A sex difference in seasonal timing of birth in a livebearing fish

Sex differences in seasonal timing include differences in hatch- or birth-date distribution and differences in the timing of migration or maturation such as protandrous arrival timing (PAT), which is early male arrival at breeding sites. I describe a novel form of protandrous arrival timing, as a sex difference in birth-date distribution in a live-bearing fish (Dwarf Perch, Micrometrus minimus). In this species, birth coincides with arrival at breeding sites because newborn males are sexually active. A series of samples of pregnant females and young of year was collected in Tomales Bay, CA. I analyzed the daily age record in otoliths to estimate the conception date of broods and the age that young-of-year individuals were born. Males were born at a younger age than females, as indicated by the daily age record and also by the predominance of females in broods from which some young had already been born, which was a common occurrence in pregnant females with older embryos. Sex ratio of broods varied with conception date such that early-season broods were predominantly male, possibly as a result of temperature-dependent sex determination. The combined effects of the sex difference in age at birth and seasonal shift in sex ratio were to shift the mean birth date of males relative to females by five days. The most likely ultimate explanation for PAT in the Dwarf Perch is that it arises from exploitation (scramble) competition for mating opportunities among recently-born young-of-year males.

Preference Structure and Random Paths to Stability in Matching Markets

This paper examines how preference correlation and intercorrelation combine to influence the length of a decentralized matching market's path to stability. In simulated experiments, marriage markets with various preference specifications begin at an arbitrary matching of couples and proceed toward stability via the random mechanism proposed by Roth and Vande Vate (1990). The results of these experiments reveal that fundamental preference characteristics are critical in predicting how long the market will take to reach a stable matching. In particular, intercorrelation and correlation are shown to have an exponential impact on the number of blocking pairs that must be randomly satisfied before stability is attained. The magnitude of the impact is dramatically different, however, depending on whether preferences are positively or negatively intercorrelated.

Teaching Time Preference and Human Impatience: The Billionaire Game

The Billionaire Game involves students in discussing time preference, or what Fisher (1930) calls human impatience. The game can facilitate the introduction of the material on present value and discounting or discussions on such issues as investment in human capital and the intertemporal consumption-saving decision. Thus, the game can facilitate discussions in a number of economics courses.