Robustness of movement models: can models bridge the gap between temporal scales of data sets and behavioural processes?

TL;DR

This paper introduces a mathematical framework to assess and improve the robustness of animal movement models across different temporal data resolutions, addressing challenges in data analysis and model applicability.

Contribution

It proposes a formal definition of robustness for movement models, enabling validation across varying temporal resolutions and incorporating approximate robustness concepts.

Findings

Exact robustness is rare in movement models.

Approximate robustness offers a practical alternative.

Framework applied successfully to resource selection models.

Abstract

Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale of the biological process of interest and matches the data sampling rate. Challenges arise when resolution of data is too coarse due to technological constraints, or when we wish to extrapolate results or compare results obtained from data with different resolutions. Drawing loosely on the concept of robustness in statistics, we propose a rigorous mathematical framework for studying movement models' robustness against changes in temporal resolution. In this framework, we define varying levels of robustness as formal model properties, focusing on random walk models with spatially-explicit component. With the new framework, we can investigate whether models can validly be applied to data across varying temporal resolutions and how we can account for these different resolutions in statistical inference results. We apply the new framework to movement-based resource selection models, demonstrating both analytical and numerical calculations, as well as a Monte Carlo simulation approach. While exact robustness is rare, the concept of approximate robustness provides a promising new direction for analyzing movement models.