Introduction

The length that a group of primates covers during its daily foraging is determined mainly by its travel costs (Steudel 2000). Proper measurement of day range is required to calculate the proximal travel costs of the group. One cannot always obtain the actual distance traveled under wild conditions. Many factors hamper efficiency of tracking and hence influence the measurement of daily ranging of a primate group, e.g., weather (Li 2002; McKey and Waterman 1982; Su et al. 1998), habituation of the individuals (Bennett 1986; Sigg and Stolba 1981), structure of the terrain (Gautier-Hion et al. 1981), density of the forest (Goodall 1977; Liu et al. 2004; Phillips et al. 1998), and moving velocity of the tracked group (Kirkpatrick 1996; Li 2002).

Researchers have applied various methods to collect data on day range of nonhuman primates: making marks on a topographic map on dislocation of the group (Koenig et al. 1997; Li 2002; Stevenson et al. 1994), carrying global positioning system (GPS) devices and georeferencing the group’s successive positions (Sprague et al. 2004), or directly pacing the distance the group travels (Bennett 1986; Fossey and Harcourt 1977; Goodall 1977; Shimooka 2005; Yamagiwa and Mwanza 1994). Researchers commonly used 2 measures of day range: 1) 2-point methods, i.e., measures based on straight-line displacement between 2 sleeping sites ≤24 h (Hu et al. 1980; Shi et al. 1982) or 12 h (DeVore and Hall 1965; Isbell et al. 1999; Kirkpatrick 1996; Koenig et al. 1997; Stevenson et al. 1994) and 2) multipoint methods, i.e., all the locations of the tracked group, are plotted on maps at time intervals as the group moves, and then one calculates the total distance as the sum of the distances between successive chronologic points (Isbell et al. 1999). Straight-line distance between 2 geographical sites, e.g., between adjacent mornings (Su et al. 1998) or between 2 consecutive night nests (Goodall 1977), is habitually used as a substitute for the actual pathway traveled to measure the travel costs of free-ranging primate groups (Altmann and Altmann 1970; Isbell 1983; Kirkpatrick 1996; Li 2002; Olupot et al. 1994). Johnson et al. (2003), Muoria et al. (2003), and Tarnaud (2006) studied demographic management via a GPS collar and tested feasibility of using GPS collars in free-ranging nonhuman primates (Phillips et al. 1998; Sprague et al. 2004), but no research team had employed a GPS collar to estimate the daily travel length in free-ranging primates until our study.

Measurements of day range raise several practical problems: How does one choose an appropriate method? How many fixes of the group are needed to estimate daily ranging distance reliably? At least how many monthly full-day follows are required?

Most diurnal, forest-dwelling, nonhuman primates exhibit a typical daily traveling and foraging pattern: After leaving the sleeping site in the morning, the primates head toward the first feeding site, then to the resting site for a routine siesta, then to the second feeding site, and finally to the sleeping site in the evening (Jolly 1985). Snub-nosed monkeys follow similar traveling patterns (Bai et al. 1988; Chen et al. 1983; Ding and Zhao 2004; Hu et al. 1980; Liu 1959; Long et al. 1998).

Only 13 semi-isolated natural groups of Yunnan snub-nosed monkeys inhabit northwestern Yunnan and southeastern Tibet (Long et al. 1996; Xiao et al. 2003). The rugged topography and dense forests make tracking them difficult (Wu 1991). Published data on day range of wild groups of Rhinopithecus bieti are scarce, and sample sizes were limited (Kirkpatrick 1996; Liu et al. 2004).

We employed GPS collar technology to monitor a free-ranging group of Rhinopithecus bieti on Mt. Laojunshan, Yunnan Province, China, from December 2003 to October 2004. Our objectives were 1) to calculate their daily ranging distances, 2) to compare day-range estimates calculated via different methods, and 3) to find a standard to measure day range of Rhinopithecus bieti.

Methods

Study Site and Subjects

Jinsichang (99°37′ E, 26°53′ N) lies in the eastern part of the geographic distribution of Rhinopithecus bieti (Xiao et al. 2003). The vegetation is continuous primary coniferous forests with fir (Abies spp.), larch (Larix spp.), spruce (Picea spp.), and alpine rhododendra (Rhododendron spp.) as the dominant species. The group confined its ranging to the forest belt between 3000 m and 3800 m above sea level (asl), an area densely covered with bamboo (Fargesia spp.).

Yang (2000) estimated that in 1997 and 1998, the group of Rhinopithecus bieti at Jinsichang contained 51 individuals We relocated the same group in July 2003 and found it contained ca. 180 individuals (Long et al. 1996). In most cases, the group moved and rested unobtrusively.

Subject Capture and Release

We used 2 types of collars (Telonics Inc., Mesa, AZ). One is a store-on-board GPS collar (type: TGW-3800; mass: 890 g) with a VHF beacon. The other is an ST-20 (mass: 740 g) Argos collar with a VHF beacon. Each collar has an autorelease function.

On December 17, 2003, we captured 2 healthy adult males at 1632 h with big tuck nets, fitted them with collars, and released them at 16:43, ≤11 min after capture. The subjects then immediately ran back to the group. We later noted the collared male with GPS transmitter to be the breeding male of a 1-male unit.

Data Collection

Data stored in the GPS collar included horizontal geographic positions of the individual, altitude, date, time, number of satellite signals, dilution of precision (DOP), programmed timetable to obtain a fix, and ambient temperatures when we positioned a fix. The GPS collar acted in auto 2D/3D mode, i.e., when ≥4 satellite signals were available, we obtained a 3D fix —horizontal position and altitude; if we detected only 3 satellite signals, the collar recorded a 2D fix (horizontal position only). After transferring the fixes to a computer, we refined the elevation of each 2D fix via the elevation of spatial adjacent 3D fixes. We then adjusted 2D fixes into a reliable 3D fix (Rempel et al. 1995).

We programmed the collar to attempt GPS readings (fixes) at the following times daily: 0800, 1000, 1500, 1700, and 1900 h. The times roughly correspond to the first sleeping site, morning feeding site, resting site, afternoon feeding site, and second sleeping site, respectively (Ding and Zhao 2004; Long et al. 1998). We attempted no fix around noon because of the known propensity for the species to take a midday siesta. We programmed both collars to fall off at specific dates and times. Based on the expected power lifetime, we set the GPS collar to release at 0800 h on October 22, 2004. We obtained fixes via the GPS collar over 310 running days. The total number of attempted fixes is 1550.

The GPS collar also provided several values of the DOP. DOP represents the geometric configuration of satellites with respect to the GPS collar. A greater angle between the satellites lowers the DOP value —which ranges from 1 to infinity— and provides a more accurate measurement. A higher DOP value indicates poor satellite geometry and an inferior measurement configuration (Phillips et al. 1998). We set the maximum DOP value at 6. We discarded fixes if their DOP values were >6.

Statistical Analysis

We downloaded fixes saved by the GPS collar and mapped them via ArcView® 3.2a (ESRI, Redlands, CA). We had previously digitized a map of the study area (1:50,000) via the ArcView 3.2a platform. We took a SPOT5 satellite image in November 2004 —60 km × 60 km, resolution: 2.5 m, unified the georeference of subjects via the projection of WGS_1984_UTM_ZONE_47N. Accordingly, we converted all GPS positions from latitude-longitude coordinates to UTM map coordinates. We calculated interfix distances in ArcView 3.2a via the Animal Movement Extension V.1.1 (Hooge and Eichenlaub 1997). We then imported the data into Microsoft Excel®, and performed statistical analyses in SPSS 11. Distances (m) of day range are means ± standard deviation (SD).

To conform to the calculating formulae of 2-point straight-line day ranges, we constructed 2-point distances from component time intervals available in the total data set. The constructed distances D-h-h are in Fig. 1: h-h is the time interval between the former and the latter hour, and D is the displacement from the point at the former hour to the point at the latter hour. For instance, we marked the straight-line distances between 2 consecutive morning (sleeping) sites at 0800 h as D08–08. We used a 24-h day scale and a ≤12-h day scale to compare differences between distances calculated within the 2 time intervals of a day scale.

Fig. 1
figure 1

All the different time intervals used to calculate two-point straight-line distances are illustrated and the labeling for each constructed distance is given above each line. Two consecutive days are sketched in the top figure (A), and the dotted line on the X axis indicates the night time between day 1 and day 2. A 12-hour day is illustrated in the figure at the bottom (B).

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D08-10-19 and D08-15-19 are 3-point cumulative distances, constructed from time intervals available in the total data set for a further comparison between the raw multipoint cumulative distances and the constructed 2-point straight-line distances.

We calculated multipoint cumulative daily ranging distances with varying numbers of locations, depending on the number of fixes on any given day. D-x corresponds to the days on which we obtained x fixes. D-5, D-4, and D-3 are the raw sums of the fixes obtained via the GPS collar on each day. D-2 is the 2-point displacement on days with only 2 fixes.

We used independent samples t-test and 1-way ANOVA to compare differences between and among the means of daily ranging distances computed from different criteria. All tests are 2-tailed with a default significance level at p = 0.05.

Results

Positions of the Group via the GPS Collar

We excluded 276 fixes because of a DOP value >6. In total, we obtained 1274 valid geographic locations of the group: the number of days with 5 fixes is 127; 4 fixes on 112 d, 3 fixes on 51 d, and 2 fixes on 19 d. The average number of satellites is 3.7, with a range: 3–6, n = 1274). We acquired 763 2-dimensional (2D) fixes and 511 3-dimensional (3D) fixes. 2D fixes account for 59.9% of the total 1274 fixes, and 3D fixes make up 40.1%. 2D fixes and 3D fixes do not randomly distribute among the various temporal intervals: χ2 = 49.8, df = 1, p = .000. The total acquisition rate —number of locations obtained/number of locations attempted— of the GPS collar is 82.2% (1274/1550).

Daily Ranging Distance Calculated with Different Criteria

A 100-m distance is the minimum to judge whether the group has moved. With the exception of distances <100 m, all 2-point straight-line displacements in 24 h —e.g., D08–08— 2-point straight-line distances —e.g., D08–19, D-2— and multipoint cumulative daily ranging distances —e.g., D–5, D–4, and D–3— in ≤12 h are in Table I. We provide standard deviation (SD), sample size n, minimum, maximum, and breakdown of the time intervals (in h) of each mean distance.

Table I Estimates of mean daily ranging distances of Rhinopithecus bieti at Jinsichang based on different time intervals and measuresa
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Statistical results of the day range comparisons for the 24-h interval, ≤12-h interval, and all other intervals, are in Table II. There is no significant difference among D08–08, D–15–15, D–10–10, D–17–17, and D–19–19 —1-way ANOVA: F 4, 1008 = 0.762, p = 0.550— and among D–5, D–4, and D–3: 1-way ANOVA: F 2, 285 = 0.973, p = 0.379). D08–08, D–10–10, D–15–15, D–17–17, and D–19–19 comprise 1 whole data set, and D–5, D–4, and D–3 another. There are significant differences between 24-h 2-point straight-line distances, e.g., D08–08, and ≤12-h multipoint cumulative distance, e.g., D–5; Table II).

Table II Comparisons of daily ranging distances (mean ± SD in m) calculated with different time intervalsa
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Comparisons of daily ranging distances ≤12 h are in Table III. D08–08 approximates to D08–19 (t test: t = 1.311, df = 394, p = 0.191). When a valid GPS fix is added between the 2 sleeping sites, D08–19 is changed to a 3-site cumulative distance, either D08–10–19 or D08–15–19. There is no significant difference between D08–10–19 and D08–15–19 (t-test: t = −1.820, df = 354, p = 0.195). Further, D08–10–19 and D08–15–19 are not significantly different from D–5, D–4, and D–3 (Table III).

Table III Comparisons of ranging distances calculated with different time intervals and measures within 12 h by independent t-test (p-value)
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The distances D08–19, D08–15, and D–10–19 are highly significantly different from one another (t-test, p < 0.05, Table III). Both D08–15 and D–10–19 are very significantly different from D08–08 (t-test, p < 0.01, Table II) and D08–19 (t-test, p < 0.05, Table III).

We also calculated the overnight distance between the group’s location at 1900 and 0800 h (D–19–08 in Fig. 1: the mean of D–19–08 is 127 ± 109 m: range: 4–592 m; n = 213.

Estimates of daily ranging distances vary depending on the number of fixes obtained via the GPS collar per day. Estimates of day range based on > 2 fixes are longer than those based on 2 fixes (t-test, p = 0.000).

The sample size of D–3 is relatively small (n = −51). D–3 does not significantly differ from other multipoint cumulative distances, regardless of whether the distances are raw data, e.g., D–4 or D–5, or constructed distances, e.g., D08–10–19 and D08–15–19; Table III). On 19 positioning days, only 2 sites are fixed via the GPS collar: 17 d after excluding distances <100 m. This 2-site distance is marked as D–2. There is no significant difference between D–2 and D08–19, D08–15, D08–17, and D–10–19 (Table III). D08–08 does not differ significantly from D–2.

Discussion

Suitability of GPS Collar in Yunnan Coniferous Forests

The choice of an appropriate set of tracking devices is of major concern. Becoming familiar with the applicability and shortcomings of the tracking instrument is essential before performing the study (White and Garrott 1990). We decided to apply GPS tracking primarily because of the enormous difficulty of following the unhabituated snub-nosed monkey group on foot. Satellite reception, and hence location accuracy, determines whether GPS technology is a suitable tool. The reception of the GPS collar is seriously attenuated by thick vegetation (Phillips et al. 1998; Sprague et al. 2004). We achieved a total acquisition rate of 82.2%, which is lower than that in a temperate forest at fixed locations at the James H. Barrow Field Station, Hiram College, OH (ca. 97%, Phillips et al. 1998). Acquisition rate in our study was higher than that in a study on Japanese macaques (20%: Sprague et al. 2004) and at fixed locations in neotropical forests of Costa Rica and Trinidad (34%: Phillips et al. 1998). We conclude that GPS collars are useful tools to track snub-nosed monkeys in their high-altitude habitat with complex terrain and dense conifer forests.

Estimating Daily Ranging Distances

Various methodologic factors have a pronounced effect on the estimate of daily ranging distance in Rhinopithecus bieti: definition of a day —12-h vs. 24-h day— time intervals, number of obtained fixes per day, and number of tracking days per mo.

The distances covered between 0800 h and 1900 h (D08–19) and between 0800 h and 1500 h (D08–15) are significantly different from each other. D–10–19 and D08–19 are also different. Hence, D–10–19 and D08–15 are not reliable estimates of day range. The variation was likely caused by extensive foraging or moving after 1500 h and before 1000 h, respectively (Ding and Zhao 2004; Long et al. 1998). However, in line with Bai et al. (1988) and Long et al. (1998), nighttime sleeping sites and daytime resting sites were rather fixed points in the daily activity cycle of Rhinopithecus bieti.

Daily ranging distances, calculated from 2 consecutive points ≤24 h (D08–08), and from 2 points ≤12 h (D08–19), are not significantly different, confirming that the group of Rhinopithecus bieti did not move after sunset. After entering the sleeping site, groups of Rhinopithecus rarely change their positions, and they can be relocated at the same place the following morning (R. roxellana: Hu et al. 1980; Li et al. 2000; Liu 1959; Ren 1999; R. brelichi: Yang et al. 2002; R. bieti: Xiang 2005). Distances between 2 locations at the same hour ≤24 h, e.g., D08–08, D–10–10, D–15–15, D–17–17, and D–19–19, and distances between the morning and evening sleeping site in the daytime, e.g., D08–19, can substitute for one another. The observation that the group covered a short distance during the interval D–19–08 –<130 m— further confirms that points at 0800 h and 1900 h are sleeping sites. In case we are unable to locate the morning and evening sleeping site ≤12-h day (daytime), we can instead position the locations at the same hour on 2 adjacent days, e.g., D–17–17, to estimate day range.

Estimates of daily ranging distances based on 2-point straight-line displacements were 43% shorter than those based on cumulative multiple sites in Rhinpoithecus bieti. We thus conclude that the multipoint cumulative daily ranging distance is a far more reliable estimate of day range and associated travel costs (Isbell et al. 1999).

We employed a 5-point cumulative ranging distance as an estimate of day range. Ideally, we could have determined the daily travel distances via continuously recording GPS readings; however, the procedure requires enormous storage and battery power, which is not available in this application. As a result, we were limited to taking readings 5 times per day. Moreover, we attempted the 5 readings at times previously determined to be important in the monkeys’ activity schedule, i.e., sleeping, resting, and feeding sites, as preliminarily evaluated (Ding and Zhao 2004; Long et al. 1998). We did not consider possible seasonal changes in activity budgets. Estimates of cumulative daily ranging distances based on 3, 4, and 5 fixes (D–3, D–4, and D–5) are not significantly different. Our results thus suggest that 3 fixes per day are sufficient to study day range of Rhinopithecus bieti: however, 5 fixes would be ideal.

The cumulative 3-point daily ranging distance based on the distance between morning sleeping site and daytime resting site, e.g., D08–15, plus distance between daytime resting site and evening sleeping site, e.g., D–15–19, can be an economic method to estimate the day range of Rhinopithecus bieti. If one cannot locate the study group at the fixed hours e.g., punctually at 0800 or 1500 h, etc.— then one can alter the schedule; if the resting site had been recorded, then one can also use 1 geographic position in the morning, before 12:00, and another in the evening to estimate the day range.

On some days, the study group stayed in 1 valley for a whole day and did not engage in long-distance movement. Nevertheless, we recorded traveled distances from the collared individual on those days. The day ranges of individuals and of the group can be very different in some nonhuman primates (Isbell et al. 1999). Thus it is necessary to set a minimum distance to judge whether the group has moved. We set the minimum distance at 100 m. Based on our observations, a group member seldom moved >50 m horizontally when the group was resting. When an individual moved >100 m, this usually resulted in the departure of the whole group. Thus we did not include distances <100 m in the calculation of day range.

Another problem concerns the number of days that should be spent each month tracking the study group to achieve a reliable estimate of the group’s mean day range. Some earlier studies adopted a 5-d observation period per mo to record the locations of the study group (Defler 1996; Harrison 1983), yielding a total sample size of 60 d in 12 mo. We obtained 1 data set (D–3) whose sample size was below 60 d (n = 51 d) with higher S.D. (497 m). There is no significant difference among the mean cumulative day ranges, e.g., D–5, D–4, and D–3. We expected that the small sample size of D–3 would make the ranges not significantly different among D–5, D–4, and D–3. In addition, D–2 showed no significant difference from D08–19 and other 24-h, 2-point straight-line displacements. Long investigation days on the day range are needed to clarify suspicions about the effect of small sample size on ranges. We therefore speculate that 5 d/mo might not be enough time to obtain a sample size large enough to measure the day range accurately. We suggest that 10 tracking days per mo is the minimum requirement to obtain a total annual sample size of >100 d ranges.