal range of structural and energy capital (in absolute or % values) and an optimal distribution of this capital among different body components. In other words, the proportional or absolute amount of energy stores can be expected to change with normal growth processes, even in an optimal environment (e.g. one free from pathogens and disturbance, with non-limiting resources). It would therefore be erroneous to assert that adults were in better ‘condition’ or ‘well being’ than juveniles because of a greater absolute amount of fat or protein, or that juveniles were in better condition than adults because of a greater relative content (as %fat, %protein, etc.). The same generally applies to comparisons between sex or subspecies (Gallagher *et al.* 1996). Kotiaho’s premise has profound implications for condition estimates and the search for a suitable method. Essentially, a method is required that accounts for normal growth processes (i.e. scaling), thus allowing a valid comparison between individuals of a different body size.

Growth leads to strong correlations between *M* and most linear body measurements (*L*) (Hoppeler & Weibel 2005; Peig & Green 2009). Because increases in both *M* and *L* are parts of the same growth phenomenon (Thompson 1961), both *M* and *L* are indicators of body size *per se* which require some type of mutual standardisation. Strictly speaking, however, as body growth involves not only variation in body size but also in body composition (Huxley 1932; Calder 1984), the aim of any CI is not to control for body size but rather for growth effects as a whole and their consequences for scaling (Peig & Green 2009).

Virtually all work on biological scaling assumes a power function of the form *Y *= α*X*^{β} where the parameter α is a constant and the parameter β, the ‘allometric or scaling exponent’, determines the dimensional balance between *Y* and *X*. The power (nonlinear) relationship is supported by the notion of growth as a multiplicative process of living matter (Shea 1985). β equals the ratio of the specific growth rates of the dimensions *Y* and *X* (i.e. *dY*/*Ydt* and *dX*/*Xdt*, Shea 1985). As the same time interval applies for changes in *M* and *L*, estimating body condition from *M*-*L* data is time-independent and unaffected by the rate of growth.

Morphogenesis is the mechanism controlling the body proportions (i.e. between *M* and *L*) and thus determines the scaling exponent β (Roth & Mercer 2000). This process is largely controlled by genes which regulate how body parts differentiate and orientate to form a well-structured organism (Conlon & Raff 1999; Hogan 1999). As monomorphic species have their own body plan distinct from other species, the assumption that β is species specific (or sex specific for dimorphic species) is likely to be an adequate approximation for representative sample sizes. This is supported by variation in scaling trends between *M* and *L* at inter- and intraspecific levels (e.g. Green, Figuerola & King 2001). Comparisons of CIs are valid when made among groups sharing the same β value for *M*-*L* relationships, regardless of variation in growth rate between individuals, populations or sex. Other comparisons of CIs (e.g. between sex that lack a common morphogenetic pattern) are nonsensical.

According to the dimensional balance between volume *V* (closely related to *M*) and length *L* (i.e. M ≅ *V *∝ *L*^{3}), under ‘isometry’ the scaling exponent that relates *M* and *L* is 3. This provides a rationale for the formulation of the Fulton’s index (*K *= *M*/*L*^{3}). In practice, β for *M* against *L* usually deviates from the predicted value of 3, owing to ‘allometry’. Body condition should be estimated at no higher than the species level, which comprises the scaling effects owing to ‘heterauxesis’ and ‘individual allomorphosis’ (Gould 1966). ‘Heterauxesis’ (also called ‘ontogenetic allometry’ or ‘growth allometry’) refers to scaling during the growth of an individual, whilst ‘allomorphosis’ (or ‘static allometry’) is scaling among conspecifics at the same stage of determinate growth (usually adults), but varying in size. Although heterauxesis and allomorphosis require different types of data, both types of scaling are relevant to body condition as they are parts of a common morphogenetic phenomenon (Stern & Emlen 1999).

To enable a meaningful comparison between individuals of different sizes, a CI method must remove the effects of ontogenetic growth on the *M*-*L* relationship through standardisation. Unless some factor affects the well-being of animals at a specific growth stage (e.g. iguanas can become inefficient foragers when they reach a certain size, Wikelski, Carrillo & Trillmich 1997), mean condition scores should be equal for different age classes, and confirmation of this indicates that size and composition have been properly standardized (i.e. growth effects have been accounted for). Similarly, even if a species shows sexual size dimorphism, if the sexes have a similar body design (i.e. a similar morphogenesis), we should expect no differences in CIs (i.e. well-being) between sex.