The distribution and numbers of cheetah (Acinonyx jubatus) in southern Africa.

Assessing the numbers and distribution of threatened species is a central challenge in conservation, often made difficult because the species of concern are rare and elusive. For some predators, this may be compounded by their being sparsely distributed over large areas. Such is the case with the cheetah Acinonyx jubatus. The IUCN Red List process solicits comments, is democratic, transparent, widely-used, and has recently assessed the species. Here, we present additional methods to that process and provide quantitative approaches that may afford greater detail and a benchmark against which to compare future assessments. The cheetah poses challenges, but also affords unique opportunities. It is photogenic, allowing the compilation of thousands of crowd-sourced data. It is also persecuted for killing livestock, enabling estimation of local population densities from the numbers persecuted. Documented instances of persecution in areas with known human and livestock density mean that these data can provide an estimate of where the species may or may not occur in areas without observational data. Compilations of extensive telemetry data coupled with nearly 20,000 additional observations from 39 sources show that free-ranging cheetahs were present across approximately 789,700 km2 of Namibia, Botswana, South Africa, and Zimbabwe (56%, 22%, 12% and 10% respectively) from 2010 to 2016, with an estimated adult population of 3,577 animals. We identified a further 742,800 km2 of potential cheetah habitat within the study region with low human and livestock densities, where another ∼3,250 cheetahs may occur. Unlike many previous estimates, we make the data available and provide explicit information on exactly where cheetahs occur, or are unlikely to occur. We stress the value of gathering data from public sources though these data were mostly from well-visited protected areas. There is a contiguous, transboundary population of cheetah in southern Africa, known to be the largest in the world. We suggest that this population is more threatened than believed due to the concentration of about 55% of free-ranging individuals in two ecoregions. This area overlaps with commercial farmland with high persecution risk; adult cheetahs were removed at the rate of 0.3 individuals per 100 km2 per year. Our population estimate for confirmed cheetah presence areas is 11% lower than the IUCN's current assessment for the same region, lending additional support to the recent call for the up-listing of this species from vulnerable to endangered status.

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

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.