American Journal of Primatology 29:93-108 (1993) Estimation of Density of Gibbon Groups by Use of Loud Songs WARREN Y. BROCKELMAN AND SOMPOAD SRIKOSAMATARA Department of Biology, Faculty of Science, Mahidol University, Bangkok, Thailand The density of gibbon populations may be estimated by listening for the loud duetted songs of monogamous territorial groups. This method requires a correction factor which must be estimated from the frequency of singing of an adequate number of known study groups. The correction factor and its error were estimated for pileated gibbons (Hylobates pileatus) in Khao Soi Dao Wildlife Sanctuary in southeastern Thailand. Among 30 groups studied, 47% sang per day, on average, but the variation between days and the variation in singing frequency between groups were large. Weather conditions, especially windiness, explained some variation in singing. During an area-wide survey of groups in the sanctuary, unexplained variation in singing from day to day accounted for approximately half of the sample error of group density estimated from 1-day listening samples. Error due to day-to-day variability can be reduced by listening for more than one day a t each site. Correction factors based on the cumulative proportion of groups heard during longer (2-5-day) sample periods of listening were closer to 1.0, therefore leaving less room for error and bias of the correction factor. o 1993 Wiley-Liss, Inc. Key words: auditory census, population density, gibbons, gibbon songs, Hylobates pileatus, Thailand INTRODUCTION Forest primates are difficult to census accurately. The most commonly used methods for estimating the density of primate populations have been the strip census and the line transect [e.g., Southwick & Cadigan, 1972; Struhsaker, 1975; Cant, 1978; Green, 1978; Chivers & Davies, 1979; National Research Council, 1981; Johns, 1985a,b; Brockelman & Ali, 19871. Line transect and strip census methods are not very reliable for hylobatids because of their low visibility in the forest and relatively unpredictable behavior on detecting humans: they may give mobbing calls, hide in the canopy, or flee secretively. Marsh and Wilson [19811 found that the line transect method tended to underestimate gibbon density. The social characteristics of gibbons [reviewed by Chivers, 1977; Gittins & Raemaekers, 1980; Brockelman & Srikosamatara, 1984; Leighton, 19871 which Received for publication May 10, 1991; revision accepted September 15, 1992. Address reprint requests to Warren Y.Brockelman, Department of Biology, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand. 0 1993 Wiley-Liss, Inc. 94 / Brockelman and Srikosamatara allow reliable determination of the number of breeding groups in small study areas are: (1)relatively stable and cohesive groups (2 to 6 individuals; usually 3-4) in permanent territories; (2) groups easy to recognize individually from age and sex composition; and (3) regular singing by mated pairs. Crude estimates of density over large regions are often extrapolations from one or a few intensively studied or typical areas [Brockelman, 1975; Chivers, 19801. Some workers have relied on auditory information to estimate group density over large unknown areas [e.g., Ellefson, 1974; Chivers, 1977; Wilson & Wilson, 1975; Tilson, 1979; Chivers & Davies, 1979; Marsh 8z Wilson, 1981; Kappeler, 1984; Johns, 1985a1. The use of loud songs to obtain reliable population estimates requires knowledge about the frequency and variability of singing behavior. In general terms, to estimate the density of a population from samples one must determine what proportion of the true number of animals are detected by the sampling procedure [Overton, 19711. One then multiplies the number of signs or animals actually detected (X) within the sample area by a correction factor (f> to estimate the number present. The correction factor in auditory sampling is equal to llp, where p is the proportion of individuals (or groups) that are expected to sing during one sample period. It may be estimated from a study population of known numbers of individuals or groups. Correction factors such as this are estimates and may contain appreciable random error. The purpose of this paper is to analyze the major factors which affect singing frequency in an intensively studied population of pileated gibbons (Hylobates pileatus) in Southeast Thailand. We investigated the effect of time of day, weather, and season on singing frequency, and analyzed the variation in singing between groups and between days. We present a simulation technique for studying the effect of variability in singing behavior on population estimates, and suggest a method for minimizing sample variability in singing frequency to improve the precision of population estimation. The method may be applicable to other species of primates which give regular loud vocalizations, but modifications may have to be made if their social systems or ranging patterns differ. General procedures for estimating populations from loud songs have been summarized in Brockelman and Ali [19871. METHODS Study Area Our intensive study area is located in seasonal tropical rain forest in Khao Soi Dao Wildlife Sanctuary, Chanthaburi Province, Southeast Thailand [Srikosamatara, 1980,19841.The forest is undisturbed with a somewhat broken canopy 20-30 m high, with some emergents exceeding 50 m. Rainfall is seasonal with 2,0003,000 mm falling annually, mostly from May through October. The study area is in a steep-sided valley of 9 km2 in area and 250-900 m in elevation (12" 59' N, 102" 9'E). At least 31 groups were within hearing distance of our listening posts, at a density of about 6 groups per km'. Five groups around the listening posts were observed regularly and their ranges were well known. Acoustical Data Collection Pileated gibbons sing duets consisting of female great-calls and overlapping male responses, repeated a t intervals of 1-3 min. Duets last 5-20 min and can be heard at least 2 km under favorable conditions [Marshall et al., 1972; Srikosamatara, 1980; Srikosarnatara & Brockelman, 19831. Males sometimes give solo bouts, but these vary somewhat more in loudness and vigor than do duets and are given Estimation of Density of Gibbon Groups / 95 by both mated and subadult males. As unmated individuals do not duet, the duet is the best evidence for the existence of a breeding group. The data reported here were collected on 91 days during 5 visits to the study area from April to December of 1978 and a 31-day visit during MayJune, 1979. The main listening posts were located on a hillside on one side of the valley; occasionally second listeners occupied positions on hills up to 1 km away. Field equipment consisted of a magnetic pocket compass accurate to within 2”, a protractor, and a digital wristwatch. Listeners collected the following information: beginning time (to nearest 2 or 3 sec) of each duet and each great-call within it, compass direction, and estimated distance of each singing group or individual. Song characteristics of use in identifying groups were also noted; most groups in the area could be recognized from a combination of acoustical and directional cues. The great-calls of gibbons are so stereotyped that minor differences in pitch, note form, or length can be used to recognize groups. Weather was recorded at 10-min intervals while listening, and was subjectively classified as sunny, cloudy (sunlight not falling on listening post), rainy, breezy (leaves and small branches rustling), or windy (boughs shaking). Rainfall and maximum and minimum temperatures were measured daily. Each day’s song data were relisted in order of increasing compass direction and mapped a t 1:20,000 scale in order to facilitate group identification. Data from a second listener sometimes permitted more accurate group location by triangulation [Brockelman & Ali, 19871. With experience, group distances could be estimated by a single listener to within 20%accuracy if groups were not behind hills. Our method assumes that all groups that sing are heard. Thus, the area of the sample must be carefully delineated on a topographic map so that no groups within it are inaudible, and weather conditions should be favorable. Methods of selection of the “listening area” have been discussed by Brockelman and Ali t19871. Estimation of Correction Factors We estimated the contribution of daily variability in the number of groups singing to sample error in p, and investigated a number of different ways of reducing this error, using Monte Carlo simulations. The simulations allowed us to place confidence limits on the proportion of groups detected using a variety of methods of subsampling the data. One strategy which can improve sampling accuracy is to listen for more than one day at each sample location. Even during good weather, not all groups sing. As one spends more days listening a t each sample location, one hears more of the groups present, hence a correction factor based on a larger number of days per location will be closer to unity. This means, however, that fewer locations can be sampled. To determine the optimal sample period, we subsampled our data for each of two different assumptions: (1)the listener can recognize groups individually from acoustical and directional information and therefore knows which groups heard sang on previous days, and (2) the listener knows only how many groups called on each day of listening and cannot identify individual groups with certainty. In the first case the group count is cumulative; in the second the estimate is simply based on the largest number heard on any single day. With experience, one can recognize many-perhaps mostgroups from one day to the next. As a rule of thumb, song locations that map more than 500 m apart (the approximate width of a territory) may be assumed to be in territories of separate groups. Using the data from May 8 to June 7,1979, we tabulated frequency distributions ofp, the proportion of groups heard per sample period, for all possible samples 96 / Brockelman and Srikosamatara of size m ranging from 1 through 5 consecutive days, with samples overlapping. Four “bad weather” days (see Results) were excluded. This yielded 27 1-day Samples, 26 2-day samples, 25 3-day samples, and so on, from which to estimate p and its distribution by each of the above methods. The variance of the percentage or proportion (p) of groups calling should be inversely related to the total number of groups (n) within hearing distance. This is simply a statistical property of the numbers, unrelated to biology. The estimate of sample variation in p obtained from a study area of known density is thus valid only for survey areas containing approximately the same number of groups which, of course, is not known beforehand. We investigated the magnitude of this effect in our simulations by subsampling from the total pool of groups heard. Thirty gibbon groups is an unusually large number to be able to hear from one place; most sites we have surveyed in Thailand have smaller listening areas. We therefore divided our study site into 2 nearly equal areas, each containing 15 groups. We then calculatedp separately for each section for each day. After tabulatingp for 5 values of m, we repeated the process after subdividing the valley into 3 sections of 10 groups each, and 5 sections of 6 groups each. This procedure increased the numbers of listening “samples.” For each combination of m and n we tabulated mean p and its variance. Although increasing the number of samples results in smoother frequency distributions and more precise standard error estimates, the samples are not truly independent for two reasons: samples 2 2 days overlap, and the gibbons in different parts of the valley can hear each other. The implications are discussed further in the Results. We have further explored the question of how to estimate the standard error of p based on varying numbers of samples. The empirical sample distributions of p follow no obvious simple frequency distribution (we test for binomiality below), and therefore we have not attempted to find a normalizing transformation. Instead, we have used a bootstrap method [Efron & Gong, 1983; Diaconis & Efron, 19831 to generate approximate confidence limits on the mean of s samples. By computer we generated new distributions of p(s,m,n), the mean of s (s = 1-12) samples of m days each by sampling the empirical distributions 300 times with replacement. This was done only for n = 15; the general conclusions reached should apply for any n. The major advantage of the bootstrap method is that it does not make any assumptions about the frequency distribution of p. The means were tested for normality (Kolmogorov-Smirnovtest). For example, in order to obtain a confidence interval for an estimate ofp based on 6 listening samples of 3 days each, we produced an artificial distribution of means of s samples by randomly drawing 300 groups of 6 samples each from the pool of 3-day samples, computed the mean of each group, and tabulated the distribution of these means, ~(6~3,151. The interval was determined by counting 116 of the distribution in from each tail. Summary of Problem Our methodology can be divided into two phases: determining the correction factor based on singing frequency estimated in a well known study area, and censusing other populations by means of auditory samples using the correction factor. These phases are not independent because determination of the correction factor depends on the methods of sampling to be used during the census. There are so many possible sources of error and bias in the entire process of population estimation from auditory data that it does not seem feasible to place reliable confidence limits on final estimates. As stated above, error enters into both Estimation of Density of Gibbon Groups / 97 correction factor determination and population sampling. Error is associated with the number of groups studied, number of samples, and number of days each group was observed. Bias may be associated with variation in habitat, weather, season, and density of groups. Our purpose is to identify the most important sources of error and bias and suggest ways of minimizing them. RESULTS Time of Singing We found that pileated gibbon duets are nearly always confined to 07001300 h. The data for 5 periods covering both wet and dry seasons (Fig. 1) illustrate the percentage of groups beginning singing in the study area by any given time of morning. Sunrise rdawn”) a t sea level varied between 0546 h (May and June) and 0615 h (Dec.) [Royal Thai Navy, 19831. The prime duetting time in this species is 0900-1100 h, but on 8 out of the 57 days shown in Figure 1, some groups started before 0800 h. In surveying for pileated gibbons it is necessary to listen during the whole period between 0730 and 1200 h. The increase in the cumulative percentage of groups singing during these hours is fairly gradual; no chorusing is evident. Usually not more than 2 or 3 groups sang at one time. The time of singing of a particular .group cannot be predicted accurately, although groups that sing often tend to begin earlier than groups that sing less. Frequency of Singing The frequency of singing by individual groups during the 31-day 1979 period varied from 23 to 61% of days (Fig. 21, and averaged 43.1% (SE = 2.03%, n = 30 groups). The mean for the 7 nearest groups was 44.6% (range 29-58%), and for the other more distant groups, 42.5%. Of the nearby groups, the one that called most frequently had formed only 11months before, and the group singing the least was a large group that must have formed at least 10 years earlier. How many groups are sufficient for obtaining a reliable estimate of the correction factor? The predicted standard error ofp during the 31-day period increases as the number of groups analyzed decreases. Figure 3 shows the width of 2 SE (which have about 2/3 chance of including the true mean p) and the 95% confidence limits on the mean. This interval is more than 0.10 if it is based on less than 5 groups, and the 95% limits exceed 0.21. With 10 groups, 2 SE are about 0.07 and the 95% limits are under 0.14. Effects of Weather on Singing Rain. Gibbons seldom sang during rain (exceptions occurred only during territorial conflict), but they did sing if rain ceased during the morning. Cloudiness. p was significantly but weakly correlated with the percentage of morning intervals with cloud cover per day during MayJune (P < 0.02; Spearman rank correlation). In fall and winter, cloudiness was usually confounded with windiness, which had a major inhibiting effect. Temperature. Singing was not correlated with daily mean temperature during any season. Wind. Wind during morning markedly inhibited singing (Fig. 1).The association between windiness and below average percentage of groups singing was highly significant in the fall monsoon (0ct.-Dec.) samples (P < 0.001; chi-square test). Even among “nonwindy)’days, breeziness was significantly associated with low singing (P = 0.029; Fisher’s exact test). An average of 3.9% of groups sang on windy days, 18.5% on breezy days, and 62.3% on calm days. Although audibility of 98 I Brockelman and Srikosamatara 100 80 so $0 20 0 TIME OF DAY Fig. 1. Cumulative percentage of groups singing in the study area in relation to time of day, during five sampling periods in 1978. Each line represents one day. The time data for 2 days in June were lost (cf.Table 1). r = rainy most of morning; b = breezy; w = windy. distant groups may be reduced by wind, this cannot fully explain the dramatic reduction; singing of nearby groups was also inhibited. The purpose of analyzing effects of weather on singing is to improve our ability to predict the number of groups in the area. Eliminating “bad weather” days from Estimation of Density of Gibbon Groups I 99 40 50 PERCENT OF DAYS 60 70 Fig. 2. Frequency distribution of proportionof days of singing per group during May 8 J u n e 7,1979. The seven closest groups are shaded. D . B . .. . 1 5 10 95% confidence interval I5 20 25 30 NUMBER OF GROUPS Fig. 3. Predicted error in estimates of p (proportion of group singing per day) in relation to the number of gibbon gi-oups used for estimation. our listening sample involves a trade-off between sample variance and the number of samples obtainable. We decided post fact0 to eliminate all days classified as windy and rainy during more than 113 of listening hours, in which singing was 100 / Brockelman and Srikosamatara TABLE I. Population Statistics for Singing Behavior for Five Periods in 1978 and One Period in 1979, Including Mean Proportion of Groups Singing Per Day @) and Its Variance, Predicted Binomial Variance, and Chi-squareTest of Agreement Period of listening Statistic Apr 22-30 May 15-18, 24-27 9 0.558 0.036 0.011 26.6 8 0.525 0.057 0.011 36.5 Jun 7-19 Oct 16-30 Nov 19 -Dec 3 Apr-Dec good weather May 8Jun 7, 1979 13 0.663 0.062 0.010 80.1 15 0.290 0.057 0.009 89.0 15 0.330 0.123 0.010 178.5 41 0.593 0.051 0.010 194.5 31 0.430 0.040 0.008 149.2 ~ No. of days, k P 4 Binomial u2 y2 (df = k-1) dramatically reduced, and days in which cloud cover was dense during more than 90% of intervals. This left a sample of 27 days during the 31-day M a y J u n e period for simulation study, during which the mean proportion of groups singing was 47.3%. Seasonal Variation Two major seasons were included in our survey: the warm summer monsoon (May-August) and the cool monsoon weather (SeptemberJanuary).The hot, dry season (February-April) is not represented. More groups sang during the warm monsoon than the cool monsoon (Table I), but when breezy, windy, and rainy days are eliminated from all 1978 samples, there are no significant differences in singing frequency between periods (KruskalWallis l-way ANOVA) [Siegel, 19561. The pooled estimate of mean % singing for good weather days in 1978 is 59.3, which is higher than that for the M a y J u n e 1979 estimate. We now know that this was due to underestimation of the total number of groups within hearing distance during 1978, as the estimate was taken from the highest number heard on a single day, 23 groups. In 1979 it was determined that there were at least 30 groups within hearing. Correction of p (mean proportion singing) for 1978 leads to 0.593 x 23/30 = 0.455, close to the estimate for 1979. The Distribution of Proportion Singing Over Days If variation in proportion of groups singing per day were binomially distributed, it would be relatively easy to normalize the data and place confidence limits on estimates of p . We calculated the predicted variance, u2 = pqtn (where q = 1 p and n = number of groups), under the assumption of binomial variation and compared it with the actual variance of p , s2. The significance of departure of s2 from 2 was tested with chi-square [Bliss, 1967: 391. For all sample periods, departure from binomial variation is highly significant (P < 0.001; Table I), even if bad weather days are omitted. The nonrandom distribution of the number of groups singing per day could be partly due to their independent responses to atmospheric conditions (especially during October-December) and partly due to mutual stimulation. The latter hypothesis is difficult to test because beginning times of songs are not highly clumped in time (Fig. 1) and most bouts are initiated with no apparent stimulation from neighbors. But nearly all groups within any listening sample area can easily hear each other. Estimation of Density of Gibbon Groups / 101 SAMPLE SIZE, M 100 93 P 87 a a 80 g 73 2 69 $ 60 (3 w c) a 1 b D I (DAYS) 4 5 53 lL 0 7 3 47 40 33 II 27 rm 20 m m m 13 7 0 ..,....,... .rr o s ..,....,.. 1 0 0 5 . ioo s 100 s 100 5 101s FREQUE NCY Fig. 4. Frequency distribution of percentage of groups detected per sample period of m days ( m = 1-5) using the noncumulative method of counting (maximum number heard on any single day). Variability of p in Relation to Sample Size The proportion of the groups heard during a single sample period (1 to 5 days) is affected both by the number of days per sample (m) and by the method of counting groups (Figs. 4 and 5). For both methods the variance of the proportion is reduced as the number of days per sample (m)is increased, but for the cumulative method this proportion rapidly approaches 1.0 and the error is asymmetrical (Fig. 5). The frequency of singing in the two sections of the valley containing 15 groups each, is not independent (product moment r = 0.51, P < 0.01), but dividing up the groups has not affected the variance appreciably. The use of overlapping samples for m > 1 also did not affect the variance in comparison with non-overlapping samples; this may not hold true for smaller numbers of independent samples, however. The distributions of p in the study area for increasing numbers (s = 1-15) of samples of m days each were compiled for both the noncumulative and cumulative methods. The approximate upper and lower limits of 1standard error were read from these distributions and are plotted in Figure 6 for the cumulative counting 102 / Brockelman and Srikosamatara SAMPLE SIZE, M (DAYS) 2 I loo 93 l--r 3 5 4 llllnlllllllllllllllllln mrrrrn mm m 0 a 80 2 69 3 U 60 0 53 8 47 tz w 0 U r I 40 33 27 20 13 7 0 d s 10 o s ioo s 10 o 5 101s I 5 10 I5 2 0 25 FREQUENCY Fig. 5. Frequency distribution of percentage of groups detected per sample period of m days, counting groups cumulatively. method. This graph indicates the gain in precision by increasing either m or s. Table I1 shows the calculated SD (of single samples) for varying m for both methods of sampling. Standard deviations ofp in relation to m for n = 6,10, and 15 groups, for both sampling methods, are also shown in Table 11. Reducing n from 15 to 6 increases the SD an average of 55% for sampling noncumulatively and 31% for sampling cumulatively. Sample Error for Estimated Density When conducting an area-wide survey, an estimate of density will contain error from two major sources: (1) error resulting from day-to-day variation in singing frequency, and (2)error due to site factors, including variation in density and perhaps differences in behavior between groups. In a series of replicated auditory samples these sources of error cannot be separated but we may roughly estimate the first from our simulations based on data from our study area. We examine a series of 11 l-day samples scattered throughout Khao Soi Dao Wildlife Sanctuary collected during April and October of 1977. Fifty-seven groups were Estimation of Density of Gibbon Groups / 103 1 2 3 4 5 6 7 8 9101112131415 NUMBER OF SAMPLES Fig. 6. Limits of standard errors above and below p , in relation to sample size (rn = 1-5 days) and number of sample periods (s = 1-15), based on simulated distributions produced by random sampling of data shown in Figure 5. heard in sample areas totaling 72.9 km', for a mean density of about 0.8 groups per km2 heard, which divided by p gives an estimated total of about 1.7 breeding groups per km2. The listening area was determined for each sample site from a topographic map [Brockelman & Ali, 19871. Variability in the number of groups heard due to differences in listening area size was removed by correcting the number of groups heard (G) to a mean area of 5.58 km'. The SD of corrected G is SD(G') = 3.67, and VAR(G') = 13.44. In order to compare this variability with that found in our study area due to variation in calling frequency, we must try to standardize n, the mean number of groups present. The mean number of groups present per sample area is estimated to be 5.3W0.473 = 11.3, which is closest to n = 10 (Table 11; for m =1)in our simulations. We correct the SD from our simulations to the approximate value expected for 11.3 groups calling: predicted SD = 0.226 x 11.3 = 2.55, and predicted variance is approximately 6.52. The actual variance is twice this value, but = 2.16, P > .05; 2-tailed test). Although the the difference is not significant number of samples from the survey is not large, the results indicate that roughly half the variance of auditory samples of gibbon groups could be due to variation in calling behavior alone. We can now show how to select the optimal combination of m and s to minimize standard error of the mean. Our model partitions the total sample variance into 2 components: 104 I Brockelman and Srikosamatara TABLE 11. Means and Standard Deviations of the Proportion of Groups Calling @) for Varying Numbers of Groups Present (n)and Days of Listening Per Site (m). m I 2 3 4 5 Noncumulative sampling n=6 0.473 (0.255) n = 10 0.472 (0.226) n = 15 0.474 (0.202) 0.615 (0.203) 0.599 (0.168) 0.582 (0.139) 0.681 (0.180) 0.653 (0.142) 0.624 (0.122) 0.724 (0.160) 0.689 (0.123) 0.656 (0.100) 0.752 (0.140) 0.706 (0.110) 0.678 (0.071) Cumulative sampling n=6 0.473 (0.255) n = 10 0.472 (0.226) n = 15 0.474 (0.202) 0.718 (0.220) 0.712 (0.193) 0.715 (0.160) 0.844 (0.183) 0.841 (0.153) 0.840 (0.131) 0.911 (0.137) 0.910 (0.120) 0.911 (0.094) 0.954 (0.090) 0.954 (0.083) 0.943 (0.084) where si is variance between sites and s$ is variance in day-to-day vocal behavior within sites. Assume that in l-day listening samples the 2 components are of equal magnitude, and that s%is reduced by increasing m,but sg is not. Estimates of s2 are taken from our simulated distributions. We have examined the behavior of the standard error of the estimated number of groups for 1to 15 samples of varying size. It was found that for both methods of sampling, increasing sample size m from 1to 2 days usually lowered the error at least the same amount as increasing the number of samples (s) by 2. However, this probably underestimates the value of increasing m and p , as the error on p is not symmetrical (see below). DISCUSSION Assumptions in the Use of Auditory Correction Factors The use of mean singing frequency (p) determined from a study area to survey an unknown population assumes that this singing frequency is characteristic of the survey area as a whole. Several factors bear on this assumption. First is the adequacy of the sample of groups. As groups vary greatly in singing frequency, an estimate based on 5 or fewer groups has an unacceptably high standard error. It should be based on more than 5 groups, and preferably at least 10. Secondly, in applying estimates of singing frequency based on a sample size of 1 day to other populations, we must assume that the mean singing frequency is a species-specific character that does not vary erratically from place to place and is not highly sensitive to environmental influences. The consistent behavior in different months of the year (allowing for weather variation) supports this idea, but it must be tested by comparing singing behavior from different locations within and betureen species. There are few comparable data available from other H . pileatus sites. In the zone of overlap in Khao Yai National Park between Hylobates lar and H . pileatus, three pileatus groups had a lower frequency of duetting ( p = 0.28) Estimation of Density of Gibbon Groups I 105 than three interspersed lar groups 0, = 0.41) [Brockelman & Gittins, 1984; E. Ranson, R. Mather, & N. Gould, unpublished report; Davies, unpublished report]. But both of these frequencies were lower than averages from pure species populations. Gibbon groups may sing less when they have fewer neighbors of their own species. Data from 5 different populations of H . lar summarized by Brockelman and Ali  indicate a p ranging from about 0.51 to 0.85 with a mean of about 0.68 (weighted average including only 18 nearby groups; SD = 0.125). Some of the variation is probably due to small sample sizes and some due to differences in season and weather conditions. Ecological changes could also affect singing behavior. For example, Johns [1985al reported that singing of H . lar groups was depressed after logging operations had disturbed the forest. There is some evidence that the density of groups influences singing frequency, and that groups with few neighbors may sing less than groups surrounded by neighbors [Chivers, 1974; Brockelman et al., 19741. Gibbon density could thus be underestimated in areas of low density. Our study area in Khao Soi Dao has a very high density of groups; we would consider less than about 2 groups per km2 to represent "low density" [see Chivers, 19771. Lack of singing in an area does not necessarily mean that no gibbons are present. Groups partially decimated by hunting would not sing much, as only mated pairs duet. Widowed females, however, have been found to solo with high frequency in H . pileatus [Brockelman & Srikosamatara, 19841 and in H . lar [Caldecott & Haimoff, 19831. Improving Estimates The cumulative number of groups singing during m days can be predicted reasonably accurately using data for 1-day samples alone, using the formula [Brockelman & Ali, 19871: p(m) = 1- E l - p(1)l". The major assumption this makes is that singing on successive days is independent. For example, we would predict that the proportion of groups calling within 3-day samples would average 1 - (1 - 0.47313 = 0.851. The actual proportion calling within 3 consecutive days was 0.840 (Table 11; n = 15),on average. The predicted proportions for 2 through 5 days are, respectively, 0.719, 0.851, 0.921, and 0.958, which all are slightly larger than the observed values, suggesting a small degree of nonindependence. Figure 7 shows values of p ( m ) for arbitrary values ofp(1) ranging between 0.30 and 0.80. For m 2 3, the sample statistics tend to converge and approach 1.0. More extensive data on the total error variance of numbers of groups heard would be desirable, to obtain a better estimate of the proportion of error due to variation in p . A higher value of s$ would make it more profitable to increase sample size m. Any method of sampling which makes the correction factor closer to 1.0 is desirable because this reduces possible effects of bias, and alters the error. The upper confidence limit on p cannot exceed 1.0 and as p approaches 1.0 the upper limit converges rapidly on 1.0. When noncumulative sampling is replaced by cumulative sampling, p is increased but the error is affected asymmetrically, being reduced only on the upper side. Increasing m, however, causes p to converge toward 1.0 and the error to converge toward zero. This also reduces the possible bias. The upper limit on p provides the minimum estimate of population density, 106 / Brockelman and Srikosamatara *.I*0 OI 0 I 2 3 4 1 5 SAMPLE SIZE M(DAYS) Fig. 7. Predicted cumulative proportion of groups heard in relation to the number of days ( m )spent listening, calculated under the assumption that calling is random (see text). The actual proportion heard in study area in relation to m is shown with dashed line. which is of most interest in surveying endangered or threatened species such as gibbons. For m 2 3, when sampling cumulatively, the upper limit of the standard error of p (containing the true mean with 83.3%confidence) does not exceed the expected number of groups heard in one sample by more than 14%, for pileated gibbons. For m 2 4, one expects to hear a t least 90% of the total population of breeding groups. For H . lar, sampling with m = 2 (excluding windy days) should yield around 90% of groups, on average. CONCLUSIONS Based on our experience, the following guidelines are offered to persons intending to survey a given species of gibbon using auditory methods. Rigid rules are difficult to establish, because of the large number of variables and uncertainties involved. 1. Establish the average proportion of groups singing per day in an intensive study area. Use group songs or duets and not solo songs. At least 10 groups should be studied. 2. Establish the number of groups heard per sample period for samples varying from 1 to 4 days. Approximately 8-10 sample periods (with good weather) are adequate to obtain a sufficiently precise estimate of p . 3. Develop the ability to recognize and distinguish groups so that the cumulative number singing during 2-, 3-, and 4-day periods can be determined. If time does not permit obtaining such samples, the cumulative estimate of the proportion singing based on binomial probabilities can be estimated using the formula given above. Estimation of Density of Gibbon Groups / 107 4. The correction factor p (proportion of groups singingkample) used in surveys should be above 0.5, and preferably above 0.8, as both possible bias and the upper confidence limit are reduced as p approaches 1.0. This is especially important if the number of groups used in the estimate is below 10. 5. Estimates of p should be made for 2 or 3 different seasons, and weather conditions should be recorded as accurately as possible. For H . pileatus, wind and rain had the greatest effect on singing behavior and explained the observed seasonal differences, but this may not be true for all species and all climates. 6. If gibbon groups are a t low density or have been broken up by hunting, they may not vocalize as much as those in an undisturbed study area. The upper limit on gibbon density therefore will never be as certain as the lower limit. ACKNOWLEDGMENTS We thank Kumpol Meeswat and Jeremy Raemaekers for their assistance in the field, and Rauf Ali for help in computer programming. Rauf Ali, Robert Fagen, Ken Green, John Oates, Alan Rabinowitz, and Richard Thorington kindly read the manuscript and offered helpful comments, as did several reviewers. The support of the Charles A. Lindbergh Fund, Inc. and the New York Zoological Society is gratefully acknowledged. REFERENCES Bliss, C.I. STATISTICS IN BIOLOGY. Vol. 1.New York, McGraw Hill, 1967. Brockelman, W.Y. Gibbon populations and their conservation in Thailand. NATURAL HISTORY BULLETIN OF THE SIAM SOCIETY 26:133-157,1975. Brockelman, W.Y.; Ali, R. Methods of surveying and sampling forest primate populations. Pp.23-62 in PRIMATE CONSERVATION IN THE TROPICAL RAIN FOREST. C.W. Marsh, R.A. Mittermeier, eds. New York, Alan R. Liss, 1987. Brockelman, W.Y.; Gittins, S.P. Natural hybridization in the Hylobates lar species group: Implications for speciation in gibbons. Pp.498-532 in THE LESSER APES: EVOLUTIONARY AND BEHAVIOURAL BIOLOGY. H Preuschoft, D.J. Chivers, W.Y. Brockelman, N. Creel, eds. Edinburgh, Edinburgh University Press, 1984. Brockelman, W.Y.; Ross, B.A.; Pantuwatana, S. Social interactions of adult gibbons (Hylobates lar) in a n experimental colony. Pp. 137-156 in GIBBON AND SIAMANG. Vol. 3. D. Rumbaugh, ed. Basel, Switzerland, S. Karger, 1974. Brockelman, W.Y.; Srikosamatara, S. Maintenance and evolution of social structure in gibbons. Pp. 298-323 in THE LESSER APES: EVOLUTIONARY AND BEHAVIOURAL BIOLOGY. H. Preuschoft, D.J. Chivers, W.Y. Brockelman, N. Creel, eds. Edinburgh, Edinburgh University Press, 1984. Caldecott, J.O.; Haimoff, E.H. Female solo singing by a wild lar gibbon in peninsular Malaysia. MALAY NATURE JOURNAL 36~167-173, 1983. Cant, J.G.H. Population survey of the spider monkey Atelcs geoffroyi at Tikal, Guatemala. PRIMATES 19525-535, 1978. Chivers, D.J. The siamang in Malaya: A field study of a primate in tropical rain forest. CONTRIBUTIONS TO PRIMATOLOGY. Vol. 4. Basel, Switzerland, S. Karger, 1974. Chivers, D.J. The lesser apes. Pp. 539-598 in PRIMATE CONSERVATION. Prince Rainier 111, G.H. Bourne, eds. New York, Academic Press, 1977. Chivers, D.J., Davies, G. Abundance of primates in the Krau Game Reserve, Peninsula Malaysia. Pp. 9-32 in TRANSACTIONS OF SIXTH ABERDEEN-HULL SYMPOSIUM ON MALESIAN ECOLOGY. A.G. Marshall, ed. Hull, U.K., Department of Geography, University of Hull. 1979. Diaconis, P.; Efron, B. Computer-intensive methods in statistics. SCIENTIFIC AMERICAN 248 (May):96-108,1983. Efron, B.; Gong, G. A leisurely look at the bootstrap, the jackknife, and cross-validation. AMERICAN STATISTICIAN 37:3648, 1983. Ellefson, J.O. A natural history of whitehanded gibbons in the Malay Peninsula. Pp. 1-136 in GIBBON AND SIAMANG. Vol. 3. D.M. Rumbaugh, ed. Basel, Switzerland, S. Karger, 1974. Gittins, S.P.; Raemaekers, J.J. Siamang, lar and agile gibbons. Pp. 63-105 in MA- 108 I Brockelman and Srikosamatara LAYAN FOREST PRIMATES. D.J. Chivers, ed. New York, Plenum Press, 1980. Green, K.M. Primate censusing in northern Columbia: A comparison of two techniques. PRIMATES 19537-550, 1978. Johns, A.D. Differential detectability of primates between primary and selectively logged habitats and implications for population surveys. AMERICAN JOURNAL OF PRIMATOLOGY 8:31-36, 1985a. Johns, A.D. Selective logging and wildlife conservation in tropical rain-forest Problems and recommendations. BIOLOGICAL CONSERVATION 31:355-375, 1985b. Kappeler, M. The gibbon in Java. Pp. 19-31 in THE LESSER APES: EVOLUTIONARY AND BEHAVIOURAL BIOLOGY. H. Preuschoft, D.J. Chivers, W.Y. Brockelman, N. Creel, eds. Edinburgh, Edinburgh University Press, 1984. Leighton, D.R. Gibbons: Territoriality and monogamy. Pp. 135-145 in PRIMATE SOCIETIES. B.B. Smuts, D.L. Cheney, R.M. Seyfarth, R.W. Wrangham, T.T. Struhaker, eds. Chicago, Illinois, University of Chicago Press, 1987. Marsh, C.W.; Wilson, W.L. A survey of primates in Peninsular Malaysian forests. Kuala Lumpur, Universiti Kebangsaan Malaysia, 1981. Marshall, J.T.; Ross, B.A.; Chantharojvong, S. The species of gibbons in Thailand. JOURNAL OF MAMMALOGY 53:479486, 1972. National Research Council, US. TECHNIQUES FOR THE STUDY OF PRIMATE POPULATION ECOLOGY. Washington, D.C., National Academy Press, 1981. Overton, W.S. Estimating the numbers of animals in wildlife populations. Pp. 403455 in WILDLIFE MANAGEMENT TECHNIQUES. R.H. Giles, ed. Washington, D.C., The Wildlife Society, 1971. Royal Thai Navy. TIDE TABLES. Bangkok, Thailand. HvdroeraDhic DeDartment. Royal Thai Navy, f985. Siegel, S. NONPARAMETRIC STATISTICS FOR THE BEHAVIORAL SCIENCES. New York, McGraw Hill, 1956. Southwick, C.H.; Cadigan, F.C. Population studies of Malaysian primates. PRIMATES 13~1-18, 1972. Srikosamatara, S. ECOLOGY AND BEHAVIOUR OF THE PILEATED GIBBON (HYLOBATES PILEATUS) IN KHAO SO1 DAO WILDLIFE SANCTUARY, THAILAND. Bangkok, Thailand, M.Sc. Thesis, Mahidol University, 1980. Srikosamatara, S. Ecology of the pileated gibbon (Hylobates pileatus) in Southeast Thailand. Pp. 242-257 in THE LESSER APES EVOLUTIONARY AND BEHAVIOURAL BIOLOGY. H. Prueschoft, D.J. Chivers, W.Y. Brockelman, N. Creel, eds. Edinburgh, Edinburgh University Press, 1984. Srikosamatara, S.; Brockelman, W.Y. Patterns of territorial vocalization in the pileated gibbon. Pp. 19-22 in PRIMATE BIOLOGY. P.K. Seth. ed. New Delhi. India, T.T.P.P. Publishers, 1983. Struhsaker, T.T. THE RED COLOBUS MONKEY. Chicago, University of Chicago Press, 1975. Tilson, R.L. Behaviour of hoolock gibbons (Hvlobates hoolock) during different seasons in Assam, India. JOrikNAL OF THE BOMBAY NATURAL HISTORY SOCIETY 7611-16, 1979. Wilson, C.C.; Wilson, W.L. The influence of selective logging on primates and some other animals in East Kalimantan. FOLIA PRIMATOLOGICA. 23:245-274, 1975.