A two-dimensional geostatistic method to simulate the precision of abundance estimates

Abstract

In this paper, we outline a geostatistic method to simulate the relative precision (coefficient of variation, CV) of total abundance estimates of one species in a predetermined, stratified area when it is appropriate to treat the observations within each stratum as realizations of a second-order homogenous and ergodic random process. To model the spatial correlations, a variogram is fitted to normal-transformed values of the original observations. Based on the variogram and its corresponding covariance matrix, extensive simulations on a fine grid that includes the sample locations provide random realizations of the process. The normal values are back-transformed to original observation space by nonparametric reversed bootstrap, as well as by a parametric Weibull approach. The method is applied to a total of 1069 shrimp (Pandalus borealis) abundance observations from 11 annual surveys in the Barents Sea (1992–2002) where a 20 nautical mile sampling grid has been applied. On average, the CV was estimated to be 6.4% for the applied regular grid when the simulations were conditional on the observations, compared with 8.1% when the sampling locations within each of the six strata were random.