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

Abstract

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.

Estimation of Pup Production of Hooded and Harp Seals in the Greenland Sea in 2007: Reducing Uncertainty Using Generalized Additive Models

“…In the survey analysis developed in Salberg et al (2009) the data was analyzed using spatial modeling methods based on Generalized Additive Models.…”

“…Hence, the GAM provides us with a smoothed expected seal density surface over the entire survey area. To estimate the total pup production in the patch, we numerically integrate the expected seal density over space (Augustin et al, 1998;Borchers et al, 1997;Salberg et al, 2009) The method used to calculate the variance of the pup production follows exactly the procedures described in detail in Salberg et al (2009), and has the following compact form…”

“…We refer to the original manuscript for a detailed explanation of the various quantities (Salberg et al, 2009).…”

“…This method does not take into account spatial seal density variability along transects, but extrapolates the mean density along a transect to areas between the transects (e.g., Stenson et al, 2003). According to Salberg et al, (2009), the underlying assumption behind the classical way of estimating the variance for this type of surveys is equal mean values between two neighboring transects. This can lead to an overestimate of the variance if the data are highly clustered.…”

“…This can lead to an overestimate of the variance if the data are highly clustered. For this reason, Salberg et al, (2009) have suggested a new method to estimate the seal pup production, where the expected seal density (or seal counts) in a patch is modeled as a function of spatial position using a General Additive Model (GAM).…”