The Complex Linear Home Range Estimator: Representing the Home Range of River Turtles Moving in Multiple Channels
Abstract
We studied the home range and habitat use of northern map turtles (Graptemys geographica) in Québec, Canada, in a river comprised of multiple channels and islands. To better represent the home range of turtles in such complex river landscapes, we developed the complex linear home range (CLHR), a generalized estimator designed to more accurately represent turtle home ranges based on their movements in multiple channels, unlike the simple well-known linear home range and the minimum convex polygon estimators. The CLHR appears to be an estimator that can permit the interstudy comparison of turtle home ranges in other rivers characterized by multiple channels and can be calculated easily using GIS software.
A major challenge to understanding and representing the spatial ecology of turtles is the estimation of home range because no single estimator is appropriate in all settings (Kenward et al. 2001). Numerous definitions of home range have been proposed (Bury 1979) and debated (Row and Blouin-Demers 2006). The most common conceptions of home range are the fundamental measure of space use by animals (Hemson et al. 2005) or the area repeatedly traversed by an animal (Kenward 2001). This has led to the development of home range estimators that seek to permit comparisons of habitats among individuals and species. For terrestrial species, the space potentially traversed by an individual is often largely contiguous and thus can often be reasonably represented by a polygon enclosing observation points. This is usually done with the minimum convex polygon (MCP; Buhlmann and Vaughan 1991; Jones 1996; Tucker et al. 2001; Greaves and Litzgus 2007; Tran et al. 2007; Greaves and Litzgus 2008). For aquatic species, however, tight constraints on the utilization of habitat can make the straightforward calculation of an MCP less desirable than for a terrestrial species: a simple polygon enclosing observed points can contain large amounts of land that are very unlikely to be traversed by an individual (Kenward 2001). This has led some researchers to simply subtract the terrestrial portion of an MCP, leaving only the part of the polygon that touches water as the measure of home range. Although both MCP and the related “MCP−” calculation are reasonable in many settings, their ability to consistently represent traversed habitat and opportunities for interaction can break down, particularly in rivers with multiple channels (Fig. 1). In part because of such methodological difficulties, broad interstudy comparisons of home ranges sizes are few in freshwater turtle literature (Bury 1979; Plummer et al. 1997).
Citation: Chelonian Conservation and Biology 10, 2; 10.2744/CCB-0847.1
Other estimators commonly employed in turtle literature are also difficult to apply appropriately for mobile aquatic species in multiple river channels. These include 1) the linear home range (LHR), also called “home range length,” “range length,” or “range span” (Pluto and Bellis 1988; Yabe 1992; Kramer 1995; Harrel et al. 1996; Jones 1996; Plummer et al. 1997; Tucker et al. 2001; Doody et al. 2002; Fachín-Terán et al. 2006; Riedle et al. 2006; Chen and Lue 2008); 2) the river channel area, formed by multiplying the LHR by the average river width (Plummer et al. 1997; Doody et al. 2002; Kay 2004; Souza et al. 2008); and 3) kernel density (Tucker et al. 2001). Of these, the LHR is one of the simplest ways to represent home range for animals moving in a geographically restricted environment (Kay 2004). Yet despite its simplicity, because it is computed from a single line, the application of LHR is most useful in a single-channel setting and problematic in a multiple-channel river. The other common estimators have substantial limitations as well. Estimating the river channel area by multiplying the channel width by the LHR can enclose large areas not actually used by animals if applied in wide channels. Kernel density estimators are useful to quantify the intensity of habitat use, though it has been demonstrated that they are not appropriate home range estimators for herpetofauna (Row and Blouin-Demers 2006). An estimator that realistically represents movements in multiple river channels is needed to more accurately assess home ranges of turtles and other mobile aquatic species.
In this study, we compare and contrast existing home range estimators with a new estimator that we have developed, the complex linear home range (CLHR) estimator, which is suitable for animals moving in multiple river channels. We illustrate and assess the estimators using data collected on northern map turtles (Graptemys geographica) in the complex habitat of the Mille-Îles River, Québec, Canada.
Methods
Radiotracking was conducted in an approximately 4.3-km-long stretch of the Mille-Îles River encompassed by the municipalities of Terrebonne and Laval (Québec, Canada). In the section studied, there are 9 islands of various sizes, the 2 major ones being Île Saint-Joseph and Île aux Vaches, which creates a complex river landscape characterized by multiple channels. Channel width is variable and extends up to approximately 390 m. Aside from a few houses on western Île Saint-Joseph and isolated summer houses on other islands, dense housing developments line the shores of the Mille-Îles River, in particular on most parts of the southern bank of Terrebonne and on the northern bank of Laval (Fig. 1).
Turtles were caught at the southern border of Île Saint-Joseph using hoop nets, basking traps, and dip nets. Six adult females and 6 adult males were fitted with SI-2F transmitters (weight: 16 g) and SB-2F transmitters (weight: 6 g), respectively (Holohil Systems Ltd, Carp, ON, Canada). Transmitters were bolted and glued with marine epoxy at the posterior margin of the carapace of males and on the anterior margin of the carapace of females to avoid mating difficulties. The total mass of the transmitter and the fixing material did not exceed 5% of the animal weight, ensuring that movements were not negatively impacted. Turtles were tracked approximately every 10 days from late May to late October 2007, thus spanning all movements during the active season except those associated with early spring emergence. Radiotracking activities were performed with a R-1000 telemetry receiver and a Yagi antenna (Communications Specialists, Orange, CA) from a canoe equipped with an electric trolling motor. GPS coordinates were noted for each turtle relocation.
First, we calculated and assessed the performance of 3 established home range estimators: the LHR, the MCP, and the aquatic portion of the minimum convex polygon (MCP−). For our assessment of home range using these estimators, we used ArcGIS 9.3 (ESRI, Redlands, CA) and 3 add-on packages: Hawth's Analysis Tools for ArcGIS (Beyer, H.L., www.spatialecology.com/htools), ET GeoWizards 9.9 for ArcGIS 9.2 (ET SpatialTechniques, Pretoria, South Africa), and XTools Pro (Data East, Novosibirsk, Russia). We used 100% of turtle locations to compute home ranges.
Second, we developed and calculated a new CLHR estimator for assessing home range of turtles in multiple channels. The CLHR is similar in spirit to and is a generalization of the LHR estimator; however, where the LHR is restricted to a measure of a single channel segment, the CLHR explicitly considers a network of channel segments joined by vertices. For a given individual, we define the CLHR estimate as the minimum-length centerline-based tree that spans all observed location points of the individual (Fig. 2). That is, in a network of channel centerlines connected at confluences and forks, the CLHR is the minimum spanning tree that includes all observations. For this study, we computed the centerline of each channel by drawing several hundred minimum-length river crossings in a GIS and then used the coordinates of the end points to find the coordinates of the crossing segment's center. For each animal, we then joined the points in a tree of minimum total length, forming a centerline-based structure, such as in Figs. 3 and 4. A path to a straightforward automated computation of the CLHR is presented in the “Discussion” section.
Citation: Chelonian Conservation and Biology 10, 2; 10.2744/CCB-0847.1
Citation: Chelonian Conservation and Biology 10, 2; 10.2744/CCB-0847.1
Citation: Chelonian Conservation and Biology 10, 2; 10.2744/CCB-0847.1
Results
Of the 4 estimators considered, only the CLHR produced a consistently realistic representation of probable animal movement in this multiple-channel system. The total length of used habitat was not consistently captured by the simple LHR estimator because all but 1 of the 10 radiotracked turtles were observed in multiple channels. Because of this multiple-channel habitat use, only 4 of the 10 MCP polygons realistically reflected plausible movement paths and potential relocation points. In effect, the complex configuration of islands and channels created imprecision in MCP estimates in 2 senses by both overestimating and underestimating habitat. First, it meant that MCPs missed potentially crucial habitat that turtles were likely to use (see Figs. 2 and 3). Second, calculated MCPs were often comprised mostly of land area: because G. geographica is a highly aquatic species, home range estimates that encompass large amounts of land are not realistic. Likewise, simply subtracting the terrestrial area to form an aquatic-only MCP, or MCP−, does not adequately capture the habitat use of individuals either spatially (Figs. 2 and 3) or numerically (Table 1). Although the calculated values of MCP− are perhaps more correlated with the CLHR than are the others (see rankings of individuals in Table 1), it corrects only for the problem of the overestimate of terrestrial habitat. As with the MCP, the MCP− misses substantial areas of aquatic habitat that must logically be used by an animal moving between 2 relocation points (Fig. 2).
Using the CLHR estimator, males mostly had shorter home ranges than females (male average: 2734 m, range 1349–4164 m; female average: 3637 m, range 2418–4402 m). Although the sample size was too small for a formal test of differences, we note that of the 5 smallest CLHR home ranges, 4 belonged to males (Table 1). Additionally, the spatially referenced tree that underlies a numerical CLHR estimate permits the identification of areas of possible overlap among animals' home ranges (e.g., Fig. 2). Mapped CLHR estimates for individual turtles in this study suggest substantial home range overlap between all radiotracked individuals. This important characteristic is unreliably computed by the other estimators (see Figs. 2 and 3).
Despite the imprecision in this multiple-channel setting, each of the 3 estimators would have been able, to varying degrees, to detect the apparent systematic gender differences between the home ranges of males and females. For most of the estimators, the average value for males was lower than for females. Yet none of the estimators behaved identically to the CLHR (or, in fact, to each other) at the individual level in terms of either calculated numbers or rankings (Table 1). This suggests that the ability in these estimators to detect this gender pattern may have been more an accident of landscape configuration than a reliable estimator characteristic. On the whole, although some aspects of the amount and location of habitat occupied by individual turtles were captured in part by each of the other estimators, none were as clear, free of bias, or conceptually satisfying as the CLHR.
Discussion
River turtle home range size and shape may be affected by factors such as the river size, habitat, search for food and mates, spatial arrangement of structures used, and possibly their swimming performance (Pluto and Bellis 1986; Yabe 1992; Kramer 1995; Tucker et al. 2001; Bulté et al. 2008). In our study site, males appeared to have smaller home ranges than females, although the sample size precluded a formal significance test. If this pattern is confirmed by further work, it would be consistent with the study of Carrière et al. (2009), which reported larger home ranges for females in the St. Lawrence River. In contrast, however, Pluto and Bellis (1988) found that males had significantly larger home ranges in their study.
Using the CLHR, we were able to simply and clearly represent satisfactory home ranges for every radiotracked individual in our study. Unlike the other estimators considered in this study (LHR, MCP, and MCP−), only the CLHR computes the likely size and shape of home ranges of turtles without needing to compensate post hoc for obvious under- or overestimation of the actual habitat used. The CLHR estimator is a simple and intuitive method to produce home range estimates for animal movement in habitats that restrict movement to multiple channels. The CLHR permitted comparison between organisms within our study and can also facilitate comparison between home ranges in this and other multiple-channel settings. Because it is a generalized version of the LHR, it should be possible to compare CLHR estimates with LHR estimates from a single-channel study, particularly if the LHR is computed along the river's centerline. Moreover, because it is both spatially explicit and easy to calculate, the CLHR would seem to allow for hypotheses about territoriality and mating opportunities that could be quite difficult to formulate and test with other estimators. Of course, depending on the number and configuration of the channels (e.g., contrast Figs. 2 and 3), as well as the amount and shape of land between channels, one of the other estimators might behave roughly similarly to the CLHR for a given setting. Nevertheless, it bears repeating that none of the 3 established estimators could reliably be used in place of the CLHR in this study.
Despite its success, there are some caveats when considering the depiction of home range using the CLHR. One of them is that the CLHR estimator does not render cross-sectional movements in channels. This could be addressed, particularly in narrow channels, in 1 of 2 ways. First, by multiplying the CLHR length by average channel width, one could crudely estimate a complex areal home range (CAHR). Second, if the data are in a GIS, one might more precisely and quickly compute the CAHR by extracting the part of the river polygon along the minimum spanning tree that forms the CLHR. These approaches are analogous to what has been sometimes done with the linear estimates of the LHR (Plummer et al. 1997; Doody et al. 2002; Kay 2004; Souza et al. 2008). An additional caveat to consider is that the CLHR might underestimate home range size because it uses the most parsimonious network. Despite potential limitations, the CLHR was the most appropriate home range estimator to use in this multiple-channel setting.
Because the CLHR explicitly considers and incorporates movement in channels between relocation points, it would appear to have a much smaller risk than other estimators of misestimating home range because of the number and particular locations where relocations occur. Moreover, ongoing miniaturization can be expected to increasingly allow the production of a steady stream of location data rather than the relatively few isolated relocations. The CLHR is the only one of these 4 estimators that could be best compared to such a stream of points. As a result, none of the 3 other established estimators described here is as conceptually satisfying, in our opinion, as the CLHR in these multiple-channel settings.
A few authors have computed home ranges that are reminiscent of the CLHR for other turtle species and organisms, including Maremys japonica (Yabe 1992) and Crocodylus porosus (Kay 2004). However, these studies did not explicitly describe their methodology, especially regarding individuals entering more than 1 channel. We hope that the clear definition and direct comparison with other estimators presented here can aid others deciding how to calculate home ranges in similar settings.
The limited possibilities of quantitative interstudy home range comparison now faced by river turtle researchers might be improved through the use of the CLHR, a generalized and ecologically relevant home range estimator. Comparison is currently difficult because home range estimates vary when different estimators, parameters (e.g., percentage of location inclusion), and methods of turtle location acquisition (e.g., telemetry vs. mark–recapture) are used (Schubauer et al. 1990; Yabe 1992; Tucker et al. 2001). The CLHR estimator developed in this study should be able to facilitate the intercomparison of river turtle home range studies, especially in rivers characterized by multiple channels. If it is generally applicable, the CLHR could lead to a better broad-scale understanding of home range patterns exhibited by riverine turtles.
Future work could focus on incorporating graph theory–based indices related to the numbers of vertices and segments (Rayfield et al. 2011), thus allowing CLHR comparisons based on parameters other than size and overlap. Additionally, the development of an automated tool for CLHR computation would be straightforward. Our manual method of finding centerlines with which to form CLHR segments was accurate but tedious. The practical aspects of computing CLHRs could be greatly improved with a robust open-source program requiring a river GIS layer and the coordinates of recapture locations as input. This would involve generating centerlines of each channel from the polygon information, associating each observation point to the nearest centerline, and calculating the minimum spanning tree of the segments connecting all the points. We plan to provide a tool to the research community using a free GIS like GRASS or QGIS, a cross-platform language like Python, and a free statistics program like R that can find a minimum spanning tree in a graph.
Studied section of the Mille-Îles River, Québec, Canada, located approximately between lat 45°40′48″N, long 73°42′33″W, and lat 45°41′24″N, long 73°39′44″W.
Illustration of the utility of the Complex Linear Home Range (CLHR) to describe home ranges in multiplechannel aquatic systems. Of the four measures considered, only the CLHR (shown in the dashed line) would properly indicate that animal A traversed a distance at least 10 times that of animal B. (The entire dashed line is the CLHR of animal A; the part of the dashed line joining the west-most and east-most locations of animal B represents its CLHR.) In contrast, a typical Minimum Convex Polygon (MCP) calculation would indicate (improperly) that animal A has a home range only about 3 times that of animal B, with no overlap between the ranges. A modified MCP calculation that subtracts the terrestrial part of the range (termed MCP- in the text) would indicate that animals A and B had approximately the same size of home range. A typical LHR calculation (dotted lines) would indicate that the home range of animal A was only two times the range of animal B. In addition to its advantage in estimating home range size, the overlap between the mapped CLHRs suggests that the two animals had substantial opportunity for interaction, unlike the representations given by the LHR, MCP, and MCP- estimators.
Comparison between calculations underlying the Minimum Convex Polygon estimator (dashed line), the MCP-estimator formed by subtracting the terrestrial portion of the MCP, and the CLHR (black line along channel centerlines).
Complex linear home range of male G. geographica “D” in the Mille-Îles River, Québec, Canada (CLHR length = 3478 m).
