Animal density and track counts: understanding the nature of observations based on animal movements.

Derek Keeping,Rick Pelletier,Alfred L Roca

doi:10.1371/journal.pone.0096598

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.

Highlights

Estimating animal numbers is often a basic requirement for determining the status of species
Animal track surveys are used in a range of efforts, such as large-scale biodiversity monitoring in northern Europe [6,7], North America [8], and Australia [9], habitat and land use impact assessments [10,11,12,13,14,15,16], planning sustainable harvest of ungulates and furbearers [17,18,19,20,21,22,23], managing invasive species [24,25,26,27], and monitoring endangered populations such as black rhino Diceros bicornis [28], tigers Panthera tigris [29,30], Florida panther Puma concolor [31], wolverine Gulo gulo [32,33], and polar bears Ursus maritimus [34]
Because the mean encounter rates did not change, the FMP formula estimated densities accurately regardless of the shape taken by the travel paths

Summary

Introduction

Estimating animal numbers is often a basic requirement for determining the status of species This task is deceptively simple and no single best approach exists; techniques that work well in some situations are useless in others [1]. Many terrestrial mammals are nocturnal, cryptic in appearance, and generally adept at avoiding being seen, which limits well-developed methods of direct observation, including distance sampling [2,3,4,5]. These challenges leave indirect observation, for example via animal tracks or remote photography, as often the only realistic option. Liebenberg [35] notes that a fully modern human brain evolved when all humans were hunter-gatherers and argues that efficient tracking techniques necessary for successful acquisition of prey still practiced by contemporary hunter-gatherers were the origin of creative hypothetico-deductive thought processes made explicit by modern science

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