Ecol Res DOI 10.1007/s11284-007-0421-9
NOTE AND COMMENT
Erlend B. Nilsen Æ Simen Pedersen Æ John D. C. Linnell
Can minimum convex polygon home ranges be used to draw biologically meaningful conclusions?
Received: 9 March 2007 / Accepted: 10 August 2007 The Ecological Society of Japan 2007
Abstract Many conclusions about mammalian ranging behaviour have been drawn based on minimum convex polygon (MCP) estimates of home range size, although several studies have revealed its unpredictable nature compared to that of the kernel density estimator. We investigated to what extent the choice of home range estimator affected the biological interpretation in comparative studies. We found no discrepancy when the question asked covered a wide range of taxa, as real and very large differences in range size were likely to have masked smaller differences due to the choice of home range estimator. However, when the question asked concerned within-species characteristics, the choice of home range estimator explained as much of the variation in range size as did the ecological variable in question. The implications for macro-ecological and intraspecific studies are discussed. Keywords Comparative studies Æ Home range size Æ Kernel Æ MCP Æ Variance components analysis
Introduction Most animals use the same area repeatedly over time, and a useful concept to define animal movements is the home range (see, e.g., Tufto et al. 1996). However, although the home range is a fundamental concept in ecology, the very concept of home range has been subject to renewed interest, and some authors have even questioned the existence of a home range (Gautestad E. B. Nilsen (&) Æ S. Pedersen Department of Forestry and Wildlife Management, Hedmark University College, 2480 Koppang, Norway E-mail:
[email protected] Tel.: +47-624-30876 Fax: +47-624-30851 J. D. C. Linnell Norwegian Institute for Nature Research, Trondheim, Norway
and Mysterud 1995). Nevertheless, developments in GIS software and VHF/GPS telemetry hardware have enabled researchers to follow individuals intensively for longer time periods. The results strongly indicate that the area traversed by an individual in a given time can be described as a probability function, although not necessarily well described by a continuous distribution (Getz et al. 2007). Hence, different approaches have been developed to describe the home range size (Worton 1987; Seaman and Powell 1996), and several simulation studies have shown that the kernel density estimator (KDE) represents the home range much better than does the minimum convex polygon (MCP) method (see, e.g., Worton 1987). Recently, Borger et al. (2006a) investigated the performance of the KDE and the MCP methods in an empirical setting and confirmed the conclusions of simulation studies; the KDE method performed far better than the MCP method did, and the MCP method was subject to unpredictable bias. This raises the important and fundamental question: can we draw biologically meaningful conclusions from comparative studies based on MCP home ranges? Although the absolute home range size in itself might be important for conservation management, more interesting ecological questions are concerned with the relative contribution of different ecological factors to the variation in home range size. Such factors could include differences caused by seasons, between classes of individuals (Borger et al. 2006b), by habitats (Nilsen et al. 2005; Tufto et al. 1996) and comparison across species (Jetz et al. 2004; Nilsen and Linnell 2006). To the extent that the MCP method introduces unpredictable bias into the estimates of home range size, such comparisons could be complicated if the bias in the estimator were so large that it swamped any meaningful biological information. Nevertheless, most studies comparing home ranges across species (Gompper and Gittleman 1991; Harestad and Bunnell 1979; Jetz et al. 2004; Kelt and Van Vuren 2001; Mysterud et al. 2001; Nilsen and Linnell 2006) and within species (Grigione et al. 2002; Herfindal et al. 2005) have, so far, used the MCP
method. One important reason for this is the fact that a far larger number of studies (especially older studies) have reported home range sizes based on MCP than on KDE. Consequently, the trade-off between basing the analysis on a limited set of studies reporting home range size based on the more robust KDE and a much larger set including the unpredictable MCP home ranges has, so far, gone in favour of quantity. To date, no studies have investigated to what extent this decision has affected the interpretation of interspecific and intraspecific patterns of variation in home range size. Drawing on a large database of home ranges and body masses of mammalian carnivores, we estimated the contribution of some ecological and methodological factors to the total variation in home range sizes. We did this by addressing three specific questions, central to the question of the utility of the MCP method. First, we looked for systematic biases in the relative difference between KDE and MCP in relation to body mass and number of fixes. Then, we evaluated to what extent the conclusions drawn from ecological analysis depended on the choice of home range estimator. This was addressed by the use of two contrasting examples of ecological analyses, the first a macro-ecological example (scaling between body mass and home range size; see, e.g., Jetz et al. 2004), the second an intraspecific comparison between male and female home range sizes (see, e.g., Nilsen et al. 2005). Finally, we estimated the relative contribution of some ecological variables (family, species, sex), comparing the choice of home range estimator, to total variation in home range size, again at the levels described above.
Materials and methods Data We obtained information on annual home range sizes of adult individuals from the literature, and from unpublished sources by contacting researchers. As we did not have control over the design of the studies we included, we decided to include only studies from which we were able to find both MCP and KDE estimates of home range size. Consequently, tracking schedules and other factors known to affect home range size (Borger et al. 2006a) should not have biased the results presented here. After an extensive literature review we obtained annual home range sizes from 468 studies on mammalian carnivores, of which 38 reported both KDE and MCP home range estimates. These 38 studies included home range sizes for 25 species from seven families of mammalian carnivores. A list of the studies included in the analysis is available from the senior author upon request. Body masses were also derived from the literature, but, when we were not able to obtain original values from a given study area, we used the values reported in Silva and Downing (1995), preferably from the geographically closest site. Where possible, we used the
average of the within-sex means; otherwise, we used the average of values where the sex was unspecified. Statistical analysis All analyses reported in this paper were performed using R version 2.4.1 (R Development Core Team 2006), and parameter estimates are given as b ± SE. On basis of the data set described above, we addressed the three specific questions raised in the Introduction. We fitted linear mixed effects models (package nlme in R, using the ML method to estimate parameters) to address the three questions. To evaluate the first question, we fitted relationships between the logarithmic ratio of site-specific and species-specific KDE and MCP estimates and the ecological variable body mass, as well as the methodological variable number of fixes. Secondly, we investigated whether the scaling between body mass and home range size would differ if we based our home range size estimates on KDE home ranges and MCP home ranges. These models were fitted with a random intercept term for species nested in families (Pinheiro and Bates 2000). We also evaluated the relationship between the KDE and MCP estimator. If no systematic bias existed, we would expect the slope to be 1. Then, we investigated whether the ratio of male:female home range size was dependent on the choice of home range estimator. This part of the analysis was performed at the intraspecific level, where we fitted individual models for two solitary felids (Eurasian lynx, Lynx lynx, and cougar, Puma concolor), for which we had ‡5 studies reporting both KDE and MCP home range size for each species. These models were fitted with a random intercept at the study area level, as it was likely that the ratio differed at this level due to differences in ecological factors and tracking schedules (see also Skrondal and Rabe-Hesketh 2004). Finally, we performed variance component analyses (Pinheiro and Bates 2000) to investigate to what extent variation in home range size could be attributed to ecological factors (taxonomic family, species or sex) and the choice of home range estimator. In addition, we included study site as a random factor, appreciating that this factor could include both ecological (Nilsen et al. 2005) and methodological (Blundell et al. 2001; Borger et al. 2006a) differences between the studies. In the macro-ecological comparison, we fitted linear mixed-effects models, with the logarithm of the home range size as the response variable and nested random terms (from outermost to innermost): family, species, sex, study site and type of home range estimator. This allowed us to partition the variance in home range size between differences among families, species, sex and type of home range estimator. To investigate the effects of ecological factors further, we fitted the model both with and without log body mass as a fixed effect. At the intraspecific level, we again fitted linear mixed-effects models, with nested random terms (from outermost to innermost): study area, sex and home range estimator.
Results When comparing the sex-specific and study-specific ratios of MCP to KDE home range size, we could not find any consistent increase or decrease with increasing body mass (b = 0.02 ± 0.04, t = 0.69, p = 0.49), or with the number of fixes (b = 0.001 ± 0.02, t = 0.15, p = 0.88; Fig. 1a). This might be somewhat surprising, given that the MCP method is widely regarded to be strongly dependent on the sample size of locations (Borger et al. 2006a). When fitting the model with
Fig. 1 a Study-specific logarithmic (MCP/kernel) ratio plotted against mean number of fixes used to calculate the home ranges. Note that the analysis revealed no consistent pattern. b Logarithm (home range size) is plotted against logarithm (body mass) for MCP (open circles, dotted line) and kernel home ranges (filled circles, solid line). In both cases the data come from a total of 38 studies covering 25 species
intercept only, we could not find evidence of any systematic over- or under-estimation of the MCP method compared with the KDE method (overall log ratio 0.04 ± 0.06, t = 0.67, p = 0.51). Also, when regressing study-specific log KDE on log MCP estimates, we found no systematic bias (b = 0.993 ± 0.02, R2 = 0.97; p = 0.716 for the test that the slope is not equal to 1). When fitting mixed-effects linear regression models with log body mass as a fixed predictor and log home range size as the response variable, we found no difference between the model fitted with KDE home ranges and the model fitted with MCP home ranges (MCP model b = 0.97 ± 0.19, t = 5.11, p < 0.001; KDE model b = 0.9 ± 0.18, t = 5.44, p < 0.001; Fig. 1b). These values are very close to the 1.0 scaling parameter that should be expected (Jetz et al. 2004), and, thus, our analysis at the macro-ecological level suggests that no systematic bias is introduced into comparative studies when the MCP method is used. Turning to the intraspecific level, we investigated whether the ratio of male home range size to female home range size differed depending on the choice of home range estimator. However, neither for the Eurasian lynx (p = 0.33) nor for the cougar (p = 0.26) did the ratio differ when the analysis was based on MCP or KDE. Indeed, when both the MCP method and KDE were used, the conclusion was that the marginal (population mean) ratio was quite similar both for the lynx (MCP, 1.88 ± 0.15; KDE, 2.09 ± 0.22) and the cougar (MCP, 2.03 ± 0.14; KDE, 1.91 ± 0.21). Differences between the studies were not investigated further, as we were mainly concerned with a comparison of the MCP and KDE methods. Finally, we investigated to what extent variation in home range size could be attributed to ecological variables and to the choice of home range estimator. Firstly, we did this at the interspecific level. These analyses revealed that ecological factors explained much more of the variation in home range sizes than did the choice of home range estimator, whether conditioned by log body mass (i.e. body mass fitted as a fixed effect) or not (Table 1). Note, however, that when fitting the model without any fixed effects, a larger part of the variation in home range sizes appeared to be attributable to taxonomic family, probably due to the fact that the different families differ considerably in body mass and diet. At the intraspecific level, on the other hand, the choice of home range estimator had a much larger influence, and, for the cougar in particular, the same amount of variation in home range size could be attributed to home range estimator as to any of the two ecological factors (Table 2).
Discussion Detecting sources of variations in the spatial scale of animal range use is of crucial importance, and here we have contrasted two commonly used home range estimators in their ability to detect biologically meaningful
Table 1 Amount of total variation in the macro-ecological analysis of carnivore home range sizes that could be attributed to the ecological variables (family, species and sex) and to type of home range. Study site could represent both methodological and ecological factors (see text). Model A contains only random effects, model B also contains the fixed effect of body mass Variance components (%)
A (%)
B (%)
Family Species Sex Study site Home range estimator Residual
9 71 6 13
