Empirical tests for the importance of population mixing in constraining adaptive divergence have not been well grounded in theory for quantitative traits in spatially discrete populations. We develop quantitative-genetic models to examine the equilibrium difference between two populations that are experiencing different selective regimes and exchanging individuals. These models demonstrate that adaptive divergence is negatively correlated with the rate of population mixing (m , most strongly so when m is low), positively correlated with the difference in phenotypic optima between populations, and positively correlated with the amount of additive genetic variance (G, most strongly so when G is low). The approach to equilibrium is quite rapid (fewer than 50 generations for two populations to evolve 90% of the distance to equilibrium) when either heritability or mixing are not too low (h 2 Ͼ 0.2 or m Ͼ 0.05). The theory can be used to aid empirical tests that: (1) compare observed divergence to that predicted using estimates of population mixing, additive genetic variance/covariance, and selection; (2) test for a negative correlation between population mixing and adaptive divergence across multiple independent population pairs; and (3) experimentally manipulate the rate of mixing. Application of the first two of these approaches to data from two well-studied natural systems suggests that population mixing has constrained adaptive divergence for color patterns in Lake Erie water snakes (Nerodia sipedon), but not for trophic traits in sympatric pairs of benthic and limnetic stickleback (Gasterosteus aculeatus). The theoretical framework we outline should provide an improved basis for future empirical tests of the role of population mixing in adaptive divergence.Natural selection should lead to the adaptive divergence of populations in different environments, whereas the exchange of individuals (and their genes) should oppose that divergence. Theoretical models have confirmed that high levels of population mixing (or gene flow) can indeed constrain adaptive divergence (e.g.the relative importance of population mixing in the wild remains a matter of debate (Ehrlich and Raven 1969;Slatkin 1987;Storfer 1999). In the absence of a clear consensus, empirical tests become increasingly important. Moreover, it is often of interest to determine if maladaptive traits within specific populations are the result of immigration from elsewhere (e.g., Stearns and Sage 1980;Dhondt et al. 1990;Riechert 1993;King and Lawson 1995; Storfer and Sih 1999). Despite the obvious importance of empirical work, tests for the role of population mixing have been surprisingly haphazard in certain contexts, particularly for quantitative traits in spatially discrete populations. We feel that this deficiency can be attributed to the lack of a clearly outlined theoretical framework on which to base such tests.Our goal is to show how theory can be used as a guide for empirical tests. We first outline quantitative-genetic models for how selection and popula...