Model-supervised kernel smoothing for the estimation of spatial usage

The analysis of telemetry data obtained from tagged animals often requires that a smooth surface of spatial usage is fitted to the observations. Well-established statistical techniques for doing this, such as kernel smoothing (KS), are based on asymptotic arguments that guarantee the convergence of their estimates to the truth with increasing sample size. Often, in addition to telemetry data, ecologists have access to a wealth of information relating to the animals' distribution and movement. This additional information is potentially useful for the estimation of spatial usage but currently remains unused by existing methods. In this paper, I outline and begin the validation of model-supervised kernel smoothing (MSKS), a modification of KS that uses such information to supervise surface-fitting to telemetry data. MSKS initially requires an ad-hoc synthesis of all the available information, excluding telemetry, into an auxiliary usage surface (the model). This is then combined with the kernel-smoothed telemetry data into a hybrid surface that is the weighted average of the two. Automatic selection of the smoothing coefficient and the weight associated with the model is done by means of likelihood cross-validation. I examine the performance of MSKS first, by extensive, numerical exploration on simulated data in one-dimensional space and second, on two-dimensional data obtained from an individual-based simulation of a central-place forager. The results for different models and sample sizes indicate that MSKS has three important properties. Firstly, it generally outperforms KS by an extent that depends on the quality of the auxiliary model. Secondly, when the auxiliary model is not informative, MSKS automatically reverts to a similar output as KS. Finally, in practical terms, MSKS is easy to implement and adds little to the computational requirements already made by KS methods. I illustrate the application of MSKS and further validate its performance on satellite telemetry data collected from a grey seal on the cast coast of Scotland.