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Estimation of density of gibbon groups by use of loud songs.

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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
[1987] 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.
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