## Introduction

In the face of complexity, ecologists often strive to identify models that capture the essence of a system, explaining the observed distribution and perhaps ultimately permitting prediction. A first step toward this aim is to collect data on the response of interest, together with data on factors that it is believed might influence that response. Frequently data are observational (i.e. the variance in the data set has not been generated by experimental manipulation) leading to difficulties in determining which causal factor or factors best explain the observed responses. In these situations, scientific possibility is limited to describing the system and identifying models consistent with the observed phenomenon. One of the most commonly used techniques for this purpose is multiple regression or, more generally, a general linear model with multiple predictors. The statistical theory underlying this methodology is well understood (e.g. Draper & Smith 1981; McCullagh & Nelder 1989), as are the assumptions and limitations of the approach (e.g. Derksen & Keselman 1992; Burnham & Anderson 2002).

Although the scientific primacy of a principle of parsimony is without clear support (Guthery *et al*. 2005), it is usually the case that models with fewer variables also contain fewer nuisance variables and have greater generality (Ginzburg & Jensen 2004). For that reason, research is usually directed towards identifying a relatively parsimonious model that is in general agreement with observed data. A suite of model simplification techniques has been developed, and the notion of a minimum adequate model (MAM) has become commonplace in ecology. A MAM is defined as the model that contains the minimum number of predictors that satisfy some criterion, for example, the model that only contains predictors that are significant at some pre-specified probability level. Finding such a model is not straightforward, and most statistical packages offer algorithms for model selection in multiple regression. These include algorithms that operate by successive addition or removal of significant or nonsignificant terms (forward selection and backward elimination, respectively), and those that operate by forwards selection but also check the previous term to see if it can now be eliminated (stepwise regression). Collectively, these algorithms are usually referred to as stepwise multiple regression.

In spite of wide recognition of the limitations of stepwise multiple regression (Hurvich & Tsai 1990; Steyerberg *et al*. 1999; Grafen & Hails 2002; Wintle *et al*. 2003; Johnson *et al*. 2004; Stephens *et al*. 2005), use of the technique in ecology remains widespread (see further below for a review of applications in major journals). In particular, three problems with the approach are frequently overlooked in ecological analyses, all of which may lead to erroneous conclusions and, potentially, misdirected research. These include bias in parameter estimation, inconsistencies among model selection algorithms, and an inappropriate focus or reliance on a single best model, where data are often inadequate to justify such confidence.

In this paper, we give a brief review of the major problems with stepwise multiple regression and we analyse how frequently the technique is used in leading ecological and behavioural journals. We present an example of how focusing on a single model may lead to difficulties of interpretation. Finally, we discuss the problems of analysing and modelling data from complex multivariable ecological data sets.