## Introduction

The role of natural selection and micro-evolution in the ecological dynamics of naturally occurring populations has become the focus of an increasing number of studies (Hairston *et al.* 2005; Saccheri & Hanski 2006; Carroll *et al.* 2007; Pelletier *et al.* 2007). However, we can say nothing about evolutionary processes without a means of measuring and understanding the way that genetics underpins variation in demographic rates and fitness (Ellegren & Sheldon 2008; Kruuk, Slate & Wilson 2008). Quantitative genetics, a discipline with a long and distinguished history within evolutionary biology and animal breeding, provides a potentially powerful means for estimating the genetic architecture and predicting the evolutionary potential of phenotypic traits (Falconer & Mackay 1996; Lynch & Walsh 1998). The recent application of quantitative genetic methodology to long-term field studies of vertebrate populations has yielded new insight into the complexities of and constraints on evolutionary dynamics under realistic ecological conditions (Kruuk 2004; Ellegren & Sheldon 2008; Kruuk *et al.* 2008). These studies have typically used a form of mixed-effects models known as the ‘animal model’ to decompose phenotypic variance into different genetic and environmental sources and to estimate key parameters such as the heritability of a trait or the genetic correlations between traits (e.g. Réale, Festa-Bianchet & Jorgenson 1999; Kruuk *et al.* 2000; Milner *et al.* 2000; Kruuk, Merila & Sheldon 2001; Garant *et al.* 2004; Wilson *et al.* 2005; Gienapp, Postma & Visser 2006). This approach, as with any in the field of quantitative genetics, requires knowledge of the relatedness of individuals in a population. Such information, although challenging to come by in field populations, is increasingly available for studies of a range of taxa (Pemberton 2008), fuelling a growing interest in the application of quantitative genetics to studies of natural, rather than laboratory or domestic, populations. Animal models are not difficult to implement, given appropriate data, but correctly specifying and interpreting them is a potentially fraught business.

In this paper, we present a practical guide aimed at the ecologist wishing to use the animal model for the first time. Our aim is neither to provide a comprehensive treatment of the theoretical and statistical models used in quantitative genetics, nor to review the empirical results of their application to ecological data sets. Rather our goal is to provide a practical guide for ecologists interested in exploring the potential to apply quantitative genetic methods to their research. In what follows we briefly lay out some of the key concepts involved. We describe the parameters that quantitative genetic methods attempt to estimate, why these parameters are of interest to ecologists, and how we can use statistical models – particularly the animal model – to estimate them. We also provide code (and example data sets) to run models with several common software applications. Whilst we have consequently tried to avoid technical terminology and issues as far as possible, in a mathematical and statistical subject like quantitative genetics technical details do assume vital importance. We have therefore tried to highlight some of the most likely pitfalls to be wary of, whilst referring the reader to the original literature and, where appropriate, more detailed reviews on specific topics. Thus this paper is intended to serve as a useful starting point and a way into the literature for the uninitiated. We do not wish this paper to be treated as a replacement for or an excuse to skip over the original quantitative genetics literature and we would always advise against a ‘black box’ approach when using complex statistical models to analyse data. However, we recognize that for many empiricists, ourselves included, grappling with the theory and mathematics underlying a technique is much more rewarding given a clear sense of the end goal. We very much hope this paper will provide a useful clarification of both the ultimate goals and the key considerations and pitfalls for any field ecologist interested in applying quantitative genetic analyses to their data.