Comparison of Kernel Density and Local Convex Hull Methods for Assessing Distribution Ranges of Large Mammalian Herbivores

Abstract

When assessing distribution range shifts, precise information is required on distribution limits, densities in occupied regions, unoccupied gaps, and changes in these measures over time. The local convex hull method recently developed for home range delineation to provide these measures was compared with that of the widely applied parametric kernel density estimation and with the commonly used tile method. The assessment used location records from 14 years of aerial surveys on four mammalian herbivores selected because of their distinct distribution patterns. Impala showed an almost continuous distribution with few gaps, wildebeest a wide distribution with regional concentrations, waterbuck a linear distribution along rivers, and sable antelope a widespread but patchy distribution. The kernel method tended to extend ranges beyond observed records, obscuring gaps within distributions. With parametric kernel approaches, bandwidth obtained via Least Squares Cross Validation techniques was not optimal when the local abundance was widely disparate, as was the case for wildebeest. The LoCoH method most effectively revealed meaningful gaps. The LoCoH method is advantageous for precisely mapping the distributions of conspicuous species for which the absence of records indicates true gaps in occurrence.

Expansions and contractions of occupied range by large mammalian herbivores in Kruger Park, South Africa: a response to rainfall variability

“…Thereafter, the joint MSCH values of for a and k were used to model and map range occupation per period. Following Chirima & Owen-Smith, 44 the 95% isopleths represented total distribution and the 75% isopleths distinguished core from marginal regions.…”

“…Range occupation patterns were modelled, mapped, and distribution changes per species assessed for periods 1977-81, 1982-86, 1987-91, and post-1991-2005, applying the Adaptive Local Convex Hull (a-LoCoH) method 43,44 in Arc Map 10.3 (Esri, Redlands, CA, USA). The method is highly accurate at identifying nonoccurrence gaps within a range.…”

“…44,45 The Adaptive Local Convex Hull applied the minimum spurious hole covering (MSHC) values of a and k derived following a procedure outlined in Getz et al 42 and Chirima & Owen-Smith. 44 Initially, the value of k (minimum neighbouring points required to construct a polygon) was fixed at 3, and the value of a (including all points within a radius such that the distances of these points to a reference point sum to a value <a) was fixed at 1 m following Chirima & Owen-Smith. 44 A curve of the area of the estimated distribution range was then plotted versus increasing values of a and k (one at a time) to find a plateau (i.e.…”

“…A KNP 5 x 5 km tile shape file was used as the basis for all analyses, following Chirima & Owen-Smith. 44 Tiles covering less than a third (8.3km 2 ) of the species' home range area extents and occurring along park boundary fences were excluded. Range was considered occupied if a herd was recorded on at least on two occasions from 1977-2005 in that same tile.…”

A Model for Animal Home Range Estimation Based on the Active Learning Method

“…Getz and Wilmers [1] noted that an HR is subject to two types of statistical errors: type I (excluding valid areas) and type II (including invalid areas) errors. Chirima and Owen-Smith [9] introduced several criteria to assess the performance of alternative HR estimation methods. These criteria are as follows: (1) ability to naturally represent the probability or possibility of the distribution of an animal;…”