Abstract.-Self-fertilization is a common form of reproduction in plants and it has important implications for quantitative trait evolution. Here, I present a model of selection on quantitative traits that can accommodate any level of self-fertilization. The "structured linear model" (SLM) predicts the evolution of the mean phenotype as a function of three distinct quantities: the mean additive genetic value, the directional dominance, and the mean inbreeding coefficient. Stochastic simulations of truncation selection demonstrate the accuracy of the SLM in predicting changes in the mean and variance of a quantitative trait over the full range of selfing rates. They also illustrate how complex interactions between selection and mating system determine the population distribution of inbreeding coefficients and also the amount of linkage disequilibrium. Changes in the genetic variance due to linkage disequilibria, which are commonly referred to as the "Bulmer effect," are greatly magnified by selfing. This complicates the relationship between selfing rate and response to selection. Like the random mating theory, the parameters of the SLM can be estimated from phenotypic data.Key words.-Quantitative genetics, selection response, self-fertilization.Received May 4, 1998. Accepted October 20, 1998 The number of studies applying quantitative genetic models to data from natural populations has increased dramatically over the last 15 years. These studies have focused on two broad objectives: (1) to measure therelationship between phenotypic variation and components of fitness such as survival and/or reproductive success; and (2) to determine the "evolutionary potential" of natural populations to respond to selection. Quantitative genetic theory suggests appropriate measures of both phenotypic selection and quantitative trait inheritance. It also indicates how these two sources of information can be combined to yield quantitative predictions for evolutionary change (Pearson 1903;Lande and Arnold 1983;Falconer 1989;Kirkpatrick and Heckman 1989;Houle 1992;Lynch and Walsh 1997).Quantitative genetic predictions depend to an important extent on the assumed mating system of a population. Most applications of the theory to natural populations have used models that assume random mating. Many species do not mate randomly in nature, however (Lande and Schemske 1985). In fact, a majority of plant studies have focused on self-fertilizing species (either partially or completely). Quantitative interpretation of results from such studies is hindered by the lack of an appropriate quantitative framework.Inbreeding changes the joint distribution of genotypic and phenotypic variation in a population and thus has important implications both for measuring phenotypic selection and the evolutionary potential of populations (Pederson 1969a; Wright and Cockerham 1985;Mitchell-Olds and Rutledge 1986;Willis 1996). In random mating models, the selection differential (8) characterizes directional selection on a single trait. The selection differentia...