Incorporating vertical dimensionality improves biological interpretation of hidden Markov model outputs

Abstract

Quantifying animal movement is a central component of ecological inquiry. Movement patterns provide insights into how animals make habitat decisions in pursuit of their life‐history requirements. Within this context, animals are expected to modulate their movement when navigating landscape complexities like steep or uneven slopes. However, the analytical tendency to predict animal movement as a function of bivariate (x, y) telemetry data (i.e. 2D methods) excludes such complexities and presumes that the landscapes over which this movement occurs are completely flat. Failure to consider vertical dimensionality may inhibit quantification and interpretation of animal behaviors, such as outputs of hidden Markov models (HMMs) built upon geometric measurements of animal movement like step length and turning angle. To explore the analytical consequences of this assumption, we utilized a dataset of GPS collared pumas Puma concolor in the Santa Cruz mountains of central California. We fit HMMs using traditional 2D step lengths and turning angles and compared them to HMMs built upon movement geometries in which we incorporated vertical dimensionality (i.e. 2D+). We then used a combination of quantitative inspection of model outputs and visual evaluation in 3D rendering software to understand what new states and biological interpretations can be facilitated by using 2D+ data. We found that 2D+ HMMs outperformed 2D HMMs in their ability to explain variation in vertical dimensionality. Furthermore, 2D+ models were able to isolate distinctive behavioral states associated with vertical dimensionality, such as movements on and off ridgelines. Our results show that 2D+ techniques enable researchers to directly investigate variation in animal movement and behavioral states across complex landscapes. We discuss the implications of our results for future study of animal behavior and energetics as well as illustrate how our methods can be tractably incorporated into HMMs to enable researchers to gain greater insights into animal movement ecology.