Natural Primate Troops and a Stochastic Population Model

A simple stochastic population model which assumes constant birth, loss (death or emigration), and immigration rates equally and independently applicable to all individuals in a theoretical population predicts at equilibrium a negative binomial distribution of population size if all three rates are strictly positive and a Poisson distribution of population size if only the birth rate is zero or if births occur at a rate independent of population size. If the theoretical population of the model is interpreted as a troop of free-ranging primates (and not necessarily as a genetic or ecological population), several species of primates appear to confirm the equilibrium predictions of the model. The observed frequency distributions of size of troops of howler monkeys approximate a truncated negative binomial except after an epidemic which removed young monkeys; the size distribution, then, is nearly truncated Poisson, as expected. In gibbons, whose troops have a birth rate independent of troop size, the observed distributions appear to be truncated Poisson. Though few data are available, colobus monkeys seem consistent with this pattern. Sizes of bisexual troops of hanuman langurs approximate a truncated negative binomial distribution. Baboon troops have approximately truncated negative binomial distributions of size, but the parameters of the distributions appear to differ more from one species to another than to the parameters of the distributions fitted to different gibbon species. The only available detailed vital statistics on a single baboon troop suggest that the simple dynamics of the stochastic model is not faithful to what actually happens, even though the equilibrium distributions are. A statistical technique apparently new to biology, called the "jackknife," indicates that the variability of the baboon data is not sufficient to account for the difference between the estimate of a parameter of the truncated negative binomial obtained by fitting the troop size distribution and the estimate of the same parameter obtained from vital statistics. Hence the innards of the model may be faulty. Both better models and better data, especially in combination, are needed.