Variable-r in sex ratios: Formulas in honor of Jim Vaupel

BACKGROUND Two seminal studies in the 1980s, by Preston and Coale (1982) and Arthur and Vaupel (1984), generalized the Lotka equations developing the variable-r methods. OBJECTIVE Time changes in sex ratios (males:females) are studied from the perspective of the variable-r method to estimate the contributions of fertility, mortality, and net-migration. METHODS The time change in sex ratios can be calculated as a comparison of the growth rates of the sexes. The difference is then decomposed into population composition, and the age-specific components of fertility, mortality, and net migration. Thirteen countries with long historical demographic series are used to illustrate the time trends in sex ratios.