Estimation of seal pup production from aerial surveys using generalized additive models

In this paper, we estimate the pup production of harp seals (Pagophilus groenlandicus) using generalized additive models (GAMs) based on thin-plate regression splines. The spatial distribution of seal pups in a patch is modelled using GAMs, and the pup production is estimated by numerically integrating the model over a fine grid area of the patch. Closed form expression for estimation of the the standard error of the pup production estimate is derived. The estimators are applied to simulated seal populations to investigate their properties. The results show that the proposed pup production estimator is comparable with the conventional pup production estimator. However, the bias of the standard error estimator of the proposed method is much lower than the bias of the conventional standard error estimator. The decrease of standard error bias results in a considerable reduction of the coefficient of variation estimate using the proposed GAM-based method. The proposed method is also applied to real survey data of harp seals obtained from aerial surveys in the Greenland Sea pack ice in 2002. We show that the number of pups counted from aerial photographs possess a good fit to the negative binomial distribution when a logarithmic link function is applied. The approach described here is applicable to many situations where georeferenced counts or measurements are available.