Comparison of Model Based Geostatistical Methods in Ecology: Application to Fin Whale Spatial Distribution in Northwestern Mediterranean Sea

Abstract

Characterizing spatial distribution of wild species as fin whales is a major issue to protect these populations and study their interaction with their environment. Accurate maps may be difficult to obtain with very heterogeneous observation efforts and unfrequent sightings. This paper proposes to compare two geostatistical methods associated with the Poisson distribution which models the observation process. First, assuming few weak hypotheses on the distribution of abundance, we improved the experimental variogram estimate using weights that are derived from expected variances and proposed a bias correction that accounts for the Poisson observation process. The kriging system was also modified to interpolate directly the underlying abundance better than data themselves. Second the Bayesian approach proposed by Diggle in 1998 was run on the same dataset. In both case results were substantially improved compared to classical geostatistics. Advantages and drawbacks of each method are then compared and discussed.