Modelling Animal Activity as Curves: An Approach Using Wavelet-Based Functional Data Analysis

Abstract

Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an inherently continuous process, even being recorded as a time series. The discreteness of the data set is clearly due to data-acquisition limitations rather than a true underlying discrete nature of the phenomenon itself. Therefore, curves are a natural representation for high-frequency data. Here, we fully model temporal activity data as curves integrating wavelets and functional data analysis, allowing for testing hypotheses based on curves rather than on scalar and vector-valued data. Temporal activity data were obtained experimentally for males and females of a small-bodied marsupial and modelled as wavelets with independent and identically distributed errors and dependent errors. The null hypothesis of no difference in temporal activity pattern between male and female curves was tested with functional analysis of variance (FANOVA). The null hypothesis was rejected by FANOVA and we discussed the differences in temporal activity pattern curves between males and females in terms of ecological and life-history attributes of the reference species. We also performed numerical analysis that shed light on the regularity properties of the wavelet bases used and the thresholding parameters.

Smoothing splines of apex predator movement: Functional modeling strategies for exploring animal behavior and social interactions

“…The apparent complexity of jaguar movement and interaction in the Taiamã Ecological Station is driven by the high density of jaguars (Fontes et al, 2021;Morato et al, 2016). Monitoring the complex fine-scale movement of multiple animal with shifts in territorial and social nature differs from previous examinations of animal movement using smoothing spline models (Buderman et al, 2016;Hefley et al, 2017;Henning et al, 2017;. This work provides a preliminary strategies for monitoring movement, behavior, social interactions, and the strength of association between animal movement, all of which are best explored on a refined and unified time grid smoothed using spline models.…”

“…FDA methods provide a viable and accessible option for examining an estimated complete path and the speed and acceleration (and deceleration) along this path, which are vital in the classification of various types of animal behavior. There have been recent basis function models proposed to model animal movement (Anderson‐Sprecher & Lenth, 1996 ; Buderman et al, 2016 ; Hefley et al, 2017 ; Henning et al, 2017 ; Hooten & Johnson, 2016 ), but there is great need to incorporate a wide array of strategies for an appropriate and application‐specific exploration using smoothed spline models.…”