## Introduction

The heritability (*h*^{2}) of a phenotypic trait is defined as the proportion of phenotypic variance that is attributable to additive genetic effects, and is a key parameter in determining the evolutionary response to selection (Falconer & Mackay, 1996). As such, evolutionary biologists have long been interested in heritability, both for predicting selection responses, and as a tool to assess more general questions. For example, can laboratory-based estimates be usefully extrapolated to wild populations (Weigensberg & Roff, 1996)? Are some types of trait more heritable than others (Merilä & Sheldon, 1999)? Does heritability change consistently with the quality of the environment (Hoffman & Merila, 1999; Charmantier & Garant, 2005)? However, whereas it is well known that heritability is specific to a trait and a population, it is rather less appreciated that parameter estimates are also heavily determined by the structure of the model used for their estimation. This issue has enormous potential to confuse and mislead evolutionary ecologists, particularly researchers who are less familiar with quantitative genetic techniques.

Over recent years, there has been a surge of interest in the application of quantitative genetic models to data from natural populations (Kruuk, 2004; Postma & Charmantier, 2007). To a large extent, this endeavour has been facilitated by the adoption of the animal model, a form of mixed effects model that has long been used by animal breeders (Henderson, 1984). Mixed effects models contain both fixed and random effects. Fixed effects are used to model population-level average responses to explanatory variables, whereas random effects allow remaining variance to be partitioned into components attributable to any grouping factors present in the data (Galwey, 2006). By definition, an animal model includes an individual’s additive genetic merit (or breeding value, Lynch & Walsh, 1998; as a random effect, and as genes are shared among relatives, this allows estimation of the additive genetic variance (*V*_{A}) for a trait of interest. By comparison with more traditional analytical techniques (e.g. parent–offspring regression), this method offers greater power and flexibility, particularly when dealing with complex pedigree structures typical of natural populations (Kruuk, 2004).

A further advantage of animal models is that fixed effects can readily be included, such that an individual’s phenotype is ‘corrected’ for known sources of variation, such as age and sex, or environmental conditions, such as density or food abundance. For animal breeding applications, the inclusion of fixed effects is used to protect against downward bias in heritability estimates. For example, if one is interested in estimating the heritability of body weight, but individual animals have been measured at different stages of growth, then fitting age as a fixed effect in the model corrects for this allowing a more meaningful comparison among individuals. This same argument also applies to studies of natural populations and a brief survey of the literature shows that studies using animal models to estimate *h*^{2} in the wild have, almost without exception, included fixed effects in the models (for some recent examples, see Wilson *et al.*, 2005; Qvarnström *et al.*, 2006; Thériault *et al.*, 2007).

Whereas heritability is determined as the ratio of additive (*V*_{A}) to phenotypic (*V*_{P}) variance, *V*_{P} is most often defined as being the variance around the fixed effects mean. That is, to say, *V*_{P} is determined as the sum of the variance components associated with each random effect, and will therefore not include any variance explained by the fixed effects of a model. Consequently, heritability estimates will be critically determined by the fixed effects structure of the model used. The purpose of this note is to draw attention to the consequences of this practice, encourage discussion on the appropriate use of fixed effects, and demonstrate the vital importance of interpreting *h*^{2} estimates in the context of the model used for estimation.