Input counts of individuals during many seasons are converted into an estimate of total population size each season. This covers a scenario where there is asynchrony, so that there is never a day when all individuals are present at once. The degree of asynchrony is estimated using the mean length of time each individual remains in the study area (referred to as tenure of individuals). If the duration of the entire season is much longer than the mean tenure, then asynchrony is high (ie synchrony is low); then the maximum count is much lower than the total population. At the other extreme, if the tenure equals the duration of the season, there is complete synchrony, and the count of individuals is the same as the population size.
The model requires prior estimates of mean tenure per individual, and the variance of tenure among individuals. Without that, there are too many parameters to fit. Ideally, tenure is known from observations of some marked individuals. Both mean and variance of tenure must be input as prior probabilitiy distributions in a Bayesian sense. Some background on the use of priors is helpful in understanding the method.
On the other hand, the distribution of arrival and departure dates of individuals are estimated by the model. No knowledge of either is needed in advance. Both distributions are assumed to follow a Gaussian. The model will also estimate the correlation between arrival and tenure, ie, if late arriving individuals have shorter (or longer) tenure on the colony.
The power of the multi-season approach is that some seasons with poor coverage will still yield good population estimates as long as other seasons have many counts. This is based on the assumption that individual phenology is consistent (but not identical!) across seasons. Some knowledge of multi-level statistical modeling will be helpful in understanding how this works.
The model assumes all individuals present on any day are detected counted. Incomplete detection would have to be estimated with additional information.
To execute the model, a table of counts per day in one or more seasons must be input (see text box below), along with basic input parameters needed to initiate the model. Detailed instructions follow, along with a sample data table. Details of the procedure are published in "Estimating population size in asynchronous aggregations: a Bayesian approach and test with elephant seal censuses".