HOME RANGE SIZE ESTIMATES BASED ON NUMBER OF RELOCATIONS

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1 HOME RANGE SIZE ESTIMATES BASED ON NUMBER OF RELOCATIONS JOSEPH T. SPRINGER, Department of Biology, University of Nebraska at Kearney, Kearney, Nebraska USA Abstract: Regardless of how animal location data are obtained, using such data to delineate and measure home range sizes has posed some problems: the kind of locations that should be included, how the home range should be delineated, and the number of relocations needed to make useful estimates. Randomly generated points were plotted within a known area to provide a table of correction factors to be used for home range size estimates. Over 50% of the entire home range is included after plotting only 12 locations, yet 100 locations account for a little less than 90% of the home range. Using the correction factors with as few as 3 independent locations (with the minimum area method) a useful estimate of home range size and shape can be found. Key words: area estimates, delineation, home range, minimum area method, point method. Springer, J. T Home range size estimates base on number of relocations. Occasional Wildlife Management Papers, Biology Department, University of Nebraska at Kearney 14:1-12. Using radio telemetry data to estimate home range sizes of different wildlife species has been done since the 1960 s (Sanderson 1966). Most researchers have come to realize that the exact location of an animal s home range and how large it is are parameters difficult to determine due to intrinsic errors in data collection (Springer 1979) and the somewhat subjective manner in which the data are analyzed (Laundré and Keller 1984). Problems associated with error in radio telemetry data collection have been addressed elsewhere (e.g. Cederlund et al. 1979; Springer 1979; Hupp and Ratti 1983; Lee et al. 1985; Saltz and Alkon 1985; White and Garrott 1986,1990; Samuel and Kenow 1992). Parameters of concern in home range data analysis were outlined by Laundré and Keller (1984). They listed 3: methods by which data were collected (many times over a period of several hours versus once or twice a day); how home range boundaries are delineated; and determining how large a sample size is needed to adequately delineate an animal s home range. Sample size is the parameter that this paper will address primarily, although all 3 aspects will be discussed. My own interest in the subject of home range is the result of studying coyote home ranges using radio triangulation (Springer 1977, 1979, 1982) as well as live trap studies of small mammals in prairie habitats (Springer and Schramm 1972; Springer 1988a, 1988b). Odum and Kuenzler (1955) recognized that when plotting location data in an effort to delineate a home range, an area observation (AO) curve will result. That is, calculated sizes of home ranges tend to increase asymptotically as the number of locations increases (Springer 1982). Laundré and Keller (1984) felt that an adequate sample size was reached when the AO curve approached an asymptote. In this paper, I will show that the asymptote itself is the true home range size. I will also show x

2 Occasional Wildlife Management Papers Springer Estimating home range size 2 how to achieve better estimates of the home range size, even with a small data base. Burt (1943) defined home range as everywhere an animal travels in carrying out its normal activities. Movements by an animal within its home range will tend to be random. A predator cannot know where the next prey item will be beyond some general vicinity included within the predator s home range. Herbivores might move about in search of food more deliberately, but much research has shown that movement itself has been selected for so that resources do not get overly depleted. Furthermore, herbivores need to remain aware of predators and cannot stay long in a single place. METHODS My investigation into home range size estimation began with the graphing of areas of known size and with different shapes as simulated home ranges. The shapes used were squares, triangles, and ellipses. Ten of the squares measured 25 in 2, and 15 squares measured 100 in 2. All other shapes measured 100 in 2. All computer work was done on a Macintosh LC with System7.01 ( Apple Computer Corporation). This system was needed so that several applications could be run simultaneously, allowing me to change among them rapidly and effortlessly. Under System6.07 it would have been possible using the Multifinder ( Apple Computer Corporation), but there were frequent system crashes. A total of 100 randomly generated binomial coordinates was produced for each simulated home range. Three different methods were used to generate coordinates: random numbers from a Casio pocket calculator, random numbers generated by Microsoft Works version 2.00 e spreadsheet ( Microsoft Corporation), and random numbers generated by ClarisWorks version 1.0v2 spreadsheet ( Claris Corporation). All coordinates fell within the graphed area. Coordinates were plotted using MacDraw II version1.1 ( Claris Corporation). This program allows precise 2-dimensional measurement of length and angles. The first 3 coordinate pairs were connected by lines to form a triangle, and the area of the triangle was measured. The result was recorded on a Microsoft Works spreadsheet. As each new pair of coordinates was plotted, a new area was calculated if the new point fell outside the current delineation. If not, the same area was recorded for the new point as was recorded for the previous point. Where the total area of the home range was 100 in 2, each measured area represented the percentage of the total area. Where the total area of the home range was 25 in 2, measured areas were recorded in true size, but also as a percentage of the total area. Areas versus location numbers were averaged, standard deviations and standard errors were calculated for all data on the Microsoft Works spreadsheet. Although Microsoft Works spreadsheets will produce graphs automatically from data such as these, the graphs are too coarse. The data were therefore plotted manually using the MacDraw II program. To show the adjusted home range size based on a given number of plotted locations, a convex polygon was plotted around the outermost points. This polygon was copied and inserted into a SuperPaint 2.0a ( Silicon Beach Software Inc.). MacDraw allows for resizing by dragging object handles, but one cannot simply type in a resizing factor. SuperPaint does allow

3 Occasional Wildlife Management Papers Springer Estimating home range size 3 Table 1. Percentage of home range delineated by a convex polygon, depending on the number (N) of locations used so far. Standard Error (SE) based on 45 polygons. N Area SE N Area SE N Area SE 1 XXX XXX XXX XXX

4 Occasional Wildlife Management Papers Springer Estimating home range size 4 100% 90% 80% 70% Average 60% Percentage of Total 50% Area 40% 30% 20% 10% 0% Number of Relocations Fig. 1. Percentage of the total home range delineated as a function of the number of relocations. The horizontal marks indicate the percentages. Vertical marks indicate + SE.

5 Occasional Wildlife Management Papers Springer Estimating home range size 5 precise resizing of shapes, and each home range polygon was increased by the appropriate factor. The resized polygon was copied and centered on the original MacDraw home range file. RESULTS The home range areas versus number of locations plotted were averaged and are shown in Table 1. Since 3 points are required to form a polygon, no area or standard error are shown for N = 1 or 2. These results are also shown graphically in Fig. 1, clearly illustrating the asymptotic nature of the curve. The asymptote at the upper limit is 100%. DISCUSSION Methods of Data Collection Laundré and Keller (1984) compared several studies of coyote home ranges, identifying different methods that have been used to collect radio telemetry data. The Sequential Method involved finding a location at regular time intervals over a period of 6 to 24 straight hours. The Point Method involved finding a location only once or twice a day. Anderson (1982) pointed out that the degree of statistical independence of these 2 methods differs substantially. Dunn and Gipson (1977) had already shown that the sequential method would produce locations that were clearly not independent. Swihart and Slade (1985) showed how to test for independence using the Schoener (1981) ratio of t 2 /r 2, where t = mean distance between successive locations and r = mean distance from the center of activity. The amount of time needed between successive locations would be found using a nonsignificant one-tailed test of the t 2 /r 2 ratio (P >.25), where the null hypothesis is t 2 /r 2 = 2.0. This was about 4.5 h for their work on cotton rats (Sigmodon hispidus). Swihart and Slade (1986) justified their choice of P >.25. In general, then, it would be safe to assume that locations obtained by the point method are independent. Exceptions would be when animals repeated are found at the same place: den site, nest site, roost site, water hole, salt lick, etc. When plotting such locations in order to delineate a home range, each should be counted as a single relocation instance regardless of how many times the animal was found there. Since it is a basic assumption in home range analysis that successive locations of an animal must be independent (Hayne 1949), the points plotted in this study are not comparable to those obtained by the sequential method. These randomly selected points are independent of each other, and are therefore comparable to a properly conducted point method. Delineation of Boundaries Another problem with data analysis is the matter of delineating home range boundaries. Laundré and Keller (1984) pointed out (with regard to coyotes) that the array of location data can be assessed several ways. One method has been Hayne s (1949) ellipse method. This establishes a long and a short diameter, and creates an ellipse that encompasses most location points. Since it does not include all points, and since it has a fixed shape (the ellipse) that may or may not include important habitats that the animal uses, its primary value is in estimating home range size. Another failing in this method would be not showing territorial boundaries that could be shown if other methods were used. This method yields size estimates that may be larger than or smaller than estimates based on the other methods (Laundré and Keller 1984). That does not necessarily

6 Occasional Wildlife Management Papers Springer Estimating home range size 6 make it less accurate than other methods, but it does make comparison to results from other methods difficult. The most widely used method to delineate home ranges has been called the minimum area method or convex-polygon method, originally described by Mohr (1947), who did not name it. In this method, the outermost locations are connected by a convex polygon, and everything within the polygon is considered to be the animal s home range. Burt (1943:351) excluded occasional sallies outside the area, perhaps exploratory in nature. This is why some researchers have described animals home ranges using a modified minimum area method: a certain percentage of location points are excluded. Either all locations are excluded that exceed some specified distance from the next nearest location (Barbaur and Harvey 1965), or the 5% of all locations lying the greatest distance from the center of activity (Bowen 1985, Holzman et al. 1992). In an earlier paper (Springer 1982), I argued that such sallies should not necessarily be excluded, particularly when a home range is comprised of 2 or more core areas separated by some distance. Burt s (1943) idea was to eliminate the occasional sally outside of the home range from being considered part of the home range. Fig. 2 shows that with randomly distributed locations some locations seem remote such as #57. As the 57th location plotted, it was 2.40 units from the next nearest location, and definitely 1 of the 5% farthest from the center of activity. The modified minimum area method would have eliminated this point from consideration, yet it was within the home range. Other points tend to be clustered indicating an area of significance that might be truly important or might simply be the result of a random distribution of points. Fig. 2 also shows what might be considered core areas within a home range: several locations that fall within a short distance of each other. Only 10 of the locations fall outside a core area in this example. Locations that are truly independent of all others will tend to form clusters and voids. Simple proximity of points should not be the only measure of a core area or a home range. Burt s (1943) definition of home range included everywhere an animal travels in carrying out its normal activities. His concept of the occasional sally should apply only to rare travels that are excessively long in distance but short in duration. Otherwise, it seems possible (if not likely) that such travels are in fact within the home range and the area encompassed should be so designated. Sample Size The third aspect of data analysis that has caused concern in respect to home ranges is determining how many relocations are needed to adequately delineate an animal s home range. Researchers have simply used all the locations they had available within a year or a designated season. Laundré and Keller (1984) tentatively established 100 relocations as the number needed to adequately delineate a home range. As Fig. 1 shows, however, even when 100 locations have been plotted, less than 90% of the true home range has been delineated. Laundré and Keller (1984) discussed the AO curve, and looked for the data to approach an asymptote. They concluded that when the increase in area from one sample to the next was less than 5%, they had reached an adequate sample size. They used the sequential method, so that a single sample included 24 to 48 locations over a 24 hr period. This point was reached with 4 or 5 such samples.

7 Occasional Wildlife Management Papers Springer Estimating home range size (56) Fig. 2. Ellipse #8, after 100 relocations. Points that lie within 1.0 unit (total area is 100 square units) of at least 1 other point have been connected with a convex polygon. Center of true home range =. Center of estimated home range =.

8 Occasional Wildlife Management Papers Springer Estimating home range size 8 Table 2. Correction factor for home range size calculation based on number (N) of locations used so far. Data based on 45 polygons. N Correction N Correction N Correction 1 XXX XXX

9 Occasional Wildlife Management Papers Springer Estimating home range size 9 A B C D Fig. 3. Triangle #09 showing delineated polygons and adjusted polygons after different numbers of relocations. A = After 10 relocations. B = After 20 relocations. C = After 40 relocations. D = After 70 relocations. Center of true home range =. Center of estimated home range =.

10 Occasional Wildlife Management Papers Springer Estimating home range size 10 From Table 1, using the point method, the rate of increase drops to less than 5% at the 14th location (an increase from square units to square units is a 4.9% increase). Yet, only 56.4% of the home range has been delineated. Thus the 5% increase in area is not an adequate point at which to say the home range has been delineated. On the other hand, would 100 locations be enough to fully delineate the home range? Table 1 shows that even after 100 locations have been plotted, the average area delineated is still <90% of the true home range. In fact, on the average only 93.4% of the home range was delineated after 200 locations were plotted, 96.9% at 400 locations, and 98.9% at 800 locations. Table 1 can be used to determine what percentage of the home range has been delineated. Then the true home range size based on the AO curve in Fig. 1 can readily be calculated. Table 2 shows the conversion factors based on any number of relocations between 3 and 100. (Few researchers using the sequential method would have even as many as 100 relocations in any given season.) Since area is 2-dimensional, the area calculated for a convex polygon based on N locations would be multiplied by the square of the correction factor to get an estimate of the actual size of the animal s home range. As can be seen in Table 1, error associated with the estimated home range size will be higher as N approaches 3. Thus a larger sample size would yield a more accurate estimate. Nevertheless, even a sample as low as 3 locations can yield a useful estimate. Fig. 3 illustrates how the estimates can be applied to home range data. The convex polygon of a home range can be increased in size by the appropriate correction factor (vertically and horizontally) and centered over the calculated center. Even after only 10 relocations (Fig. 3a), the size and shape of the corrected polygon makes a fair approximation of the true home range. The southwestern edge has been missed, and some area has been included to nearly the entire east side. After 40 relocations (Fig. 3c), only a little of the northeast has been missed. MANAGEMENT IMPLICATIONS Data points used for home range size calculations, however they are gathered, must be independent of each other. Although such independence cannot be found in all the data collected using the sequential method, independent points can be pulled from those data. The point method generally would yield independent data. All locations should be included in the analysis with rare exception. The ellipse method and the modified minimum area method of delineating home ranges exclude some locations that are almost certainly part of the animal s home range. The minimum area method does not, and is therefore preferable. The minimum number of locations needed to generate an estimate of home range size and shape is 3 using Table 2. Estimates will be more accurate with more data, but large numbers of relocations are not necessary. LITERATURE CITED Anderson, D. J The home range: a new nonparametric estimation technique. Ecology 63: Barbaur, R. W., and J. J. Harvey Home range of Microtus ochrogaster as determined by modified minimum area. Journal of Mammalogy 46:

11 Occasional Wildlife Management Papers Springer Estimating home range size 11 Burt, W. H Territoriality and home range concepts as applied to mammals. Journal of Mammalogy 24: Cederlund, G., T. Dreyfert, and P. A. Lemnell Radiotracking techniques and the reliability of systems used for larger birds and mammals. Swedish Environmental Protection Board, Solna, pm pp. Dunn, J. E., and P. S. Gipson Analysis of radio telemetry data in studies of home range. Biometrics 33: Hayne, D. W Calculation of size of home range. Journal of Mammalogy 30:1-18. Holzman, S., M. J. Conroy, and J. Pickering Home range, movements, and habitat use of coyotes in southcentral (sic) Georgia. Journal of Wildlife Management 56: Hupp, J. W., and J. T. Ratti A test of radio telemetry triangulation accuracy in heterogeneous environments. Proceedings of the International Wildlife Biotelemetry Conference 4: Laundré, J. W., and Keller, B. L Home range size of coyotes: a critical review. Journal of Wildlife Management 48: Lee, J. E., G. C. White, R. A. Garrott, R. M. Bartmann, and A. W. Alldredge Accessing (sic) accuracy of radiotelemetry system for estimating animal locations. Journal of Wildlife Management 49: Mohr, C. O Table of equivalent populations of North American small mammals. American Midland Naturalist 37: Odum, E. P., and E. J. Kuenzler Measurement of territory and home range size in birds. Auk 72: Saltz, D., and P. U. Alkon A simple computer-aided method for estimating radio-location error. Journal of Wildlife Management 49: Samuel, M. D., and K. P. Kenow Evaluating habitat selection with radiotelemetry triangulation error. Journal of Wildlife Management 56: Sanderson, G. C The study of mammal movements a review. Journal of Wildlife Management 30: Springer, J. T Movement patterns of coyotes in south central Washington as determined by radio telemetry. Ph. D. Dissertation, Washington State University, Pullman. 108 pp Some sources of bias and sampling error in radio triangulation. Journal of Wildlife Management 43: Movement patterns of some coyotes in south central Washington. Journal of Wildlife Management 46(1): a. Immediate effects of a spring fire on small mammal populations in a Nebraska mixed-grass prairie. Proceedings of the North American Prairie Conference 10: Paper # (5 pp). 1988b. Individual responses of some small mammals to a prairie fire. Proceedings of the North American Prairie Conference 10: Paper # (6 pp)

12 Occasional Wildlife Management Papers Springer Estimating home range size 12, and Schramm, P The effect of fire on small mammal populations in a restored prairie with special reference to the short-tailed shrew, Blarina brevicauda. Proceedings of the North American Prairie Conference 2: White, G. C., and R. A. Garrott Analysis of wildlife radio-tracking data. Academic Press, Inc., San Diego. 383 pp. Swihart, R. K., and N. A. Slade Testing for independence of observations in animal movements. Ecology 66: , and The importance of statistical power when testing for independence in animal movements. Ecology 67: White, G. C., and R. A. Garrott Effects of biotelemetry triangulation error on detecting habitat selection. Journal of Wildlife Management 50: To cite this paper: Springer, J. T Home range size estimates base on number of relocations. Occasional Wildlife Management Papers, Biology Department, University of Nebraska at Kearney 14:1-12.