JOSEPH T. SPRINGER, Department of Biology, University of Nebraska at Kearney, Kearney,. Nebraska 68849-1140 USA. Using radio telemetry data to estimate.
HOME RANGE RELOCATIONS
SIZE
ESTIMATES
BASED
ON
NUMBER
OF
JOSEPH T. SPRINGER, Department of Biology, University of Nebraska at Kearney, Kearney, Nebraska 68849-1140 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. 2003. 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
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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 in2, and 15 squares measured 100 in2. All other shapes measured 100 in2. 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
Springer • Estimating home range size
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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 in2, each measured area represented the percentage of the total area. Where the total area of the home range was 25 in2, 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
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Springer • Estimating home range size
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
35
77.37
0.956
69
85.70
0.708
2
XXX
XXX
36
77.71
0.972
70
85.83
0.705
3
8.510
1.029
37
78.13
0.970
71
85.99
0.692
4
14.59
1.218
38
78.66
0.912
72
86.16
0.687
5
21.56
1.424
39
78.97
0.901
73
86.36
0.670
6
27.06
1.386
40
79.49
0.824
74
86.47
0.664
7
32.42
1.427
41
79.82
0.800
75
86.63
0.649
8
37.93
1.576
42
80.11
0.792
76
86.84
0.646
9
41.67
1.614
43
80.41
0.779
77
87.02
0.645
10
45.13
1.416
44
80.62
0.787
78
87.12
0.652
11
48.06
1.404
45
80.81
0.775
79
87.36
0.615
12
50.85
1.377
46
81.15
0.785
80
87.49
0.612
13
53.77
1.387
47
81.41
0.795
81
87.61
0.604
14
56.40
1.438
48
81.82
0.760
82
87.74
0.602
15
58.55
1.461
49
82.12
0.774
83
87.82
0.609
16
60.18
1.380
50
82.40
0.781
84
87.95
0.601
17
61.88
1.416
51
82.57
0.773
85
88.08
0.593
18
63.06
1.360
52
82.72
0.785
86
88.17
0.573
19
64.35
1.234
53
82.83
0.776
87
88.23
0.561
20
65.52
1.223
54
82.96
0.788
88
88.32
0.553
21
66.82
1.215
55
83.10
0.784
89
88.36
0.550
22
67.70
1.241
56
83.19
0.793
90
88.43
0.553
23
68.62
1.214
57
83.40
0.782
91
88.55
0.552
24
69.41
1.233
58
83.58
0.793
92
88.66
0.535
25
70.31
1.290
59
83.92
0.802
93
88.75
0.527
26
71.15
1.248
60
84.11
0.791
94
88.87
0.526
27
72.00
1.172
61
84.37
0.799
95
88.93
0.521
28
72.73
1.167
62
84.49
0.802
96
89.03
0.524
29
73.49
1.179
63
84.66
0.796
97
89.13
0.496
30
74.14
1.119
64
84.90
0.772
98
89.22
0.494
31
74.91
1.045
65
85.04
0.761
99
89.29
0.496
32
75.76
0.998
66
85.24
0.749
100
89.42
0.474
33
76.48
1.004
67
85.37
0.721
34
77.14
0.975
68
85.51
0.719
3
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Springer • Estimating home range size
100%
90%
80%
70%
Average
60%
Percentage 50%
of Total Area
40%
30%
20%
10%
0% 0
10
20
30
40
50
60
70
80
90
100
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.
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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 t2/r2, 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 t2/r2 ratio (P >.25), where the null hypothesis is t2/r2 = 2.0. This was about 4.5 h for their
Springer • Estimating home range size
5
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
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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.
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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.
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Springer • Estimating home range size
61 79 42 19 76
20
92
4 13
89
80
33
2
81 50 67 21
30 49
72 84
46
69
43
48 98 73
12
36
25
55
39
75
44 62
53
65
9
78
52
22
95 47 15 37
97
90
96 99
8 32
66
18
87
60
63
100
41
74
23
82 94 34 35 (56)
58
16 86
24 27 54 29 59
71
40
70
17 51
88
14
45
5
6
7
1 31
77
10
64
91
3
93
28 26 85
68
38 11
57
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 =
.
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Springer • Estimating home range size
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
35
1.1369
69
1.0802
2
XXX
36
1.1344
70
1.0794
3
3.4282
37
1.1313
71
1.0784
4
2.6184
38
1.1275
72
1.0773
5
2.1538
39
1.1253
73
1.0761
6
1.9224
40
1.1216
74
1.0754
7
1.7563
41
1.1193
75
1.0744
8
1.6237
42
1.1173
76
1.0731
9
1.5491
43
1.1152
77
1.0720
10
1.4886
44
1.1137
78
1.0714
11
1.4424
45
1.1124
79
1.0699
12
1.4024
46
1.1101
80
1.0691
13
1.3637
47
1.1083
81
1.0684
14
1.3316
48
1.1055
82
1.0676
15
1.3069
49
1.1035
83
1.0671
16
1.2891
50
1.1016
84
1.0663
17
1.2712
51
1.1005
85
1.0655
18
1.2593
52
1.0995
86
1.0650
19
1.2466
53
1.0988
87
1.0646
20
1.2354
54
1.0979
88
1.0641
21
1.2233
55
1.0970
89
1.0638
22
1.2154
56
1.0964
90
1.0634
23
1.2072
57
1.0950
91
1.0627
24
1.2003
58
1.0938
92
1.0620
25
1.1926
59
1.0916
93
1.0615
26
1.1855
60
1.0904
94
1.0608
27
1.1785
61
1.0887
95
1.0604
28
1.1726
62
1.0879
96
1.0598
29
1.1665
63
1.0868
97
1.0592
30
1.1614
64
1.0853
98
1.0587
31
1.1554
65
1.0844
99
1.0583
32
1.1489
66
1.0831
100
1.0575
33
1.1435
67
1.0823
34
1.1386
68
1.0814
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Occasional Wildlife Management Papers
A
C
Springer • Estimating home range size
B
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 = .
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Occasional Wildlife Management Papers
From Table 1, using the point method, the rate of increase drops to less than 5% at the 14th location (an increase from 53.77 square units to 56.40 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
