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Recent research has shown how process variability and measurement error in ecological time series can be separated using state-space modeling techniques to combine individual-based data with population counts. We extend the current maximum likelihood approaches to allow the incorporation of sex- and age-dependent counts and provide an application to data from a population of Soay sheep living on the St. Kilda archipelago. We then empirically evaluate the performance and potential of the method by sequentially omitting portions of the data available. We show that the use of multivariate time series extends the power of the state-space modeling approach. The variance of measurement error was found to be smaller for males and the sex ratio of lambs to be skewed toward females and constant over time. Our results indicated that demographic parameters estimated using state-space modeling without relevant individual-based data were in close agreement with those obtained from mark-recapture-recovery analyses alone. Similarly, estimates of population size obtained when the corresponding count observations were unavailable were close to those from the entire data set. We conclude that the approach illustrated here has great potential for estimating hidden demographic parameters, planning studies on population monitoring, and estimating both historical and future population size.

Original publication




Journal article


Am Nat

Publication Date





722 - 733


Animals, Demography, Female, Fertility, Likelihood Functions, Male, Models, Biological, Population Density, Sex Ratio, Sheep