Animal Density and Track Counts: Understanding the Nature of Observations Based on Animal Movements

Abstract

Counting animals to estimate their population sizes is often essential for their management and conservation. Since practitioners frequently rely on indirect observations of animals, it is important to better understand the relationship between such indirect indices and animal abundance. The Formozov-Malyshev-Pereleshin (FMP) formula provides a theoretical foundation for understanding the relationship between animal track counts and the true density of species. Although this analytical method potentially has universal applicability wherever animals are readily detectable by their tracks, it has long been unique to Russia and remains widely underappreciated. In this paper, we provide a test of the FMP formula by isolating the influence of animal travel path tortuosity (i.e., convolutedness) on track counts. We employed simulations using virtual and empirical data, in addition to a field test comparing FMP estimates with independent estimates from line transect distance sampling. We verify that track counts (total intersections between animals and transects) are determined entirely by density and daily movement distances. Hence, the FMP estimator is theoretically robust against potential biases from specific shapes or patterns of animal movement paths if transects are randomly situated with respect to those movements (i.e., the transects do not influence animals’ movements). However, detectability (the detection probability of individual animals) is not determined simply by daily travel distance but also by tortuosity, so ensuring that all intersections with transects are counted regardless of the number of individual animals that made them becomes critical for an accurate density estimate. Additionally, although tortuosity has no bearing on mean track encounter rates, it does affect encounter rate variance and therefore estimate precision. We discuss how these fundamental principles made explicit by the FMP formula have widespread implications for methods of assessing animal abundance that rely on indirect observations.

A camera‐based method for estimating absolute density in animals displaying home range behaviour

“…Another advantage of the proposed method is that, neither stringent assumptions nor precise data on movement features are needed to estimate densities (but to define the optimal sampling settings some rough idea is required, Appendix S1). When using wildlife video recording methods, specific models that relate animal density with encounter rates have been widely considered: the random encounter model (REM), derived from ideal gas models (Hutchinson & Waser, ), and a closely related approach based on the Formozov–Malyshev–Pereleshin (FMP) formula (Keeping & Pelletier, ; Stephens, Zaumyslova, Miquelle, Myslenkov, & Hayward, ), for which animal speed is assumed to be known (Cusack et al., ; Rowcliffe et al., ). A drawback of the REM and FMP is the non‐instantaneous nature of encounters, which account for the speed‐related bias (Ward‐Paige et al., ).…”

“…detections are equivalent to encounters), distance sampling methods record distances from the observation point (typically line transects) to any detected animal (Buckland et al., ) and claim reasonable accuracy only if animals move at less than half the speed of the observer (Ward‐Paige et al., ). Thus, in general, encounter‐related methods are highly dependent on the assumptions on how animals move (Cusack et al., ; Glennie et al., ; Keeping & Pelletier, ; Rowcliffe et al., ). Different alternatives for circumventing this problem have been proposed (Hutchinson & Waser, ; Lucas et al., ; Ward‐Paige et al., ).…”

Simplified large African carnivore density estimators from track indices

“…Methods used to estimate densities of African large carnivores include intensive studies (Smuts, 1982; Maude, 2010), call in surveys (Cozzi et al, 2013; Mills, Juritz & Zucchini, 2001; Ogutu & Dublin, 1998), camera trap surveys (Balme, Hunter & Slotow, 2009; Kent & Hill, 2013), track counts (Funston et al, 2010; Keeping & Pelletier, 2014; Stander, 1998) and measuring track dimensions to identify individuals (Gusset & Burgener, 2005). This paper focuses on the use of track indices to estimate large carnivore densities in Africa.…”

A preliminary survey of medium and large‐sized mammals from Lebu Natural Protected Forest, Southwest Showa, Ethiopia

“…The variety of conditions created in a given ecosystem that harbors diversified-habitats that serves as home to a large number of endemic mammal species (Bantihun & Bekele, 2015;Yalden & Largen, 1992). A basic requirement for determining the status of species is surveying mammals (Keeping & Pelletier, 2014). Mammal inventories are essential tools to efficiently forward conservation strategies and management practices (Legese, Bekele, & Kiros, 2019).…”