Improving the precision of the daily egg production method using generalized additive models

Generalized additive models (GAMs) are used to model spatial variation in egg density and increase the precision of biomass estimates from the daily egg production method. Application of GAMs to survey data from the western mackerel (Scomber scombrus) and horse mackerel (Trachurus trachurus) stocks result in a substantial reduction in coefficients of variation of egg abundance. In developing GAM methods for the daily egg production method, we generalize Pennington's method, in which presence-absence is modelled separately from nonzero observations, and use a new form of the bootstrap that accommodates clustered count data without requiring explicit modelling of the form of clustering. In addition to increasing estimation precision, the use of GAMs has several advantages over stratified sample survey methods. To a large degree they allow the data to determine the form of functional dependence of the response on explanatory variables; they accommodate a wide variety of forms of stochastic variation of the response; they provide maps of the predicted density within the survey area; they provide an objective means of interpolating into unsampled areas; and estimation does not assume random sampling with respect to location.