D (2011) “The Population Dynamics of Black-White-Mulatto Racial Systems,” American Journal of Sociology forthcoming

Abstract Building on the two-sex model of intergenerational transmission devel-oped by Preston and Campbell (AJS 1993), this paper provides a theoretical analysis of the dynamics of the racial distribution in black-white-mulatto racial systems (with black-white systems as a special case). We introduce the concept of “boundedness” for racial classification and racial switching, and show that bounded classification and switching imply long-run racial homogeneity. We also show that differential repro-duction (even with bounded classification and switching) not only permits long-run racial heterogeneity but also more complicated outcomes such as limit cycles. Be-yond our theoretical analysis, we also address the empirical case of Puerto Rico in the early 20th century, attempting to account for the dramatic growth of the white population share. While the nature of our (discrete-generations) model limits our ability to make precise short-run population projections, we show that the observed social norms governing the racial classification of children would have promoted the growth of the mulatto (not the white) share. Because the effects of racial classifi-cation and differential reproduction were roughly offsetting, the observed growth of the white share can be attributed almost entirely to racial switching. ∗For helpful comments and suggestions, I am grateful to Phil Bonacich, Mara Loveman, John Martin, Jenna Nobles, and participants in the demography seminar at UW-Madison. 1