LoCoH: nonparameteric kernel methods for constructing home ranges and utilization distributions

Parametric kernel methods currently dominate the literature regarding the construction of animal home ranges (HRs) and utilization distributions (UDs). These methods frequently fail to capture the kinds of hard boundaries common to many natural systems. Recently a local convex hull (LoCoH) nonparametric kernel method, which generalizes the minimum convex polygon (MCP) method, was shown to be more appropriate than parametric kernel methods for constructing HRs and UDs, because of its ability to identify hard boundaries (e.g., rivers, cliff edges) and convergence to the true distribution as sample size increases. Here we extend the LoCoH in two ways: "fixed sphere-of-influence," or r-LoCoH (kernels constructed from all points within a fixed radius r of each reference point), and an "adaptive sphere-of-influence," or a-LoCoH (kernels constructed from all points within a radius a such that the distances of all points within the radius to the reference point sum to a value less than or equal to a), and compare them to the original "fixed-number-of-points," or k-LoCoH (all kernels constructed from k-1 nearest neighbors of root points). We also compare these nonparametric LoCoH to parametric kernel methods using manufactured data and data collected from GPS collars on African buffalo in the Kruger National Park, South Africa. Our results demonstrate that LoCoH methods are superior to parametric kernel methods in estimating areas used by animals, excluding unused areas (holes) and, generally, in constructing UDs and HRs arising from the movement of animals influenced by hard boundaries and irregular structures (e.g., rocky outcrops). We also demonstrate that a-LoCoH is generally superior to k- and r-LoCoH (with software for all three methods available at http://locoh.cnr.berkeley.edu).     

Estimating utilization distributions with kernel versus local convex hull methods

Estimates of utilization distributions (UDs) are used in analyses of home-range area, habitat and resource selection, and social interactions. We simulated data from 12 parent UDs, representing 3 series of increasingly intense space-use patterns (clustering of points around a home site, restriction of locations to a network of nodes and corridors, and dominance of a central hole in the UD) and compared the ability of kernel density estimation (KDE) and local convex hull (LCH) construction to reconstruct known UDs from samples of 10, 50, 250, and 1,000 location points. For KDE, we considered 4 bandwidth selectors: the reference bandwidth, least-squares cross-validation (LSCV), direct plug-in (DPI), and solve-the-equation (STE). For the sample sizes and UD patterns tested here, KDE achieved significantly higher volume-of-intersection (VI) scores with known parent UDs than did LCH; KDE also provided less biased home-range area estimates under many conditions. However, LCH minimized the UD volume that occurred outside the true home range boundary (V_out). Among the KDE bandwidth estimators, relative performance depended on the type and intensity of space use patterns, sample size, and the metric used to evaluate performance. Biologists should use KDE for UD and home range estimation within a probabilistic context, unless their objective is to exclude potentially unused areas by defining the area delimited by data. © 2011 The Wildlife Society.     

Evaluating distributional shifts in home range estimates

A variety of methods are commonly used to quantify animal home ranges using location data acquired with telemetry. High‐volume location data from global positioning system (GPS) technology provide researchers the opportunity to identify various intensities of use within home ranges, typically quantified through utilization distributions (UDs). However, the wide range of variability evident within UDs constructed with modern home range estimators is often overlooked or ignored during home range comparisons, and challenges may arise when summarizing distributional shifts among multiple UDs. We describe an approach to gain additional insight into home range changes by comparing UDs across isopleths and summarizing comparisons into meaningful results. To demonstrate the efficacy of this approach, we used GPS location data from 16 bighorn sheep (Ovis canadensis) to identify distributional changes before and after habitat alterations, and we discuss advantages in its application when comparing home range size, overlap, and joint‐space use. We found a consistent increase in bighorn sheep home range size when measured across home range levels, but that home range overlap and similarity values decreased when examined at increasing core levels. Our results highlight the benefit of conducting multiscale assessments when comparing distributions, and we encourage researchers to expand comparative home range analyses to gain a more comprehensive evaluation of distributional changes and to evaluate comparisons across home range levels.     

Effects of sampling regime on the mean and variance of home range size estimates

1. Although the home range is a fundamental ecological concept, there is considerable debate over how it is best measured. There is a substantial literature concerning the precision and accuracy of all commonly used home range estimation methods; however, there has been considerably less work concerning how estimates vary with sampling regime, and how this affects statistical inferences. 2. We propose a new procedure, based on a variance components analysis using generalized mixed effects models to examine how estimates vary with sampling regime. 3. To demonstrate the method we analyse data from one study of 32 individually marked roe deer and another study of 21 individually marked kestrels. We subsampled these data to simulate increasingly less intense sampling regimes, and compared the performance of two kernel density estimation (KDE) methods, of the minimum convex polygon (MCP) and of the bivariate ellipse methods. 4. Variation between individuals and study areas contributed most to the total variance in home range size. Contrary to recent concerns over reliability, both KDE methods were remarkably efficient, robust and unbiased: 10 fixes per month, if collected over a standardized number of days, were sufficient for accurate estimates of home range size. However, the commonly used 95% isopleth should be avoided; we recommend using isopleths between 90 and 50%. 5. Using the same number of fixes does not guarantee unbiased home range estimates: statistical inferences differ with the number of days sampled, even if using KDE methods. 6. The MCP method was highly inefficient and results were subject to considerable and unpredictable biases. The bivariate ellipse was not the most reliable method at low sample sizes. 7. We conclude that effort should be directed at marking more individuals monitored over long periods at the expense of the sampling rate per individual. Statistical results are reliable only if the whole sampling regime is standardized. We derive practical guidelines for field studies and data analysis.     

Incorporating Movement Behavior and Barriers to Improve Kernel Home Range Space Use Estimates

Abstract: Kernel-based utilization distribution (UD) estimates are powerful tools to investigate home range space use and resource selection in many vertebrate species. By ignoring local movement information provided by the serial correlation between successive locations and the constraints to movement imposed by obvious boundaries, the classical kernel method results in loosely estimated UDs that tend to overflow into never-visited areas and eventually in possibly biased estimates of space use and habitat selection. We improved biological relevance of kernel home range space use estimates by incorporating both movement (and activity) information and boundary constraints.     

The use of spatial ecological modelling as a tool for improving the assessment of geographic range size of threatened species

We analysed endemic threatened tree and reptile species of Socotra Island (Yemen), characterised by different ecological requirements and spatial distribution, in order to evaluate the usefulness of spatial ecological modelling in the estimation of species extent of occurrence (EOO) and area of occupancy (AOO). Point occurrences for the entire species range were used to model their spatial distribution by Random Forest (RF) and Generalised Linear Model (GLM). For each species the suitability area (SA) was obtained by applying the 0% omission error criterion on the probability map, and compared or integrated with EOO and AOO area obtained by topological methods such as the minimum convex polygon (MCP), α-hull and 2 km × 2 km grid.RF showed a lower prediction error than GLM. Higher accuracy was achieved for species with higher number of occurrences and narrower ecological niche. SA was always greater than AOO measured with the 2 km × 2 km grid method. SA was greater than EOO, measured by both MCP and α-hull methods, for species with localised distribution, while it was smaller for widely distributed species. EOO-α-hull area was equal or smaller than that calculated by MCP depending on the spatial distribution of species. AOO measured considering the SA within the EOO-MCP was greater than that measured using the standard 2 km × 2 km grid. Conversely, AOO calculated considering the suitable area within the EOO-α-hull showed variable results, being smaller or greater than the 2 km × 2 km grid AOO depending on the ecological niche and spatial distribution of species. According to our results, SEM does not provide an effective alternative to topological methods for the estimate of EOO and AOO. However, it may be considered a useful tool to estimate AOO within the boundaries of EOO measured by the α-hull method, because it reduces some potential sources of inconsistency and bias.     

Estimation of Shark Home Ranges using Passive Monitoring Techniques

We examined a population of blacktip sharks, Carcharhinus limbatus, within a coastal nursery area to define how individuals use the nursery habitat throughout the summer. We used a series of acoustic hydrophones to passively monitor the movement patterns of sharks for periods up to 167 days. We used passive monitoring data to calculate home range estimates using minimum convex polygon (MCP) and fixed kernel estimators. MCP calculated the extent of an individual's range. Kernel estimates provided information regarding the utilization of space within the home range including core area (50% kernel) and larger excursions outside the core area (95% kernel). Individuals within the nursery area typically used a consistently small core area. All sharks monitored in the study site underwent a home range expansion during the month of July, suggesting a synchronous population-level change in habitat use. This change in habitat use was reflected in all home range calculations. Passive monitoring revealed that young sharks remain within the nursery area for up to 6 months. The long-term use of this nursery area reflects its critical importance to young blacktip sharks.     

A scaled line-based kernel density estimator for the retrieval of utilization distributions and home ranges from GPS movement tracks

Utilization distributions (UDs) can be used to describe the intensity with which an animal or human has used a certain geographical location. Within the domain of wildlife ecology, a density distribution model represents one way to describe an animals' home range. Several methods have been developed to derive UDs, and subsequently home ranges. Most of these methods, e.g. kernel density estimation (KDE), and local convex hull methods, have been developed with point-based datasets in mind, and do not utilize additional information that comes with GPS-based tracking data (e.g., temporal information). To employ such additional information we extend the point-based KDE approach to work with sequential GPS-point tracks, the outcome of which is a line-based KDE. We first describe the design criteria for the line-KDE algorithm. Then we introduce the basic modeling approach and its refinement through the introduction of a scaling function. This scaling function modifies the utilization distribution so that a bone-like probability distribution for a single GPS track segment is obtained. Finally we compare the estimated utilization distributions and home ranges for two datasets derived using our line-KDE approach with those obtained using the point-KDE and Brownian Bridge (BB) approaches. Advantages of the line-based KDE by design are (i) a better representation of utilization density near GPS points when compared against the BB approach, and (ii) the ability to model and retain movement corridors when compared against point-KDE.     

Effects of Point Pattern Shape on Home-Range Estimates

Abstract: Home-range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home-range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home-range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space-use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home-range estimation: 1) KDE with reference bandwidths, 2) KDE with least-squares cross-validation, 3) KDE with plug-in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home-range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home-range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home-range estimation.     

Home Range Analysis of <Emphasis Type="Italic">Perodicticus potto edwardsi</Emphasis> and <Emphasis Type="Italic">Sciurocheirus cameronensis</Emphasis>

Because the spatial arrangements of nocturnal prosimians are often used to indicate their social systems, it is important to assess the reliability of methods used to analyze ranging patterns. We compared methods of home range analysis for 2 species of nocturnal prosimians: central pottos (Perodicticus potto edwardsi) and Cross River Allens galagos ({Sciurocheirus cameronensis}). We conducted radio-tracking studies of 10 pottos and 8 galagos from October 1999 – November 2000 in the montane rain forests of southwest Cameroon. We calculated home ranges via minimum convex polygon (MCPs) and kernel analyses. Adult potto home ranges averaged 145.2 ha (MCPs) versus only 28.4 ha via kernel analysis; the difference is statistically significant. The mean home range of galagos is 18.3 ha via MCPs and 2.19 ha via kernel analysis; the difference is statistically significant. Neither MCP nor kernel analyses revealed a sex difference in adult home ranges for pottos and galagos. Kernel analysis gave more reliable estimates of home ranges than the minimum convex polygon method used in many studies of nocturnal prosimians. Minimum convex polygon analysis tended to overestimate the range sizes and to include many areas not traversed by the animal. We compared our findings with those from an earlier study of similar species in Gabon, where little attention was given to the home range analysis, technique. Together with studies of lemur spatial systems they highlight the importance of considering the method of home range analysis when it is to be applied to understanding social systems.     

Patterns of Spatial use and movement of the Poóuli – a critically endangered Hawaiian honeycreeper

The Poóuli (Melamprosops phaeosoma) is a highly endangered Hawaiian honeycreeper endemic to Maui, and is currently one of the World's rarest birds. Only two wild individuals of this species are now known to exist, and they are restricted to the windward slopes of Haleakala volcano on east Maui. Studies of the more common honeycreepers on the Hawaiian islands describe a diverse array of spatial use and movement patterns, which vary according to specific ecological needs. In contrast, spatial use and movement of Poóuli are very poorly known, despite continuous field monitoring of all three individuals since 1997. We analyzed annual data by breeding season between 1995 and 2001 for three individuals, and eight days of telemetry data derived from the radio-tracking of one individual in 2002, using GIS and conventional methods, to estimate home range size, and to interpret these data alongside those for other honeycreepers. We estimated mean home range sizes of 8.43 hectares (ha) from annual re-sights using kernel analysis and 2.14 ha using minimum convex polygons, and 8.44 and 3.51 ha respectively from telemetry data. Our estimates conform to those derived for other insectivorous honeycreepers, but indicate that Poóuli may forage widely to support their diet of forest snails. Our home range size estimates are compatible with estimates of population density for Poóuli that were derived from field transects between 1975 and 1985, suggesting that such field methods may be a reliable density estimator for rare forest birds. Jim J. Groombridge and Bill Sparklin: Joint first author     

Comparing Global Positioning System and Very High Frequency Telemetry Home Ranges of White-Tailed Deer

ABSTRACT Use of Global Positioning System (GPS) collars on free-ranging ungulates overcomes many limitations of conventional very high frequency (VHF) telemetry and offers a practical means of studying space use and home range estimation. To better understand winter home ranges of white-tailed deer (Odocoileus virginianus), we evaluated GPS collar performance, and we compared GPS- and VHF-derived diurnal home ranges (for the same animals) and GPS-derived home range estimates for diurnal and nocturnal locations. Overall, the mean fix success rate of our GPS collars was 85% (range = 14–99%). Kernel density estimates of home range (using the 95% probability contour) derived from GPS and VHF locations were generally similar, as were GPS-derived diurnal and nocturnal home ranges. Overlap indices between GPS and VHF utilization distributions (UDs) ranged from 0.49 to 0.78 for the volume of intersection (VI) index and from 0.67 to 0.94 for Bhattacharyya's affinity (BA); overlap indices for GPS-diurnal and nocturnal UDs ranged from 0.29 to 0.81 for VI and from 0.56 to 0.94 for BA. Despite similarities of home ranges estimated from GPS versus VHF locations and GPS-diurnal versus nocturnal locations, our data also indicate that differences may have important implications for studies focused on deer use of space, habitat, and resources at a finer scale.     

固定核空间法和最小凸多边形法估计藏狐家域的比较

最小凸多边形法(MCP)和固定核空间法(FKE)是目前最常用的家域计算方法,但受空间自相关性、偏远位点等问题的影响,两种方法均存在明显的局限性。本文根据2006 年和2007 年在四川省石渠县和青海省都兰县的7 只藏狐352 个活动位点数据,分析MCP 和FKE 家域估计的效果和存在的问题。结果显示:(1)利用概率百分比≤95% 时,MCP 计算结果和FKE 没有显著差异;(2)极端点对高百分比(85% ～ 100% ) 下MCP影响显著,而FKE 对极端点影响控制较好;(3)FKE 家域外形复杂,计算结果受平滑度系数设置影响显著。因此,研究领域行为时,应同时使用FKE 和95% MCP 两种方法。当数据分布较理想时,FKE 能够给出更为准确的面积估计,而MCP 则因其通用性,使得研究数据与其他研究的结果更具可比性。
     

Home range dynamics of the yellow‐footed rock‐wallaby (Petrogale xanthopus celeris) in central‐western Queensland

Analyses of the interspecific differences in macropod home range size suggest that habitat productivity exerts a greater influence on range size than does body mass. This relationship is also apparent within the rock‐wallaby genus. Lim reported that yellow‐footed rock‐wallabies (Petrogale xanthopus xanthopus) inhabiting the semi‐arid Flinders Ranges (South Australia) had a mean home range of 170 ha. While consistent with the hypothesis that species inhabiting less productive habitats will require larger ranges to fulfil their energetic requirements, the ranges reported by Lim were considerably larger than those observed for heavier sympatric macropods. The aim of the current study was to document the home range dynamics of P. x. celeris in central‐western Queensland and undertake a comparison with those reported for their southern counterparts. Wallaby movements were monitored at Idalia National Park, between winter 1992 and winter 1994. Male foraging ranges (95% fixed kernel; 15.4 ha, SD = ±7.8 ha) were found to be significantly larger than those of female wallabies (11.3 ha, SD = ±4.9 ha). Because of varying distances to the wallabies' favoured foraging ground (i.e. an adjacent herb field), the direction in which the wallabies moved to forage also significantly affected range size. Mean home range size was estimated to be 23.5 ha (SD = ±15.2 ha; 95% fixed kernel) and 67.5 ha (SD = ±22.4 ha; 100% minimum convex polygon). The discrepancy between these two estimates resulted from the exclusion of locations, from the 95% kernel estimates, when the wallabies moved to a water source 1.5 km distant from the colony site. The observed foraging and home ranges approximated those that could be expected for a macropod inhabiting the semi‐arid zone (i.e. 2.4 times larger‐than‐predicted from body mass alone). Possible reasons for the disparity between the current study and that of Lim are examined.     

Home range and movements of male feral cats (Felis catus) in a semiarid woodland environment in central Australia

There is a paucity of data on the movement patterns of feral cats in Australia. Such data can be used to refine control strategies and improve track‐based methods of monitoring populations of feral cats. In this study the home ranges and movements of male feral cats were examined over 3.5 years in a semiarid woodland environment in central Australia. Two home range estimators were used in the examination: (i) minimum convex polygon (MCP); and (ii) fixed kernel. The most widely used method of estimating home range in feral cats is MCP, while the fixed kernel method can be used to identify core areas within a home range. On the basis of the MCP method, the long‐term home ranges of feral cats in central Australia were much larger than those recorded elsewhere (mean, 2210.5 ha). Twenty‐four hour home ranges were much smaller (mean, 249.7 ha) and feral cats periodically shifted their 24 h ranges within the bounds of their long‐term home ranges. Core area analysis indicated marked heterogeneity of space use by male feral cats. Several instances where feral cats moved large distances (up to 34 km) were recorded. These long distance movements may have been caused by nutritional stress. Using data from the literature, it is shown that prey availability is a primary determinant of long‐term home range size in feral cats. The relevance of the results to the design of management strategies for feral cats in central Australia is also discussed.     

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

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.     

Use of space and home range characteristics of Lepilemur mittermeieri,an endangered sportive lemur endemic to the Ampasindava peninsula,north‐west Madagascar

Lepilemur mittermeieri, a little‐studied sportive lemur of north‐west Madagascar, endemic to the Ampasindava Peninsula, faces habitat loss through forest degradation and rapid fragmentation. Understanding its habitat requirement is the first step toward preservation of this threatened forest‐dependent species. In this study, we gathered data on the use of space and home range characteristics of L. mittermeieri. We studied individuals from early March to the end of June 2015 and 2016, in three sites of the Ampasindava peninsula. We radio‐tracked 15 individuals to obtain detailed information on the size and location of home ranges (around 450 hr of tracking). Direct observation and morphometric measurements provided additional data sets. Both kernel density estimation (KDE) and minimum convex polygon (MCP) methods yielded similar home range sizes (an average of 2.01 ha with KDE method and 1.96 ha with MCP method). We did not find differences in home range size between males and females, with respect to forest type or proximity to the forest edge. Home ranges overlapped and individuals showed low levels of territoriality. We highlighted a sexually‐dimorphic trait: males have longer upper canine than females. Our results constitute the first set of ecological information on Lepilemur mittermeieri and could be the basis for a conservation strategy for this endangered species with a very small distribution area.     

洪雅县人工林赤腹松鼠活动范围及栖息地利用

2009年3～8月期间,通过观察并利用无线电遥测等方法对洪雅县林场赤腹松鼠(Callosciurus erythraeus)的活动范围和栖息地利用进行了研究。研究结果显示,赤腹松鼠的最小凸多边形(minimum convex polygon,MCP)巢域面积为(1.90±0.59)hm2,95%和60%固定核法(fixed kernel,FK)巢域面积分别为(1.06±0.19)hm2和(0.16±0.03)hm2。处在求偶高峰期的雄鼠会显著地扩大活动范围。栖息地利用的研究结果表明,赤腹松鼠对栖息地因子有明显的选择性,倾向在坡度大、灌木生长繁茂、靠近人居和水源及有藤本植物覆盖的区域活动。