Suitability of distance metrics as indexes of homerange size in tropical rodent species
Abstract
Estimators of homerange size require a large number of observations for estimation and sparse data typical of tropical studies often prohibit the use of such estimators. An alternative may be use of distance metrics as indexes of home range. However, tests of correlation between distance metrics and homerange estimators only exist for North American rodents. We evaluated the suitability of 3 distance metrics (mean distance between successive captures [SD], observed range length [ORL], and mean distance between all capture points [AD]) as indexes for home range for 2 Brazilian Atlantic forest rodents, Akodon montensis (montane grass mouse) and Delomys sublineatus (pallid Atlantic forest rat). Further, we investigated the robustness of distance metrics to low numbers of individuals and captures per individual. We observed a strong correlation between distance metrics and the homerange estimator. None of the metrics was influenced by the number of individuals. ORL presented a strong dependence on the number of captures per individual. Accuracy of SD and AD was not dependent on number of captures per individual, but precision of both metrics was low with numbers of captures below 10. We recommend the use of SD and AD instead of ORL and use of caution in interpretation of results based on trapping data with low captures per individual.
 Akodon montensis
 Atlantic forest
 Brazil
 Delomys sublineatus
 minimum convex polygon
Size of home range provides basic information on animal ecology and is linked to various lifehistory traits, such as territorial behavior (Jennings et al. 2010; Leiner and Silva 2009), use of resources (AliagaRossel et al. 2008; Borowski 2003; Hubbs and Boonstra 1998; Lira et al. 2007; Relyea et al. 2000; Zabel et al. 1995), and mating systems (Blondel et al. 2009; Fernandes et al. 2010). Furthermore, changes in homerange size are associated with seasonal changes (Getz and McGuire 2008; Getz et al. 2005), population density (Abramsky and Tracy 1980), and age of individuals (Fernandes et al. 2010).
Different methods have been proposed to estimate homerange size, all of which require spatially explicit information on the location of individuals at different points in time, which is used to infer the outer boundaries of home ranges and patterns of habitat use (e.g., minimum convex polygon [MCP—Mohr 1947; Stickel 1954], bivariate normal utilization distribution [Jennrich and Turner 1969], fixed and adaptive kernel methods [Worton 1989], or mechanistic homerange models [Mitchell and Powell 2004]). Such spatially explicit information is frequently obtained using radiotelemetry or capturerecapture methods. However, because these methods for estimating homerange size require a large number of independent captures per individual to provide reliable estimates of homerange size (Boyle et al. 2009; Kie et al. 2010; Stickel 1954; Worton 1989), their use is frequently limited to species that are easy to observe, radiotrack, or capture. Data limitation is a serious problem, especially for small, shortlived vertebrates such as nonvolant small mammals studied mainly by capturerecapture techniques and for which recaptures are usually not numerous.
To deal with this limitation, different distance metrics between points of capture have been used as indexes of homerange size (Slade and Russell 1998). The most commonly used indexes of home range are the mean distance between successive captures (SD—Stickel 1954) and the observed range length—the maximum distance among all possible distances between points of capture of an individual (ORL— Stickel 1954). Another less commonly used metric is the mean distance between all capture points (AD—Koeppl et al. 1977), which was proposed as an extension of the SD with 2 advantages: increased number of distances included in the calculation, and distinction between different spatial patterns (e.g., SD does not distinguish between 3 sequential linear movements and 3 nonlinear movements of the same length [see Koeppl et al. 1977]).
Although these metrics represent merely an index of homerange size and do not allow investigations of homerange shape or overlap between individuals, they offer obvious advantages; for example, individuals with as few as 2 captures can be included in calculations, increasing sample size substantially, they are free from distributional assumptions, and they are easy to calculate (Slade and Swihart 1983). Moreover, because these metrics provide a relative index of homerange size, they allow temporal and spatial comparisons as well as comparisons between groups of individuals (e.g., sex or species—Slade and Swihart 1983). Indeed, both ORL and SD have been widely used as indices for homerange size of small mammals in studies comparing groups of individuals (e.g., males versus females or juveniles versus adults) or species (ORL [Abramsky and Tracy 1980; Gaines and Johnson 1982; Matic et al. 2007; Moorhouse and Macdonald 2008; Nakagawa and Cuthill 2007] and SD [Getz and McGuire 2008; Odhiambo et al. 2005; Püttker et al. 2006; Slade and Swihart 1983; Wells et al. 2008; Yunger et al. 2007]). Despite its advantages, AD has been used much less frequently, probably because of limited exposure in the literature (Connor and Leopold 2001).
Regardless of the wide application of these homerange indexes, few studies evaluated the correlation of distance metrics to area estimates of homerange size. Previous studies included only North American small mammals and in general found high correlation coefficients (Connor and Leopold 2001; Faust et al. 1971; Getz and McGuire 2008; Slade and Russell 1998). However, no study compared the 3 metrics investigated here, and only a few investigated the robustness of the metrics to low numbers of individuals or recaptures (Faust et al. 1971; Stickel 1954).
In this study, we tested the generality of former results on the suitability of distance metrics as indexes for homerange size in tropical rodents. We used an extensive data set from a capturerecapture study on Atlantic forest small mammals to investigate the correlation between 3 distance metrics (SD, AD, and ORL) and an estimate of homerange size (MCP) in 2 rodent species. Additionally, we tested the robustness of distance metrics as indexes of homerange size to low numbers of both individuals captured and captures per individual.
Materials and Methods
Study area.—Small mammals were sampled in 9 trapping grids located in the Atlantic Plateau of Sao Paulo, Brazil, in the municipalities of PiedadeTapiraí (between 23°57′S, 47°27′W and 23°49′S, 47°24′W), and CotiaIbiúna (between 23°35′S, 46°45′W and 23°50′S, 47°15′W). The region was once covered with Atlantic forest classified as lower montane Atlantic rain forest (OliveiraFilho and Fontes 2000). Elevation ranged between 800 and 1,000 m above sea level, annual rainfall was between 1,222 and 1,808 mm, and mean annual temperature was between 18.9°C and 22.2°C among the 6 municipalities (CEPRAGI 2007). All grids were placed in secondary forest; 6 in forest fragments of similar size (13.9–19.6 ha) and 3 in a continuous forest area of approximately 10,000 ha.
Trapping.—Each of the grids covered 2 ha and consisted of 11 parallel 100m lines, 20 m from each other, with trapping stations located every 10 m containing 1 Sherman trap (37.5 × 10.0 × 12.0 cm or 23.0 × 7.5 × 8.5 cm; H. B. Sherman Traps, Inc., Tallahassee, Florida) placed on the ground. Additionally, pitfall traps (60liter buckets, 53.0 cm in depth and 40.0 cm in diameter) connected by a 50cmhigh plastic fence were placed at each trap station in 5 of the 11 lines. Two different types of traps were used to maximize both capture and recapture rates, because pitfall traps result in higher capture rates and a higher proportion of young individuals (Umetsu et al. 2006), whereas recapture rates are higher in Sherman traps (C. Barros, pers. obs.). All traps were baited with a mixture of sardines, peanut butter, banana, and corn flour. In all 9 grids, animals were captured during five 5day capture sessions between February and June 2008; an additional seventeen 5day capture sessions between June 2008 and November 2009 were carried out in the 3 grids placed in continuous forest. Total trapping effort was 84,480 trap nights, and time between capture sessions in each grid varied from 19 to 27 days. Captured animals were marked with a numbered ear tag (Small Animal Tags OLT; A. Hartenstein GmbH, WürzburgVersbach, Germany). We used only 1st captures of each capture session in the analyses to guarantee independence between captures and because the pitfall drift fences constrain movements of individuals within capture sessions. The minimum time between 2 captures of the same individual was 23 days. All capture, handling, and tagging protocols followed the guidelines of the American Society of Mammalogists (Sikes et al. 2011).
Estimation of home range.—Because of low numbers of captures per individual and the resulting inability to implement more sophisticated methods of homerange estimation, we used MCP to estimate homerange sizes of the rodents. Despite its limitations (Börger et al. 2006; Worton 1989), MPC is widely used in studies of small mammals (e.g., Bowers et al. 1996; Brown et al. 2005; Cáceres and MonteiroFilho 2001; Jonsson et al. 2002; Pires and Fernandez 1999; Tristiani et al. 2003) because low capture rates and small body size, which do not allow for the use of tracking devices, lead generally to low numbers of samples and impede the use of other methods. Homerange size estimated by MCP depends on the number of captures per individual and tends to be underestimated in individuals with low numbers of captures (Anderson 1982; Worton 1987). Number of captures proved to be influential also in calculation of MCP in Akodon montensis (montane grass mouse) and Delomys sublinetaus (pallid Atlantic forest rat; Fig. 1), and we therefore only included individuals with 5 or more captures in the analysis. The limit of 5 captures per individual for estimating homerange size by MCP was used in several studies on neotropical small mammals and rodents from temperate regions (Adler et al. 1997; Batzli and Henttonen 1993; Bergallo and Magnusson 2004; Bowers et al. 1996; Cáceres and MonteiroFilho 2001; Gentile et al. 1997; Lidicker 1966; Pires et al. 1999; Priotto and Steinmann 1999; Seamon and Adler 1999). However, because we were interested in using the best possible estimates of homerange size, we excluded 7 individuals from the analyses (4 individuals of A. montensis and 3 of D. sublineatus; Fig. 1) that proved to have moved exceptionally large distances between captures and therefore were assumed to have not established homerange areas.
Study species.—Despite the large trapping effort, sufficient independent captures were only obtained for 2 species, A. montensis and D. sublineatus. Both species are small, nocturnal rodents (mean adult body mass for A. montensis = 31.9 g; for D. sublineatus = 46.1 g) with terrestrial locomotion. D. sublineatus is a forest specialist, with its geographical range restricted to the Atlantic forest at large spatial scales and occurring only in native vegetation at local scales (Umetsu and Pardini 2007). In contrast, A. montensis is a habitat generalist, found in the open biomes that surround the Atlantic forest, and occurs in all major habitat types in fragmented landscapes at a local scale (Umetsu and Pardini 2007).
Data on 25 individuals of A. montensis (155 captures in total; mean captures per individual: 6.2; range 5–10), and 11 individuals of D. sublineatus (59 captures in total; mean captures per individual: 5.4; range 5–6) were included in the analyses.
Data analysis.—We calculated SD, ORL, AD, and MCP for each individual using Hawth's Analysis Tools extension (Beyer 2004) in ArcMap 9.2 (ESRI, Redlands, California). The correlation between the 3 distance metrics and MCP were tested using Spearman's rank correlation, because the KolmogorovSmirnov test indicated samples deviating from a normal distribution.
To investigate the robustness of the distance metrics to varying numbers of individuals we followed a 2step approach. In the 1st step, we selected randomly 3, 5, 10, or all individuals captured (considering all captures per individual) from the data set and calculated 4 secondorder means (i.e., mean values of the means calculated for each individual) of SD, AD, and ORL among individuals of each species. The individuals included were chosen randomly, because seasonal changes might influence the homerange size of small mammals (Getz and McGuire 2008) and sequential inclusion of the first 3, 5, and so on individuals would lead to the inclusion of individuals sequentially captured in subsequent seasons. In order to evaluate whether mean distance metrics differed between calculations obtained by the inclusion of different numbers of individuals, we used a KruskalWallis test. In the 2nd step, we repeated the analysis using simulated data sets with different numbers of individuals with equal number of captures, because low sample sizes and varying number of captures per individual might impair inferences about the precision and accuracy of the estimate of the mean value of distance metrics. By investigating the deviations from the estimated mean in response to the number of simulated individuals included in the analysis, we expected to be able to make recommendations about minimum numbers of individuals necessary to precisely and accurately estimate the mean value of distance metrics. We simulated 2, 3, 4, 5, 20 individuals by randomly selecting 10 distance values from the data set of each species and compared between mean values of distance metrics obtained by the inclusion of different numbers of simulated individuals.
Similarly, we investigated the influence of varying numbers of captures per individual on the distance metrics. First, we calculated 5 secondorder means of SD, AD, and ORL among individuals of each species by including the first 2, 3, 4, 5, and all captures of each individual. In order to evaluate whether mean distance metrics differ between calculations obtained by the inclusion of different numbers of captures per individual, means were compared by a KruskalWallis test. Afterward, we repeated the analysis using new simulated individuals varying in number of captures per individual. We randomly chose 2, 3, 4, 5, …, 20 values from the data set of each species 100 times and calculated mean SD, AD, and ORL for each of the sets of 100 simulated individuals. The distance metrics obtained by inclusion of varying numbers of captures per simulated individual were compared by KruskalWallis test. Statistical analyses were performed in the STATISTICA 7 program (StatSoft, Inc., Tulsa, Oklahoma).
Results
Mean size (mean ± SD) of home range was 0.079 ± 0.009 ha for A. montensis and 0.076 ± 0.015 ha for D. sublineatus. Overall mean distance moved between successive captures was 31.1 ± 3.4 m and 26.3 ± 2.8 m, observed range length was 61.6 ± 5.9 m and 55.2 ± 6.7 m, and mean distance between trap locations was 32.0 ± 2.7 and 34.0 i 3.4 m (all values are mean ± SE reported for A. montensis and D. sublineatus, respectively).
All correlations between distance metrics and MCP were significant for A. montensis (Fig. 2), whereas for D. sublineatus the correlation between AD and MCP proved to be marginally not significant (Fig. 2). For A. montensis, the weakest correlation was detected between SD and MCP (Fig. 2a), with other correlation coefficients above 0.7 and highly significant. The highest correlation between MCP and distance metrics was observed for ORL (Fig. 2b), and among distance metrics, between AD and ORL (Table 1). For D. sublineatus, on the other hand, the correlation was lowest between AD and MCP (Fig. 2f). The highest correlation between MCP and distance metrics was observed for SD (Fig. 2d), and among distance metrics between SD and ORL (Table 1).
SD  AD  ORL  

r_{s}  n  P  r_{s}  n  P  r_{s}  n  P  
SD  0.894  25  < 0.0001  0.799  25  < 0.0001  
AD  0.791  11  0.0037  0.915  25  < 0.0001  
ORL  0.860  11  0.0007  0.920  11  < 0.0001 
For both species, mean values of distance metrics were not influenced by the number of individuals included and did not differ significantly (Fig. 3; A. montensis: SD: χ^{2}_{3} = 3.71, P = 0.29; AD: χ^{2}_{3} = 2.95, P = 0.40; ORL: χ^{2}_{3} = 3.14, P = 0.37; D. sublineatus: SD: χ^{2}_{3} = 0.11, P = 0.99; AD: χ^{2}_{3} = 0.47, P = 0.93; ORL: χ^{2}_{3} = 0.23, P = 0.97). Comparison between mean values of simulated data resulted in no difference between mean values of distance metrics (A. montensis: SD: χ^{2}_{4} = 6.42, P = 0.17; AD: χ^{2}_{4} = 1.38, P = 0.85; ORL: χ^{2}_{4} = 1.73, P = 0.78; D. sublineatus: SD: χ^{2}_{4} = 3.62, P = 0.46; AD: χ^{2}_{4} = 2.44, P = 0.65; ORL: χ^{2}_{4} = 5.99, P = 0.20). Precision of the mean distance metrics measured by the deviations from the mean values decreased slightly while accuracy increased with inclusion of more individuals, leading to a more stable value after inclusion of 4–6 individuals in all 3 distance metrics and both species (Fig. 4).
For both species, mean value of ORL among individuals proved to be strongly dependent on the number of captures per individual included in the calculation (A. montensis: χ^{2}_{4} = 24.41, P < 0.001; D. sublineatus: χ^{2}_{4} = 21.84, P < 0.001), whereas the mean values of SD and AD among individuals proved to be unaffected by the number of captures per individual (Fig. 5). Mean values of SD and AD did not differ significantly between calculations including different numbers of captures per individual for A. montensis (SD: χ^{2}_{4} = 1.99, P = 0.74; AD: χ^{2}_{4} = 2.82, P = 0.59) and D. sublineatus (SD: χ^{2}_{4} = 1.71, P = 0.79; AD: χ^{2}_{4} = 7.51, P = 0.11).
Analysis of the simulated data lead to similar results with ORL being highly dependent on number of captures in both species (A. montensis: χ_{18} = 461.80, P < 0.0001; D. sublineatus: χ_{18} = 403.03, P < 0.0001), whereas SD and AD were independent of the number of captures per individual (A. montensis: SD: χ_{18} = 14.26, P = 0.72; AD: χ_{18} = 18.29, P = 0.44; D. sublineatus: SD: χ_{18} = 14.26, P = 0.72; AD: χ_{18} = 15.29, P = 0.64). The precision of the mean SD and AD measured by the deviation from the mean increased with increasing number of captures and stabilized after 10 captures per individual (Figs. 6a, 6b, 6d, and 6e). Precision of the mean ORL did not increase with increasing number of captures within the range of numbers of captures investigated (Figs. 6c and 6f).
Discussion
All distance metrics were significantly correlated with each other as well as to the MCP estimate for both species. Therefore, given a sufficient number of captures per individual, all 3 distance metrics represent a useful index for the homerange size estimated by MCP. The results extend the generality of the suitability of distance metrics as indexes of homerange size revealed in former investigations on nontropical rodents (Faust et al. 1971; Slade and Russell 1998; Slade and Swihart 1983; Swihart 1992).
Only 2 studies investigated the same distance and area metrics, and both revealed similar results. Faust et al. (1971) found a correlation coefficient of 0.8 between SD and MCP using the combined data of 3 species: Blarina brevicauda (northern shorttailed shrew), Ochrotomys nuttalli (golden mouse), and Peromyscus gossypinus (cotton mouse), which is somewhat larger than what we found for A. montensis, but coincides with the value for D. sublineatus. Faust et al. (1971) also found a high correlation of r = 0.84 between adjusted range length (ORL + the distance between traps) and SD, as observed in this study. On the other hand, Slade and Russell (1998) found a significant, but lower, correlation between SD and MCP for Microtus ochrogaster (prairie vole, r = 0.58) and Sigmodon hispidus (hispid cotton rat, r = 0.71).
The comparison of AD and SD revealed interesting details on the effects of uncommon movements on distance metrics. For A. montensis, the correlation between SD and MCP was lower than between AD and MCP, whereas the opposite was found for D. sublineatus. The comparatively lower correlation between SD and MCP for A. montensis was caused by 1 individual with a low homerange area but high SD (Fig. 1a). This particular individual moved, in general, short distances, but undertook 1 uncommonly long movement and returned, causing a high SD. Because in AD all distances between points of capture are considered, it is less affected by the exceptional long movement. In contrast, the comparatively low correlation between AD and MCP for D. sublineatus is caused by 1 individual with a very high AD but low MCP (Fig. 1f). This individual moved small distances in a linear fashion, thereby increasing the AD but maintaining a low SD. These uncommon movements became evident by comparing the values of distinct metrics, highlighting the usefulness of calculating and using different metrics in order to reveal details of animal movements.
Precision or accuracy of none of the 2ndorder means of the distance metrics representing a group of individuals were influenced strongly by the number of individuals included in the calculation, indicating mean values could be estimated with few individuals, given a considerable number of captures per individual. Conversely, mean ORL was strongly affected by the number of captures per individual and proved to underestimate the index of homerange size when numbers of captures per individual were low. It is not surprising that ORL was more affected by number of captures than SD or AD, because unlike SD and AD, ORL is a single maximum value for each individual and not a mean of several distances. Indeed, ORL had been shown to be dependent on the number of captures and usually reaches an asymptote after a number of observations (Stickel 1954). Clearly, the maximum distance moved was not reached in both species, because an asymptote was not reached. On the other hand, both SD and AD mean values were similar irrespective of the number of captures per individual for both species, as previously observed for SD in 3 North American rodents (Faust et al. 1971). Although low numbers of captures per individual allowed for accurate estimation of the mean of SD and AD in this study, the precision of the estimate was dependent on number of captures, as shown by both real and simulated data. The stabilization of the deviation from the mean after about 10 captures per individual highlight the limited possibility of inference when comparisons of SD and AD between groups are based on few captures per individual.
The results of this study confirm the correlation of distance metrics with home range estimated by MCP. Nonetheless, given the comparatively low sample size in this study and the resulting limitations of estimating home range by MCP (Anderson 1982; Börger et al. 2006; Worton 1989), further studies are needed to investigate the relation between distance metrics and homerange size estimated by other methods (e.g., kernel density estimators) in order to confirm the correlations found in this study. Such datademanding methods for estimating home ranges are frequently not feasible in studies of small mammals, especially in the tropics where abundances of several small mammal species are low (Umetsu et al. 2006) and even extensive effort does not result in high numbers of individuals or independent captures per individual (this study). In larger small mammal species, homerange estimates and movement distances might be achieved by using telemetry data (e.g., Lira and Fernandez 2009). However, because we investigated 2 small rodent species with similar size as well as habitat preference, questions remain whether the results are transferable to larger species or species inhabiting other habitats (e.g., arboreal species).
Based on the results of this study, we recommend using SD and AD before ORL when using distance metrics as indexes for home range of terrestrial rodents. Given the advantage of possibly revealing differences in movement patterns that might be overlooked using only SD, it is not clear why AD has rarely been used in former studies. Because the distance metrics were highly correlated to each other, comparisons among groups of animals using different metrics should lead to similar results. However, although accurate estimation seems to be feasible with low numbers of individuals and captures per individual, precision of the estimates depends on number of individuals and captures, which limits the possibility of inference when comparing between different groups of animals; caution should be taken when captures per individual are below 10.
Resumo
Estimadores da área de vida requerem um grande número de observações para a estimativa e dados escassos, típicos de regiões tropicais, muitas vezes impedem seu uso. Uma alternativa pode ser o uso de métricas de distância como índices de área de vida. Entretanto, testes de correlaçõo entre métricas de distância e estimadores de área de vida existem apenas para roedores norteamericanos. Nós avaliamos a adequação de 3 métricas de distância como índices de tamanho área de vida (distância média entre capturas sucessivas [SD], comprimento no intervalo observado [ORL] e distância média entre todos os pontos de captura [AD]) para 2 espécies de roedores Akodon montensis (ratodochão) e Delomys sublineatus (ratodomato). Além disso, nós investigamos a robustez dos índices de área de vida à baixos números de captura por indivíduo e poucos indivíduos. Nós observamos uma alta correlação entre as métricas de distância e estimadores de tamanho de área de vida. Nenhuma das métricas foi influenciada pelo nóméro de indivíduos. ORL apresentou forte dependência ao número de capturas por indivíduo. Acurácia de SD e AD não foi dependente do número de capturas por indivíduo, mas a precisão de ambas as métricas foi baixa com numerous de capturas menores que 10. Nós recomendamos o uso de SD e AD invés de ORL e precaução na interpretação dos resultados baseados nos dados de captura com poucas capturas por indivíduo.
Acknowledgments
We thank T. K. Martins, R. Bovendorp, T. R. D. Reis, N. da Câmara Pinheiro, M. Coelho, E. J. Feragi, G. S. Limbardi, and ail other field assistants for invaluable help during fieldwork. We thank C. Cassano, A. P. Fernandez, and 2 anonymous reviewers, who provided helpful comments on an earlier version of the manuscript. We acknowledge assistance from BMBF Germany (German Federal Ministry of Education and Research, 01 LB 0202), Conselho Nacional de Desenvolvimento Científico e Tecnológico, and Fundaçâo de Amparo à Pesquisa do Estado de São Paulo (05/ 565554) for funding our research. This study is part of the BIOCASP project (Biodiversity Conservation in Fragmented Landscapes on the Atlantic Plateau of São Paulo, Brazil).
Footnotes

Associate Editor was Michael A. Steele.
 © 2012 American Society of Mammalogists