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4 Census Methods for Estimating Densities BACKGROUND FOR CALCULATIONS DERIVED FROM TRANSECT CENSUSES MEASUREMENTS FOR TRANSECT METHODS AND CALCULATION OF DENSITY The aim of a census is to estimate the density of a sample popula- tion in a defined area so that the total population of a larger census area can be estimated. The basic formula for calculating density, which is the number of animals per unit area, is Estimated animal Number of animals seen population, N in sample area, n Census area, A Sample area, a When utilizing a transect, the area censused is found by multiply- ing the length by the width (A= Iw). For sample areas based on transects, / = the length of the transect line and 2w = the strip width, which is twice the transect widthâthat is, the width lo- 36
Census Methods for Estimating Densities 37 cated on one side of the transect line. The above relationship is usually solved for N, and the basic formula for estimating the number of animals in a population of census area a = 2 â¢ Iw becomes 2-/w where A is measured in the same units as the distance measure- ments. Several types of density estimates are recognized, and these are discussed in Chapter 8. Transect width is estimated from the following measurements, which can be collected when an animal is sighted along a transect line: P = the perpendicular distance, that is, the shortest distance from the detected animal to the transect line. It is often called the animal-to-transect distance. S = the animal-to-observer distance, or sighting distance from the observer to the animal at the moment of detec- tion. 0 = the sighting angle, or the angle between the transect line and the animal-to-observer line at the moment of detec- tion. The angle 6 may be measured with a field compass. On the basis of the trigonometric relationship P = S sin 6, any two of the three measurements shown in Figure 4-1 can be taken for convenience. Estimation errors can sometimes be caught when all three measurements are taken by using trigonometry to check accuracy. Usually a measurement is made only for the per- pendicular distances or for both the sighting angle and the sight- ing distances from which the perpendicular distances can be com- puted. Different methods for determining a valid transect width have led to a variety of formulas, usually through the substitution of w by some specifically defined value. The transect width has been variously defined as the maximum sighting or perpendicular dis- tance, as the mean distance, and as some distance between the maximum and mean that is considered an effective strip width.
38 TECHNIQUES IN PRIMATE POPULATION ECOLOGY FIGURE 4-1 Measurements for per- pendicular and sighting distances. Three measurements may be taken when an animal is sighted from a transect line: P, the animal-to-path distance; 5, the ani- mal-to-observer distance; and 6, the sight- ing angle. The length of the transect line, 7", is a measured distance; the transect width, tv, may be established as a fixed or variable distance. These intermediate widths have been attempts to estimate a 100% detection distance or a distance at which observations be- come markedly less frequent. It is obvious from the initial equation, TV â nA/2-lw, that de- creasing the size of the sample area relative to the sample popula- tion, n, has the effect of decreasing the denominator and thereby increasing the population estimate, N. Thus, formulas that util- ize mean sighting or perpendicular distances will produce smaller estimates of the sample area and larger population estimates than will equations that utilize maximum values for these estimates of transect width. Formulas that are used to derive some estimate of effective strip width will provide intermediate estimates of population size. The latter formulas often rely on establishing a fixed width and excluding from analysis those sightings that lie beyond this fixed width. These estimates are made to avoid one of the problems encountered when using the maximum distance: the possibility that the maximum record represents an extreme
Census Met hods for Estimating Densities 39 value that is beyond the distance within which one could normally detect animals. Burnham et al. (1980) reviewed census methods and tested several probability functions under the assumption that the prob- ability of detection can be best expressed by a family of probability curves. Their estimates depend on use of a computer to generate probability functions and on access to a statistician. Although their methods will probably be used increasingly as census meth- ods and analysis become more accurate and statistically robust, it is assumed that the investigator using this manual will not have access to a computer and will therefore be obliged to use the sim- pler analytical methods even though these may depend on some assumptions that only approximate the real situation. A variety of methods were reviewed by Burnham et al. (1980) and Robinette et al. (1974), and additional discussions can be found in the references cited by them. Several of these methods are mentioned below. Selected methods that have been useful in censusing primates are discussed later in this chapter. Robinette et al. (1974) reviewed several strip census methods that use either sighting or perpendicular distances. They con- ducted field tests in which they used stationary objects (blocks and carcasses) and found that all but three methods overesti- mated the actual numbers by more than 10%. Formulas based on sighting distances could be ranked by the size of the population estimates that they produced from lowest to highest as follows: King's method, which uses the arithmetic mean for the sighting distance; Gates III, which is based on a geometric mean; Hayne's method, which uses the harmonic mean of the sighting distance; and Gates II, which substitutes 2Â« â 1 for Â« and uses the arithmetic mean for the sighting distance. The Gates II method gave population estimates that were almost twice that of King's. Robinette and his colleagues found that several methods based on perpendicular distances also overestimated the population of stationary objects. These included Webb's method, the Gates I method, and Leopold's method. Webb's method uses the mean sighting distances and mean sighting angles to determine perpen- dicular distances; the other two methods use the mean perpendic- ular distances. The Gates I method also uses n â 1 for Â«. Meth-
40 TECHNIQUES IN PRIMATE POPULATION ECOLOGY ods developed by Kelker and Anderson and by Pospahala gave mean estimates within 10% of the actual numbers; in this way they were like King's method. Kelker used an estimated perpen- dicular threshold distance within which all animals were probably observed but beyond which some animals were probably missed, and he used an n in his formula that is equal to the number of animals seen within twice the threshold distance. Anderson and Pospahala also developed a correction factor for animals not observed. ASSUMPTIONS FOR LINE TRANSECT SAMPLING The theory of line transect sampling depends on four assump- tions outlined by Burnham et al. (1980): 1. Animals directly on the line will never be missed. It is also understood that all of the animals in the sample area will not be detected, and the farther an animal is from the line, the less likely it is to be detected. 2. Animals are fixed at the initial sighting position; they do not move before being detected and none are counted twice. 3. Distances and angles are measured exactly, thus avoiding both measurement errors and rounding errors. 4. Sightings are independent events. The investigator attempts to design the study and the data analysis to minimize violations of these assumptions. It is assumed that a plot of the sighting data, like the frequency of many classes of measurements, approximates a normal distri- bution. Figure 4-2 illustrates a normal distribution fitted to a fre- quency histogram. The value x is the mean or the sum of all values divided by the number of individual measurements, x = Ex/En. The standard deviation, s, indicates the dispersion of the values for the measured variable around the mean. The usual no- tation for the mean plus or minus the standard deviation is x + s. One calculates s by the formula: s = VP" where s2 is variance. The variance is calculated from the following formula:
Census Met hods for Estimating Densities 4 1 E(x - *)2 = n â 1 where A: is any measured value in your sample, x is the mean, and n is the number of observations. In practice, the term (x â x)2 is reduced to: V 2 / , = LXI n â 1 /!-( T \â- / - s= Ex2 n â 1 A census method that can be used for data that are not normally distributed but follow a Poisson distribution is given on p. 65. A good census is one that avoids bias and is both accurate and precise. The introduction of bias due to terrain, vegetation, or human activity is avoided by selecting transects in a way that ran- domly distributes them in the census area. The use of existing roads as transects strongly biases the counts because a road sys- tem almost never randomly traverses an area. Roads are generally constructed along rather than across contours. In addition, roads affect the exposure of animals and habitat to human activity by providing an access to nearby areas for hunting, cutting for fire- wood, and lumbering. Lastly, road or river edge habitat is very different from nonedge habitat because of the increased light penetration and prevalence of secondary growth species. There are a few special situations, e.g., the flat agricultural plains of the upper Gangetic Basin in India, where roads provide valid tran- sect routes for surveys of primates in rural areas (Southwick et al., 1965). An accurate census is one in which the estimate of a population closely approximates the true value; a precise census is one in which repeated measurements or replicates of the same quantity
42 TECHNIQUES IN PRIMATE POPULATION ECOLOGY â J3 g i_ a > 0) o c 0> 3 CT (V -8j [fa + s Values for the measured variable FIGURE 4-2 A normal distribution. The diagram shows the observed frequency of a variable in the form of a histogram (rectangles) together with a fitted normal distribution (smooth curve). Data may show some variation from a bell-shaped curve and still be considered as normally distributed. The x = the mean, the s = one standard deviation. (in this case, the number of animals present) are close to each other. To obtain a census that is both accurate and precise, it is necessary to determine the sample size, the number or length of transect lines, and the number of sightings (sample points) from inspection of preliminary data drawn from the sample area. Ex- amples are given in subsequent sections of this chapter. Tables of random numbers can be found in general statistics texts, and an elaboration of these statistical concepts can be found in discus- sions of population estimates in Burnham et al. (1980), Caughley (1977), Norton-Griffiths (1975), and Overton (1971). Several examples of primate censuses illustrate that there can be considerable variability in the results, but the estimates tend to increase in accuracy and precision with replication. Thus, Neville (1976) showed that counts of a population of howler monkeys in Venezuela doubled between the 50th and 80th hours of observa- tions. Altmann and Altmann (1970) found a clear-cut tendency for censuses to become more accurate with time when they mea- sured the amount of sampling error by matching the results of censuses against the true composition of groups of baboons deter-
Census Methods for Estimating Densities 43 mined by independent methods. MacKinnon (1974a,b) calcu- lated the density of orangutans as 0.8 individuals per km2 on the basis of a count of nests along a transect, but increased the esti- mate to 4.6 organutans per km2 after making a more detailed count of all nests in a plot within the same census area. Not all census methods have high accuracy or precision but represent compromises between size of survey area, cost, time, and manpower. Southwick et al. (1965) "calibrated" roadside surveys by repeating runs over 168 km of Indian roadside. The counts, based on 10 replications of the trip, ranged between 3 and 11 groups with an average of 7. Later they found that 14 groups lived in the census zone, indicating that for small sample sizes roadside surveys of rhesus macaques have low accuracy and, on the average, underestimate actual numbers by half. Assumption 3 emphasizes the theoretical importance of esti- mating distances to the nearest unit of measure, such as a meter, because grouping distance measurements into classes, as the data are taken, sets the limits for data analysis and requires that the data be analyzed as frequency counts rather than as a set of con- tinuous measurements. Thus, an observation should be recorded as a sighting at 36 m rather than as one in the interval between 30 and 40 m. Burnham et al. (1980) point out that there are valid statistical methods for estimating densities on the basis of grouped perpendicular distances, but none have been developed for analyzing grouped sighting distances and angles. Assumption 2 presupposes that animals do not move before they are detected. Movement away from an observer by animals initially close to a transect line has the effect of increasing width estimates (such as means) and thereby decreasing density esti- mates. Such bias is suggested in graphed data (Figure 4-3) when- ever the number of close sightings is less than the number of in- termediate sightings (Janson and Terborgh, in press). Figure 4-3 also illustrates a method for determining a reliable detection dis- tance by using the graphed data to identify the distance at which the frequency of detections drops sharply. Where there is no sharp separation between a plateau and a decline in observation distances, it is useful to compute density estimates for more than one possible maximum cutoff distance and to present the range of resulting density estimates.
44 TECHNIQUES IN PRIMATE POPULATION ECOLOGY 10 - 9 - 2 a. Ul CO en O UJ CD 5 - 4 - 2 - 7 14 21 28 35 42 49 56 63 D1STANCE (M) FIGURE 4-3 Distribution of perpendicular sighting distances for Cebus. Redrawn from Janson and Terborgh (in press). Burnham et al. (1980) recommend the use of perpendicular distance data and believe that when sighting distances are used they should be used with sighting angles. Robinette et al. (1974) also recommend the use of methods based on perpendicular dis- tances but note that there are some conditions, such as uneven terrain, in which sighting distances are useful because measure- ment of perpendicular distances from the transect lines is dif- ficult. Thomas Struhsaker reports finding a high frequency of sightings over the transect line. In such instances, the use of methods based on sighting distances is preferred over those based on perpendicular distances because the latter underestimate the area (the perpendicular distance overhead is a "zero" width) and overestimate the number of animals.
Census Methods for Estimating Densities 45 The fundamental problem in utilizing the perpendicular dis- tance from the transect line derives from the fact that primate habitat space is three-dimensional. We are in effect attempting to estimate density in terms of area rather than density within a volume. The problem becomes critical when the sample size is small and the area surveyed is restricted in size. Large sample sizes over wide areas reduce the vertical dimension relative to the transect length and width and thus reduce apparent variability, but the problem is a genuine one in small transect survey opera- tions. Density expressed as numbers of animals per volumetric units are common in fisheries but have seldom been applied to terrestrial vertebrates. In most primate surveys of limited scope, the observer-to-animal distance will probably yield the most use- ful results for estimating density per unit of area, but the record- ing of perpendicular distances as well as sighting distances and angles will provide the greatest flexibility in later statistical analy- ses of the data. GENERAL GUIDELINES AND FIELD PROCEDURES Standardization of methods is essential to minimize the variables and thereby allow comparisons between investigators and study sites. Unless distances are to be measured with a tape, an ob- server should develop experience and confidence in pacing and visually estimating metric distances prior to starting a census. Pacing is an effective method for determining horizontal distance provided the terrain is relatively level and unobstructed. A pace may be empirically determined by counting one's steps along a straight line premeasured by a metric tape and then dividing the paces into this linear distance. A person can accurately determine his average pace or step by pacing the measured line several times and by using care in regulating his stride. Experience and interobserver reliability also are gained by esti- mating horizontal and vertical distances in the habitat where the census will be done and by making visual estimates along mea- sured distances. The trick is to think in multiples of known dis- tances and heights, whether the basis of comparison is an imag- ined 90-m football field or an 8-m two-story building. An 18-m
46 TECHNIQUES IN PRIMATE POPULATION ECOLOGY tree can be considered simply as a tree that is 12 times the height of your 1.5-m-tall partner, who is standing at its base. Measuring treefalls is another way of developing a sense of scale. After mea- suring a few 50-m treefalls with a metric tape, it becomes easier to recognize the standing height of comparable emergents and to estimate the height of smaller trees as a fraction of the tallest trees in the forest. Censuses should be made at about the same time of day. The first 4 to 6 h and the last 3 h of the day are recommended because these periods are usually coincident with peak activity of pri- mates. Published surveys show that primates are easier to detect when they are active than when they are resting (Freese, 1975; Green, 1978a,b). It is not possible to census during rainstorms or windstorms. During a census the observer moves along a transect line and stops frequently (every few minutes or meters) to listen and scan the surrounding area. The optimal walking pace is about 1 km/h. By noting in your notebook the distance paced at every stop or every hundred meters, or by punching a number counter, you can accumulate an accurate record of the total distance paced. It may be advisable to work a transect line alone in order to reduce the noise from the movement of other people, but under some condi- tions the eyes and ears of a partner increase the chance of detect- ing primates. When a primate group is seen, a standarized time should be spent observing it (10 min is recommended). It is suggested that the observer remain on the census route and not follow the ani- mals away from the predetermined line. When beginning each transect, the observer should record se- veral standard items including the location, date and starting time, weather, census method, and participating personnel. These items can be recorded on a data sheet modified as neces- sary from the sample provided in Appendix C for all types of tran- sects, from broad surveys to random compass line transects. Each time an animal or group of animals is encountered, the observer should record the following information: â¢ Species. â¢ Number of individuals actually counted. In addition, the
Census Methods for Estimating Densities 47 group size should be estimated when conditions prevent a com- plete count. â¢ Mode of detection (whether by sight, vocalization, or sound produced by the animal moving through the vegetation). â¢ Time sighted. â¢ Observer's location along the transect. â¢ Animal-observer distance. This is the distance from the ob- server's position to the animal when it is first detected. It is fre- quently referred to as the sighting distance. â¢ Shortest transect-animal distance. This is the perpendicular distance from the transect line to the animal. Both the sighting distance and the perpendicular distance should be checked by measuring or by pacing until confidence and reliability in esti- mating distances are built up through experience. â¢ Height of the first animal sighted. â¢ Activity when first detected. â¢ Age (body size relative to adults) and sex of individuals in each group. Since one is rarely able to make a complete group count of forest species within 10 min, in the final analysis one is concerned primarily with the number of social groups and soli- tary animals encountered. â¢ Vocalizations. Tabulating bouts of loud calls may be useful in evaluating relative abundance in study sites. â¢ Time encounter ended. Carbon copies of field notes are a cheap form of insurance against loss when the original is held by the observer and the copy is sent back to the institution supporting the study. Blank sheets and notes of the day are best carried in an aluminum loose-sheet holder, which are available in a variety of sizes from most Ameri- can forestry suppliers. Daily field notes should be cataloged on summary census sheets at the end of each day and summarized at the end of each week or month. Catalog entries should include date, location, species sighted, number of individuals, page num- ber of the entry in the daily notes, and a brief description of what the specific entry contains. Daily cataloging permits rapid refer- ence to specific events and greatly facilitates data analysis. The catalog entries can be stored in ring files (looseleaf notebooks). The catalog entries are greatly expanded in long-term studies to
48 TECHNIQUES IN PRIMATE POPULATION ECOLOGY include whatever behavioral topics are the focus of attention, such as interactions between specified age and sex classes or in- dividuals, feeding observations, vocalizations, progressions, or group encounters. ASSESSING THE IMPACT OF HUMAN ACTIVITIES In conducting initial surveys, investigators will find that interviews with local inhabitants, government officials, and biologists help determine the amount and selectivity of hunting pressure, the utilization of forest products, and the extent of recent land clear- ing. In many parts of both the New and Old World tropics, mon- keys are hunted for food for local consumption and for markets, which can be visited to verify interview reports. Where primates have been subjected to continuing hunting pressures, their detectability will be seriously altered. A field investigator should keep in mind that more precise methods of data gathering and analysis can be used in protected areas than in hunted areas where reliable estimates of depleted populations may be beyond the scope of an initial survey. When entering an unprotected census area in which animals are hunted, investigators will want to know what species are hunted, for what purpose primates are hunted, and about how many animals are killed each year. This information is usually available from local inhabitants. Several interviews may be neces- sary. If hunters are active in the area, it may be a good idea to ac- company one of them. The value of the interview method is illustrated by the results of a survey that J. F. Eisenberg (1976, unpublished) conducted in an area of Territorio Amazonas in Venezuela, where six species of primates were known from museum collections to have occurred 15 yr previously. It quickly became apparent from interviews that local hunters had removed great numbers of primates to support a population of colonists. The bearded saki (Chiropotes) was rated as extremely palatable, as were the spider monkey (Ateles) and howler monkey (Alouatta). The hunters confessed that the capuchin monkey (Cebus) was very unpalatable and that the squirrel monkey (Saimiri) was too small to be profitably hunted
Census Met hods for Estimating Densities 49 with a rifle. The night monkey (Aotus), because of its nocturnal- ity and difficulty of detection, seemed not to be worth the effort for sustained hunting. Again its small size made it somewhat un- economical. As could be predicted from this information, the only primate species seen during diurnal boat surveys were the less favored species Saimiri and Cebus. The other larger species and the highly prized bearded saki were not detected by normal sur- vey techniques. BROAD SURVEYS The broad survey attempts to cover large geographical areas in a relatively short period of time (Scott et al., 1976a,b). When deal- ing with forest habitats, the most one can hope for in this kind of survey is data on geographic distribution, relative abundance in different areas of habitats, and limited information on age and sex composition of the populations. In open-savanna habitats and certain types of rural and urban settings, one may be able to collect relatively accurate data on group size, age and sex compo- sition, and density, but it is difficult to collect these data in most situations (Southwick and Siddiqi, 1977; Struhsaker, 1976). For broad surveys in forests and with little time available, ob- servations are usually made along existing roads, trails, or foot- paths. In special situations, counts may also be made from ca- noes along streams and in swamps. If time permits, a rough trail can be cut through the forest, preferably in a straight line and 4 km or more in length. No attempt should be made to census the same day that rough trails are cut. For broad surveys in open habitats and along river edges, vehi- cles and boats or canoes greatly expand the area that can be cen- sused, but the detectability of animals may be reduced in areas where animals move back from the edge in response to motor noise. Vehicles have been used extensively in India (Mukherjee and Mukherjee, 1972; Neville, 1968; Southwick and Siddiqi, 1966; Southwick et al., 1961, 1965) to survey primates along rural roads and canal banks. Modifications of this procedure have also been used in Malaysia (Southwick and Cadigan, 1972), Indonesia
50 TECHNIQUES IN PRIMATE POPULATION ECOLOGY (Wilson and Wilson, 1974), Bangladesh (Green, 1978b), and Africa (Taub, 1977; Altmann and Altmann, 1970). In most forest regions, suitable roads are limited in their extent and distribution and may be impassable during the wet season. Also, noisy vehicles reduce auditory cues from the animals. The practicality of counts from vehicles is therefore restricted. Favor- able conditions include good visibility, accessibility, and reason- able tolerance of vehicles by primates. Vehicles may be the only reasonable method for surveying large land areas, and they are well suited for surveying in savannas and agricultural areas. Researchers have censused by canoe or motorized boat areas not otherwise accessible. Flood plains that can be surveyed by foot during dry seasons may be passable only by water transport during the rains. Therefore, censusing in different seasons may require two survey methods. The approximate distance traveled on a river can be computed by determining the time required to travel a measured distance along a shoreline (e.g., 1 km), both upstream and downstream; computing the speed (km/h) at which the measured distance is traveled; and multiplying this speed by the total travel time. APPLICATIONS OF LINE TRANSECT CENSUSES IN AN AFRICAN FOREST Many of the data identified in the previous section can be used in a comparison of relative abundance of animals in study sites. However, because results of primate censuses along the same route are extremely variable from one day to the next, the data from broad surveys cannot give an accurate estimate of the ab- solute density. To reduce variability in transect censusing, a large number of censuses must be made over the same census route and over a long period of time (usually a year or more). But this is beyond the scope of the broad survey. The number of transects established and the distance between transects depend on the size of the study area, the heterogeneity of the habitat, and the distribution of the primate community within the study area. Although there is no fixed rule on this point, the following discussions of the number of censuses to be made and of estimating densities are relevant to planning an ac-
Census Methods for Estimating Densities 51 curate census program. Clearly, more research needs to be done on this aspect of censusing forest primates. The same methods and precautions listed in the preceding sections of this chapter should be followed. In the line transect census, the trail should be of predetermined length and established randomly within the study area. It should not be biased according to terrain, vegetation, or other factors (e.g., hunting) that may affect primate abundance along the transect. One usually establishes a transect along an arbitrary compass bearing and assumes that the area included will be rep- resentative of the vegetation types of the site. For instance, if the forest encompases 80% forest, 10% grassland, and 10% swamp, then ideally the transect will reflect this. Straight-line transects are preferable to routes following a cir- cle, square, or rectangle because they reduce the chances of inad- vertently counting the same animals more than once. A transect of about 4 km is appropriate for a morning's census. ZONATION If the vegetation along a transect varies in type (e.g., forest and swamp, woodland and savanna), it is important to divide the transect into zones or strata within which the vegetation is homo- geneous. Censuses and density estimates are made for each zone (habitat type) and weighted according to the proportional repre- sentation of each zone in the study area. This technique, called zonation or stratification, is intended to reduce variability be- tween samples and thereby increase precision. Although developed and used most extensively in aerial counts of large mammals, in principle it should be applicable to any kind of line transect cen- sus (Caughley, 1977). Use of this method usually requires prior knowledge of the habitat types, their abundance, and the habitat preferences of the animals. In most cases the technique has been of limited value in cen- suses of tropical forest primates because this kind of information has not been available. Observers should keep accurate notes on the exact locations of sightings along the transect line and the type of vegetation so that it is possible to zone the census transect after the censuses have been completed.
52 TECHNIQUES IN PRIMATE POPULATION ECOLOGY Zonation techniques are most applicable when dealing with a mosaic of strongly contrasting vegetation types in which one can quickly form impressions about primate densities from prelimi- nary walks through the study area. For example, this technique would be employed when comparing low-stature swamp forest with contiguous upland tall forest or a block of undisturbed mature rain forest with an adjacent forest that has been selec- tively felled for timber. One can, of course, zone the census tran- sect after it has been established and after the cenuses have been completed as long as accurate notes are kept on the exact location of each sighting and the vegetation is described accordingly. In this way one can combine segments of the transect that are simi- lar in vegetation. Such zonation would not only increase the pre- cision of density estimates by reducing variability between cen- suses for each zone but would also reveal habitat preferences of the primates being censused. Two outstanding problems are posed by the line transect method: (1) determining the appropriate sample size (length) and (2) estimating densities (width) from the data. As mentioned earlier, the extreme variation in counts from one day to the next makes it necessary to conduct several counts along the same tran- sect. SAMPLE SIZE DETERMINED BY 95% CONFIDENCE LIMITS How many censuses should one make along a particular transect? This will depend on the precision required, which in turn depends on the variability of the censuses. Although, basically, the larger the sample size, the more precise the results, a point is usually reached where more samples will not reduce variability signifi- cantly. Since this point cannot be determined before the study has begun, one must analyze the data as the study progresses so that the results and estimates of precision can be monitored. As outlined by Norton-Griffiths (1975, pp. 34-36), the precision of an estimate is the 95% confidence limits expressed as the per- centage of the estimated mean. In the case of censuses of primate groups, precision can be expressed as the 95% confidence limits divided by the estimated mean number of groups per census mul- tiplied by 100. The lower this percentage, the more precise the
Census Methods for Estimating Densities 53 estimated mean. One then plots this estimate of precision against the cumulative number of censuses completed. The point on the curve where any further increase in effort is not repaid by a pro- portional increase in precision can either be calculated exactly or found where the curve begins to flatten out. An example from the Kibale Forest, Uganda, demonstrates the value of computing estimates of precision (Table 4-1). A total of 44 censuses were made over an 18-mo period on a single 4-km census transect that traversed relatively mature tropical rain forest. No samples were made in 4 mo, and 2-4 censuses were conducted during each of the remaining 14 mo. TABLE 4-1 Results from 44 Censuses of Red Colobus Along the Same Transect Census Number Number of Red Colobus Groups Seen (x) Census Number Number of Red Colobus Groups Seen 1 7 23 3 2 3 24 4 3 5 25 4 4 2 26 3 5 3 27 0 6 5 28 3 7 2 29 3 8 2 30 3 9 3 31 3 10 5 32 1 11 6 33 3 12 4 34 6 13 8 35 4 14 7 36 2 15 4 37 3 16 3 38 3 17 6 39 5 18 3 40 0 19 4 41 6 20 3 42 3 21 5 43 4 22 6 44 5
54 TECHNIQUES IN PRIMATE POPULATION ECOLOGY Confidence limits were computed for the mean number of groups seen per census for the two most common primate species (red colobus and redtails). Although this could have been done at the end of each census, for simplicity the censuses were divided into units of 10. Calculating the standard deviation (s) was the first step in cal- culating the 95% confidence limits. An example of the calcula- tions for the s of the first group of 10 red colobus samples is shown below from the original census data provided in Table 4-1. /v 2 ILX2 n - 1 163- II) (7h II) . = 1.7029. In the present example of two species selected from Kibale, the 95% confidence limits and the percentage precision are given in Table 4-2. For illustration, the first value for the 95% confidence limits in the table was obtained by using the following formula: s 95% confidence limits = <o.o5<n-o X ~r ' v/i where t = the critical values of Student's ^-distribution obtained from two-tailed t table (used when dealing with small samples of fewer than 100) found in any standard statistical textbook (e.g., Sokal and Rohlf, 1969), Â« = the number of censuses, Â« â 1 = the degrees of freedom, and s = the standard deviation of the mean number of groups per census. Thus, the 95% confidence limits are: 1.7029
Census Met hods for Estimating Densities 55 = 2.26 X .538 = 1.218. The 95% confidence limits are computed cumulatively in units of 10; thus, they were computed for each species for the first 10 censuses, then the first 10 and second 10 censuses were combined for the next computation and so on until the final computation included all 44 censuses. 95% confidence limits The % precision = â X 100 Mean number ot groups seen for that unit of census 1.218 X 100 3.7 = 32.9%. The results are graphed in Figure 4-4 and clearly show that for both species precision began to level off after the first 20-30 cen- suses. To account for seasonal variation, one should conduct censuses uniformly throughout the year, preferably during every month. The number of censuses per month will again depend on the vari- ability of the results. In most cases it will not be possible to con- duct enough samples every month to demonstrate statistically sig- nificant differences between months, unless the differences are very pronounced. How many censuses are required to make comparisons with other areas or with the same transect in different time periods? Through modification of a formula presented in Sokal and Rohlf (1969), Janson and Terborgh (in press) suggest that the minimum sample (N) necessary to distinguish with 95% confidence a given
56 TECHNIQUES IN PRIMATE POPULATION ECOLOGY TABLE 4-2 Estimates of Precision for 44 Censuses of Red Colobus and Redtails Along the Same Transect 95% Mean Census Confidence Number % Species Number Limits Groups Precision Red colobus 1-10 1.218 3.7 32.9 1-20 0.844 4.3 19.9 1-30 0.654 4.0 16.5 1-40 0.570 3.7 15.3 1-44 0.532 3.8 14.0 Redtails 1-10 1.237 3.1 39.9 1-20 0.816 3.3 25.1 1-30 0.594 3.1 19.0 1-40 0.501 2.8 17.7 1-44 0.463 2.8 16.7 degree of difference between two means is roughly approximated by N = 4 X C.V. degree of difference between means + where C.V. = coefficient of variation, which is the standard devi- ation divided by the mean (s/x). For example (following Janson and Terborgh), suppose we want to be able to detect at least a 25% change in the red colobus population at Kibale. From the 44 censuses we calculate a C.V. of the mean number of red colobus groups seen per census, which is 0.46; thus, the minimum sample size required would be 4 X 0.46\2 0.25 + 1 = 55 groups of red colobus, which would indicate 15-20 censuses. Janson and Terborgh sug- gest, however, that because the data are usually not normally dis- tributed, the samples should be at least 10-20% larger than pre- dicted from their formulas.
Census Methods for Estimating Densities 57 ESTIMATING DENSITIES BY USING DIFFERENT STRIP WIDTHS The main problem in estimating group densities from line tran- sect samples is determining the size of the area sampled. The length of the transect can be easily measured, but how does one determine the width of the strip sampled? This will be affected by the perceptiveness of the observer, visibility and audibility in the 10 - Red Colobus 20 Cumulative number of censuses FIGURE 4-4 Precision of estimated mean number of social groups per census as a function of number of censuses completed. Vertical axis is the 95% confidence limits expressed as the percentage of the mean number of groups per census, i.e., 95% confidence limits divided by the estimated mean number of social groups per census times 100. This is a measure of precision, and as this percentage decreases the precision increases. The horizontal axis is the cumulative number of censuses completed. Data were collected during 44 censuses along one 4-km transect in mature forest (compartment 30) of the Kibale Forest, Uganda, during 1970-1972. Adapted from Struhsaker, 1975.
58 TECHNIQUES IN PRIMATE POPULATION ECOLOGY habitat censused, and detectability of the animals. Animal de- tectability can, in turn, be affected by group size, group spread, frequency of vocalization, activity at the time of census, sound made in movement through the vegetation, and the height of veg- etation most frequently used. Several methods for determining strip width are reviewed by Caughley (1977), Janson and Terborgh (in press), and Robinette et al. (1974). (K. M. Green discusses the subject in an unpublished report; to borrow a copy, write to the National Zoological Park, Washington, D.C.). Selected methods are tested here by compar- ing census results with the known group densities obtained from detailed, long-term studies of individual groups (see below). There are two basic approaches to determining strip width: Transect-to-animal distance is the estimated perpendicular dis- tance from the line transect to the first animal of each group seen. Observer-to-animal distance is the estimated distance between the observer and the first animal of each group seen. Both of these estimates give some indication of visibility and detectability. The first method, however, gives an estimate of width regardless of the actual detection distance from the ob- server, whereas the second method is based on the actual detec- tion distance (see Figure 4-5). Transect-to-Animal Distance Mean Perpendicular Distance Several formulas use the mean perpendicular distance of all first sightings to calculate the width of the transect. The methods indicated in Table 4-3 were tested with the red colobus census data (Struhsaker, 1975), but were re- jected because of unacceptably high overestimates of group den- sity. On the basis of detailed studies of individual groups, the red colobus density in the cenused area of the Kibale Forest was esti- mated at 6 groups per km2. Maximum Perpendicular Distance In this formula, the maxi- mum perpendicular distance of all first sightings of a particular species is used to estimate transect width (unpublished report by K. M. Green). This means that all groups detected will be within this distance. In order to cover both sides of the transect, this
Census Methods for Estimating Densities 59 maximum distance is doubled and then multiplied by the transect length to give the area censused. The number of groups seen is di- vided by the area to give the density. Example: 44 censuses along a single 4-km transect was 776 km. (1) Maximum perpendicular distance from transect to a red colobus group was 110 m or 0.11 km. (2) During all 44 censuses a total of 168 sightings of red col- obus groups were made. sum of sightings on number of different or repeat â.,. , . groups sighted transects (3) Density = â area censused 2 sides C length X widtrA of of 1 side of transect (_ transect in km J 168 2(176 X 0.11) = 4.34 groups/km2. This figure of 4.34 groups/km2 is an underestimate of 27.7%. The direction and magnitude of error were similar for redtails at Kibale, but for blue monkeys at Kibale this method overesti- mated by around 22%. Maximum Reliable Transect-to-Animal Perpendicular Distance A more critical method was first set forth by Kelker (1945) and modified by several others (see Robinette et al., 1974, and Janson and Terborgh, in press). In this approach, one plots the fre- quency distribution of all estimates of the perpendicular distance between the transect and the first animal seen. On inspecting this frequency distribution, one attempts to determine thje distance within which all groups were probably detected but beyond which some were missed. This maximum reliable distance is most read- ily determined when the frequency distribution curve shows an obvious plateau or asymptote that is followed by a sharp drop in
60 TECHNIQUES IN PRIMATE POPULATION ECOLOGY Comparison of distance from animal to 1) Observer 8 2) Transect â A' Animal T = Transect 0â¢Observer M 100 Â£ a D 'c .Â«> .5 < O Q A1 100 100 A2 100 9O A3 100 70 A4 100 30 A5 100 0 80 - 60 - 40 - 20 - 20 40 60 80 100 FIGURE 4-5 Diagram illustrating distinction between animal-to-observer and animal-to-transect distances. frequency. The maximum reliable distance or cutoff point is where the curve begins its sharp drop. In cases where the fre- quency distribution of transect-to-animal distances does not show a clear plateau and sharp decline, one is faced with the problem of deciding the maximum reliable distance. In such cases it may be advisable to compute density estimates for more than one pos- sible maximum reliable distance and to present the range of re- sulting density estimates. Take, for example, the case of the red colobus census data. Figure 4-6 suggests at least two possible cut- off points of maximum reliable transect-to-animal distances: 40 m and 60 m. With these distances, Kelker's method allows us to estimate group density as follows: (1) Length of censuses: 776 km (44 censuses along the same 4-km transect).
Census Methods for Estimating Densities 61 (2) Width of transect: 80 m or 0.08 km (40 m X 2, both sides of transect). (3) Total number of red colobus groups seen within 40 m of transect: 138 (from Figure 4-6). (4) Density: 138/176 X 0.08 = 9.8groups/km2. This value represents an overestimate of 63.3%. If one uses 60 m as the maximum reliable transect-to-animal distance, the esti- mate becomes 156 groups/176 X 0.12 = 7.39 groups/km2 or an overestimate of 23.3%. Janson and Terborgh (in press) applied a modification of this method to their raw data from Manu, Peru, and found that it gave enormous overestimates, usually of several hundred percent. Only with a number of correction factors derived from their de- tailed studies of specific groups could this method give reasonable estimates. A fundamental difficulty with the transect-to-animal distance is that many sightings will be made of animals directly over the trail and ahead of the observer. In such instances, the distance from trail to animal will be zero (see Figure 4-5). In the 44 cen- suses at Kibale, Uganda, referred to above, nearly 40% of the 166 sightings of red colobus were over the census transect and were scored as zero meters from the trail, although usually they were more than 20 m from the observer. Consequently, methods employing transect-to-animal distances will usually overestimate TABLE 4-3 Rejected Methods of Estimating Group Density of Red Colobus Monkeys Estimated Number of Method Source Groups per km2 Overestimate Leopold et al. (1951) Eberhardt (1968) Emlen (1971) Robinetteef al. (1974) Caugh ley (1977) Emlen (1971) 22.0 33.5 21.0 266.7 458.0 250.0
62 u l/l TT TT c ^ UO **) fN O H III 1 â c â¢0 00 x o ^c 2P T3 i/5 1 C OO f-l (N â 4> -o CS e > 0 ^ 1 * .1 o r"- 1 ,N 1 a, ^c <l 0 00 ^c "g Â£ TT 1 r^ c 3 4C 8 I I S A _f^ ^*â¢ ^ .- 1 g [>. Q> to rt ,>. O O/) "c3 as S 2 Â° 1 iÂ° 5 -"" 65 ^ c^ 3 '*J *^" o â d o .c S "^ f^ 00 00 ro bt ^ flj e Â§ & s OS ,0 ^* _H o o r"- o ^^ ^rt fN g C 0 S S3 Â° i > Ql --*1 â â 00 00 iO .s -i ffl 53 1 i | <Â« S> o 3 o o K C o i i i E Â«"Â° 1 | ^ 1 "S Q ..Â£ c -- ~ (-; 1 i 3 "> 1 O. -4 Estimates her of Initial S istances (m) 1 f tllll 17 censuses along i were considered- T. Struhsaker, un .5 Â« â¢Â§ E Â§ ^ S â¢o â¢o | | || j W 3 u J Z "n 1 " 1 Â« = i TO .â O H 'S Q g v>
Census Methods for Estimating Densities 63 0-10 11-20 21-30 31-40 41-5O 51-60 61-70 71-80 91-90 91-100 101-110 FIGURE 4-6 Frequency distribution of initial perpendicular animal-to-transect distance. Data are from the same 44 censuses that are dealt with in Figure 4-4. Red colobus sightings total 166. the density because they underestimate the size of the area cen- sused. Observer-to-Animal Distance Estimates of the initial distance between the observer and the first animal seen overcome the problem of zero distance inherent in the transect-to-animal method, although Janson and Terborgh (in press) discuss some of the theoretical difficulties. Mean Distance The King method (in Robinette et al., 1974) is based on the mean value of such estimates. By applying King's method to data from 17 censuses made in Kibale, Uganda, dur- ing 1974 and 1976 (when observer-to-animal distances were recorded; see Table 4-4) one finds that it tends to overestimate by a substantial factor: 80% for red colobus, 85% for redtails, and nearly twice this for blue monkeys. Similar gross overestimates
64 TECHNIQUES IN PRIMATE POPULATION ECOLOGY resulted when Janson and Terborgh (in press) applied this method to their raw data from Peru. Maximum Distance Applying the maximum distance (90 m) of all sightings of red colobus groups during the same 17 censuses to the basic formula gives: 55 sightings/68 km (i.e., 4-km transect X 17) X (2 X 0.09 km, the width) = 4.49 groups/km2 or an un- derestimate of about 25%. The same method applied to the red- tail data gave an underestimate of 30.5%, but for blue monkeys it yielded an overestimate of about 2-17.4%. Maximum Reliable Sighting Distance More accurate estimates were obtained by inspecting the frequency distribution of ob- server-to-animal distances and, as with the Kelker method, deter- mining the cutoff distance or maximum reliable sighting distance within which all animals were probably observed, but some missed (e.g., Ghiglieri, 1979). As discussed above, there may be a prob- lem in determining the cutoff point, and it may be necessary to use more than one distance and to compute more than one den- sity estimate. In any case, when this method was applied to the data from Kibale, Uganda (Table 4-4), the density estimates were generally closer to those from the detailed studies than to any of the other line transect analyses. For the red colobus, the cutoff point would appear to be 50 m. Applying the basic formula: 45 sightings within 50 m/(length = 17 X 4 km) X (width = 2 X 0.05 km) = 6.6 groups/km2. This represents an overestimate of only 10% when compared with the estimate of 6 groups/km2 from detailed studies of specific groups. A similar analysis for redtail monkeys in the same series of censuses gave an overestimate of 20% when 40 m was used as the maximum reliable sighting distance and 6.5% when 50 m was used. In contrast, estimates for blue monkeys were too high. With a 50-m cutoff, the results gave an overestimate of 47-67%, and with a 70-m cutoff an overestimate of 21-45%. It would ten- tatively appear that this method is most useful for primate species of generally high densities. For species of low density, it tends to overestimate.
Census Methods for Estimating Densities 65 Summary In summary, it would seem that the observer-to-animal distance, at least for the Kibale data, gives more accurate estimates in gen- eral than the transect-to-animal distance; that the mean distance in both methods tends to grossly overestimate; that the maximum distance tends to underestimate except for species of low density; and that the maximum reliable sighting distance, depending on the species and how one determines the cutoff point, gives the most accurate density estimate. NONLINEAR DENSITY PLOT METHOD When time and resources are limited and information from inter- views has confirmed that the species of interest is not selectively hunted, the first tasks in visiting a new area are to conduct a pre- liminary exploration of the region, making notes on vegetation height and quality and on soils and general topography. During the initial encounters with primates, attempts should be made to estimate group size, to estimate the distance from which the group was detected, and to determine what the animals were do- ing when detected. After a few days of the initial survey, select a troop and attempt to study it through an entire day. In this way one can begin to focus on the number of animals in a group and the approximate size of its daily foraging range. Of course, in so short a time it is not possible to estimate the entire home range of group or to ob- tain a very accurate idea of the mean group size, unless the sam- ple is very large. However, this approach provides sufficient data to permit one to estimate densities if the data are not normally distributed. By contrast, so far as methods described earlier in this section, it has been assumed that the data are normally dis- tributed. The data set approaches a Poisson distribution if the standard deviation approximates or exceeds the value of the mean. This simply means that the number of replicate samples (transects walked) is insufficient to generate a normal distribution of the variable that one is trying to measure: primate density.
66 TECHNIQUES IN PRIMATE POPULATION ECOLOGY One need not despair if this circumstance occurs. For example, if the species of interest has a mean group size approximating the size that has been noted in other areas, and if the preliminary in- vestigation indicates that its daily range-use pattern approaches the value for the ranging of the same species studied in another habitat, then the following technique may be used with con- fidence. Remember, however, that the method assumes that there is more accurate knowledge of the density of the species in question for another area and that there is reason to believe that the physical conditions of the new area are similar to those of the reference area. Even though high standard deviations are found in the analysis of the data, transect census data will positively covary with the real density. The preliminary data are thus a useful indicator of relative abundance. The number of transect samples may be in- creased or reanalyzed according to the following procedure: Set each transect length so that for a known detection width one will cover an area equal to 0.5 the average home range of the species in question. Each transect will then be treated as a single plot. Express the result of each transect as either the presence or ab- sence of a group or subgroup. Run transects until at least 10 sam- ples are available. Since the transects are randomly placed in the habitat, one can use a Poisson distribution for estimating the real density of groups per unit area from the percentage frequency of groups per sampling unit or plot. The proportion of plots with no groups will be 1 â / = e~* (Caughley, 1977), where/is the mean frequency of sightings per plot and the proportion of plots containing one or more groups will be / = 1 â e ~*. The value of â x can be found by using a table of exponentials. The relationship between the frequency of sightings and density can also be approximated from Figure 4-7. The transformed data can then be expressed as groups per unit area, which can be converted to individuals per unit area by multiplying by the mean group size. In the example provided in Table 4-5, the average home range of howler monkeys determined independently by following troops at the Smithsonian Tropical Research Institute, Panama, was found to be 10.5 ha, or 0.10 km2, in 1973. A plot with a transect width of 50 m (a detection or strip width of 25 m) and a length of
Census Methods for Estimating Densities 67 a E o u> \_ O) Q. >> O O) u cr <D Density per sampling unit FIGURE 4-7 Nonlinear relationship between fre- quency of sightings and density in plots that are one- half the average home range of the species studied. From Caughley, 1977. 1,000 m gave an area one-half the average home range of these monkeys, or 0.05 km2. Groups were sighted with a frequency (/) of 10 sightings per 18 transects, or/ = 0.55. The proportion of transects with no troops was (!â/) = 0.45. A table of exponen- tials was used to find the value of â x for 1 â / of 0.45â0.8 group per plot. By multiplying by the mean group size (10) and converting the density estimate for the 0.05-km2 plot to whole numbers (20 plots/km2), the density was estimated to 0.8 X 10 X 20 = 160 howlers/km2. This density estimate was higher than that determined from direct counts of groups or individuals. Note that the standard deviation, s, approximates the mean in Table 4-5, indicating that the data set follows a Poisson rather than a normal distribution. The density estimates calculated by the plot method for 1973 were also higher than the overall estimate of 95 howlers/km2 dur- ing this year (crude densities) for the entire island. This is ex- pected because the above transect was made in the central part of the island, which supported the highest number of howlers, and
68 TECHNIQUES IN PRIMATE POPULATION ECOLOGY may be considered an estimate of the ecological density (see dis- cussion, Chapter 8). This method was studied further in Venezuela and was found to generate density estimates comparable with those estimated from detailed studies (Eisenberg, 1979). QUADRAT CENSUSES This method involves covering a predefined area (the quadrat) and counting all the groups within that area at one time. It is most applicable to open habitats and areas with natural bound- aries, such as islands and forest patches where the animals are necessarily confined. This method has seldom been used in cen- susing forest primates. Janson and Terborgh (in press) have used a method termed "synchronous sightings," which is essentially a combination of the line transect and quadrat methods. Two or preferably more observers start at a baseline and each follows different equidistant and parallel transects through the quadrat. To ensure maximum coverage in a forest habitat, it would seem that observers should walk in parallel at about 100-to 150-m intervals, or at smaller intervals when censusing inconspic- uous species. When groups are encountered the same data are recorded as in line transects. The data are combined by plotting all sightings on a common map and then trying to distinguish dif- ferent groups. This will allow an estimate of the total number of groups present in the predefined area, which in turn allows an es- timate of density. This method was used in censusing forest popu- lations of rhesus monkeys in northern India (South wick et al., 1961). In addition to requiring several observers, transects, and rea- sonable maps of the study area, this method requires some knowledge of the characteristics of each species. For instance, in order to distinguish between groups and to avoid duplicate count- ing, one should have some idea of the distance over which social groups of the different species can be spread and their rate of travel. A widely spaced group may be considered two groups by two observers if they see opposite edges of the group, even though the distance between them may be more than 100 m. A fast-mov- ing group counted by one observer may be counted again, if
Census Methods for Estimating Densities 69 another observer happens to see it later. The crucial factors are the time elapsed between the sightings and knowledge of how fast the species can travel. A major deficiency of this method is that it fails to resolve the problem of individuals or groups living partly in the sample quad- rat and partly outside it. (This causes no difficulty where quad- TABLE 4-5 Use of the Nonlinear Density Plot Method to Estimate the Density of Alouatta palliata in Panama" Conditions: Transect length = 1 km; transect width = 50 m Plot Number Animal Counts Group Counts Frequency of Plots with Sightings 1 7 2 1 2 3 1 1 3 0 0 0 4 0 0 0 5 3 1 1 6 4 1 1 7 2 1 1 8 0 0 0 9 3 1 1 10 0 0 0 11 0 0 0 12 5 1 1 13 0 0 0 14 4 1 1 15 0 0 0 16 5 1 1 17 3 1 1 18 0 0 0 Total number of animals per 0.90 km2 Mean number of animals per 0.05 km2 s Estimated density of animals per km2 39 2.167 + 2.256 43 11 0.611 Â±0.608 122 10 160 "Data from J. F. Eisenberg (1974, unpublished).
70 TECHNIQUES IN PRIMATE POPULATION ECOLOGY rats consist of distinct forest patches.) It is also probably inade- quate for relatively cryptic species (Janson and Terborgh, in press). Modification of the block or quadrat sampling method may be used for both small and large census areas. Figure 4-8 shows the process of dividing the census area, which may be a province, state, or country, into convenient sample units. Next, representa- Quodrat sampling X X 3 X 5 X 6 X 8 X 10 X \ X FIGURE 4-8 Quadrat sampling. Grids are drawn on maps of very large areas to subdivide the areas into quadrats until the sample quadrats represent about 15% of the study area. Each choice of quadrat is made randomly. In the illustration, four quadrats (e.g., Nos. 3, 5, 6, 8) are chosen randomly in each of the five sampling units, A-E, giving a total of 20 quadrats to be surveyed in detail.
Census Methods for Estimating Densities 71 tive sample units are selected randomly. Five sample quadrats (A-E) are shown in the example. Within each sample unit, sub- units are selected on a random basis (e.g., Nos. 3, 5, 6, 8). One tries to choose a sample space equal to about 15% of the total area surveyed. In this figure, the sampling space consists of 4 of 10 randomly chosen subunits in each of the 5 sample quadrats. All potential monkey habitats contained in those subunits are censused. Calculations for population estimates using the quad- rat method are shown in Table 4-6. SPECIALIZED CENSUS METHODS FIXED-POINT COUNT In this method the observer remains at one point and records all primate groups seen or heard. It seems best suited for large, con- spicuous, diurnal primates that give loud calls at predictable times of the day. Few primate studies have used this method (e.g., Chivers, 1969, 1974; Green, 1978a; Pollock, 1975). Unless the terrain is very steep and the lookout point is well positioned, TABLE 4-6 Estimates of Population Based on a Random Sample of Four Quadrats as Illustrated in Figure 4-8 Quadrat number 1 2 3 456 7 8 9 10 10 Sample quadrats 3 5 6 8 4 Number of groups/sample quadrat 14 9 10 9 42 Number of animals 140 90 99 91 420 Variable Total 42 groups Mean number of groups/subunit or sample quadrat = = 10.5 groups 4 quadrats Estimated number of groups in 10-quadrat sample grid = 10.5 groups X 10 quadrats = 105 groups Estimated population = 105 groups X 10 animals/group = 1,050 animals
72 TECHNIQUES IN PRIMATE POPULATION ECOLOGY this method has limited use for enumerating primates by sight alone. Counting the number of sources of loud calls assumes that each source represents a social group and that all groups call. Until further refinements have been made in this method, it is best used to determine relative abundance only, rather than to ex- trapolate estimates of absolute density. TRAP, MARK, AND RELEASE Mark-recapture techniques have been used extensively in popula- tion studies of small mammals (particularly rodents), birds, and fish (see Overton, 1971, and Caughley, 1977, for review of analytical methods). In such studies, one makes use of the pro- portion of marked-to-unmarked individuals in a series of catches in order to determine population size and density. This method is often inappropriate for estimating primate densities, particularly for arboreal species, because it can be harmful to the animals, time-consuming, and expensive. Although several studies of primates have involved capturing by means of traps and immobilizing darts, marking, and releas- ing (e.g., Brockelman and Kobayashi, 1971; Dawson, 1977; Fog- den, 1974; Neyman, 1977; Scott et al., 1976a), this method has not been used to estimate densities. In studies of nocturnal or otherwise secretive species (e.g., Charles-Dominique, 1977; Thorington et al., 1976), censusing by direct observation may be inadequate. In such cases, marking in combination with radio tracking may be the only way of estimating densities and home range size. Methods for marking such species are included in Chapter 5. Small primates, such as marmosets, may actually be live- trapped and marked with a suitable tag. Other primates, such as howler monkeys (Thorington et al., 1979), have been successfully darted and marked for long-term studies. When marking individ- uals for easy visual recognition, one can conduct censuses that give an estimate of the population density. Suppose you have marked 30 monkeys, and after a week you conduct a transect cen- sus through the same forest. During the transect you count 110 monkeys of the species under study and of these, 25 are marked.
Census Methods for Estimating Densities 73 The "Lincoln Index" is used to determine a rough estimate of the population size: No. marked animals seen Total no. marked animals Total no. animals seen Total population of animals _25_-30 110 ~ X X= 132 The above calculation assumes that the 30 marked animals are from randomly selected groups. If, for example, all 30 animals were from one large primate troop, the application of the index would be invalid. The Lincoln Index was developed for species that are not grouped into large groups of mixed-sexed adults, but instead tend to have single individuals uniformly distributed in space. Thus, the application of the method assumes that you have selected animals randomly from within the area that you wish to census. The method assumes that there is no loss of marked animals from the survey area and no immigration of unmarked animals into the survey area; that the means of marking is permanent; and that there is no differential observability between marked and unmarked animals. These conditions are not often met in practice (Caughley, 1977). NEST COUNTS Few primates build nests and only four species build nests large enough to be readily counted: gorillas, orangutans, and two species of chimpanzees. Several studies have used nest counts to estimate population densities of great apes (Ghiglieri, 1979; Kano, 1972; MacKinnon, 1974a; Schaller, 1961, 1963; Yoshiba, 1964). The field method consists of counting the nests in a predefined area, usually a transect of known length and fixed
74 TECHNIQUES IN PRIMATE POPULATION ECOLOGY width. The total number of nests divided by the area searched gives nest density. However, in order to extrapolate primate den- sity, it is necessary to refine the formula to take into account the age of the nests and the fact that some animals do not make nests (e.g., infants). Observer efficiency is also an important factor and can be estimated by recounting nests along segments . of the transect soon after the original census (Ghiglieri, 1979). In his study of chimpanzees in the Kibale Forest, Uganda, Ghiglieri (1979) derived the following formula: No. nest-building animals/km2 = no. nests/area sampled in km2 X I/mean nest life span X 1/observer efficiency X total no. animals/total no. nest builders (excluding infants). The last factor depends on hav- ing some detailed information on the population age structure based on a detailed study of at least a portion of the study popula- tion. This formula can be further refined by computing a weighted mean nest life span that takes into account differences in nest life span. Life spans differ according to the kinds of trees or other vegetation in which the nests are built. According to Ghiglieri (1979), in order to gain a representative sample of chimpanzee nest density for an area of 4-5 km2 it was necessary to enumerate at least 9 km of transect that was 20 m wide. Furthermore, since the chimpanzees' use of certain parts of the forest was extremely variable and often at very irregular time intervals, Ghiglieri recommended that each transect be sampled at intervals of 4-6 months. The main advantage of the nest- enumeration technique is that it allows a single observer to collect in 3 or 4 days a sample that will give a fairly reliable index of animal density. Prior knowledge of nest life span and other fac- tors mentioned above are necessary for greatest accuracy. LONG-TERM MONITORING OF SPECIFIC GROUPS This method is the most accurate for determining densities; how- ever, it is also the most time-consuming. It requires an extensive network or grid of trails, detailed maps of the study area, and nu- merous observations and counts of specific social groups, prefer- ably for several days of each month for at least 1 year. One usu- ally has time to study only one group intensively, but in order to
Census Methods for Estimating Densities 75 ensure greater accuracy it is advisable to follow one or two others. Each group must be individually recognizable. How long must one observe a group before it can be confidently stated that the home range is known? This, of course, will depend on the species and the habitat. Species with large home ranges will usually take a longer time to cover their whole range than those with smaller ranges. Therefore, in order to determine sam- ple size, one must monitor the data as the study progresses. Monthly samples (to cover seasonality) of 5-10 days with 10-12 h of obser- vation for each day are recommended. One plots on a map at reg- ular time intervals the location of the group (or preferably indi- viduals in the group). By dividing the map of the study area into a grid of 0.25-ha quadrats, one is able to calculate the accumula- tion of new quadrats for each sample and to plot a cumulative range curve against study time (Figure 4-9). As the study pro- gresses, the group will continue to enter new quadrats until the curve begins to level off. When a plateau or asymptote is reached, one can be fairly confident that the entire home range is known. In extremely seasonal habitats, however, one might anticipate a cumulative area curve consisting of several steps (e.g., Altmann and Altmann, 1970, Figure 37). Because a long step might be confused with an asymptote, caution should be taken in such sit- uations. Figure 4-9 clearly shows major interspecific differences within the same study plot. A group of 15 mangabeys at the Kanyawara study site in the Kibale Forest had an enourmous home rangeâ some 400 ha. After more than 1,200 h of observation during 12 mo of study, the group was still entering new areas with no sign of approaching an asymptote. In contrast, the smaller redtail mon- key, living in the same area in groups of 35 members, visited its entire home range of some 28 ha after about 370 h of observation during 10 monthly samples spread over a 12-mo period. Fifty per- cent of its range was visited within the first 63 h of observation. Waser (1976) emphasizes that the shape of the cumulative area curve is influenced by the choice of the quadrat size: the larger the quadrat, the sooner the leveling off of the curve. To estimate densities it is critical to know not only the home range of the study group, but also the extent to which other con-
76 TECHNIQUES IN PRIMATE POPULATION ECOLOGY FIGURE 4-9 Cumulative increase in home range size as function of hours of observation. Each curve is for one social group. These three species are om- nivorous. The home range of the mangabey group of 15 completely overlapped that of the blue (24 in- dividuals) and redtail (35 individuals) groups, and the range of the blue group overlapped the redtail group. Home range increase was plotted in in- crements of 0.25-ha quadrats. Data are from com- partment 30 of the Kibale Forest, Uganda. Data from Rudran, 1978; T. T. Struhsaker, unpublished; Waser, 1976.
Census Methods for Estimating Densities 77 specific groups share this home range. Parts of the home range used by more than one group must be apportioned according to the number of groups using them (Janson and Terborgh, in press). For example, if two groups share an area of 24 ha, each group is allocated half, or 12 ha. The group density per km2 can be obtained by dividing 100 by the average home range of the groups in hectares (1 km2 = 100 ha). This calculation gives a density of 8.3 groups/km2. If three groups use this same 24 ha, then each is apportioned a third, or 8 ha (100 ha/km2/12 ha/group), giving a density of 12.5 groups/km2. In reality, however, the situation is generally more complex. Usually the home range of the main study group is only partly shared, and the home ranges of neighboring groups are incom- pletely known. One can make a crude estimate of overlap by plot- ting the limits of incursion of these groups into the range of the main study group. In the schematic diagram in Figure 4-10, the main study group has a home range of 100 ha. Area A of 39 ha is not shared with any other group and is apportioned entirely to the main group. In areas B, C, and D, there is overlap with one other group per area. This area of overlap, totaling 52 ha, is therefore divided in half, giving a total of 26 ha to the main group. In area E, consisting of 9 ha, there is overlap between the main group and two other groups. Thus, the area is divided by 3 to give 3 ha to the main group. Summing these figures gives a total of 68 ha (39 + 26 + 3) to the main group, or a density of 1.47 groups/ km2. Partitioning areas of overlap between groups provides a more accurate estimate of density than the estimate of 1 group/ km2 obtained if overlap between neighboring groups is not taken into account. Although this method involves an investment in time that is considerably greater than that required by any of the others de- scribed, the results are far more accurate and the kinds of addi- tional data on the status of the population that can be collected are much greater. The most accurate counts of group size and composition are usually made during these studies. These counts are, of course, imperative for extrapolation from estimates of group density to estimates of numerical density, while composi- tion of age and sex classes gives an indication of the status of the population in terms of fecundity and survivorship.
78 TECHNIQUES IN PRIMATE POPULATION ECOLOGY < = Â£ ' A 39 B 24 C 16 D 12 E 9 GROUP DENSlTY COMPUTATlON FROM HOME f s I RANGE OVERLAP I o 100 ha. home range boundary of main study group ]f 39 12 6 68 ha. total A â¢ area used exclusively by main group B, C,D,E = areas of overlap with neighboring groups B A D FIGURE 4-10 Group density computation from home range overlap. SUMMARY OF IMPORTANT CENSUS METHODS FOR DIURNAL PRIMATES When time to cover large areas is limited and replication of cen- suses along the same route is not plausible, emphasis should be placed on obtaining indices of relative abundance of social groups. These indices are usually expressed as numbers of groups seen per kilometer of transect and per hour of searching. Some indication of visibility, such as distance between the first animal seen and the transect or observer (or both), permits more realistic comparison of data between sites and habitats. If time allows, many replications should be made along the same line transects throughout the year. Determination of sample
Census Methods for Estimating Densities 79 size is outlined above. Comparative data from the Kibale Forest, Uganda, demonstrate that the method of maximum reliable sighting distance gives results most consistent with detailed, long- term studies of specific groups, especially for species of high den- sity that are frequently seen. In order to verify this conclusion, however, there is clearly a great need for more case studies com- paring these various methods with detailed group studies of a var- iety of species in different habitats. The most accurate method of estimating primate densities is the detailed study of specific groups. It is also the method that gives the best data on group size and age/sex composition. EXTRAPOLATION OF DENSITY ESTIMATES FROM CENSUS AREA TO OTHER AREAS After determining estimates of density from the more accurate methods of repeated line transects and detailed studies, one would like to be able to extrapolate densities in similar habitats. This would permit population estimates to be made for areas much larger than the one studied. Unfortunately, such extrapola- tion has many shortcomings. Within the same gross habitat type or even within the same forest, one can find large differences in primate densities. An ex- ample is provided by two study sites in the Kibale Forest, Uganda. These sites, which we will call A and B, differ significantly in pri- mate densities although they are only about 10 km apart in the same continuous forest. At site A, blue monkeys are nearly 7 times more abundant than at site B; and at site B, mangabeys are about 1.5 times more abundant than at site A (T. T. Struhsaker, personal communication). Baboons were encountered on 10 occa- sions during 24 censuses at one site, but were not seen in any of the 44 censuses at the other site. Although the two sites differ in some of the predominant tree species, both are classified as medium-altitude tropical evergreen forests. This is usually the gross level of habitat classification that one must deal with when extrapolating densities from a small study area to a district or an entire country. Even within the same small study area, one can find striking differences in primate densities. For example, at the Kanyawara
80 TECHNIQUES IN PRIMATE POPULATION ECOLOGY study site in the Kibale Forest, within a linear distance of 2 km and in an area of 3 km2, the density of black and white colobus ranges from 1.3 to 11.6 groups/km2 (Gates, 1977, 1978; Struh- saker and Leland, 1979). Although the reason for this difference is not understood, subtle habitat differences linked to nutritional requirements may be involved (Gates, 1978). When the forest is fragmented into relatively small blocks, such as in East Africa, northern Colombia, and India, differences in primate communities and densities of particular species be- tween these forest patches can be very great. Even in large blocks of continuous forest, such as in La Macarena National Park in Colombia, one finds large differences in primate densities from one part of the forest to another (Klein and Klein, 1976; Struh- saker, 1974). What this means in terms of estimating populations over large areas is that many study sites must be established to cover a wide variety of habitat types and separate habitat blocks. At present, there is no short and simple solution. Because those attempting to manage primates for conservation or utilization are eager to have the figures that best suit their purposes, it is important that any density estimate be as accurate as possible. Census methods, especially data analysis, still need much more study to improve their accuracy and general applicability. Extrapolation can be a dangerous guess.