Optimal GPS tracking for estimating species movements

Abstract

A common approach to learning about species movements is to tag individuals with a GPS transmitter. Here we provide methodology which determines the optimal programming of the times for such a device, and in doing so allow an assessment of the benefit provided over equidistant sampling schedules. We provide an algorithm (and MATLAB code1) that computes the optimal patch in which to tag an individual, in addition to the optimal timing and number of samples in order to best estimate three parameters describing the species-habitat migration rate (assuming a common form of migration). We use this algorithm to identify some basic conditions of a network that ensure identifiability of model parameters: at least four distinct inter-patch distances. We subsequently apply our algorithm to a number of randomly-generated networks, and demonstrate the efficiency gains from optimising various components of the sampling schedule. Finally, we determine the optimal sampling schedule for a real network: the spotted owl (Strix occidentalis occidentalis) in Southern California (Lahaye et al., 1994; Shuford and Gardali (editors), 2008). The comparison of random and real networks demonstrates the improvement in efficiency as the size and heterogeneity of the underlying network increases. This is believed to be the first methodology to determine the optimal design for monitoring species movements. Our study also differs from previous optimal design methodology for stochastic models in that we evaluate the Fisher Information Matrix exactly (to computational precision) rather than adopting an approximation (Pagendam and Pollett, 2009, 2010b). Furthermore, we provide code to implement EID- optimality, which more naturally aligns with the motivation of classical D-optimality, but in the situation of prior uncertainties on parameter values as is common to the problems of interest to us here (Walter and Pronzato, 1987).