• Mirounga angustirostris;
  • breeding asynchrony;
  • pinniped colony size;
  • elephant seal population;
  • inverse modeling;
  • Gibbs sampler;
  • Bayesian


Many organisms reproduce in temporary aggregations where estimates of colony size can be made by direct counts. When individuals are not synchronous, however, early breeders depart before the last arrive, so counts underestimate the total breeding population. We present a model describing a colony's census as a function of arrival, breeding tenure, and the correlation between them, and we use it to illustrate how variance in arrival and tenure affect the census. Counts of breeding female northern elephant seals (Mirounga angustirostris) from 1975 to 2007 were used to test the model. Four of the model's parameters—population size, mean and variance of arrival date, and the correlation between arrival date and breeding tenure—could be estimated from census data using a Bayesian approach; prior estimates of two other parameters—mean tenure and its variance—had to be used to avoid overparameterization. The model's predictions fit observed censuses well and produced reliable estimates of population size and arrival behavior, showing that the maximum census was 8%–16% below the total number of breeding females. This method could be used for estimating abundance in any asynchronous aggregation, given independent information on one of the defining distributions: arrival, tenure, or departure.