Monitoring mammal populations with line transect techniques in African forests

Authors


A.J. Plumptre (fax 718 3644275; e-mail aplumptre@wcs.org).

Summary

1.  Line transect survey techniques have been used to estimate population density for a variety of mammal species in tropical forests. In many cases indirect methods, surveying signs of animals such as counts of dung or nests, have been used because of the poor visibility in these forests. The estimates of the production and decomposition rates of these signs each have their associated errors; however, for the majority of published studies these errors have not been incorporated into the estimate of the standard errors or confidence limits of the density estimate. An equation is given showing how this should be done.

2.  An equation is also given relating the resolution (R) of a density estimate to the coefficient of variation (CV) of the estimate. This shows that to detect a 10% change in a population the CV must be 3·6% (with a power of 50%) or 2·4% (with 80% power). Using this equation and data from studies in Africa, it is shown that differences of less than 10–30% change in the population are unlikely to be detected between two surveys where visual sightings of animals are made. When indirect methods of estimating the population are used, it is unlikely that less than a 30–50% change in the population could be detected.

3.  Some studies have surveyed primate groups using estimates of an average group spread. Data from primate groups in Budongo Forest, Uganda, show that group spread is highly variable and varies at different times of day and between months. This survey technique is not recommended.

4.  If line transects are used for monitoring populations, conversion factors should be minimized as each contributes to an increase in the CV and a reduction in the ability to detect small changes in population density.

5.  Monitoring trends in abundance over several survey periods can improve the detection of change, although this is costly and requires several surveys before any conclusions can be reached. Re-using transects in subsequent surveys can also reduce the variation around the estimate and will improve the resolution. Focusing survey efforts in areas of high density is an alternative strategy, but one that could lead to other errors as high-density areas may be the safest and hence the last to show change. Using biased survey methods is also a promising technique that can increase the precision of surveys. It is concluded that a combination of different survey methods will ensure that changes in abundance are identified.

Introduction

Ecological monitoring should be a vital component of any conservation project so that the effects of management can be assessed (Kremen, Merenlender & Murphy 1994). Management plans always emphasize that monitoring should take place and, more recently, some have attempted to define limits of acceptable change beyond which management action should be taken (Alexander 1996). However, if we are to define these limits, we must be certain that our survey techniques can detect them.

The use of distance sampling techniques to estimate animal population densities has become increasingly popular since the production of the computer package transect (Laake, Burnham & Anderson 1979) and subsequently distance (Buckland et al. 1993; Laake et al. 1994). In African forests this technique has mainly been used to estimate the density of primate groups (Whitesides et al. 1988; White 1992, 1994; Plumptre & Reynolds 1994), as many species are highly visible. Surveyors of most other mammals in these forests have resorted to indirect estimation techniques rather than direct observation because visibility is often poor and some species cannot be approached in safety. In these surveys animal densities were calculated from line transects, counting signs that animals leave behind, usually nests (apes: Ghiglieri 1984; Tutin & Fernandez 1984; Wrogeman 1992; White 1994; Hashimoto 1995; Ihobe 1995; Marchesi et al. 1995; Plumptre & Reynolds 1996, 1997; Hall et al., 1998a) or dung (elephants Loxodonta africana: Wing & Buss 1970; Short 1983; Merz 1986; Barnes & Jensen 1987; Dawson 1990; Ruggiero 1990; Fay & Agnagna 1991; Barnes 1993; Plumptre & Harris 1995; ungulates: Plumptre 1991; White 1992, 1994; Plumptre & Harris 1995). Indirect counts require conversion factors to be calculated to convert the count of dung or nests to animal density. These factors include the rates of production and the decay rates of dung/nests. Some studies have avoided the need to correct for the rate of decomposition of dung or nests by counting the number that appear over a certain time period. The same transects are visited repeatedly during this period at intervals shorter than the quickest time to decay. These are referred to here as marked nest counts or clearance plot dung counts (Plumptre & Reynolds 1996; Staines & Ratcliffe 1987).

Where the animals/signs of interest occur in groups, then conversions have to be made to calculate animal/sign density from group density. This has been particularly common in primate surveys (Whitesides et al. 1988; Plumptre & Reynolds 1994), where individual density has been calculated using mean group size. Whitesides et al. (1988), in addition, recommended that a measure of mean group spread be calculated for primate studies, using a perpendicular distance measure to the nearest animal to the transect to calculate the perpendicular distance from the transect to the centre of the group. They argued that this was necessary because monkeys further from the transect tended to be missed.

Each of these conversion factors has an associated error. Few studies report their standard errors or 95% confidence limits, and where they do these errors are of the count only and rarely include errors from conversion factors. If line transects are to be used for monitoring populations of mammals then the true errors of the estimate should be calculated. This paper investigates how variation in conversion factors and measures of effort affect the error of the density estimate. Table 1 summarizes the errors associated with different methods of analysis.

Table 1.  The additional errors associated with direct and indirect counts of mammals from transects. These associated errors should be calculated in addition to the error of the basic count. += error associated with survey estimate; – = no error; +/– = can be an error depending on method used
MethodProduction rateDecomposition rateGroup sizeGroup spread
Direct counts
Sightings of single animals
Sightings of groups + +   /   –
Indirect counts
Dung counts + + +
Nest counts + + +
Clearance plot dung counts + +
Marked nest counts + +

Methods

Line transect techniques

Line transects are commonly established using a stratified random sampling procedure (Plumptre & Reynolds 1994). In African forests transects have usually been walked at approximately 1 km h−1, counting all groups of animals seen from the transect. The perpendicular distance from the transect line to the centre of the group seen is measured and the number of animals seen in the group recorded (Plumptre & Reynolds 1994; White 1994). The perpendicular distances are used to calculate a probability density function that models the decrease in sightings of animals with distance from the centre line of the transect. This function is used to calculate a density of groups with standard error and 95% confidence limits (Buckland et al. 1993). Individual density can be calculated from group density by multiplying by mean group size (see below). Estimating density using line transects has been thoroughly covered by Buckland et al. (1993) and the reader is referred to this book for details.

A Z-test is used to test whether two population (Buckland et al. 1993, p. 381):

image

where Dn= density estimate of population n or the same population at time n; and se(Dn) = standard error of this estimate

The assumptions for this test are that se(D2) = se(D1) and that the sample units from the first survey are drawn independently from the sample units in the second survey. An additional assumption is that sample sizes are sufficiently large that the distribution is close to normal. Sample size in transect analyses is a function of the number of objects seen and the number of transects censused. Buckland et al. (1993) recommend that at least 10 transects are censused to meet this assumption, although studies of elephant dung in Gabon indicate that 20–25 transects are required to approach normality (P. Walsh, personal communication). With fewer than this number of transects, it is better to use a t-distribution (see Appendix 1 for a possible test).

Line transect surveying makes several assumptions (for details see Buckland et al. 1993): (i) objects on the centre line are detected with certainty; (ii) objects are detected at their initial location; (iii) measurements are exact. Some papers state that an object should not be counted on more than one transect line, but this is not in fact an assumption of this technique provided movement is random with respect to the lines (Buckland et al. 1993, p. 37).

Calculating resolution of density estimation from two independent surveys

The resolution of a density estimate is defined here as the percentage change that will be detectable between two independent surveys. Surveys in African forests are costly and there are few places where more than two surveys have been carried out to date (see Discussion). The resolution will depend on the standard errors of the two density estimates. If initially we make an assumption that the standard error of a density estimate is equal to the standard error of a second density estimate, which is changed by a factor R, i.e. D2 = D1 + D1*R, where D1= density estimate and R= proportional change or resolution (100R = % change), then we can derive a simple equation from the Z-test equation above to calculate the resolution (R). Substituting D2 = D1 + D1*R in the equation above:

image

Therefore:

image

(for P = 0·05, 2-tailed test; but see below).

Therefore:

image(eqn 1)

where CV = coefficient of variation calculated by distance.

For example, if we want to detect a 10% change in the population then R = 0·1 and CV = 3·61%. However, the power of the Z-test to detect a difference at P = 0·05 is low (see Appendix 2), only around 50%. If we want the power of the test to be around 80% (as most textbooks suggest) then we need to calculate the Z-test for 2·8 standard errors. In this case CV = 2·4% (Appendix 2).

If the standard error of the second density estimate differs from the first (a violation of one of the assumptions of the test, see above) then the number in equation 1 changes and the resolution that is detectable changes, although not greatly (Fig. 1).

Figure 1.

The percentage change detectable (resolution) with a Z-test as the coefficient of variation changes and the standard errors of the density estimates change. The lines plotted are where the standard errors of two density estimates are equal (SE1 = SE2; assumed in equation 1) and also where one is half (SE1 = 2SE2) or double (2SE1 = SE2) the size of the other. Lines are plotted where the power of the test is around 50%.

This test provides a measure of the percentage change in a population. However, a 100% increase (population doubling) is different to a 100% decrease (population extinction). One way to deal with this is to use differences between densities on a logarithmic scale and the fact that the CV of the density is approximately equal to the standard deviation of the loge transformed density (P. Rothery, personal communication). This method has the advantage that working with log densities helps to approximate a normal distribution. However, for the purposes of this paper, percentage increases/decreases will be used as examples because it is easier to visualize references to 20% changes in the text rather than differences on a logarithmic scale.

With indirect counts there are errors and CVs associated with each conversion factor used. A standard dung survey, for example, corrects the dung density for the decomposition rate and the deposition rate of dung:

T  = DP/Q

where T= density of animals; D= density of dung on transects; P= mean rate of decay (1/mean days); and Q= mean number of dung piles produced per day.

Barnes (1993) gives an equation (derived using the delta method) that provides an approximate estimate of the CV for the product of several variables:

CV2(T)=CV2(D)=CV2(P)+CV2(Q)(eqn 2)

where CV(X) = coefficient of variation of variable X (standard error/mean *100%) [CV(Q) is approximately = CV(1/Q)].

This equation assumes that the values of the component variables are not correlated (for example it is possible that dung decay is faster if dung density is high because dung beetles are more abundant, in which case this assumption would be invalid).

The variance of the corrected estimate is:

Var()=(D*P/Q)2*[(CV(D))2=(CV(P))2=(CV(Q))2]

Resolution of direct observations from transect data in africa

Primate sightings

Data from primate surveys in the Budongo Forest in western Uganda (Plumptre & Reynolds 1994, 1996) were used to investigate the effects of total distance walked and number of groups sighted. Data were used from surveys of blue monkeys Cercopithecus mitis Matschie and black and white colobus monkeys Colobus guereza Ruppell in several compartments in the forest. In each compartment five transects were established using a stratified random sampling procedure (Plumptre & Reynolds 1994), and were walked twice each month during 1993. The total length of transects was at least 10 km in each compartment. The data were analysed each time the transects were walked three times, until they had been walked 21 times. This allowed the change in the CV to be monitored with survey effort and number of groups seen.

Nest counts

Data from gorilla Gorilla gorilla graueri Matschie surveys (Hall et al. 1998b) and chimpanzee Pan troglodytes schweinfurthi Blumenbach surveys (Plumptre & Reynolds 1996; Hall et al. 1998b) were used to investigate the effect of sample size on CV of nest counts.

Effects of correction factors using data from africa

Dung defaecation rates

Standard errors and CVs of data for defaecation rates that could be found in the literature (for large African mammals) were calculated.

Nest construction rates

Estimates of nest construction rate and its CV were calculated from dawn to dusk follows of habituated individuals in a community of chimpanzees in the Budongo Forest in western Uganda. Only data from complete dawn to dusk follows were used (Plumptre & Reynolds 1997).

Nest decay rates

Mean time to nest decay has traditionally been calculated from nest decay rates in the literature, although nest decay can also be calculated in a similar way to decay of dung by fitting an equation to the decay curve and obtaining bootstrap estimates of the error (Barnes & Barnes 1992; Barnes et al. 1994; Plumptre & Reynolds 1996). Fitting a decay rate equation such as an exponential decay (Barnes & Barnes 1992) has advantages in that the slowest decomposing nests/dung do not need to be monitored until they have disappeared before an estimate for the rate can be obtained. However, this method measures the median rate of decay rather than the mean rate and it is recommended that mean rate is used (Barnes & Barnes 1992; White 1995). CVs of published mean time to nest decay studies were calculated where the data were available to do so.

Dung decay rates

Barnes et al. (1994) provided data on bootstrapped estimates of the median decay rate of elephant Loxodonta africana Blumenbach dung and its associated errors for dung monitored in Ghana and Cameroon. The effects of sample size on bootstrapped CV were analysed using these data.

The combined effects of these errors for these conversion factors were investigated using equation 2.

Effects of measures of group size and spread on primate surveys

Individual animal density is calculated by multiplying the group density by the mean group size. It is sometimes found that large groups are seen at further distances from the transects than small groups, in which case it is necessary to correct for this bias. Buckland et al. (1993, pp. 130–134) give four methods to do this: (i) calculate mean group size from observations within a strip width where there is no bias observed; (ii) use the perpendicular distance for the group to replace the group by n individuals with the same perpendicular distance (where n= number of animals seen); (iii) stratify the density estimation procedures by group size (requires a large sample size to do this); (iv) regress group size with distance or estimated detection probability. distance can carry out the last method and by default regresses log(group size) on the estimated detection probability. The effects of correcting for group size on CV was investigated with the primate data, correlating CV of group density with CV of individual monkey density calculated by distance.

Many primatologists have surveyed groups of primates by measuring the perpendicular distance to the nearest animal in a group and then computing an average group spread to calculate the true perpendicular distance to the group centre (Whitesides et al. 1988; White 1994). This method assumes that group spread on average is circular, constant throughout the day and has no error associated with its measurement. As Struhsaker (1997) pointed out, primates often move in a linear fashion and are very unlikely to be distributed in a circle. To test the assumption that group spread is fairly constant, measurements were made during dawn to dusk follows of 17 groups of monkeys (six blue monkey, six black and white colobus monkey and five redtail monkey Cercopithecus ascanius Matschie) made between October 1994 and January 1996 in the Budongo Forest. Groups were located at around 16.00 h on day 1 and followed until dusk, then from dawn until dusk on day 2 and on the third day from dawn until the time at which they were found on day 1. Each group was followed using this protocol once each month. Group spread was measured using a rangefinder (often several measurements were required to measure across the whole group as visibility was not much greater than 30 m; these would be made to tree stems and summed across the group). Group spread was measured in this manner every 30 min throughout the day.

Results

Direct observations from transects

Distance walked

Not surprisingly, increasing the distance walked reduced the CV of group density in primates in Budongo Forest (Table 2) because it increased the numbers of groups encountered. What is of interest here is that the CV remained fairly high (10–20%) even when the distance walked was large (200+ km), and the forest supports a relatively high density of primates (Plumptre & Reynolds 1994). Consequently, in order to detect this degree of change in primate populations in Africa, it is necessary to walk at least 200 km and probably further because most other sites will have a lower sighting frequency.

Table 2.  The number of groups seen, distance walked and coefficient of variation (CV) for two monkey species in different compartments in Budongo Forest
SpeciesCompartmentNumber of groupsDistance walked (km)Density (groups km−2)CV (%)
Blue monkeyB116321021·09·7
Cercopithecus mitisK11–13162102·937·9
W21762109·417·9
K4742129·413·5
N313322713·810·8
Black and white colobusB1582106·516·7
Colobus guerezaK11–13472106·616·7
K4682128·815·0
N3952279·913·7

Number of groups seen

The number of groups seen strongly reduced the CV for primate groups in Budongo Forest (Fig. 2). This was expected as standard error (and hence CV) is always reduced by increased sample size. By fitting a curve of the equation CV = a/√(N) (where N= number of groups seen; a = a constant) to these points (R2adjequals;0·93, F = 685·8, P < 0·001) it can be calculated that to detect a 10% change (CV = 3·61%) in the group density you would need to see about 1671 primate groups, and to detect a 20% change (CV = 7·22%) about 418 groups. However, as stated previously, the power to detect this change is only about 50%. For a power of 80% the respective values are 3781 (CV = 2·4%) and 1029 groups (CV = 4·6%).

Figure 2.

Changes in coefficient of variation with numbers of primate groups seen for surveys of blue and colobus monkeys in different forest compartments.

Number of nests seen

Variation around group density estimates (chimpanzees and gorillas combined) for the number of nest sites seen from transects was high. Fitting a similar curve (CV = a/√(N)) of nest sites seen on CV gives a reasonable regression (R2adj=0·67, F = 36·2, P < 0·001). Using the equation derived, 349 nests would need to be found to detect a 20% difference and 1395 nests to detect a 10% change (again with only a power of 50% to detect this change). For a power of 80% the values are 3157 (10% change) and 859 nests (20% change).

Indirect surveying

Production rates

The defaecation rates of various mammals have been calculated and published in the literature. However, few studies have published the errors around these rates. The CV for those that have are not too high (Table 3) and very much depend on the number of days over which production was measured. For elephants, production has been calculated by following the trails of a group over several days for each estimate (Wing & Buss 1970; Tchamba 1991), providing a large sample size. For other estimates individual animals have been monitored over much less time and hence the CV is larger.

Table 3.  The coefficient of variation in the deposition rate of dung for various species, and construction rate of chimpanzee nests from published studies. N= number of sample intervals over which dung/nest production was measured to obtain a mean
SpeciesNDeposition rate (no. day−1)CV (%)Reference
Dung
Elephant Loxodonta africana Blumenbach617·03·4Wing & Buss (1970)
Elephant Loxodonta africana1619·81·2Tchamba (1991)
Elephant Loxodonta africana216·22·8Plumptre (1991); A.J. Plumptre, unpublished data
Buffalo Syncerus caffer Sparrmann155·15·2Plumptre (1991); A.J. Plumptre, unpublished data
Okapi Okapia johnstoni P.Sclater55·214·1J. Hart, unpublished data
Blue duiker Cephalophus monticola Thunberg44·926·5Koster & Hart (1988)
Bay duiker Cephalophus dorsalis Gray44·429·5Koster & Hart (1988)
Bushbuck Tragelaphus scriptus Pallas519·049·6Plumptre (1991); A.J. Plumptre, unpublished data
Blackbuck Antilope cervicapra L.1210·47·7Rollins, Bryant & Montandon (1984)
Fallow deer Dama dama L.1211·311·5Rollins, Bryant & Montandon (1984)
Sika deer Cervus nippon Temminick206·94·3Rollins, Bryant & Montandon (1984)
Axis deer Axis axis Erxleben1212·611·9Rollins, Bryant & Montandon (1984)
White-tailed deer1219·611·7Rollins, Bryant & Montandon (1984)
Odocoileus virginianus Zimmermann
Moose Alces alces L.2210·92·3Miquelle (1983)
Nests
Chimpanzee P. troglodytes Blumenbach141·154·1A.J. Plumptre, unpublished data

There is no published literature on the production rates of nests by gorillas and only one for chimpanzees (Plumptre & Reynolds 1997). The mean production rate from the dawn–dusk follows of chimpanzees in Budongo was 1·15 nests per day with a CV of 4·1%. This was based on 201 dawn–dusk follows.

Decay rates

For nest decay, the mean number of days to complete decay has been calculated to correct the nest density estimate to an animal density. Two published studies have provided measures of variance/error around these mean estimates. In the Tai Forest, mean decay was 73·3 days, SE = 9·7, CV = 13·3% (Marchesi et al. 1995), and in Budongo Forest, mean decay was 45·9 days, SE = 3·6, CV = 7·8% (Plumptre & Reynolds 1996).

Barnes et al. (1994) used bootstrapping of median time to decay (1000 replications) as a procedure to calculate the standard error of the mean number of days for elephant dung to decay. Dung was monitored in different sites or at different times of year in Ghana and Cameroon to provide 12 estimates of decay rate with standard errors. The CV was about 5% with 70 monitored dung piles and 10% with 40 monitored piles.

Combining CVs for two independent surveys

A CV of 10% allows measurement of a 27·7% change in the population in a second survey (with 50% power). Counts of primates (Fig. 3) and nests rarely had lower CVs, even with large sample sizes. If CVs of dung/nest deposition and decay are around 5% as well, then the total CV of the group density estimate is:

Figure 3.

Mean group spread for three primate species at different times of day in Budongo Forest, Uganda.

CV(total)2=(CV density)2+(CV deposition>2+(CV decay)2=√(150)=12·2%

This CV will allow detection of a 34% change in the population (with 50% power) or a 67% change (with 80% power). This is using fairly optimistic estimates of CV for dung decay and deposition; several estimates given above are larger than 5%. If decay and deposition are both 10%, then only a 48% change in the population can be detected (50% power). For 80% power, not even 100% change can be detected.

Group size and spread

The primate groups followed in Budongo often split up into two or more subgroups that could be separated by 200+ m. During a survey these would be counted as separate groups, and hence the density estimate would be overestimated if these were multiplied by a mean group size calculated from following different groups and counting all individuals present. Consequently, it is recommended that the number of animals seen from the transect should be used as the group size in distance.

Density estimates of group density and total monkey density were calculated from the Budongo survey data using the corrected mean group size (observed from the transects) and the default method in distance. Regressing the CV of primate group density on the CV of total monkey density gave the following equation:

image

Therefore calculating total density from group density increases the CV by 3·3% for the Budongo data.

The CV of group spread was very low after a very large sample size for all species (blue monkeys: n = 3163, mean = 65·6 m, CV = 1·0%; redtail monkey: n = 2426, mean = 64·6 m, CV = 1·1%; colobus monkey: n = 2698, mean = 31·5 m, CV = 1·7%). This small variation should be included in the total survey variation if average group spreads are used to calculate perpendicular distance.

A repeated measures general linear model analysis was carried out to investigate the time of day and month of the year on group spread. For each species the natural logarithm of group spread was taken to normalize the data. Primate group spread varied significantly throughout the day (blue monkey: F = 8480·2, d.f. = 1,5, P < 0·001, range 6–321 m; redtail monkey: F = 4260·9, d.f. = 1,4, P < 0·001, range 7–267 m; colobus monkey: F = 8281·6, d.f. = 1,5, P < 0·001, range 1–212 m), increasing between 06.00 and 08.00 h (Fig. 3), the time when most surveys are taking place. Group spread also varied significantly between months (blue monkey: F = 7622·1, d.f. = 1,5, P < 0·001; redtail monkey: F = 5140·6, d.f. = 1,4, P < 0·001; colobus monkey: F = 5678·9, d.f. = 1,5, P < 0·001).

Due to this variation in group spread it is concluded that correcting perpendicular distance data to the nearest individual in a group with a measure of the radius of mean group spread (Whitesides et al. 1988) is not a good method and should be avoided. It is better to measure the perpendicular distance to the centre of the group of animals seen and count these, or to measure distance to every individual in the group and analyse the data for individuals (S. Buckland, personal communication).

Discussion

Monitoring

In African forests line transect surveys have mainly been used to obtain density estimates of large mammals, and few studies have established monitoring programmes. It is often implied that subsequent surveys will show whether the population is changing, but little thought is given to planning future surveys. If future surveys are to detect change then the results in this paper show that both surveys must be intensive. Where monitoring has occurred in Africa it has provided useful data for conservation. For example, detection of population changes of elephants following aerial monitoring of several populations in savannas led to the placing of this species on Appendix 1 of CITES (Douglas-Hamilton 1987; Douglas-Hamilton, Michelmore & Inamdar 1992). With the recent concessions made to allow limited trade of ivory, it is vital that elephant populations continue to be monitored. In forests this can currently only be achieved using line transect dung counts (Barnes et al. 1994).

Improving the resolution by repeated surveying or repeated use of transects

If line transect methods are to be used for monitoring animal populations in Africa, the results from this study show that at best a 10–30% change in the population will be detectable between two surveys, and if high power is required for the test then the percentage change detectable will be higher still. Estimations of density using indirect methods (dung or nest counts) will at best be able to detect a 30–50% change in the population. These results are, however, obtained on the assumption that two independent surveys are made and that the two density estimates obtained are tested for differences. The resolution can be improved in two ways if this assumption is not made:

  • 1.  carrying out regular surveys and fitting a trendline to the data obtained (Buckland & Anganuzzi 1988; Buckland et al. 1993, pp. 392–396).
  • 2.  using the same transects for the second survey. In this case the variance of the difference in the density estimate of the two surveys is reduced by the covariance of the two estimates:V(D2-D1)=V(D2)+V(D1)-2 cov (D2, D1)

In this case it would be better to estimate density for each transect separately (using the detection function obtained by pooling data across all transects), and then use Wilcoxon's signed ranks test (or a paired t-test if the data are normal) on the paired data to assess whether there has been a significant change in the population (P. Rothery, personal communication). This will be a more robust test than the Z-test.

Both these improvements assume that funding for surveys is regular, something that is rare in Africa. Transect lines can become overgrown and difficult to find after only 6 months, so that if regular surveyors are to revisit lines then it will be necessary to employ labourers to keep the lines open. Even for a single survey the costs can be prohibitive if large areas are being surveyed. The Wildlife Conservation Society's Grauer's gorilla Gorilla gorilla graueri Matschie survey in Kahuzi Biega National Park in the Democratic Republic of Congo cost around $80 000, and a recent survey of the mountain gorillas in Bwindi Impenetrable National Park in Uganda, covering only 325 km2, cost around $35 000.

Improving the resolution to detect changes in two independent surveys

Accuracy, bias and precision

The accuracy of a population estimate is a function of the bias of the estimate and the precision of the estimate. In most surveys line transects are established using stratified random sampling methods to eliminate any potential bias. However, the effort required to do this may be at the expense of a larger sample size because it takes more time to establish transects than to use paths that already exist in the forest. It is possible to census from paths in the forest, but this will give a biased estimate of the population density. However, this biased estimate is likely to be more precise for the same effort (human-days) as a transect census because more ground will be covered and a larger sample size is more likely to be obtained. In order to improve the ability to detect changes in a population, the precision of the two estimates must be high. If the bias can be corrected, obtaining biased estimates may in fact allow greater resolution.

Walsh & White (1999) have developed a method that they call ‘reconnaissance (recce) walks’ that follow a path of least resistance through the forest. They have found that elephant dung encounter rate (Walsh & White 1999) and gorilla nest encounter rate (Hall et al. 1998b) on recce walks are highly correlated with encounter rates on nearby line transects. Thus, a statistically rigorous estimate of density can be made from recce data if some effort is made to calibrate the functional relationship between recce and transect encounter rates and thereby correct for the bias. Therefore a combination of recce and transect sampling should provide a more precise estimate of density than transect sampling alone, because transect sampling requires roughly three times the effort necessary for recce sampling (Walsh & White 1999).

Decay rates

The resolution of indirect counts can also be improved by reducing the number of conversion factors involved. Transects that are visited regularly can measure the accumulation of nests and dung and thereby avoid the need to correct for decay (marked nest counts in Plumptre & Reynolds 1996, 1997; clearance counts of dung in Staines & Ratcliffe 1987). Given the inter-seasonal variation in decay rates of nests (Plumptre & Reynolds 1996) and dung (Plumptre 1991; Plumptre & Harris 1995; A. Nchanji, unpublished elephant dung data), dung and nest count resolution is poor where decay rates are calculated. It is not valid to calculate separate dung decay rates for wet and dry seasons because long-lived dung (such as elephant and buffalo) survives from one season into the next and decays at a different rate to dung deposited in that subsequent season (A. Nchanji, unpublished data). Many studies utilize nest or dung decay data from other sites but, given the variation that occurs, these data are likely to be inappropriate. However, repeatedly visiting transects is more labour intensive and costly than one-off counts, and counting only fresh dung/nests will result in lower sample sizes. Consequently there is a trade-off between the loss of precision due to lower sample sizes and the decrease in resolution as a result of correcting for decay rates. This should be investigated further.

Defaecation rates

If surveys use indirect signs to estimate population size, better estimates of defaecation rates and nest production rates are needed with smaller CVs. Many of the values for CV in Table 3 are high because the observation time was short. Elephant defaecation rates had the lowest CV because it is possible to follow a group for several days and hence obtain a large sample size. Population estimates from indirect counts should incorporate the errors of the deposition and decay rates in the error of the estimate and the errors should be published in papers.

Sample sizes

Sample sizes in surveys should reach at least 100 groups if the objective of the study is to monitor the population changes in future. A pilot study should be carried out to determine the sighting rate prior to commencing the main survey. For rare species, obtaining 100 sightings is likely to require many hundreds of kilometres of transects, and consequently line transects may not be appropriate and recce walks may be a better method. One option is to concentrate transects in areas where densities are known to be high or that are visited regularly by the animals, and to monitor these areas. In the forests of central Africa many animals visit waterholes/salt licks or ‘bais’ (Turkalo & Fay 1995), and monitoring could be better concentrated at sites such as these. This method would assume that habitat use does not change over time, however, and care must be taken to ensure that monitoring also occurs elsewhere at the same time to confirm this. It is possible that populations will concentrate at these sites when they are declining elsewhere if these sites are considered ‘safe’ or ‘good habitat’, and general population declines will not be detected until it is too late to do anything.

Monitoring of animal populations in African forests must rely on information from various sources in order to adapt management practices in time to assist declining populations. Relying solely on transect counts is inadvisable because of the low resolution of changes that can be detected. For example, if elephant populations are to be monitored in forests it would be advisable to focus dung counts in regions where the population is known to be high, whilst at the same time having some transects or camera traps in low density regions (where the data of interest will be presence or absence, rather than density or encounter rates). In addition, records of carcasses should be collected and surveys of meat in markets conducted so that additional data are available from other sources. Using a multi-method approach such as this is likely to give a clearer picture of changes in mammal abundance.

Recommendations for monitoring in tropical forests

  • 1.  Carry out a pilot study prior to a survey to determine the encounter rate along transects: are transects going to be a suitable method to use? At the same time test the possible use of recce walks or other biased survey methods that may give more precise but biased estimates (if the bias can be corrected).
  • 2.  Obtain data on decay rates of signs and, if the variation is high, consider the use of repeated surveys along transects.
  • 3.  Obtain at least 100 sightings of groups or separate sightings of individuals.
  • 4.  If possible and if the budget allows it, survey regularly and fit trendlines to the data. Re-use the same transects wherever possible.
  • 5.  Record the number of animals seen whenever a group is sighted and do not use measures of group spread to correct the perpendicular distance.
  • 6.  Obtain good measures of the production rate of signs so that the associated CV is small.
  • 7.  Think about a variety of methods that can be used to monitor the population in question and do not rely on one method.

Acknowledgements

I would like to thank many of the people who have contributed through informal discussion to the ideas in this paper. In particular John Hart (who also provided data for Table 2), Peter Walsh and Lee White have made me think hardest about survey methods and monitoring. Len Thomas, Peter Rothery and Peter Walsh have all provided helpful advice on the statistics given here, and provided solutions given in the Appendices. I am also grateful to the two anonymous referees whose advice greatly improved this paper. Data collected in the Virungas, Rwanda, on dung production was funded by Bristol University, Fauna and Flora International and the Dian Fossey Gorilla Fund. Data collected in Budongo Forest, Uganda, was funded by ODA, National Geographical Society, Jane Goodall Institute and the Wildlife Conservation Society. I am grateful to the Ugandan and Rwandan field assistants who helped collect these data, particularly Mutungire Nabert, Muhumuza Geresomu, Kyamanywa Julius, Uwimana Fidele, Tolith Alfred, Hatari Stephen, Biroch Godfrey, Tuka Zephyr, Tinka John, Kugonza Dissan, Kakura James and Akanya Martin and other staff of the Budongo Forest Project and the Karisoke Research Centre. I am also grateful to the Institute of Biological Anthropology at Oxford University and in particular Professor Vernon Reynolds for support whilst working in Uganda.

Received 10 June 1998; revision received 28 December 1999

Appendices

Appendix 1

t-test to test differences in density estimates (L. Thomas, personal communication).

This test may be more appropriate than the Z-test for small sample sizes. The only approximations available are designed for the case where the t distribution is being used to compare two sample means. Their performance when comparing two estimates is unknown. However, an approximation is as follows:

t=(density_1-density_2)/sigma

where sigma (the standard error, or standard deviation of the difference in estimates) is estimated by:

√[(SE  survey  1)2+(SE  survey  2)2]

The degrees of freedom for this t-test are:

image

d.f._1 and d.f._2 come from the formulae in Buckland et al. (1993, pp. 89–90).

Appendix 2

Statistical power of Z-test (P. Rothery, personal communication; L. Thomas, personal communication).

To approximate the power of the Z-test the actual difference and the standard error of the estimated difference are required. This can be seen as follows.

A difference is detected at the 5% level when the standardized difference D/s[D] is larger than 1·96 or less than −1·96, where D is the estimated difference. The power of the test is then given by:

Power=1-Prob(-1⋅96<D/SE[D]<1⋅96)=1-Prob(-1⋅96*SE[D]<D<1⋅96*SE[D])

If Dtrue is the true difference, then the above expression for power can be written as:

Power=1-Prob(-1⋅96*SE[D]-Dtrue<D-Dtrue<1⋅96*SE[D]-Dtrue)

or

Power=1-Prob(-1⋅96-Dtrue/SE[D]<(D-Dtrue)/SE[D]<1⋅96-Dtrue/SE[D])

If D follows a normal distribution with mean Dtrue and standard error SE[D], then the quantity Z = (D − Dtrue)/SE[D] follows a standardized normal distribution with mean zero and standard deviation of one. The power is then given by:

Power=1-Prob(-1⋅96-Dtrue/SE[D]<Z<1⋅96-Dtrue/SE[D])

The probability can be looked up in tables of the standardized normal distribution or calculated using a statistical package such as Minitab.

If we apply the above formula to calculate power for detecting a difference of two standard errors, i.e. Dtrue= 2*SE[D], then we have:

Power=1-Prob(-3⋅96<Z<-0⋅04)=0⋅52

The corresponding power for detecting a difference of three standard errors is give by:

Power=1-Prob(-4⋅96<Z<-1⋅04)=0⋅85

The method can be related to the estimation of changes in density as follows. Let D1true and D2true denote the true densities at times 1 and 2, with change in density given by:

Dtrue=D2true-D1true=R*D1true

Let D1 and D2 be estimated densities at times 1 and 2, respectively, with change estimated as D = D2 − D1. If the coefficient of variation of each estimated density is equal to C, then:

SE[D1]=C*D1,  SE[D2]=C*D2

The standard error of the estimated difference is then given by:

SE[D]=C*D1true*√[1+(1+R)2]

So:

Dtrue/SE[D]=R/{C*√[1+(1+R)2]}

For a 10% change (R = 0·10) and C = 0·036 then:

Dtrue/SE[D]=0⋅10/(0⋅036*1⋅49)=1⋅87

with corresponding power of about 53%. For 80% power, Dtrue/SE[D] = 2·8 and C = 0·024.

Ancillary