The idea of evolvability and its evolution has assumed various guises (Dawkins 1989; Cheverud 1996; Wagner and Altenberg 1996; Kirschner and Gerhart 1998; Radman et al. 1999; Hansen and Houle 2004). Evolvability can profitably be viewed as the intrinsic capacity of a genome to produce adaptive variants (Wagner and Altenberg 1996). In quantitative genetics, the concept of evolvability is closely related to the variability and standing genetic variance of phenotypic traits. With respect to a single trait affected by many genes, evolvability is dependent upon the input of new genetic variance due to mutation each generation. For a phenotype comprising multiple quantitative traits, the relevant parameter is **M**, the mutational matrix, which describes the effects of new mutations on trait variances and covariances. For a response to selection to occur, the variance due to new mutations must be translated into standing genetic variance and covariance in the population by various microevolutionary processes. The population-level additive genetic variance is described by the **G**-matrix, which has additive genetic variances on its main diagonal and additive genetic covariances elsewhere (Lande 1979; Lynch and Walsh 1998). The additive genetic covariances reflect coupling between traits that arises from pleiotropy and linkage disequilibrium. The population's greatest capacity to evolve in trait space is along the first principal component of the **G**-matrix, also known as the genetic line of least resistance (Schluter 1996). In other words, the **G**-matrix is the proximate parameter most relevant to quantitative measures of evolvability. To understand the evolution of evolvability from this standpoint, we need to understand the evolution of the **G**-matrix and its determinants, including the **M**-matrix.

At equilibrium, the **G**-matrix and hence the immediate capacity of a population to evolve can be viewed as a balance between the processes that affect genetic variation and covariation. In an infinite population at equilibrium, the input of genetic variation each generation due to mutation and recombination exactly offsets the pruning and reshaping that arises from stabilizing selection (Lande 1980). In a more realistic view of the world, finite population size imposes erratic fluctuations on top of this simple deterministic picture, causing the cloud of genetic values described by the **G**-matrix to pulsate and wobble from generation to generation (Jones et al. 2003, 2004). Thus, the primary determinants of the **G**-matrix are selection (especially stabilizing selection), mutation, recombination, and finite population size. The extent to which these determinants change over time is the central issue in the evolution of evolvability.

In two previous reports we studied the evolution and stability of the **G**-matrix under various constant regimes of population size, mutation, and stabilizing selection (Jones et al. 2003, 2004). We resorted to computer simulation because analytical work and empirical studies have failed to define the conditions under which **G** is likely to be stable or unstable. One of our main findings was that different aspects of stability react differently to selection, mutation, and drift. In particular, we found that correlational selection, correlated pleiotropic mutational effects, and large population size promoted stability of the orientation of the **G**-matrix. In contrast, stability in the overall size and eccentricity of the **G**-matrix was increased only by population size (Jones et al. 2003). The addition of a moving optimum led to two important new insights (Jones et al. 2004). First, evolution along the genetic line of least resistance increased stability of the orientation of the **G**-matrix relative to stabilizing selection alone. Evolution across genetic lines of least resistance decreased **G**-matrix stability. Second, evolution in response to a continuously changing optimum for one trait can produce persistent maladaptation in a correlated trait, even if its optimum does not change. In those simulations, as in virtually all other theoretical work, we employed a constant, nonevolving pattern of pleiotropic mutation.

In this report we consider the possibility that the pattern of pleiotropic mutation might evolve in response to selection. Although many estimates exist for the mutational variance, which corresponds to the diagonal elements of **M,** of single traits (Lynch and Walsh 1998; Lynch et al. 1999), only a few studies have assessed the rate and pattern of pleiotropic mutation, that is, the off-diagonal elements of **M** (Lynch 1985; Houle et al. 1994; Fernández and López-Fanjul 1996; Camara and Pigliucci 1999; Keightley et al. 2000; Estes et al. 2005). Comparative studies of **M** are nonexistent. Theoretical studies have modeled the composition of the **M**-matrix, but very little work has addressed the question of whether and how it evolves (Hermisson et al. 2003; Liberman and Feldman 2005). Thus, one of our goals is to provide some theoretical expectations about **M**-matrix evolution that might guide experimental and comparative studies of pleiotropic mutation. The **M**-matrix is the most important genetic parameter affecting evolvability, so the extent to which **M** evolves and responds to selection will provide direct insights into the evolution of evolvability.

Our second goal is to determine how an evolving pattern of pleiotropic mutation might affect evolvability through its effects on the **G**-matrix, the quantitative genetic parameter most directly relevant to the response to selection. If, for example, the **M**-matrix evolves toward alignment with the adaptive landscape, such evolution would also promote evolutionary alignment of **G** with the landscape. The result would be coincidence in genetic and selective lines of least resistance (Arnold et al. 2001). Alternatively, **M** might be a genetic constraint that maintains its independence in the face of selection. Thus, if the **M**-matrix does not respond to selection, we can expect the genetic line of least resistance to be a compromise between the major axes of the **M**-matrix and the adaptive landscape.

Our third goal is to determine how an evolving pattern of pleiotropic mutation might affect the stability of the **G**-matrix. Two extreme outcomes are conceivable. On the one hand, evolution of **M** that promotes alignment of **M** and **G** with the adaptive landscape might promote stability of the **G**-matrix. On the other hand, weak selection on pleiotropic mutation coupled with drift due to finite population size might make **M** prone to stochastic fluctuations that destabilize the **G**-matrix. One of our aims is to determine the conditions under which these and other outcomes might prevail. We address these issues by developing a two-trait, quantitative genetic model of **M** evolution in which the diagonal elements of the matrix are held constant, whereas the mutational correlation is assumed to be a quantitative trait determined by multiple additive loci. We use this model to explore the evolutionary dynamics of the mutational correlation under stabilizing selection, with a particular emphasis on the evolution of evolvability and the stability of the **G**-matrix.