## Introduction

There is abundant evidence that populations of the same species differ phenotypically and that such variation is frequently correlated with some geographical variable such as latitude or with an environmental variable such as temperature (e.g. Masaki, 1967; Mousseau & Roff, 1989; Smith *et al.*, 1994; Blanckenhorn & Fairbairn, 1995; Nylin *et al.*, 1996; Conover *et al.*, 1997; Arnett & Gotelli, 1999; Tracy, 1999; Merila *et al.*, 2000; McKay *et al.*, 2001; Thomas *et al.*, 2001). The former type of variable, and in some cases the latter, is not likely to be itself the agent causing variation but rather an indicator variable of some other factor that directly exerts a selective pressure on the populations. Phenotypic differences among populations are very often maintained when individuals derived from these populations are grown under common garden conditions (see previous citations), indicating that such variation has a genetic basis. Whereas considerable attention has been devoted to measuring and discussing variation in mean trait values, relatively little attention has been given to variation in the phenotypic variances and covariances (Steppan, 1997; Ackerman & Cheverud, 2000). This is unfortunate, because these statistics are an integral component of the description of variation within and among populations and species. If mean trait values are expected to evolve there seems little reason to suppose that the variances and covariances will not also be subject to selection. Selection and drift act upon the phenotype and hence also the phenotypic variances and covariances, and thus any study of evolutionary change must address both the change in phenotypic means and the change in the phenotypic variance-covariance structure.

The evolution of the mean phenotype can be modelled using the multivariate extension of the breeders equation where is the vector of mean responses, **G** is the matrix of additive genetic variances and covariances, **P** is the matrix of phenotypic variances and covariances and **S** is the vector of selection differentials (Lande, 1979). It is evident from the forgoing equation that evolutionary change is a function of the phenotypic variance-covariance matrix (hereafter the **P** matrix) and in general this matrix, as with its counterpart the **G** matrix, is assumed to be constant. This assumption has been justified by two further assumptions, namely that population size is sufficiently large that genetic drift can be ignored and that selection is sufficiently weak that variation eroded by selection is replaced by mutation (Lande, 1976, 1980, 1984). Both of these assumptions are highly controversial. Effective population sizes are frequently small enough that significant drift can be expected to occur, particularly over long periods of time (Lande, 1976; Lynch, 1990; chapter 8 in Roff, 1997). Estimates of selection coefficients in wild populations show that the strength of selection varies widely from weak to very strong (Endler, 1986; Kingsolver *et al.*, 2001), although the extent to which the estimated values represent a random sample of selection coefficients is uncertain. Nevertheless, these data indicate that the assumption that the **G** or **P** matrix will be invariant cannot be justified on theoretical grounds alone but must be verified empirically (Turelli, 1988; Arnold, 1992; Whitlock *et al.*, 2002). The question then is not whether **P** matrices vary but rather at what level do detectable differences arise and to what effects can these differences be attributed?

In the present paper, we present an analysis of geographic variation in the phenotypic means, variances and covariances of populations of two grasshopper species, *Melanoplus sanguinipes* and *M. devastator.* The purpose of the analysis is to determine: (1) if the phenotypic means and **P** matrix vary among populations and between species; (2) if such variation correlates with geographic or environmental variables, suggesting that selection has shaped the **P** matrix; and (3) if variation in the **P** matrix correlates with variation in neutral genetic markers, an indication that drift has also played a role in shaping the **P** matrix.