Dynamic approach to space and habitat use based on biased random bridges

Abstract

Background: Although habitat use reflects a dynamic process, most studies assess habitat use statically as if an animal's successively recorded locations reflected a point rather than a movement process. By relying on the activity time between successive locations instead of the local density of individual locations, movement-based methods can substantially improve the biological relevance of utilization distribution (UD) estimates (i.e. the relative frequencies with which an animal uses the various areas of its home range, HR). One such method rests on Brownian bridges (BBs). Its theoretical foundation (purely and constantly diffusive movements) is paradoxically inconsistent with both HR settlement and habitat selection. An alternative involves movement-based kernel density estimation (MKDE) through location interpolation, which may be applied to various movement behaviours but lacks a sound theoretical basis.

Methodology/principal findings: I introduce the concept of a biased random (advective-diffusive) bridge (BRB) and show that the MKDE method is a practical means to estimate UDs based on simplified (isotropically diffusive) BRBs. The equation governing BRBs is constrained by the maximum delay between successive relocations warranting constant within-bridge advection (allowed to vary between bridges) but remains otherwise similar to the BB equation. Despite its theoretical inconsistencies, the BB method can therefore be applied to animals that regularly reorientate within their HRs and adapt their movements to the habitats crossed, provided that they were relocated with a high enough frequency.

Conclusions/significance: Biased random walks can approximate various movement types at short times from a given relocation. Their simplified form constitutes an effective trade-off between too simple, unrealistic movement models, such as Brownian motion, and more sophisticated and realistic ones, such as biased correlated random walks (BCRWs), which are too complex to yield functional bridges. Relying on simplified BRBs proves to be the most reliable and easily usable way to estimate UDs from serially correlated relocations and raw activity information.

Figure 1. Utilization Distribution (UD) of an African buffalo herd for a 4-week stationary period computed using simplified BRBs (σ_min = 100 m, D = 440 m²/min and T_max>30 min) through the MKDE method (h_min = σ_min and h_max = (σ² _min+DT_max/2)^0.5).

The top panel shows how the period considered (early wet season, indicated by the white background) was delineated by marked and durable changes in mean or variance of longitude or latitude (computed over a few days in a sliding window). The bottom left panel shows the herd movement (big dots represent GPS relocations recorded at 30-min intervals and tiny dots locations interpolated along track segments at 1-min activity intervals) and the different habitat types available within 95% UD cumulative frequency isopleths (R: Rocky grounds, G: Forest galleries, P: Perennial grasses, A: Annual grasses). The bottom right panel shows the GPS relocations (black dots) and UD cumulative frequencies up to 95% (the colour attributed to a given percentage p applies to areas comprised between p and p–5% isopleths).