“Hav- “ | “in; ,-. ‘ an: to .‘l 7‘ 7": 4'1“ 2" l‘ J 'I‘ ‘ 9. . " . ~ C ‘ - r A f . . L Q . ., Lv' . ‘ s? . 9-" ' km ‘N ways" a: -—'4" w» fit? :1 - A - “$812k .. at}. ' L: $~A~ " ...L1‘~I-.;-~.-"=- . ‘ I‘, I- ' .';‘.p F. - :1 .' Jr ‘7‘: . Wi . '1 4H . 791.1. 1KIT“. 31 “"‘ ‘ 1-5 ‘ ”3 1L.r~.‘:;":.. :5; My in. wk‘icfi I“: 9,- . ;:f‘ x ‘ "I. i, . . “RS2“ ,3”? s 1-" ‘92?“- 1" . , “fink: { " ‘. 5-9:}; -- ‘95 4‘ . I “I"- .. 35? "I ‘1 fifi¢ 35%;- ‘" 11"" r32 5 . 1 a a}? _ .4; J: "-“m “'2 ,. "Hui“ {THESIS LIBRARY ' Michigan State University This is to certify that the dissertation entitled AN EVALUATION OF LINE TRANSECT CENSUS METHODS IN A WEST AFRICAN WOODED SAVANNA presented by Stanley Henry Koster has been accepted towards fulfillment of the requirements for Doctor of Philosophy degreein Fisheries and Wildlife Cm Z2“ guise Major professor Date 11- 7-84 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 .~,. [MW ......... "T7 MSU LIBRARIES 3106417” 0556 RETURNING MATERIALS: Place in book drop to remove this checkout from ‘3". your PECOY‘d. FINES will be charged if book is returned after the date stamped below. 7- 7'5“? ‘ W 0F€?Z:v;;~gz 'J AN EVALUATION OF LINE TRANSECT CENSUS METHODS IN A WEST AFRICAN WOODED SAVANNA By STANLEY HENRY KOSTER A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Fisheries and Wildlife 1984 ABSTRACT Three census methods, foot, roadside counts and aerial surveys, were compared for their usefulness to estimate population densities of 11 species of large mammals in a West African savanna woodland. For foot and roadside count data, 18 line transect estimators were evaluated for their consistency and usefulness under a wide variety of sampling conditions. Foot transect counts, though time consuming, were the most use- ful for estimating population densities. Aerial counts were reliable for buffaloes and elephants, but not for antelopes. Roadside counts were unreliable, despite a relatively good road distribution. Among the 18 estimators evaluated, three radial and four perpen- dicular distance estimators were recommended. The most consistent radial estimators included the Geometric and Modified Hayne. For certain data sets where flushing distances were small, the King estimator performed better. Among estimators based on perpendicular distances, three nonparametric estimators, the Fourier Series, Polynomial and Kelker and one parametric, the Generalized Exponential, performed well. Nonparametric estimators were preferred because of their robust properties. With small data sets, however, only the Generalized Exponential was recommended. The Hahn estimator, based on disappearing distances, consistently yielded low estimates. Among the many factors which can lead to biased estimates, animal movements prior to detection was the most serious. For 6 of the 11 species, at least 10% of the animal groups were moving rapidly when sighted, resulting in inaccurate distance measurements. Body size and group size did not significantly influence the detection of groups. The transition from group density estimates to population estimates required reliable estimates of both mean group size and species dis- tributions within the study area. Density estimates of kobs, waterbucks, bushbucks and reedbucks were most meaningful when based on acutal areas occupied along streams. ACKNOWLEDGEMENTS I wish to thank Benj Kaghan for his patience, perseverance and long hours afield in Park W. Appreciation is extended to park director Albachir Mohammed for his support and to the game guards for their invaluable knowledge, field assistance and good humor. Thanks also to Jeff Towner, Dave Maercklein, Pat McDuffie and Richard Poche for their efforts in many aspects of the study. I wish to extend special thanks to Dr. George Petrides whose advice and support throughout my graduate program was deeply appreciated. I also wish to thank the members of my committee, Drs. Carl Ramm, Stephen Stephenson, Niles Kevern and Rolin Baker. Finally, I wish to thank my wife Heidi for her patience and support, and my family for the many ways in which they helped make this dissertation possible. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES INTRODUCTION REVIEW OF LINE TRANSECT METHODS Mathematical review Historical review STUDY AREA METHODS Foot transect counts Roadside counts Aerial counts Vegetation Analysis of line transect data Description of estimators Variances of density estimators RESULTS Vegetation Distributions of animals Aerial counts Foot transect counts Summary of counts Pooled data set Park-wide survey Central study area Tests of assumptions Roadside counts Pooled data set Hahn estimator Goodness-of-fit tests Frequency distributions 1976-1978 roadside counts Comparison between foot and roadside counts Tests of assumptions Estiamtion of population size DISCUSSION Methods of surveying populations Recommendations of selecting estimators Recommendations on the use of estimators Selection process for estimators Usefulness of density estimates ii SOD-J 17 22 28 29 31 32 35 43 46 49 63 71 71 102 110 117 127 136 136 140 142 145 153 163 167 170 173 184 185 Table Table Table Table Table Table Table Table Table Table Table Table 10. 11. 12. LIST OF TABLES Numbers of transects and kilometers traversed during large mammal counts in Park W, NIger. Large mammal species in Park W, Niger whose populations were investigated in this study. A list of the eighteen estimators evaluated in this study. . Characteristics of vegetation in Park W, Niger. Selectivity indices of vegetation types of animals encountered during the censuses. A value greater than 1.0 indicates preference, and less than 1.0, partial or total avoidance. Percentages of the total vegetation burned and percentages of animals occurring in burned vegetation in Park W, Niger. Distributions of riparian species along streams as determined from ground surveys in 1976, 1977 and 1978. Density estimates of large mammals in Park W, from the park-wide aerial census. Densities are in numbers /km2. Density estimates of large mammals in the central study area from aerial transect counts. Comparisons of group sizes as determined from 1977, in Park W. Values represent numbers of observatiosn in each ground counts during February, group size class. Numbers of observations made during the 1976, 1977 and 1978 foot transect counts in the central study area in Park W, Niger. Density estimates, coefficients of variation and required sample sizes fro foot transect counts made in the central study area in 1976, 1977 and 1978 in Park W, Niger. iii Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table 13. 14. 15. 16. 17. 18. 19 20. 21. 22. 23. 24. 25. 26. 27. Results of the 1978 park-wide foot transect counts in Park W, Niger.' Basic measures of the combined foot transect 1977 and 1978 in Park W, Distances are in meters. counts of 1976, Niger. Comparisons of density estimates from pooled Rankings of density estimators for pooled foot foot transect counts in Park W, transect counts in Park W, Niger. Relative values of density estimates from the pooled foot transect counts.in Park W, Niger. Tendencies of estimators toward positive or negative bias as determined from studies on populations of known size. Goodness-of—fit tests to distributions for pooled foot transect data. Values for tests to determine the applicability of radial estimators for pooled foot transect data. Comparisons of mean disappearing distances in meterstof species in burned and unburned vegetation during the 1976-1978 W, Niger. foot transect counts in Park Disappearing distances of similarly sized large mammal species by vegetation type, Park W, Niger. Comparisons of percent coefficient of variation for estimators from truncated, pooled foot transect data in Park W, Niger. Density estimates from the 1978 park-wide survey in Park W, Niger. Rankings of density estimates from low to high from the 1978 park-wide survey, Park W, Niger. Relative values of density estimates from the 1978 park-wide data for foot transects in Park W, Niger. Results of goodness-of-fit tests to selected distributions from the 1978 park-wide survey in Park W, Niger. iv Table Table Table Table Table Table Table Table Table Table Table Table Table 27. 28. 29. 30. 31. 32. 33. 34. 35. 35. 37. 38. 39. Results of goodness of fit tests to selected dis- tributions from the 1978 park-wide survey in Park W, Niger. Test statistics on angle measurements to determine the validity of radial estimators. Density estimates from the 1976 foot transect Park W, Niger. Density estimates from the 1977 foot transect counts in the central study area, and 1977 aerial counts in the central study area in Park W, Niger. Density estimates from the 1978 foot transect Park W, Niger. 1977 and 1978 foot transect counts in Park W, Niger. counts in the central study area, Rankings of density estimates from the 1976, Relative values of density estimates from the 1976, 1977 and 1978 foot transect counts in Park W, Niger. Activities of animals when first spotted and their responses after detection during all foot transect surveys in Park W, Niger. Values are in percentages of the total seen. Correlation coefficients for relationships between group size and distance measures for the pooled foot transect data. Number of observations per unit time walked during the 1976, 1977 and 1978 foot transect counts in Park W, Niger. Comparisons between mean numbers of groups observed per kilometer walked for transects positioned parallel and perpendicular to streams during the 1978 foot transect counts in Park W, Niger. Basic measures of pooled data from roadside counts. during the 1976-1978 censuses in Park W, Niger. Density estimates from the 18 estimators from pooled data of roadside counts in Park W, Niger. Table Table Table Table Table Table Table Table Table Table Table 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. Rankings of estimates from pooled roadside transect data in Park W, Niger. Relative values of estimates from pooled roadside counts in Park W, Niger. Rankings and relative values of the totals for all species for pooled foot and roadside transect data in Park W, Niger. Values of goodness-of-fit tests to specified dis- tributions for pooled roadside count data in Park W, Niger. Basic measures of roadside counts in the study area in 1976, 1977 and 1978 in Park W, Niger. Distances are in meters. Density estimates from roadside counts in the area in 1976, 1977 and 1978 in Park W, Niger. Rankings of estimators for the 1976, 1977 and 1978 roadside counts in the study area in Park W, Niger. study Overall relative values of estimators for foot and roadside counts in Park W, Niger. Comparisons of selected density estimates between foot and roadside counts in the study area from 1976-1978 in the study area in Park W, Niger. Densities are in numbers/kmz. Comparisons between numbers of groups recorded per kilometer of foot and roadside counts during the 1976-1978 censuses in the central study area in Park W, Niger. Comparisons of numbers of groups counted per kilometer of transect for foot and roadside counts in high animal density areas within the central study area in Park W, Niger. vi Table Table Table Table Table Table Table Table Table Table 51. Density estimates for a distribution which is approximately half normal and one which is skewed (fewer observations in the first sighting class) 52.Values of goodness-of—fit tests to specified dis- 53. 54. 55. 56. 57. 58. 59. 60. tributions for the 1976-1978 roadside counts in the central study area in Park W, Niger. Test values from the goodness of fit tests to the cosine theta distribution, whether 9 is significantly different from 32.7 and sin 9 is significantly different from 0.5 for the pooled data in Park W, Niger. Test values to determine if 9 is significantly different from 32.7 and sin 9 = 0.5 for data from the 1976-1978 roadside counts in Park W, Niger. Percentages of animals observed in activity categories when first observed along road transects and percentages of animal responses to vehicles from 71976-1978, Park W, Niger. Mean numbers of groups counted per hour during the 1976-1978 roadside counts in Park W, Niger. Mean group sizes of species measured during the 1976- 1978 foot transect surveys in the central study area and total park in Park W, Niger. Estimated square kilometers occupied by species dur during the foot and roadside counts from 1976-1978 in the central study area and total park in Park W Niger Population estiamtes based on sample and total mean group sizes in the central study area from 1976- 1978. Density estimates are based on the Geometric mean estimator. Desirable characteristics and recommended qualities for estimators. vii Table 61. Simulated effects of short sighting distances on radial distance estiamtors, where L = 10km and n . 10. The number of small r values increases from tests 1 to 4. viii Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Fighre Figure Figure Figure LIST OF FIGURES 1. Diagram of the measures recorded in line transect surveys. 2. Examples of a negative exponential (NE) and a half normal (HN) detection function curve g(x). 3. Examples of data grouped into 14 (a) and 7 (b) equal class intervals. 4. Map of Park W, Niger. 5. Boundaries, roads adn major drainages in Park W, Niger. 6. Locations of foot transect counts during the 1976 survey, Central Study Area, in Park W, Niger. 7. Locations of foot transects during the 1977 survey in Park W, Niger. 8. Locations of foot transects during the 1978 survey in Park W, Niger. 9. Locations of foot transects during the park-wide survey of Park W, Niger. 10. Locations of aerial transects in survey units a-j followed during the 1977 helicopter survey of Park W, Niger. ‘ 11 An example of a splining function using a hypothetical histogram. 12.Vegetation map of Park W, Niger. l3.a. Distributions of kob and waterbuck in Park W, Niger. b. Distributions of bushbuck and reedbuck in Park W, Niger. 14.Distributions of buffalo and elephant in Park W, Niger. 15 Percentages of animal groups observed in low moderate and high density vegetation during the 1976, 1977 and 1978 line transect counts in Park W, Niger. ix Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure l6. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. Approximate dry season distribution of livestock and locations of hunting incidents observed in Park W, Niger. Numbers of observations of kobs, waterbucks, bushbucks and reedbucks made at 100 m intervals between a watersource and 3.0 km during foot transect counts from 1976-1978 in Park W, Niger. Numbers of observatiosn of 7 species at 8 km intervals between a watersource and 4.0 km during foot transect counts from 1976-1978 in Park W, Niger. Designated strata used to estimate animal densities from the 1977 aerial transects in Park W, Niger. Frequencies of density estimates for buffalo, waterbuck and kob as based on the pooled foot tran- sect data. Density estiamtes and donfidence limits for kob from the pooled foot transect data set in ascending order. Comparisons between perpendicular (P), radial (R) and disappearing (D) distances form pooled foot transect data. Sighting radius for observers when the detection of exposed animals depends on scanning the vetetation. Correlations between body size and mean perpendicular (a). for the pooled foot transect data. sighting (b) and disappearing (c) distances Percentages of animals active during 0700 and 1900 hours from January to February in Park W, Niger. Diagramatic representation of the decreasing con- centration of animals from a stream and the relative position of a transect positioned parallel to a stream. (a). sighting (b) and disappearing distances (c) for the pooled Histograms of perpendicular (a), roadside count data of kob, waterbuck, road and hartebeest. Figure Figure Figure Figure Figure 27. 28. 29. 30. 31. (b). Histograms of perpendicular (a), sighting (b), and disappearing (c) distances of the pooled roadside count data of buffalo, elephant, oribi and warthog. Frequency histograms of observed perpendicular distances for pooled roadside count data in Park W, Niger. ' Frequency histograms of foot transects (top) and roadside counts (bottom) of kobs from the 1978 park-wide survey in Park W, Niger. (n = 25). Numbers of kobs and waterbucks.observed along roads per hour driving between 0800 and 1800 hours during the 1976-1978 roadside counts in Park W, Niger. Key to the selection of a line transect estimator for estimating densities of large mammals in Park W, Niger. xi INTRODUCTION One of the central problems in the study of animal populations is that of assessing pOpulation size. Though not always necessary, know- ledge of pOpulation size and density can provide a basis for sound management decisions. Leopold (1933) felt that the game census was the first step in initiating management on an area. In spite of the interest in pOpulation studies for many years, Eberhardt (1978) noted that field biologists still do not have an array of reliable methods for population study available to them. Among the methods for counting large mammals in Africa, aerial transects are perhaps the most widely used, eSpecially in East and South Africa. In the wooded savannas of West Africa, however, air— craft may be somewhat less useful, even for the largest animals. Avail- ability and high cost, too, may restrict their use. Mark-recapture studies are also costly and time consuming, especially where multiple species are involved. The rapid disintegration of feces limits the utility of pellet group counts, too, as a technique to estimate abun- dance. Among the most feasible methods for West Africa are roadside and foot transect counts. They are relatively inexpensive, rapid, and, as shown by Hirst (1969) in southern Africa, can be reasonably accurate. While many investigators have applied line transect methods to large mammal counts (Barber, 1980; Harris, 1970; Child, 1974, Sihvonen, 1977; Bosch, 1977), evaluations of these methods in Africa have been limited. Some theoretical considerations of line transect estimators have been rigorously examined (Burnham et al., 1980, Gates, 1979), but many practical ones have not. The wildlife manager is confronted with a number of challenges in designing line transect counts. First, there is the choice be- tween aerial, roadside and foot transect counts, each having advantages and disadvantages. II'ground counts are chosen, the best estimator must be selected from among the array of more than twenty. The esti- mator selected ideally should be useful for a variety of species and under a wide range of environmental conditions. ‘ The large mammals commonly censused in Africa range in size from the dimunitive duikers to elephants, and each species is unique in behavior and habitat selection. Visibility in the wooded savannas it its highly variable and animal distributions are often clustered near water. Furthermore, some animals occur singly while others are found in large groups. The challenge for the field biologists is to design a sampling procedure which will provide reliable estimates for all or most of the large mammal species present in the diverse habitats present on this management area. The objectives of this study were first, to examine the use- fulness of foot, roadside and aerial counts for large mammals in a West African wooded savanna, and second to evaluate the vailidity of the various line transect estimators. Review of Line Transect Methods Mathematical Background Line transect history and concepts have been discussed in some detail (Eberhardt, 1978; Gates, 1979; Jolly and Watson, 1979; Burnham et al., 1980). The underlying theory is relatively straight-forward. The observer moves along a transect line (Figure 1) and, as animals are encountered either as a result of detection by the observer or as a response by the animal, one or more measurements are recorded. These measurements include radial distance r, from the observer to the animal at z; the perpendicular or right angle distance x from the line of travel; or the disappearing distance d from the line of travel. The perpendicular distance can also be obtained by either measuring both the angle 9 and r (x - sin 9 - r) or by measuring both .9 and y, the distance from the observer to a point directly perpendi- cular to the animal (x - tan 9 - y). The most common and usually recommended measures (eg. Burnham et al., 1980) are r and 9. These measures, when used with an unbiased estimator, are expected to give an unbiased estimate of the average pOpulation density. If sampling procedures were representative of the entire management area, a re- liable population estimate for that area can be obtained. The general formula used to estimate animal density for all line transect estimators is D a 2%3" where n is the number of objects counted, L is the transect length and D is the estimated density. The parameter 6 or its alternate form c', where c' 8 {E- D - gg', is the only unknown in the equation. The parameter c is determined ossuvu a Figure 1. Diagram of the measures recorded in line transect surveys. by measuring the distances x or r along the transect line, and is some- times referred to as one-half of the effective strip width. (For es- timators based on perpendicular distances, the measures of x and n represent the information required to estimate densities.) Gates et a1. (1968), Seber (1973) Gates (1979), Burnahm and Anderson (1976) and Burnham et a1. (1980) have discussed the general model that must be followed to estimate density from the above measures, and their discussions are summarized here. The model is based on the concept that the probability of detecting an animal decreases as the perpendicular distance from the line increases. This probability of detection has been represented by a function g(x), termed the detection function (Burnham et al., 1980). It is the conditional probability of observing an object (animal) at some perpendicular distance x from the transect line. The model requires only that all objects directly on the transect line are detected (eg. g(O) - 1). The form of the detection, function can assume a variety of shapes (Figure 2), depending on the objects being counted, the observer, and a wide variety of environmental factors which influence the detection of objects in the field. Thus, for any set of distances x, there is a probability density function, which forms the basis for a mathematical expression. The form f(x) has been adopted from Burnham et a1. (1980) to represent the probability density function, since it is directly re- lated to g(x) where f(x) - g(x)/c. This function can then be used to n f(O) 2L ’ since f(O) - l/c. The central problem in describing the probability represent the unknown parameter in the generalized formula D a density function, then, is finding an appropriate mathematical form for f(0). NE NH Distance Figure 2. Examples of a negative exponential (NE) and a half-normal (HN) detection function curves g(x). Grouped data Some estimators require that the data be grouped into discrete class intervals. This is normally done by constructing a frequency histogram of the data (Figure 3). The shape of the probability de- tection function often can be subjectively altered to follow a smooth curve by decreasing the class interval size. Truncation Often with line transect data, there are several observations which are very large in relation to most others. These extreme values can bias the estimation of f(O), and it has been recommended (Burnham et a1. 1980) that they be eliminated or truncated at some distance, w*. In practice, Burnham et al. found that 1-3% of the data should be ;truncated to minimize bias. Assumptions of estimators The underlying assumptions of line transect estimators were first mentioned by Hayne (1949) and later elaborated by Gates at al. (1968), Seber (1973) and Burnham and Anderson (1976). They are: (i) Objects to be sampled are randomly distributed in the area, or the transect lines themselves are randomly located. (ii) The sighting of one animal is independent of the sighting of another. (iii) No animal is counted more than once. (iv) When animals are seen upon being flushed or spotted, each animal is seen at the exact position it occupied when startled or spotted. a... ). u a f lh——- D O -l U C b o , lbw —. )- U z .‘—I b “I 3 O U 8 5 l—I 0' DISTANCE CLASSES Figure 3. Examples of data grouped into 14 (a) and 7 (b) equal class intervals. (v) The probability of sighting an animal directly on the tran- sect line is unity. (no animals on the transect line are missed). The above assumptions apply to animal groups as well as to solitary individuals. Failures of the data to meet these assumptions have been discussed by Gates et al. (1968), Seber (1973), Eberhardt (1978) and Gates (1979). Historical Review Line transects were first used for counting animals early in this century. Only in the past few years, however, have efforts been made to establish a solid theoretical framework for line transect estima- tors. Forbes and Gross (1921) were evidently the first to report using a fixed strip transect while counting songbirds in Illinois. During the 1930's and 1940's, interest in monitoring wildlife popula- tions arose out of the need for a more scientific approach to management. The first reported use of distance measures for estimating density was the procedure devised by R. T. King for ruffed grouse (Bonasa umbellus) in Minnesota, as reported by LeOpold (1933). King's method was based on measurements of r, and Leopold introduced the term "effec- tive strip width" to describe the average area sampled during the count. Breckenridge (1935), working with songbirds, felt that by con- structing a frequency table of perpendicular distances, he could de- termine the strip width to a point after which frequencies sharply declined. His strip, therefore, was based on the distance within which he was reasonably sure that all or most birds were detected. 10 Gradually, line transect methods were adapted to counts of various species in a variety of habitats and circumstances. These include white-tailed deer (Odocoilieus virginianus)(Erickson 1940; Krefting and Fletcher 1941), ruffed grouse (Bonasa umbellus) (Fisher, 1939; Frank, 1946), snowshoe hares (Lepus americanus) (Webb, 1942), songbirds (Kendeigh, 1944), and dead deer (DeBoer, 1947). Webb's approach for snowshoe hares was to use the mean perpendicular distance E, derived from f and 5, the mean radial and angle measures, as an estimate of the effective strip width. Hayne (1949) felt that estimates based on average flushing distances would underestimate population size, and proposed using the reciprocals or the harmonic:mean of r as an estimate.of the strip width. He assumed that each animal will flush if the observer approaches within a certain critical distance, and that the distance differs for each individual. His methods has been widely used. Kelker (1945) was one of the first to examine line transect methods critically, and this led to his belt or strip transect method. For estimating deer densities, he counted only those animals within a pre- determine strip width and ignored animals outside the strip. Hahn (1949) used a considerably different approach in an attempt to estimate strip width- He used a person to represent a deer, and :measured the distance at which the person disappeared from view as he.moved away from the transect line. From these measurements, he established visibility profiles in the different vegetation types encountered along roads in his study area, and thus was able to estimate the area in which animals might be seen during roadside counts. During the 1950's and 1960's many field biologists used line transect methods but made few advancements toward assessment or improvement 11 of existing line transect estimators. Yapp (1956) presented a theo- retical paper in which he attempted to develop a census methodology which took into account movements of animals prior to counting. Skellam.(1958) reviewed Yapp's method, and further developed an unbiased estimator based on motion theory. As noted later by Seber (1973), however, the methods of Yapp and Skellam had little practical appli- cation because they required measurements unobtainable during normal line transect counts. Robinette et al. (1954, 1956) provided insight into the relative precision of several estimators and the practical problems of counting inanimate objects. Their investigations into assessing numbers of dead deer and burlap sacks revealed that counts can have a considerable amount of negative or positive bias, depending on the environmental conditions and the estimator selected. In the late.1960's, several advances in line transect theory were made. Gates at al. (1968), Eberhardt (1968) and Gates (1969) were among the first to develop a more statistically-rigorous approach. Using only perpendicular distances, Gates et al. (1968) based their estimator on the probability of detecting an animal along the transect. They used g(x) to denote the probability of detection and proposed (“A“), with the maximum likeli- that g(x) is exponential, g(x) - exp hood estimate oflis equal'to n-l/in. They based this estimator on the frequency distribution of perpendicular distances for grouse flushes in Minnesota which exhibited a negative exponential distribution. This estimator is restrictive.because unless g(x) is exponential, it can lead to badly-biased results. Gates (1969) then developed an estimator 12 for radial distances r, also based on the negative exponential dis- tribution. Eberhardt (1968) introduced a more general approach. He noted that the probabilities of detecting an animal decrease with increasing perpendicular distance, and that an appropriate model for the de- creasing function is undefined. Rather than the negative exponential, he suggested adopting a more flexible model from a family of curves, either the power series or reversed logistic distributions. He developed an estimator based on the power series distribution. The work of Gates and Eberhardt led to the development of a number of other line transect estimators. Frequency distributions of obser- vations for a variety Of animals in various types of vegetation were scrutinized and it gradually became clear that detection functions can assume a variety of shapes. Thus, more than one distribution must be considered for a particular animal and its habitat. The half—normal distribution was suggested by Hemingway (1971) for Thomsonksgazelle (Gazella thomsoni) in East Africa. Sen (1974) proposed a gamma distribution, a generalized form of the exponential distribution. The log—quadratic distribution provided the basis for an estimator deve10ped by Anderson (1978), who attempted to find an equivalent to the Exponential Quadratic estimator. Quinn (1977) and Pollock (1978) independently proposed the generalized exponential distribution for g(x), which, as noted by Gates (1979), included as special cases the exponential, half-normal and uniform distributions. In his computer program LINETRAN, Gates (1981) included an additional estimator based on the triangular distribution. 13 As noted by several investigators (Burnham and Anderson 1976; Seber 1973) estimators based on any underlying distribution will give unbiased estimates of population density if the assumptions of the underlying distribution are met. Departures from these assumptions can lead to badly-biased estimates. In contrast to estimators based on parametric distributions, an- other approach was developed during the 1970's. Anderson and Pospahala (1970) used the line transect method to estimate densities of waterfowl nests in southern Colorado. They measured perpendicular distances of nests within a 16.5 ft strip and found that despite the narrow strip, frequencies of nests counted declined significantly near the limits of the strip. As a correction factor for the missed nests, they used a curvilinear regression equation. In their case, a quadratic equation performed best. This equation permitted a nest-density estimate to be calculated that was in no way dependent on an underlying distribution. Their paper laid the foundation for non-parametric approaches to den- sity estimators. Seber (1973) and Gross et a1. (1974) also implicated the use of a distribution-free approachs Nevertheless,Burnham and Anderson (1976) first recognized the full potential and fundamental differences from parametric approaches. The non-parametric estimator of Burnham .and Anderson (1976) required no assumptions about underlying distri- butions. It was an estimator based on perpendicular distances which required only that G(0) = 1, meaning that all animals on the transect line are counted. They also developed a modification of the Hayne estimator for radial distances which was not based on an underlying distribution. 14 The efforts of Burnham and Anderson led to the development of still other estimators. Crain et al. (1978) proposed an extension of the Fourier Series as an estimator. The Fourier Series estimator has since been shown to have robust properties with regard to variations in the underlying distribution and its use has been recommended over other transect estimators (Burnham et al. 1980). Eberhardt (1978) recently developed a non-parametric estimator which is simdlar to that of Kelker (1945). It is based on grouped data, and uses only the two groups nearest the line. Since their early development, efforts have been made to apply line transects to roadside counts (Nice and Nice 1921; Hosley 1936; Rasmussen and Doman 1943; Schrader 1944; Cronmiller and Fisher 1946; Taylor 1947; Hahn 1949). They were used mainly for white-tailed deer and mule deer (Odocoileus hemionus), and as index counts for bird species such as mourning doves (Zenaida macroura) and ringnecked pheasant (Phasianus colchicus). Roadside counts of animals have taken three general forms. In the first, all animals are counted along the road transect and no dis— tance measurements are made. Such counts reflect relative numbers and are used for comparisons with other areas or the same area at different times. The second approach involves establishing a fixed width or strip along one or both sides of the transect and counting all animals observed within that strip. Norton-Griffith (1978) discussed a variation of this where several fixed widths may be established to account for differences in vegetation or terrain along the transect. This method is most applicable to open country. The third is similar to Kelker's 15 (1945) belt transect except that all animals are counted and distances are measured to establish a visibility profile in the different vege- tation types along the transect lines. Several variations have have been developed to measure profiles: 1. The average perpendicular distance of animals from the transect (Dasmann and Mossman 1962). 2. The disappearing distance of animals along a pre—established route (Hirst 1969), preferably for each vegetation type and for each species being counted. 3. The distance from the transect line to the point at which the frequency of observations begin to rapidly decline. That distance determines the effective strip width and obser- vations made only within that width are included. An additional method was attempted during this study, wherein the r and 9 measures were made as done on foot transects. Norton-Griffith (1978) noted that although roadside counts have been frequently enployed in Africa and elsewhere, very little effort has been made to evaluate their accuracy. Criticisms of roadside counts. involve bias in the random coverage of an area, and their attractive- ness or avoidance of roads by animals (Norton-Griffith 1978; Gates 1979; Dasmann and Mossman 1962; Hahn 1949). Cronemiller and Fischer (1946), however felt that their roadside counts of white-tailed deer provided accurate density estimates, and Hirst (1969) showed that roadside dis- appearing distances for several species of African antelope gave reasonably—accurate population estimates. l6 Aerial transects have been widely used in Africa and elsewhere for counting large mammals. Density estimates are obtained from aerial transects by determining the strip width to be used prior to the count (Norton-Griffith 1978) and then tallying only those animals observed within the strip. Many sampling procedures have been used in aerial surveys but stratified random sampling is recommended (Jolly 1969; Jolly and Watson 1979). Despite their wide acceptance, aerial counts have been shown con- sistently to be negatively biased, even for large mammals (Caughley 1977; Pienar et a1. 1966; Jolly 1969b). There are many factors which affect the reliability of aerial estimates. Helicopters are recommended over airplanes, but even under the most favorable conditions, aircraft counts may provide only minimum population estimates. 17 STUDY AREA Park W has been in existence since 1936. It is Niger's only national park and the one remaining locality with relatively-undisturbed upland and riparian vegetation. The park lies within the Sudan savanna zone and is international with portions also located in Benin and Upper Volta (Figure 4). The portion in Niger covers 2200 km?, and lies between latitudes 11°05' and 12°35'N and longitudes 02°05' and 02°50'E. It is essentially a peneplain 250 m above sea level. The 750 mm isohyet and 350 isotherm pass through it. The Niger River, the only permanent flowing stream, forms the eastern boundary. Annual rains begin between early April and early June, usually in May, and end in September/early October. The dry season has three distinct periods: warm.and humid in October-November, relatively cool and dry from December through February, and hot in March-May. Wet season daily highs average 33°C. The upland vegetation is mainly Combretum wooded savanna, with moderately dense woodlands and shrublands interspersed with small grassy openings. Riparian vegetation consists mainly of narrow bands of fringing forest. Annual fires burn approximately 70% of the park during the dry season. Most are set by park personnel during November and December to facilitate game viewing by tourists. Park W has one of the most extensive road systems of West African parks. There are approximately 470 km of roads (Figure 5) which traverse 18 (5:3? NIGER PIII W O C I C I. ““ ' \ o I’ i ‘ . \ .0. ” 'u.. I I ‘ ,o‘, —' Gnu u . ’ \ I s I ' I . I o R I’ \‘ ’ o "'6‘ \ “ o .0 :0. O . ‘\ 0 li'.’ ... “ .0 I s a... , o. .' ' I I . o ' \ O I . , . s ~,r I o P o I . . O I ' I. ' . I n l .0 : . w ~\ 0. I , \ I ‘ ' I . I l . c ‘ I ' UPPER 2 l ‘ o ' l \ o O ' ..o ’P I . votn . mm , l ' I | a a o l I a I | c | \ . . ‘ I i ' ’ I ' I ’0 ‘. ’I |‘ . fi\‘~ ‘-‘ I' o c- , \ , o ’ O . I ““"‘| I’ \ ..' l o ,’ \ .' l ' l .\.' " | \ I \ ‘ I |\ P H \ ,’ \ ' 10 ill \ ‘ 1 \ I \ ’1 \ I ' I \ I ' I s. , ‘\ I s I I \--o ---- Park boundary --.. International boundary Figure 4. Map of Park W, Niger 19 representative types of vegetation and terrain. All roads are graded at the beginning of each dry season to permit passage by tourists. This is normally completed by December 1 of each year. Many portions of the road system become impassable soon after the first rains. Time of Census It was possible to conduct line transect counts in Park W from November to August. The period from mid-December of Mid-February, how— ever, was considered best because daily high temperatures were moderate and visibility was comparatively good. Most fires were set by early December. Counts during November were less desirable because not all areas of the park were accessible at that time and maximum visibility was only a few meters where grasses were unburned. The late-dry season also was not desirable because daily temperatures often reached 45°C (115017) and field work became noticeablydifficult. Animals responded to the heat by lying down and seeking shade making them.more difficult to spot. A census during the late-dry season also ran the risk of being interrupted by rains. In 1976, for example, heavy rains arrived in mid-April. Many animals were concentrated along streams during the late dry season but quickly dispersed following the first substantial rains. The census was seriously affected. Counts during the rainy season were difficult, too, because many areas were inaccessible and visibility was significantly reduced. 0f the three major streams bordering Niger's Park W, the Niger is by far the largest (Figure 5). Its peak flow period occurs during 20 I I ‘ ‘\ - '- -- ' Niger IIPOI’O ’I ‘-,’;,’ .. ‘ River ” — ” I.’ I I’ll, I, I- ‘ Iaoa Iiv r "“~”\ I - {\ Central \ l" \a -- ' I \\ study ‘ . ‘ ‘\ area | ~\ ‘, I-s/ 2‘ \ I . "— \‘ I I . I, I - l -\I’ l I. ’ \ . I \ ;:---.\ | - —’ \ I ’-'] ~—. . '-' _—' ' [I '\ \\ I "l \ s . \\/\ ' I\ \‘ ’I \v- \ \\ ‘- --"’ Ichou livu ,\ \ ,L/ ‘ \ I \ \ I ‘ \ I I \\ ‘ BENIN \ a \ \ /’ : \ ‘ -I ‘ \ ' \ ---IOADS X. \ ~ STREAMS I \ \ \ \ UPPER VOL” \ \ \ ,0 o I. \ ’" _.___. \ 1 km \1’ Figures, Boundaries, roads and major drainages in Park W, Niger. 21 the dry season (January-February), coincident with rainfall at the headwaters in the highlands of Guinea. The flow level is greatly reduced during the wet season. The Mekrou and Tapoa Rivers, in contrast, have seasonal flow for about five to six months after the rains commence. Except in the Tapoa Gorge, the Tapoa River is usually dry by mid-dry season, but numerous pools remain throughout the dry season in the Mekrou River. For a detailed comparison of foot, roadside and aerial transect methods, the central portion of the park was selected for study (Figure 51. It is close to park headquarters in Tapoa, has a good road distribution and contains examples of most plant and animal communities in the park. In addition, it was probably the least affected by live— stock grazing and hunting, both illegal but prevalent in the park. 22 METHODS Foot Transect Counts Counts of animals were made during each mid-dry season (January-o February) in 1976, 1977 and 1978. Counts were also attempted early and late in the dry season as well as during the wet season. The numbers of transects and distances walked were increased each year (Table 1). In 1978, the entire park was included in the survey. Because of difficulties of access and of locating random starting points, complete randomization of transects was not possible. Road- side counts were made at the same time because of personnel and equip- ment lbmitations, and it was necessary to coordinate activities to maximize distances walked and minimize fuel and time wastages. Where possible, transect starting points were randomly located along roads or major rivers. Others were sited in representative habitats in a systematic manner designed to achieve time and fuel efficiency. It is believed that the foot transects (Figures 6-9) provided a repre- sentative coverage of the study area and total park. Transects were normally traversed in cardinal directions, with a minimum of 1 km between transects to avoid duplications of observations. Most transects were walked between 0700 and 1100 hours. Usually, two persons were present on each transect. One served as observer/navi- gator and the other as observer/recorder. Transect distances were Table 1. Numbers of transects and kilometers traversed during large mammal counts in Park W, Niger. Central Study Area Total Park 1976 1977 1978 1978 Foot transects Numbers 12 22 26 63 Total distances 76 160 208 760 Roadside counts Numbers 16 31 35 51 Total distances 776 1240 1200 2120 24 liter liver Figure 6. Locations of foot transects during the 1976 survey, Central Study Area, Park W, Niger. 25 Niger liver Figure 7. Locations of foot transects during the 1977 survey in Park W, Niger. 26 'gkt.‘ Figure 8. Locations of foot transects during the 19.78 survey in Park W, Niger. 27 Figure Location of foot transects during the parkswide survey of Park W, Niger. 28 determined by pacing and confirmed from topographic maps. Pacing enabled observations to be recorded on the transect by position. For each observation along transects, the following information was recorded: Species, number, sexes and relative ages if possible, time, location on the transect, animal activity, sighting distance, angle, disappearing distance, vegetation type, burn status of the ve- getation and relative density of the vegetation. Sighting distances were defined as the number of meters from the observer to the center of a group. Group is defined here as one or more individuals. Dis- appearing distances were defined as the maximum distance that an observer could see the group. A basis for aiding judgements in disappearing distances was to estimate the maximum distance at which a group could have been spotted in vegetation of that type and density. A Mark IV range finder and pacing were used to measure distances and a compass for angles. In some instances, animals were not observed until in motion. For those observations, sighting distances and angles of their initial location were approximated or left unrecorded. The relative density of vegetation was recorded as l for low, 2 for medium and 3 for high density. Roadside Counts Roadside counts were carried out during the same time period as foot transects each year. Additional roadside counts were made during the early and late dry season, and also during the wet season until roads became impassable. Both morning and afternoon counts were made on each transect. Normally, two observers stood in the back of a 29 pickup truck which travelled between 15 and 25 km/hr. All park roads were traversed during the dry season but concentrated efforts were made in the central study area (Table 1). Transects along roads in the study area sampled approximately the same proportion of each vege- tation type as did foot transects. In cases where an animal group did not voluntarily disappear, the vehicle proceeded along the road until a disappearing distance for the group could be obtained. Aerial Counts . Aerial counts were made in February, 1977, and coincided with the locations and timing of foot and roadside counts made that month. Aerial censuses had been planned for 1976 and 1978 as well, but logistic complications prevented their completion. A Bell 206 B Jet Ranger helicopter was employed for the aerial counts. All survey units (Figure10)‘were sampled once. In high animal- density areas, three counts were made within a 3 day period. Air speed was maintained at 100 kph at an altitude of 100 m. The strip width' sampled was 100 m.on each side of the helicopter. Transects were a minimum of 2 km apart to avoid duplicate counts. Advantage was taken of natural landmarks such as roads and rivers to aid navigation and positioning of transects. During the survey, one observer sat beside the pilot and two ob- servers sat behind them. The pilot and forward observer assisted in Spotting game while the rear observers both spotted and recorded. Desired strip widths for counting were established by marks placed on the aircraft windows while hovering over a measured and marked area windows while hovering over a measured and marked area on the ground. 30 I. o. Figure 10. Locations of aerial transects in survey units a-j followed during the 1977 helicopter survey of Park W, Niger. 31 The study area was divided into two strata and the entire park into 5 strata according to relative animal densities as determined from.ground counts. Because these counts were intended to be used as a standard against ground counts, prior to and during the aerial counts, a serious effort was made to minimize bias. Five factors were specifically addressed as potentially biasing counts: 1. Animals visible but overlooked because of observer inefficiency. 2. Animals visible, but overlooked as the observer counted another group. 3. Animals concealed from.view by vegetation. 4. Animals which moved out of the transect prior to counting. 5. Species misidentification. There was no readily available check against these factors. For the first one, some measure of bias was obtained by comparing counts of the two observers on the right side. Vegetation A survey was made to determine the park's vegetation types and characteristics. The point center-quarter method (Cottam and Curtis 1956) was used to determine the species composition and density for woody vegetation. Sixty transects 100 meters in length consisting of 10 points each were established in the four types identified. From aerial photographs and after extensive ground verification, a vege- tation map was prepared. 32 The extent of burned vegetation was estimated by point samples taken during the animal counts by foot transect and roadside counts. The point at the end of each 100 m transect was sampled to record whether it was burned or unburned. Along roads, the distance between points was 500 m. Analysis of line transect data The computer program.LINETRAN developed by Gates (1981) served as the principal means of analyzing line transect data. With LINETRAN, the user has the option of specifying whether the data entered is truncated or untruncated, grouped or ungrouped, and can select one or more of 11 perpendicular distance and 4 radial line transect estimators. LINETRAN can also fit the data to the following distributions: half- normal, generalized exponential, triangular, polynomial, quadratic, and gamma distributions with o - 1.0, o - 2.0 or a variable. The test for the goodness of fit to the distributions is made by the Kolmogorov-Smirnov (K~S) statistic (Steele and Torrie, 1980). In addition, the cosine 0 distribution of the measured angles (Hayne, .1942) optionally can be fitted and tested by chi square. For estimating variance, the user has the option of selecting the interpenetrating sample or specifying natural replications in time or space. The original program.LINETRAN was developed on an IMB computer. It required modification for compatability with the CDC 6600 computer at Michigan State. Evaluation of estimators Critieria used for evaluating estimators included tests of goodness of fit to distributions on which certain estimators were based, 33 comparisons of relative density estimates with estimators of known bias, consistency of density estimates between species and between surveys and comparisons with results of aerial counts. The objective of these comparisons was to determine which estimators, if any, demon- strate consistent patterns between species and between surveys, and are generally useful for all species and habitats. LINETRAN does not select the best or least biased estimator. The choice is entirely that of the investigator. Species included in the analyses Fourteen of the fifteen large mammal species (not including predators or primates) which occurred in the park were initially targeted for counting (Table 2). Observations later showed that topis, red-flanked duikers and red-fronted gazelles were rare. Esti- mation of their population densities was not feasible and they were omitted from the analyses. Tests of Assumptions The reliability of estimators can sometimes be determined by testing the assumptions on which they are based. Radial estimators are based on the assumption that the mean angle is approximately 32.70. This can be tested by one of the two 2 tests (Burnham et a1. 1980). For E(9) - 32.70, the test statistic is n(9 - 32.7) 21.56 8' where n is the number of observations. A second test involves the sin(9), to show that it is an uniform 34 Table 2. Large mammal species in Park W, Niger whose populations were investigated in this study.- Species Scientific name Kob 52212 is; Waterbuck Kobus defassa Roan Hippotragus equinus Hartebeest Alcelaphus buselaphus Topi Damaliscus korrigum Buffalo Syncerus cafer Elephant Laxodonta africana Oribi Orebia ourebi Grimm's duiker Red-flanked duiker Bushbuck Reedbuck Warthog Red-fronted gazelle Sylvicapralgrimmia Cephalophus rufilatus Tragelaphus scriptus Redunca redunca Phacochoerus aethiopicus Gazella rufifrons 35 random variable on 0,1 . The test statistic is z = 12n (§ - 0.5) 'where § = sin (9) The other assumptions could not be directly tested. Instead, evi- dence from a variety of sources was used to determine if each assumption had been met. Description of density estimators Eighteen estimators of population density were included in the analysis. These estimators represent the majority of those developed and involve a wide range of mathematical approaches to density estimation. Several estimators including the King, Webb, and Dasmann-Mossman, have been largely replaced by others. They were included here, however, for comparative purposes. Estimators based on perpendicular distances Exponential Gates et al. (1968) developed the estimator L (n-l) D = i n 1 2L or in the f(O) form, D1 = N x A 2.0L where A = (N-1)/2(X ), x is the mean perpendicular distance, n is the number of observations and L is the transect length. This para- metric estimator requires that the detection function is negative exponential, and is sensitive to departures from this distribution. 36 Table 3. A list of the eighteen estimators evaluated in this study. Available in King Name of estimator LINETRAN Literature Source Perpendicular distances Exponential x Gates at al. (1968) Hemingway Normal x Hemingway (1971) Quadratic x Anderson and Pospahala (1970) Triangular x Gates (1981) Generalized Exponential x Quinn (1977), Pollock (1978) Spline x Gates (1981) Polynomial x Anderson and Pospahala (1970) Fourier Series x Burnham et al. (1980) Eberhardt-Cox x Eberhardt (1978) Kelker x Kelker (1945) DasmannAMossman Dasmann and Mbssman (1962) Webb Webb (1942) Disappearing distance Hahn x Hahn (1949) Radial distances Geometric x Gates (1969) Hayne x Hayne (1949) Modified Hayne x Burnham and Anderson (1976) Exponential x Gates (1969) Leopold (1933) 37 Hemingway Normal Hemingway (1971) first prOposed the half-normal distribution to fit observations based on perpendicular distances. The general form of the detection function is f(0) = exp(ax)2, where a = exp(—x2/2) For ungrouped, untruncated data, the form of the estimator is a (1r/2)15 XXZ /n n - 0.8 n D 2 ( ) The form used in LINETRAN is N/(L(02(2w))), where 02 = £(X2/N) The underlying distribution must be approximately half-normal for density estimates to be unbiased. andratic This estimator was proposed (Anderson and Pospahala, 1970) as a correction for bias caused by objects missed during strip transect counts. In this method, a quadratic curve is fitted to the detection function, and the intercept b(0) is determined. The b(0) is then used to estimate the density. The general form of the equation is 133 = N - b(0)/2 * L * w<2) where W(2) is the width of the second class interval, U02) - U(1) Triangplar For the case when the detection curve is approximately linear, this may be an appropriate estimator. The form of the estimator is D = n/(2 * 1 * W) where w = x(max)/2 38 Gates (1981) modified this equation somewhat because of its extreme sensitivity to outliers. He fits a straight line with the equation Y = 8(0) + B(l) * X + E and uses the constrained least squares to obtain D4 = N * F(O)/2 * L * W(2) where W(2) = U(s) — U(l) for grouped data, and W(2) - 1.0 for ungrouped data, and F(O) = 3(0) Generalized Exponential This model is based on an exponential power series (Quinn 1977; Pollock 1978) and can assume a variety of detection function shapes. It has the general form A DS = exp {-(x/B)a} (where x, a, +-B >0) The model used in LINETRAN is F(X) = EXP(-(X)B)a/ (8 * w 1.0 + 1.0/a)) Spline This method was suggested by Gates (1979) as an alternative to the Kelker method. Gates (1981) noted that his procedure required the researcher to define an arbitrary distance, w, from the transect line in which all animals are seen. The spline method lets the data define that distance. LINETRAN does this by fitting a splining function 0 B +B (X-Z) Z—-. . m \D S : \--- Y - I, + b‘U—l) n ' ‘fil g I \ 31 I __\_. m ' ‘L .0 O | -*—-. I... I \ O ‘ \ >. I U 8 I 3 I ‘7 I w h I Fl-I J I I Perpendicular distance Figure 11. An example of a splining function using a hypothetical histogram. 40 The curve to the right of Z can be linear, quadratic or polynomial. .The form of the estimator is A B n D =._JL___. 6 2L w(2) where w(2) is the width of the interval between Z and X. Polynomial This estimator also is derived from the work of Anderson and Pospahala (1970). It takes the form B7= nF(O)/2L where F(O) is estimated by a polynomial of degree m; pm) = 3(0) + 22,m (B(J)(x2J)) + c To avoid overfitting the data, an equation higher than the 6th degree is not permitted. Fourier Series This non-parametric approach, developed by Crain et a. (1978) used the Fourier Series expansion of a probability density function over an infinite interval. Their estimator has the form: = n f(O) 8 2L U) 1 m ~ where f(0) = -;'+ 2 w 1‘.lak ‘ s 2 knx and ak 'Efi¥ £1 COS -fi;i where W* is the truncation point and k = 1, 2, 3,... The stopping rule for the selection of m, the number of cosine terms in the Fourier Series, is l_ W* 2 % n+1 ) Z-|am + 1| ( where lam + 1| is the absolute value of am + 1 41 Kelker Index Kelker's (1945) model has as its detectability curve g(x) - 1 and has the basic form D9 = n/2Lw where W is the cutoff point specified by the user within which all animals are likely to be seen. Eberhardt-Cox This non—parametric estimator pr0posed by Eberhardt (1978) as based on the work of Cox (1969). It takes the form: A Dlo = (3N(1)-n(2))/ (4L(W(2)) where W(2) is the width of the second class interval. fiéhp_ Sometimes referred to as the "Hahn Cruise" or "Visibility Profile" method, Hahn (1949) proposed an estimator using distances in each vegetation type beyond which animals could no longer be easily detected, A D = n/(ZLg) 11 where i a Exi/n Dasmann-Mossman For their density estimates, Dasmann and Mossman (1962) used mean perpendicular distances, i, and A D = n/ZLx 12 where i = the mean perpendicular distance of actual distance measures taken during the survey. 42 Webb Webb's (1942) method is a modification of the King method (see beyond) and is based on mean sighting angles and distances, where A D13 = n/ 2L; sin 5 where f is the mean radial distance, and 5 is the mean sighting angle. Estimators based on radial distances Geometric Gates (1969) proposed this estimator to "fill the void" because the geometric mean is always less than the arithmetic mean (King estimator) and greater than the harmonic mean (Hayne estimator). The Geometric estimator takes the form: D14 = n/(ZLg) where g is the geometric mean of sighting distances. Haype This is a basic method developed by Hayne (1949), where A D15 = n/(ZLh) ( and h = n/ 2%- is the harmonic mean of sighting distances 1 Modified Hayne Burnham and Anderson (1976) added a constant C(2) to Hayne's formula to minimize bias. This modified version of Haynels estimator has the form: A D = c(2) n/ 2Lh 16 .l where h n/E r1 and C(2) = (1-A) + (A(2/n)). and A a (e - 32.7°)/ (45° - 32.7°) 43 This method requires that the average flushing angle be between 32.7° and 45°. Exponential Where radial distances are distributed negative— (-Ar) exponentially g(r) 2 r Aexp , the estimator from Gates (1969) is: _ D17 = (2n - 1)/2Lr where f is the arithmetic mean of the radial distances. King This oldest estimator was developed by R. T. King but first published by Leopold (1933). It has the form: D18 = n(1/r)/2L Variances of density estimates The variance of a density estimate can be obtained in several ways, depending on the sampling procedure and sample size. The following methods were evaluated for their applicability to density estimates in this study: 1. Interpenetrating sample variance. The interpenetrating sampling method (Cochran 1977) was designed to estimate variance from a single set of observations. Observations are randomly sampled after collection, and assigned to one of n subsamples. Densities are then estimated from each subsample, and the variance is determined from the densities of the individual subsamples. 2. Replicate samples Where separate density estimates Di can be obtained from each transect line 2, an estimator of var(D) 44 (Burnham et al. 1980) can be determined from 221(Di - D)2 L(R - 1) Var(D) = where D is the overall weighted density, L is the total tran- sect length, and R is the number of replicate lines. 3. Indirect estimation of var(D) Burnham et al. (1980) noted that in the general estimation formula D = nf(0)/2L both n and f(O) are subject to sample variation. The var(D) can be obtained indirectly by separate estimates of variances of f(O) and n. The general equation is var(D) - (D)2 (cv(n))2 + (cv(f(0)))2, where cv is the coefficient of variation. H R 2.2. - =1 H r”: The variation of n = 4. Jackknife method. From a series of subsamples, the density is estimated by omitting, one at a time, the data from each subunit, and estimating the density from the remaining subunits. These densities are termed pseudovalues, Pi, and are used to estimate the average density where i P - LP - (L - 2.1)Pi These pseudovalues are then treated like R replicate estimators of density and are used to compute Pj and var(Pj), where P = 2P1 3 L i 2 - (P - Pi) and var(Pj) -Z L(R _ 1) If a stratified sampling scheme is desired, any of the above methods can be used to obtain within-stratum variance estimates. 45 Each of these methods of estimating variance was evaluated for application in this study. Estimation of variances from strata was not possible, however, because of the small sample sizes (in- cluding zero) from many of the strata. The jackknife method is appropriate for small sample sizes, but variance estimates by this method were so small that the author felt they did not realisti- cally reflect the actual variability. For example, when coefficients of variation were between 40 and 50% for other methods, those of the jackknife method were usually less than 10%. Indirect methods of variance estimation were of limited use- fulness because variances of f(O) have not been developed for each of the estimators. For large sample sizes, in consequence, the interpenetrating sample variance was employed, and for smaller sample sizes and density estimates from the central study area, replicate samples were used to estimate variances. It was recognized that replicate samples are undesirable for small sample sizes because re- liable estimates may not exist. Habitat preferences of large mammals were determined from density estimates of each species in each vegetation type. The ratio of estimated densities in each vegetation type and the estimated average density for the entire park gave a measure of selectivity for a habitat type. Values greater than 1.0 indicate a preference. Those less than 1.0 indicate that the animals did not utilize that habitat type in pr0portion to its abundance. 46 RESULTS Vegetation Though Park W contains many plant communities (Koster 1981), only the six major categories (Table 4) were considered for this study. Combretum shrublands together with Combretum woodlands comprised most of the park's vegetation (Table 4). Combretum wood- lands were variable in height, density and composition, but consistently dominated by species of trees and shrubs of the genus Combretum and, to a lesser extent, by Terminalia. These woodlands were widely dis- tributed in the park (Fig. 12), and generally comprised the inter- mediate vegetation between Combretum shrublands and riparian habitats. Shrublands dominated by Combretum species, occurred on well-drained ironpan soils. The distinction between woodlands and shrublands was not always obvious since tree species often assumed a shrub-like growth form on poorer soils. Riparian forest occurred as a narrow band along streams. They were composed of tall trees with a mostly- closed canopy and a dense understory of smaller trees and shrubs. Riparian woodlands were found on deeper soils adjacent to streams and often appeared as open parkland with a tall,dense grass cover. Riparian grasslands occurred in small patches along streams and in' upland marshes. They were most common along the Niger River. Upland grasslands comprised openings in shrublands and woodlands. 47 Table 4. Characteristics of vegetation in Park W, Niger. .Percentage of total Vegetation Riparian grassland Riparian forest Riparian woodland Combretum woodland Combretum shrubland Upland grassland area 1.3 4.2 14.8 37.4 39.7 2.6 Average stem density/ha 78:8 851ia78 saqizoa 8981968 364:306 242192 Dominant species Mimosa pigra Jardinia congoensis Sacciolepsis africana Vetivera nigritana Sporobolis pyramidalis Diospyros mespiliformes Kegelia africana Anogeissus leocarpus Daniellia oliveri Mitragyna inermis Cola laurafolia Combretum.micranthus Acacia atataxacantha Diospyros mespiliformes Daniellia oliveri Anogeissus leocarpus Prosopis africana Pterocarpus erinaceous Terminalia avicennioides Tamarindis indica Combretum nigricans C. glutinosum C. hypopilinum Crossopteryx febrefuga Piliostigma riticulatum Combretum micranthum Guiera senegalensis Combretum micranthum C. nigricans C. glutinosum Guiera senegalensis Dicrostachys glomerata Securinega virosa Loudetia togoensis Microchloa indica Andropogon fastigiatus A. pseudapricus Acacia ataxacantha Combretum glutinosum 48 ....... ------- Combretum woodland Combretum shrubland Riparian grassland Upland grassland Riparian forest Figure 12. Vegetation map of Park W, Niger. 49 Distribution of Animals Few of the large mammal species studied were ubiquitous in the park. Most species were more numerous in the central portion and along streams (Figs. 13 and 14). Roan, hartebeest, Grimm's duikers and warthog distributions covered the entire park . The principal factors believed to have affected animal distributions were vege- tation, livestock, hunters and trappers, and water and fire. The influence of any one factor varied by animal and season. sfitbitat Utilization Patterns of habitat use as determined from foot transect counts (Table 5) indicated that each species perferences were unique. Warthogs were the most widely distributed animals, and were found in all habitat types. Only Grimm's duikers occurred regularly in up- land grasslands and Combretum shrublands, whereas riparian and Combretum woodlands were often heavily utilized by most species. There was a strong association between kob, bushbuck and reedbuck density and the several riparian habitats. Those species were nearly always observed in or near riparian vegetation. While water- bucks also were distributed along streams, they were most often in Combretum woodlands near streams. The distributions of reedbucks was patchy because of the scattered occurrences of their preferred riparian grasslands. Within certain vegetation types, and within certain vegetation types, animals also displayed preferences for dense or Open vegetation (Fig. 15). All species except bushbuck were rarely found in dense vegetation. 3:23—55 2... .. n. r) n i“ ‘\ I . .\ . 0‘ | .... s o 79“}? OKO‘\‘Q . . 1.3.: a.” .o.\s.. no: \ I u x o . (”b.3390 I C I .. | O u . a D a . . $.04. a . . . . _ 3 I oo o 0' ~ I N I l ' -I I I U l I ‘h OI “ ~ I’ll C on I C" 0' a c o s. e .. II o a o o. o. I O I. i‘ . 0 It .\ o d! I! s. on o o b I \ I0 I I. \ a o o o s ful - s Q s o o . on \ I O b \ a Q o I II I I \\ \\ \- II c s o — ‘\ \ \ I I .uowaz .3 xwmm cw soanuouma vow pox mo oceausnfiuumfia .mmH muswwm ’0 0.. .0 -0. I . I t O I s\ I .\Q‘I I I, a ill m I -\ I n 4 .‘fl 4 . 0\ ~- \\ I III] .\ ‘u.|\ " \ \ Ill/ID! I . e .I .09! I 10‘ o I r. ’0 ’ III all. I h ‘0“ ,x s I \‘0 um I \ Q 9 I §\ . a Q. 0 a ’ ICC~ I... Q ll .1 x ..v . a: I. n“- I O I--. s I of 0 ll '0’ c. D " \Il. ’ O .n O " Cl C \‘C II I \ ’ u to ~ - ! lclio o g.\ I D I \ DO - Q I! Q I" o n. .l' o c on o o o I i C D I. Q 9. II no I . I-‘\\’I a u .00 ’ o as \- . an. \\ c; .4 o . .. III '0' so “a n I u o a .o (1! II.\ a o . J‘. o .o c .k C O ‘ |‘ l O O I “ . O O us a \| \ I o o . o 1' II‘I \\ \- II 0 R “ ~ o o I? I\ \\ \ II ‘ a 00 \ K a '00 0 ~ I” Q 0. \ \Q o N 5 s 1'. ~\¢ c§l\ -. \ o‘lao u o a .I a O .0 \ Q . ‘ ' C. “ 51 I“ .I C O.- I. " ' 3 ,’ .Q‘.‘ l, t I '4', .. ‘u. ‘- ~ ' I. \. \ s -..O \ o \ \ 0‘ N o \ ‘ Q. ‘0 ‘. .0 ‘o.. ‘ X \ ‘os \ ‘\ \‘.o'."' u U ‘\ . 3 ‘, . a 9 i ‘Y."' ‘ '. . a \ " :1 In '5 .J c “I ‘ o n .' u‘ ..‘o' g Q.‘ \. 5 . . a " fl- , . ' o g t I 0'- ‘ \. I ' . \ ‘ 1' ' o" : I 1' u 4' k . I I I ‘ Q l '. 0. I 0" ~ ‘ .‘ ......O‘ .I . ‘ I \Q \ . ‘ 0 o ' U l \‘ :. o ~ ' | ‘ ‘OO‘ "-fi I .' I. .’ nus-x, ’ a ' L I ‘ ’ ‘0' ' "0 ‘\ I \‘ I o- I'.. '0 . “. .0 " , s u l I 'oo‘. ‘. a Q \ o a a I k... 0 I \ I’ \ ..‘ ‘ g..o‘. . o . 'l‘t-ooo" “” 0' ' I.“ I '0 .’ \‘ . I . I c ‘\ I. ’ .oo o m g ’ .v .' ‘~ '.. . V o...- ‘ I ‘ I I ‘0.-. I -° 1 . I 0 . \ .. I‘ . .ou’ l ’0 I I ; 'I \“ 0‘ ‘ 1. ,.-x o. n 0 n ‘5. \‘ .‘ -~ I \ ’ o ‘ | .0. .u . . .‘o x ‘\'\ ”‘5‘ U s Q .0" L D \ ‘C \. O u‘ I .00“ | C. W ‘ o \‘. l‘ | .’o D a " ' n I ‘ -- 0 \ ‘0' ~.‘ ‘I I I . I l .' a I ”0’ I " o l ' "‘ O. : " +f‘ I . ‘0’ ' '. ’ o a f. ' . é o . . s I .0 £’ “ ~ 0‘ o‘ .3 .. . ' '. ‘ .w.. “ 0'..- ’- a a, .t-i'a. ‘ " O z \\ '0'._ .‘o ‘Q. '- ' ‘ 1“, - . I I . ~hux I 0 ‘ k ‘ a ‘d , N‘ ' 0 ‘~ I "' ‘ a. 'd' 'a“ Q ' \\ I 1 ’ ‘ g. \‘ . ’I V .. \:' o f I " I \_ ,. ‘. . I ‘o’ ' I I .00. \‘ 'O.".... I . ’.€. -O'-. " ’ ’ , s ‘.o' '0‘\‘ I a .‘ '1. I s . 5 .... .o'~.:: I l . . ,‘ v 0" -‘.. I I ‘ I I .0--. I . I I ' ’ Distributions of bushbuck and reedbuck in Park W, Niger. Figure 13b. 52 a a a a. I . I X . o . d \l‘ ‘ \ Q \\ o 0‘0 ‘0 o O O \ I’-" I ‘ 0‘0 C o o o O 0".“ 0'. o O I O \ 00’ I-‘ Q o 0' o o o o o a II o «I. o o r. I'lL‘ 0' a o ’0 I o on o o \I If I r ss- 0 " I o O O o \ II o o o 0“. o I III s I-’ I, O O O I O O 0 O I o 0 II 0 o .I ’o-“’ ‘- .0 . ( . O O . . . . O I O O I 0 'IO 0 o o 0 0'0 0 o O o O O Q o no. \ o o 0 o o o o o I'.f‘ 0 J CI 0 o o c". o o o o b o o o I". o a I I o o ¥\ollo o o o o o .IC‘H \gio a. 0 fl”. 0 J'I’o o o o'r'o'e\ o o o \o o ”’0 o o 0". o o o ’ o o 0‘ s s s O O O O o o o O a I ‘ o O V‘O \ 0“ o o o o o o o o 0‘. o o s s 0’. o o \o o o f"lI. 0 o o \ I o 0 0‘0 0 o I o o o. o o o \ s ‘ c C; . . . .. . . . .\I. W o I o o 0‘ o o o o 0 Q . thIHIHII . . . o . O l C 0“. O O O 0“. I,“ O o 0’ o o o‘A o o 00"- 0 O o O O O O O (0‘“ . O C C C . 0“ ‘0‘“ O ~‘1‘. O I O O “""\O O O I O O O I O I OIIOI o “o o I’. O O o o O. O loOIoOlo 0 0 II 0 o " \\\ 10'0"“! I \\\\ s \I’l Is a II “-“ Q‘I \\ s ‘\-\“‘O n I \ .I ll \ o O I 0 hi. 9 o O I O ‘ O I 0 fi ‘ ‘ - o o 5 0 d I o ‘ o . . ..~ . . .. ..I.III . o; . .I . . . o \ o\\ I. o 0’ I. o o o o”- o o o\ o\o :4. o o o o o o o o o o o \ \ ll 0 \ o o o o. o o O o o 0 o \I O \ O O O ’ ”‘0’ O O O \ JoIIIVIV . \ . .X. . . .s... . . V o u o a o o. 0” o\ 0 Q0 0 O O ‘0' o " x .. \ Distributions of buffalo and elephant in Park W, Niger. Figure 14. 53 Table 5. Selectivity indices of vegetation types of animals encountered during the censuses. A value greater than 1.0 indicates preference, and less than 1.0, partial or total avoidance. Riparian Riparian Riparian Upland Upland Species Grassland Forest Woodland Woodland Shrubland Grassland Kob 3.28 2.18 2.53 0.98 0.80 0.00 Waterbuck 0.20 0.00 4.04 1.94 0.00 0.00 Roan 0.00 0.00 3.39 1.64 0.22 3.45 Hartebeest 0.00 0.00 8.09 0.79 0.15 0.00 Buffalo 0.00 0.10 0.46 2.32 0.28 0.00 Elephant 0.00 2.33 0.48 1.96 0.48 0.00 Warthog 9.53 1.48 1.04 1.69 0.52 ' 1.59 Oribi 0.00 0.00 0.69 1.40 0.78 0.00 Grimm's Duiker 0.00 0.00 0.26 0.62 1.36 . 0.87 Bushbuck 34.50 54.90 4.77 0.33 0.28 0.00 Reedbuck 224.10 3.25 5.12 0.63 0.00 0.00 54 Figure 15. Percentages of animal groups observed in low, moderate and high density vegetation during the 1976, 1977 and 1978 line transect counts in Park W, Niger. 95!?5! 10W MODEIAI'E HIGH [00 55 IIIIIIIIII filiflkidfiidiidiflV' WAHHOG lllllllllllllll 56?5!5525€?' IEEDIUCK illlllllll 5¢FEZF" IIIIIIIIIIIIIIIIII 36’ GIIM M's DUIKE. IUSHIUC I llllllllllllllll 5195l9§25625" OOIII llllllllllllll 55255254?’ ElE'HANI lllllllllllllllll 47569519' IUffAlO lllllllllllllllllllll Si?¢?5¢9525¢95¢952§d¥' HAI'EIEESI IIIIIIIIIIIIIIIllllllllll 4562569525¢254254957' IOAN lllllllllllllllllllll 5Z9!!5¢25¢95I95!9525€?’ WAIEIIUCK Illlllllllll § 1569525695Z95¢9€7' on. O ‘0 F U'I N sdnoifi go saSenuaoJaa 56 Hunting and trapping Hunting and trapping (snaring) of animals, though illegal in the park, frequently occurred along the park's perimeter and some- times also in the interior. According to park wardens all species were affected, but elephants, buffaloes and the larger antelopes were the most soughteafter. Hunting was observed to have a profound effect on elephants. Following the wounding or death of an elephant, the remaining in- dividuals or herds usually vacated the vicinity for a period. Popu- lations of large mammals were noticably reduced where hunters and trappers had easy access, and where frequent patrols were not possible (Fig. 16). In prime habitats along the Niger and lower Mekrou Rivers, for example, neither buffaloes nor elephants were observed during the entire study period. Livestock Livestock, mainly cattle and sheep, were commonly found along the Tapoa and Niger Rivers (Fig. 16) and less commonly in the in- terior of the park. The park was readily accessible to herders and their animals, and it contained attractive forage in an otherwise heavily-grazed region. Where villages occurred adjacent to the park, livestock could be found nearby in the park throughout the year. Along the Niger River, the heaviest livestock grazing period was the mid-to-late dry season when forage and water became scarce outside the park. An estimated 3,000 head were present during the. February, 1977 aerial survey. Some sections along the Niger River 57 Livestock distribution ‘3 Q a u + Evidence of illegal hunting \u activities I. Figure 16. Approximate dry season distributions of livestock and locations of hunting incidences observed in Park W, Niger. 58 were grazed to the extent that soils were heavily trampled and left nearly devoid of vegetation. In all areas where both livestock grazing and hunting-trapping activities occurred, large mammals were virtually absent. Water The distributions of most large mammals appeared to be affected by water availability, but it was not always clear whether water, or the vegetation associated with water most-directly influenced animal distributions. Field observations indicated that all species except warthogs and Grimm's duikers drank water on a frequent basis. Water dependency was important in determining distributions of species associated with riparian habitas, kobs, waterbucks, reed- bucks and bushbucks. The seasonal streams and most of the Tapoa River contained no_water at the time of most censuses, and therefore, the occurrence of riparian species could be expected only along streams containing water or near waterholes. The degree to which all species required water strongly influenced their distributions, and consequently, pOpulation estimates. A measure of the relationship between animals and water was obtained from the line transect data. Such transects were established perpendicular to streams. Since animal locations along transects were recorded, animal distances from known water sources could be plotted. For the four riparian species, numbers of observations declined rapidly as distance from water increased (Fig. 17). Approxi- mately 90% of kob, bushbuck and reedbuck sightings were within 0.5 km of water. Hartebeests, buffaloes and oribis were also commonly 59 no» no: " l lLl . . ‘ . W‘1[.IUC“ 5 “llllllllll111 l L. 1 . IIISIIIIICI l.-. . , . IIEDIUCI Sp llLLll L 1 1 85 1.0 1.5 2.0 2.5 3.0 DISTANCE FROM WATER Figure 17. Numbers of observations of kobs, waterbucks, bushbucks and reedbucks made between a watersource and 3.0 km during foot transect counts from 1976-1978 in Park W, Niger. 6O encountered near water, though they were less restricted by water availability than the four riparian species. Roans, elephants, warthogs and Grimm's duikers were more evenly distributed along the transects (Fig. 18). This was expected for warthogs and Grimm's duikers since those two species can exist without free-standing water. Elephants and roans, though frequently seen at water, were apparently less likely to remain nearby after watering. Elephant and roan groups were observed as far as 8 km from water. Bushbucks and reedbucks, though usually found within a few hundred meters of water, were not clearly water-dependent. Several sightings were made at considerable distances from water. Although other investigators have found these species to be in association with water (Odendaal and Bigalke 1979; Wilson and Child 1964; Holsworth 1972), it was not obvious in Park W whether water or vegetation restricted their distributions. Schoen (1971) showed that both species have little physiological adaptations to heat stress. He did not examine their water dependency, but it may be that they can exist for short periods without moisture. Fire The importance of fire in influencing animal distribution is probably less than that of vegetation and water, but all species exhibited tendencies to prefer burned or unburned areas. Because visibility was greater in burned areas and because vegetative types were unequally affected by fire, it was difficult to establish unbiased patterns of preference or avoidance for burned areas. Figure 18. 61 Numbers of observations of 7 large mammal species at 8 km intervals between a watersource and 4.0 km during foot transect counts from 1976—1978 in Park W, Niger. r‘v- t J Ibo... N|.u.'D(V '—~ LI!” (lelncv Numbers of Observations 62 101 ROAN 51 1 l l 1 I 1 4 10* HAITEIEEST y l l A 1 L j 10‘ M BUFFALO I 1 l 1 1 10* a I ELEPHANT L 1 I 1 1 1 101 5+ I O RIII 7 1 L 1 l l l J 10‘ GIIMM'S owns: 51 1 1 1 l 1 1 4 10* 5‘ WARIHOG I 1 l 1 1 . 1 0.5 1.0 1.5 2.0 2 5 3.0 3.5 4.0 63' Yet when percentages of observations were compared with total areas burned each year, certain patterns emerged. Several species were consistently observed in burned areas in approximately the same proportions as the total area burned, whereas other species were found in greater or lesser proportions (Table 6). Species such as oribi and hartebeest evidently were attracted to the green flush of perennial grasses which occurred after burning whereas bushbuck and reedbuck sought unburned areas. In areas burned during the mid-dry season, herbaceous vegetation was almost totally consumed and the green flush was minimal. These areas were mostly avoided by animals. For later use in estimating the population sizes of riparian species, their presence or absence along all streams was recorded. Kobs and waterbucks were mainly restricted to the Niger, Mekrou and Tapoa Rivers, whereas buckbucks and reedbucks also were found along many of the small seasonal streams (Table 7). Nearly the entire distance of each stream had been visited during the study, yet bushbucks and reedbucks were not often seen. It is questionable whether these species were indeed absent. They were secretive during the day and flush only when closely approached. They may have been missed. Kobs and waterbucks, conversely, were quite visible and their distributions were more easily verified. Aerial Counts During aerial counts, attempts were made at counting all large mammal species. But because of difficulties in spotting the 64 Table 6. Percentages of the total vegetation burned and percentages of animals occurring in burned vegetation in Park W, Niger. 1976 1977 1978 Percentage of .gggetation burned 68% 76% 71% Species Kob 68 73 81 Waterbuck 58 77 80 Roan 88 83 81 Hartebeest 88 82 94 Buffalo 55 73 68 Elephant 33 48 36 Oribi 93 96 88 Warthog 83 87 72 Grimm's duiker 63- 81 82 Bushbuck 38 27 46 Reedbuck 35 43 44 Table 7. Distributions of riparian species along streams in Park W, Niger, as determined from ground surveys in 1976, 1977 and 1978. Stream Total kilometers Estimated kilometers occupied Kob Waterbuck Bushbuck Reedbuck Mekrou Niger Tapoa Dyerikomoso Bata Nyafarou Gomandi Diamonpinga Ribs Tyeri Fouanou Kibatyerou Bossegata Gorou Boguel Bonkogou Hari Kwara Anana Doundou Kidyoapienga Kargaougwa Tyeri Kirimkouandi ernmoana Meydyaga Samboanli Soanda Otem Fouanou Layar Gorou Moussiemou Tyalkoey Borofwanou Ousmandyoari Dyodyonga Ouskwafwanou Filimaze Mamasse Gourou Tapoa Gorge Totals 141 73 78 HH bomO‘J-‘m H OQO‘U‘O‘O@®G\\JUI\OUJUIGJH\OLn-L\J>w N lmwoxsoboo 514 141 15 19 N I 1.2qu wHNwt-‘l I ID—‘F-‘l 141 5 19 ? 2 I “WU-2| UHNO‘NI IHHI 141' 73 78 Hr—H—I1—-HI-H—tr—o1-Hbemt—H—IHHHHO‘NHHHHHHHHHHH 344 141 8+ I NbHNNWI le-‘(DIF-‘II-‘U-‘l—‘mlmi-‘l - Species absent ? Species present but not on a regular basis -+ Not observed but likely occurs 66 smaller antelOpes, only counts of elephants, buffaloes, roans, hartebeests, waterbucks and kobs were included. On the basis of information obtained during ground surveys, the park was divided into five strata (Fig. 19). Strata 2 and 4 corresponded to the study area which was intensively sampled by foot and roadside counts. The results of the aerial survey (Tables 8 and 9) reflected those factors which influence animal distributions. Strata 1 and 3, for example, which were most accessible to herders and hunter- trappers, had considerably lower density estimates of elephants than other starta. And in stratum 3, which is bordered by the Niger River, animals were mainly found along the lower Mekrou River. Separate estimates were calculated for buffaloes in bachelor male groups and those in breeding herds. Bachelor males occurred in groups of 1 to 11, whereas breeding herds ranged in size from 12 to 160. Density estimates for breeding herds represented group densities. Population estimates can be obtained by multiplying group density by the mean group size, 40. As a check on whether smaller groups were more likely than large groups to be overlooked by observers, a comparison was made with group sizes determined from ground counts made during the same time period. Comparisons between small, intermediate and large groups revealed that for all species differences between frequencies of group sizes were not significant (Table 10). 67 IPPEI lllIl Figure 19. Designated strata used to estimate animal densities from the 1977 aerial transects in Park W, Niger. 68 Table 8. Density estimates of large mammals in Park W from the park-wide aerial census. Densities are in numbers/kmz. Total Strata Average Population Species 1 2 3 4 5 Density, Estimate Kob 0.000 0.000 0.021 0.089 0.075 0.047 101 i_68 Waterbuck 0.000 0.164 0.146 0.270 0.439 0.177 402 i 194 Roan 0.000 0.069 0.020 0.412 0.312 0.120 286 :_177 Hartebeest 0.173 0.385 0.043 0.081 0.015 0.123 262 i 152 Buffalo (T) 0.000 0.027 0.021 0.019 0.015 0.020 43 i, 27 Buffalo (B) 0.057 0.069 0.065 0.358 0.222 0.141 295 i 145 Elephant 0.056 0.290 0.020 1.419 0.733 0.359 768 i_266 T - Breeding herds of buffalo. B 8 Bachelor herds. Estimates are for herd density. 69 Table 9. Density estimates of large mammals in the central study area from aerial transect counts. Strata Total Population Species 1 2 Density, Estimate Kob 1.680 .724 1.100 53 1:40 Waterbuck 0.544 .800 0.972 103 :L66 Roan 0.060 .571 0.259 141 1:87 Hartebeest 0.340 .090 0.244 133 :1146 Buffalo (T) 0.027 .019 0.024 13;: 11 Buffalo (B) 0.069 .2110 0.200 109 i 48 Elephant 0.290 .429 0.728 397 t 144 T - Breeding herds of buffalo. Estimates for for herd density 3 a Bachelor herds 70 Table 10. Comparisons of group sizes as determined from ground and aerial counts during February, 1977, in Park W, Niger. Values re- present numbers of observations in each group size class. Group sizes Chi-square Species 1 2-3 4-6 7+ values Kob Ground 22 29 5 5 Aerial 6 7 4 0 2.70 ns Waterbuck Ground 7 18 14 5 Aerial 7 11 6 4 0.84 ns Roan Ground 21 5 7 15 Aerial 12 2 2 4 1.50 ns Hartebeest Ground 4 6 5 5 Aerial 1 5 4 1 1.18 ns Buffalo Ground 4 5 4 7 Aerial 10 6 7 15 1.25 ns Elephant Ground 2 1 4 9 Aerial 3 2 6 15 0.00 ns Warthog Ground 5 18 6 0 Aerial 1 5 3 0 0.67 ns 71 Foot transect counts Results of the study area and firk-wide surveys During the preliminary foot transect survey in the central study area, only 8 of 14 large mammal species were observed (Table 11). Because of the small sample sizes, variances and coefficients of variation were large (Table 12). Required sample sizes projected from this survey were extremely large, even at the 20% coefficient of variation level. Subsequent observations in the park indicated that topi, red-fronted gazelle and red-flanked duiker occurred in very low numbers. They were omitted from further consideration in this study. During the 1977 survey, although sampling efforts were doubled and all species were observed, the numbers of observations of each species were still small (Table 11). In spite of the large number of transects, required sample sizes were unrealistically large. The positioning of transects parallel to streams resulted in a relatively insignificant increase in sightings of riparian species. In 1978, the study area was nearly saturated with foot transects, but numbers of observations were still small for most species (Table 11). Several factors were responsible for the few encounters. First, relative densities of animals were low, especially in upland woodlands and shrublands. Second, the uneven distribution of animals affected the sampling intensity of the different species. Since some species were widely distributed and others clumped near water, efforts to obtain estimates for all species required that all areas be sampled and not just the high density areas. Third, visibilities in all vegetation types were limited over most of the park. In many areas, observers could see no more than 50 m and often less. 72 2 m 2 m 2 a month: m q N N 1 o mosnpoom «a 0H q c N a xosnnasm AH 0H m m N N umxasp m.eaauu NH N m o a N inane 3 .V 3 N 1 o 0:283 N a o m . MN m ofimumom NN a o a 1 o ammonouum: mg m Nfi 0 ON m seem ofi m N m CH m xosnuoums o~ 0 NH m o N pox pm>uomno maoaum>uomno vo>uomno macaum>ummno vo>uomno adowum>uomno mowoomm .oz Hmuoa mo usaasz .oz Hmuoe mo Honasz .oz Hmuoh mo nonasz mmmg humfi onmg .uowaz .3 xumm a“ noun husum Hauuaoo any a“ mucsoo uommcwuu uo0w mnmd new NN¢~ .onm~ ecu magnum mama maowum>uouno mo muonasz .- manna 73 >0>usm 0:0 wcwu3p v0>uomno moo: «x NON mo >0 0 you aumcoa uuomcmuu vmuusvou n A NON mo >0 0 you mean manamm poufiswmu 1 mm coauowum> mo 0:0H0awu0o0 1 >0 Nax\mu0na:: cw 0N xuwmooak mNm NN o.~q oHN.o qu w N.mN HHN.o mmo om c.mm mom.o monuumz cm NH N.mm mm~.~ Nome Hm m.o~H OON.H « « xosnwmmm Nn o N.mH OmN.N “Non mm m.ow ooo.H «mag «N m.mm cam.o Mosnnmsm «mmH Hm ¢.¢m NNm.o «we ma m.0 zuwmamn A mm >0 .Nuwmcma A an >0 «huamC0a mofiommw mmma mmma chad .uowaz .3 gumm cw msma can snag .onmfi a“ noun meson Hmuuao0 050 :a mums mucsoo uoomcmuu uoow you woman madamm.vouwsuou can coauowun> mo musowoammooo .moumaaumo huamcon .N~ manna 74 Fourth, individuals of most species tended to occur in groups. Encounters with groups were less likely than if animals occurred singly. The combination of these four factors translated into low probabilities of encounters with groups. Though numbers of observations were small, groups observed per kilometer walked were consistent between years. Density esti- mates, therefore, were relatively similar for the three years. The results of the 1978 park wide survey were similar to those in the central study area with respect to distance and angle measures and density estimates. The number of groups counted were roughly proportional to the distances walked. The'number of observations of any species, though, did not exceed 36 (Table 13). The recommended minimum number of observations for line transect estimators is 40 (Burnham et al. 1980). This figure was impossible to attain for many species unless the park had been saturated with transects. Furthermore, for species which occurred in large groups such as roans and hartebeests, the majority of the population would need to be counted. Because the number of observations for any one survey was small, observations were pooled into a single sample for the purpose of evaluating estimators (Table 14). The objective was to detect patterns and relationships between estimators with a larger data set, because estimators perform better with larger numbers of observations. Following these analyses, individual surveys were reviewed to determine whether general patterns found for larger data sets held true for the smaller number of observations encountered during actual surveys. 75 Table 13. Results of the 1978 park-wide foot transect count in Park W, Niger. Number of Total No. Species observations observed Density_ CV 33' L Rob 25 72 1.240 26.3 114 146 Waterbuck 17 64 1.402 38.4 181 283 Roan 19 46 0.231 39.6 176 2046 Hartebeest 8 51 0.025 19.5 - - Buffalo 10 19 0.120 42.6 86 2300 Elephant 6 51 0.057 43.6 208 1766 Oribi 21 38 0.310 27.4 90 1014 Grimm's duiker 23 25 0.845 31.2 63 1390 Bushbuck 17 23 3.151 10.9 - - Reedbuck 20 30 4.842 41.6 112 341 Warthog 36 92 0.449 42.3 411 3408 Density is in km2 cv - coefficient of variation in percent 33 8 required sample size for a 20% coefficient of variation L a required transect length for a 20% cv Table 14. Basic measures of the combined foot transect counts of 1976, Distances are in meters. 1977, and 1978 in Park W, Niger. Mean Mean Mean Sample perpendicular disappearing sighting Mean Species size distance distance distance angle Kob 63 30.04* 99.70 57.46 33.37 Waterbuck 61 30.15 96.41 71.64 27.30 Roan 64 37.52 101.60 83.08 30.84 Hartebeest 27 44.10 115.72 80.40 35.19 Buffalo 60 29.15 92.40 58.97 33.07 Elephant 12 39.53 115.00 73.50 34.58 Oribi 70 32.06 95.04 66.77 30.14 Grimm's duiker 66 12.08 48.05 23.15 34.24 Bushbuck 50 13.34 48.40 22.54 40.04 Reedbuck 50 15.30 53.14 25.40 41.28 Warthog 64 32.60 77.80 57.60 36.60 *meters 77 Evaluations of estimators A comparison of density estimates from the 18 estimators (Table 15) demonstrates, as also found by other investigators, that they may give widely differing results. Inferences about estimates of population density may vary greatly, depending on which estimator is selected. 0n closer examination of the estimators, however, certain patterns emerge. Among the estimates based on perpendicular distances, the Dasmann- Mossman and Webb estimators consistently gave the highest estimates or nearly so. The Hahn estimator, conversely, nearly always gave the lowest estimate. Several estimators typically gave estimates which were between the highest and lowest ones, including the Hemingway Normal, Quadratic, Triangular, Generalized Exponential, Polynomial, Fourier Series and all those estimators based on grOuped data. Among the radial estimators, only the Geometric and King esti- mators gave estimates which were consistently between the high and low estimates. Estimates from the Exponential estimator were always higher than other radial estimators and all perpendicular distance estimators except the Dasmann-Mossman. In general, the rank relation- ship between radial estimators was in ascending order: King<=Geometric< Hayne and Modified Hayneaom n~.N mo.m q~.m~ o~.o mm.c am.o nn.m m~.e No.0 .dxm pouwamuocmu om.c cc.m 0N.q mo.n am.m om.m Nq.m mN.N oc.¢ Nm.q NN.o unasmamaua mm.m ow.o mo.< No.o mm.m co.¢ ¢H.m mo.m mo.m mm.m mq.m 0Humupmno 03wcwamm no.3 om.u000o 300 ooaa 55.0 00.0 00.00 00.N0 05.0 00.0 00.0 00.0 00.0 00.0 00:0000 00.0 No.0 00.00 00.00 50.0 00.0 00.0 00.0 50.0 00.0 xoolueum0uo0m 00.0 00.0 N0.0 00.00 0N.0 00.0 00-0 55.0 50.0 00.0 0000mm 55.0 00.0 00.00 00.N0 05.0 00.5 00.0 00.0 00.0 05.0 000aoa00om 00.0 05.0 N0.0 00.00 00.0 00.0 00.0 0N.0 00.0 00.0 00umuum:0 00.5 N0.0 00.00 00.50 00.0 « 00.5 00.N 00.0 00.0 00.5 0mauoz 0030:0800 0000:0H0 .0muwoc:uev 00.0 N0.0 00.00 N0.N0 00.0 00.0 5N.0 00.0 00.0 N5.0 000000 H00u:om 00.0 00.00 00.0 00.0 00.0 00.0 0N.0 0N.0 No.0 N0.0 0m0SoG00om 00.0 50.0 00.0 00.0 00.0 00.0 NN.0 5N.0 N0.0 00.0 H00:0:m0uH 00.0 00.5 00.0 00.0 00.0 00.0 50.0 N0.0 00.0 00.0 00umunmac 00.0 0N.0 00.00 0N.00 05.0 « 50.0 N0.0 00.0 00.0 00.0 0000:06o0x0 0000:ou0:: .00000::uuv 000:00000 ~00:000:00000 00.0 00.0 05.0 . 0N.00 0N.0 N0.0 00.0 00.0 00.0 0N.0 00.0 0:00 No.00 N5.50 0N.50 0N.0N 00.00 50.0 00.00 00.0 00.5 00.0 00.00 0m0ucmconxm 00.N0 00.5 00.0 55.5N 00.0 50.0 00.5 00.0 00.0 00.0 N0.0 0:00: 000000oz 00.00 N0.00 N0.00 00.0N 00.0 N0.0 0N.5 00.N N5.0 00.0 00.0 000 .umcoo 0:00: 00.5 50.0 50.0 N0.00 05.0 50.0 00.0 00.0 0N.0 00.0 N0.0 00uumaomw 000:00000 000000 wo0uum3 00:0 00:0 umx0:0 00000 0:000. o0mmw:0 00000, :mom 00:0 0oM muoums0umm 10000 100:0 0.350u0 1000 10000: 1u0003 0.0.uco00 .m0 00000 80 As an aid for evaluation, density estimates were ranked from 1, the lowest estimate, to the highest (Table 16). Though this did not necessarily reveal information concerning bias, it did aid in exposing patterns among estimators. For each species, there was a wide range of values. There also tended to be a group of estimates with similar values and which were approximately between the highest and lowest values. Examples of this range in values have been shown for buffalo, waterbuck and kob by plotting frequency histograms of density estimates (Fig. 20). For those species, there is a clumping of estimates near some central value and several estimates which are somewhat higher or lower. A plot of density estimates and con- fidence limits for kob further illustrates this range of values (Fig. 21). The lowest and highest values are markedly below and above the cluster of moderate values. Unfortunately, it could not be assumed that the median value had the least bias. In reality, none or several of the values between the highest and lowest may have relatively small bias. Based on these results, estimators could be further categorized to illustrate relationships between density estimates. Values of low (L), low to moderate (L-M), moderate (M), moderate to high (M—H) and high (H) were assigned to estimates based on their values rela- tive to other estimates (Table 17). It is evident from Table 17 that not all estimators are consis- tently low, moderate or high. Among estimators based on ungrouped data, only the Dasmann-Mossman, Webb and Exponential estimators, are always high, the Hahn estimator always low, and the Hemingway- Normal, Generalized Exponential, Geometric and Fourier Series nearly 81 on N m: m m m m m o m m 0:00 mm: 0: 0N m: a: a: 00 N0 oN N: oN 000uamcoaxm an: a: N0 0 N: m0 m0 0: o: a: 00 0:N00 000000o= mmfi ON a: 00 0: o: 00 m: m: 00 00 .000 .umaou 0:000 mm 00 m0 O0 00 n o 0 cl N m 00000Eo00 . 000000000 000000 00 0 N H 0 0 0 m m 0 0 :00: .0000 000000000000 N0: 00 0 m: N0 N0 0: 0: 00 0: N: 000=m=00ua ea N m m o 00 N0 N :0 o0 o: 000000000 N00 o: 0 0_ o m: 0: N0 N a N0 000eoaN0om 0N 0 N a N m N o m: N N 0000000 on 0 m a N H: m c N 0 m0 xouuuoumaumnm m0 0 m a N 0 N 0 0 n a 000000 00000 000:0000 «N: 0: 00 N: m: 00 00 m: 00 ON 0: 0002 00: N: ON 00 00 ON oN 00 :N :N. a: cmammoz 0 0020000 :5 0: 0 0: m N: a m 0 m0 0: 00000m 0000000 Nm 0 0: 0 0 N N 0 a 0 N 000aoaN0om N: o: o: w 0: m m N .axm 00000mumcmo 00 w 0: m m m m N N0 N0 0 0005000000 am e 0: N N . N 0 0: N0 0: 0 000000000 N00 0 N0 N 0: 0: o: 00 m: m: 00 0050oz Nmaw=0amm :w m: 0 N0 :0 0 N: 0 0 :0 o 0000:00oaxm .um00 000:000000000 00uoH 0000003 00:0 00:0 “000:0 00000 0:000 o0000:0 00000 0000 00:0 000 0ou0a0umm 10000 1:95 m .3000 .1000 1300: 1030: 0000000 .00002 .3 0000 00 00::o0 00000000 uoow 000oo0 you 00o00a0000 0000000 0o mwa0xcmm .0: 00000 Frequency 82 V .UFFAlO I V 9.0 WATEIIUCK N 9‘ 5 KOI Figure 20. Frequencies of density estimates for buffalo, waterbuck and kob as based on the pooled foot transect data. u m 'u u o on c ”.4 '8 m _ u m * m w a _ *4 m _ H _ o — u — m S — u — m a: — 3:0 7.0 510 63 7.'o (.0 93 1010 H‘ Density (kmz) Figure 21. Density estimates and confidence limits for kob from the pooled foot transect data set in ascending order. 84 2-; z z z 274 x :14 z z A 2 mass m a m m m m m m m m m Hmauamaoaxm m m m z z x z z z z 2 .cm« umaoo mass: z z z m a z z z m.: z 2 «can: concave: z z z z z z z z 2 2-4 2 unnumEooo a. a a a a a a a A a a saw: 2 z z z z z z z z z z umaawcmfiue z z z z z z z z z z z uaumucmso z z z z z z z z z z z Hmaaoazaom z z z z z z z z z z z nmafiaam z z z z z z z z A z z xoouuuumnomnm z z z z z z z z z z z umxamx : m m m m m m a m m m ppm: : m m z m m m z = m m swammozuacmamma : z z z z z. z a z z : magnum “masses z mu: a a 2-4 a a a z z A Hmfiaoasflom z z z z z z z z z z z .axm cmuaamumamo z m.: a A z a z a z z : “maswcmaue z z a a z m z m an: an: x ofiumoumso mu: 2 2 mu: m z :1: z z z mu: Hmauoz mmawcaamz m a z z z m m a a 2 :1g Hmfiuamaoaxm mew—PMS; £059 #059 va‘Hfi—u HDHHO uflmfiq OHmmem umwmfl Cmom Juan DOM HoumEHumm Ivmmm Inmsm m.aafiuu Imam Iowan: Iuouma .uomaz .3 sham as muummcmuu uOOm yew mumv uummamuu uOOu vmaooa mzu Scum wouMEAumm zufimcmv mo mmaam> m>wumamm .m~ manna 85 always moderate. All estimators based on grouped data are consistently moderate. The relative values of the remaining estimators are con- siderably less consistent. Estimates from the Exponential (x) estimator, for example, are very low or very high for several species. The effects of truncation on density estimates varied from none to great.‘ Only the Exponential, Quadratic, Triangular, Poly- nomial, Fourier Series, Kelker, Spline and Eberhardt-Cox estimators are influenced by truncation (Gates 1981). The exponential estimator was very sensitive to truncation. The truncated estimate was usually much lower and more in-line with other estimators. The Splined, Kelker and Eberhardt-Cox estimators were virtually unaffected by truncation. Density estimates from the Fourier Series, Quadratic and Polynomial estimators increased slightly with truncation, while estimates of the Triangular estimator were decreased by a large amount. The overall effect of truncation was to raise or lower un- truncated estimates to more moderate values. Comparisons with other studies For those estimators which were consistently higher or lower than others, it was of interest to know whether they over-cnrunder- estimated population densities. Fortunately, there have been several simulation and field studies in which the population size was known (Table 18). Several estimators in those studies consistently ex- hibited negative or positive bias. The Webb and Exponential estimators, which yielded the highest estimates from the pooled data, were found in other studies to overestimate true population sizes. The King estimator usually gave low estimates in this study Table 18. Tendencies of estimators toward positive or negative bias as determined from studies on populations of known size. Literature Source Estimator 1 2 4 5 6 7 Exponential, Gamma + + + + Hemingway Normal 0 Quadratic Generalized Exponential 0 Polynomial - Fourier Series Dasmann and Mossman - + Webb + + + Kelker - 0 0,+ Hahn - + Geometric ' + Hayne +,0 Exponential, Gamma + + King ‘ ‘ ' 1. Dasmann and Mossman (1962) - a negative bias 2. Hirst (1969) 0 - small bias, either direction 3. Burnham et a1. (1980) + = positive bias 4. Evans (1975) S. Robinette et al. (1974) 6. Gates (1969) 7. Quinn (1977) 87 and in several independent investigations was found to be negatively biased. Most other estimators examined displayed little bias or were not consistent in the direction of bias. The prediction by Kranz (1973) and the results of a field study by Evans (1975) indicated that the Hahn procedure overestimated densities were not confirmed by this study. For each species in Park W, the Hahn estimator gave estimates which were below all others, often by a considerable amount. Goodness-of-fit tests to detection functions A basic requirement for parametric estimators is that the detection function of perpendicular or radial distances closely match that of a known distribution. A calculated value that is larger than the suprama (critical value) indicates that the observed distribution significantly differs from the expected. If the under- lying distribution is significantly different from the expected, the estimator based on that expected distribution may be biased. Goodness-of-fit tests applied to the detection functions re- vealed that for each species there were several distributions which were not significantly different from the detection function (Table 19). For perpendicular distances, fitting the exponential distribution with a - 1.0. In several cases, it provided the best fit. Values for the half-normal distribution were all well below the suprama for each species, indicating that the detection functions were all approximately half-normal. Fits to the generalized ex- ponential distribution were not significantly different for seven species, but highly significantly for four others. These poor fits, 88 .Ho>oH monocumaoo ch msu um uanHmwcwwm « Hug. «cg. «cg. cod. «cg. cdq. mud. new. and. cma. mn~.. coauouwuc umme «cca. «caq. cac. cmc. mma. ccc. «mom. «cc. «mum. «chm. ccc. Hmfiaocmaom {cc~. «cue. mmc. ccc. NQH. «cmc. «mmm. *cNN. «cmN. «end. «mum. afiumucmsc . mummu uwm mo mmmccooww uguumemquIcoz cmc. ccH. find. Ncfi. mac. ccfi. «no. mcg. mad. cc“. «cc. adamaum> m maamc ccc. «ccc. «ccc. ccc. «no. Ncg. ccc. «mcc. «ccm. «no. ccc. .axw coufiamumcmc ccc. «cNN. cc“. «mg. «mum. mac. nfid. ccm. sacm. uma. ama. A u m .maEmc acc. aafi. «fine. sumo. «NRA. kmcm. «mam. «ccc.~ NH“. cda. una. umaawcmwue ccfi. mod. sea. cad. acc. cmfi. ccc. NMN. cud. csc. ccd. Hmauoznmamm muoumsfiumm umaauficamauom ccc. know. end. Hmc. ch. mom. «cc. cqm. «com. «cum. and. N n m .maamc mmc. acc. cmc. ncc. ccc. mam. mwa. cmfi. Ncc. «ccc. «cc. manmwum> m .masmc mucumafiumo Howcmm wonuumz 30:: 30:3 umxfisc wnfiuc uaonm‘ oamwwam ummmn zoom xoan cox mcoauanauumfic .6me 1:95 m .EfiEc Imam Imuumm Iuoumz .mumc uommcmuu uOOm cmaooa you mcowuanfiuumwc cu mummu uwm mo mmoscooc .c~ canoe 89 however, may reflect problems encountered with the program LINETRAN rather than the data. Tests to the Triangular distribution indi- cated poor fits in five of the 11 species. The usefulness of the Quadratic and Polynomial estimators was indicated by goodness-of-fit tests against their respective equations. Values for the quadratic distribution were non-significant for three of the 11 Species, though several of these had values only slightly above the suprama. Similarly, fits to the polynomial distribution were non-significant for only five of the 11 species. Goodness-of-fit tests with radial distances indicated that distributions for all species were exponential when thecxa variable was used. Forcx= 1.0, fits to four of the Species were significantly different from the K-S criterion. V Goodness-of-fit tests were useful for explaining the variabi- lity of some estimators such as the Triangular and Quadratic. The wide range of density estimates for the Triangular estimator, for example, was probably due to the lack of triangularity of the de— tection function. For hartebeest, this estimator yielded an esti- mate considerably higher than all others. The goodness-of-fit test to the triangular distribution for hartebeest was significantly different from the critical value. Similar variability in density estimates was found for Grimm‘s duiker and bushbuck when poor fits were obtained for the triangular distribution. When goodness-of- fit tests to the triangular were non-significant, as with warthog, estimates were moderate. 90 These results reflected the general pattern for many estimators, in that when the goodness-cf-fit tests indicated close agreements, the estimator based on that distribution tended to yield moderate density estimates. The value of goodness-of-fit tests in selecting a single best parametric estimator appeared to be limited. For each species, usually several distributions were not signiffcantly different from the detection function of a species. With kob, for example, fits to the half-normal, triangular, exponential and generalized expo- nential distributions were all below the test criterion. The estimators based on these distributions, however, gave different estimates ranging from 5.50 to 7.63/km2. The fit to the exponential distribution for radial distances and the polynomial also gave non- significant results. While estimates from all those estimators were moderate in ranking and between the highest and lowest estimates, certainly not all of these estimates are unbiased. These estimates were relatively clOse to eachother, but different enough to be of ecological importance. Thus, the value of goodness-of-fit tests as a basis for selecting an estimator is questionable. This is especially true for the Exponential estimator for radial distances, which was higher than most other estimators whether or not the detection function was exponential. It could only be concluded that if a goodness of fit tests indicates a good fit, the estimator based on that distribution will give a moderate but not necessarily unbiased estimate. Tests of angle measures Goodness-of-fit tests to the Cosine 9 distributions were significant for all species except roan (Table 20), indicating that angle measures were not made uniformly over the sighting radius. This may be attributed to observer's methods of searching for animals along the transect. They concentrated on the area directly in front of them. If so, fewer observations would be made at the larger angles. Table 20. Values for tests to determine the applicability of radial estimators for pooled foot transect data in Park W, Niger. Tests Cosine Critical Theta E(G) - 32.7 E(sin 9)==0.5 Species value: 12.59 1.96 1.96 Kob 24.67** 0.24 1.38 Waterbuck 24.02** 1.59 1.12 Roan 5.59 0.69 0.35 Hartebeest * 0.60 1.37 Buffalo 23.60** 0.13 1.23 Elephant * 0.30 0.81 Oribi 19.87** 0.99 1.82 Grimm's duiker 46.39** 0.47 1.76 Bushbuck 19.47** 2.41** 3.51** Reedbuck 23.9** 2.81** 3.91** Warthog l3.96** 1.45 2.67** *Too few observations were available to fit the Cosine Theta distribution. ** Significant at the 952 level. 92 Despite the few observations made at the larger angles, mean sighting angles were clOse to the theoretical 32.7o except for reedbuck and bushbuck (Table 20). Similarly, the test for whether the sin 9 = 0.5, was significant for only bushbuck, reedbuck and warghog. These results indicate that radial estiamtors are useful for most species. Hahn estimator Compared to other estimators, the Hahn consistently yielded estimates which were low (See Table 15). In most cases, those estimates were 25% to 50% lower than moderate ones and usually 2 to 3 times lower than the highest estimates. The Hahn estimtor was always ranked lower than the King estimator. The only instances in which the Hahn was not the absolute lowest was when other estimates, usua usually those from the exponential (x), were completely out-of-line with all others. These results were in direct contrast with findings in other studies. Evans (1975), working with white-tailed deer in Texas, reported that both in theory (as found by Kranz, unplublished thesis) and in practice, the Hahn mehtod overestimated population densities. Hirst (1969) found the Hahn method to yield nearly unbiased estimates of a blusbok (Damaliscus dorcas) in South Africa. Other investigators (Lamprey 1964, Sihvonen 1977, Van Lavieren and Bosch 1977) felt that disappearing distances gave reliable results. 93 Comparisons between the King and Hahn estimators in Sihvonin's study on antelopes in Upper Volta revealed that the Hahn estimator was always lower than that of King. An examination of diaappearing distances in thsi study, however, indicated that the Hahn method, as applied here, was subject to several biases which will be discussed below. Comparisons of frequency distributions For the Hahn estomator to have yielded unbiased estimates, all animals between the observer and the disappearing distance should be detected. With the live populations of animals, it was not possible to directly test whether or not animals were missed. An examination of frequency histograms of perpendicular, radial and disappearing distances of each species, though was informative. For each species, there were marked differences between the three histograms (Fig. 22). Perpen- dicular distances at which the animals were seen declined rapidly as distances from the transect line increased. Apparently, fewer animals were seen at the further distances. Frequencies of disappearing distances, by contrase, were often the highest at approximately the maximum perpendicular distances, while radial distance frequencies usually peaked somewhere between the two. These results imply that disappearing distances overestimated the area in which all animals could be seen, and in app probability, underestimated group densities. his discrepency between perpendicular and disappearing distances was especially large for bushbuck, reedbuck and Grimm's duiker. 94 'AIIIOO Fr‘ L53:- ‘ _- _l-—l--r—1 ' ‘ j uuuuut ' "UN“ "'"‘ F— . FREQUENCY "'""'"r— wuuo uncut: l . ItI'IAN' IIIIOUCI D O M .—.. u I. no no no loo 0 U20 onsunc: cussesm) ousuuce cusseshn) Figure 22. Comparisons between perpendicular (P), radial (R), and disappearing (D) distances from pooled foot transect data. 95 There are several possible explanations for the scarcity of detection at the longer disappearing distances. First, it was noticably more difficult to Spot animals as distances from the transect line increased. Vegetation usually did not abruptly conceal animals. Instead, visibility gradually declined as the distance and amount of obstructing vegetation increased. At the longer distances, it was often possible to see only parts of animals. Under those circumstances, even an experienced observer might miss such an animal while scanning the.vegetation. When the observer was watching animals disappear and thus knew the animal was present, the observer might have con- sidered that animal to be easily observable. It was quite possible that disappearing distances overestimated the effective area because it is easier to follow a moving animal through the brush than to spot it at that same distance. A second factor was that of response behavior. Some species ‘may have used Open vegetation as escape cover, and so were visible at a greater-than-average distances. Thirdly, habitat preferences ’may have distorted the.mean disappearing distances. The vegetation in which animals occurred most often may not have been representative of their visibilities in the average vegetation type. This appeared to have been true for waterbucks and oribi which avoided dense vegetation. Possibly, bias due to this factor was not large, however, since disappearing distances of the larger mammals were similar to those of smaller species even though their preferred habitats differed. A fourth factor involved the manner in which observers scanned vegetation for animals. Ideally, the two observers on foot transects 96 should have scanned an area from the transect line to the point of ‘maximum.visibility at 900 on both sides of the line as well as the entire area in front of them (Fig. 23). An examination of the sighting angles recorded, however, revealed that comparatively few observations werexmade between 750 and 90°. Furthermore, the mean angle should have.been near 45° if the entire area had been scanned equally well. Instead, most mean angles were considerably below 45°, indicating that sighting efforts were directed more toward the central portion of the transect than the sides. A fifth.factor was fire. Approximately two-thirds of the park was burned annually, and most species demonstrated either a preference for or an avoidance of burned areas (see Table 6). Visibilities in burned areas were considerably greater than those in unburned vege- tation.(Iable.21). 'As a result, mean visibilities were based not only on relative proportions of habitat use, but also the proportions of burned areas traversed, and thus, may have been further biased. Biases from these five factors was minimized to some extent in other studies (Hahn 1949, Lamprey 1964). These authors measured the.disappearing distances of an assistant who walked at right angles to the transect lines. Where a sufficient number of distances along transects were thus averaged, the total area sampled could be calcu- lated. This was also done during this study, but regrettably those data were lost while in air transit. In recalling the distance measures, however, they were.quite similar to those obtained by the actual ‘measurements of disappearing animals. It was felt that a visibility profile, as determined from disap- pearing distances of an assistant, was subject to biases from.the 97 \OIsenu Figure 23'. Sighting radius for observers when the detection of exposed animals depends on scanning the vegetation. 98 Table 21. Comparisons of mean disappearing distances in meters of species in burned and unburned vegetation during the 1976-1978 foot transect counts in Park W, Niger. Species Unburned Burned .Kob 76 90 Waterbuck 91 109 Roan 97 107 Hartebeest 92 109 Buffalo 82 110 Elephant 76 . 114 Oribi 81 101 Warthog 56 86 99 several factors discussed above. It was, for example, likely that a moving person in dense cover was easier to observe than spotting an animal at that distance. Also, as assistants moved, there was a tendency to select a "path" through the vegetation, especially when thorny shrubs were encountered. This would result in longer distance- measures, a problem which was not reported in other studies. Comparisons of distance measures for similar sized species. A common application of the Hahn method in Africa has been to make observations of Similar—sized Species, and combine the data into a common visibility profile. This has been based on the premise that the larger the.animal, the greater the distance at which it could be seen, and that animals of similar size disappeared at approximately the same distance. This was the case in this study for many Species (Table 22), but some did not fit this pattern. Elephants and oribis, the largest and smallest Species Studied for example, had nearly the same mean disappearing distance per vegetation type. This was mainly because oribis were commonly observed in clearings and open woodlands whereas elephants were often in dense vegetation and sought conceal- ment cover when detected. Large Species including roan, hartebeest, waterbuck.and buffalo also had similar profiles in woodlands and shrublands (Table 22), in Spite of their dissimilar coloration, size and habitat preferences. Correlation coefficients between animal size (shoulder height) and perpendicular, Sighting and disappearing distances indicated no significant difference.between those measures (Fig. 24). Habitat preferences undoubtedly influenced these results. Nost Species uti- lized habitats in which.visibilities were Similar. Too, the vegetation 100 .oamu oowuouowo> manu ow coaaauouoc mum: mouomumwclwawumooommwc oz « ch cad a a a a a * comammmuc canoe: cm ccH ccH am mm mca Ham mm comaosunm mm qu mm . mcH ficH «Ha ~c~ cc odomcooz uamfiap no co co cHH mod ccH cca ac comacooz amaumoam He a a a a a a no umouom oofium>fim mca a « mc~ meg mod mad NNH comflmmmuc omwumofim wonuumz aofinc \Luamaooam oamwmam umoooouumm swam xosououmz pox maze mowooow soauMuowo> .uowwz .3 xumm .oo>u cowumuowo> an mowooom Hmaama owuma woman mHHmHHEHm mo moosmumfio wcaumoooomac .NN manna 101 100 f =.sn so £004 Instalcuuuu) Figure 24. Correlations between body Size and mean perpendicular (a), sighting (b), and disappearing (c) distances for the pooled foot transect data. 102 was not stratified in a manner such that smaller animals were less visible at the further distances. In many areas, the vegetation above 1.5 m was more dense than it was near the ground, and the smaller animals could be observed at longer distances. Efficiency of estimators Comparisons of coefficients of variation (Table 23) showed consi- derable differences in variability between estimators. No estimator consistently had a low or high coefficient of variation. Park—wide survey To determine if patterns were consistent for smaller sample sizes, analyses applied to the pooled foot-transect data were performed Similarly on the results of the park-wide survey. The patterns among estimators were similar to those of the pooled data set despite the smaller sample sizes (Table 24). The Hahn estimators, as expected, generally gave the lowest density estimate and had the lowest overall ranking. The King estimator, too, consistently had low rankings. The Webb and Dasmann-Mossman estimators consistently ranked high. The Fourier Series estimators, surprisingly, tended to give low estimates rather than moderate ones as found in the pooled results. In several instances, the Fourier Series estimates were lower even than the King and Hahn results. Other notable differences involved the Quadratic and Exponential estimators which yielded some estimates that were among the highest. The Quadratic ranked even higher than the Webb estimator (Table 25). The Exponential also ranked higher than the Webb estimator and achieved the same rank as the DasmannéMossman estimator. Comparisons of percent coefficient of variation for estimators from truncated, pooled foot transect data in Park W, Niger. Table 23. Reed Bush— buck Grimm's Harte— beest Water- Warthog buck Oribi duiker Buffalo Roan buck Kob Estimator 7.5 15.2 42.2 17.3 18.1 14.9 54.1 14.8 22.0 11.1 30.4 28 Exponential 18.2 18.8 14.5 58.5 12.1 20.5 52.5 .4 12.5 Hemingway Normal Quadratic 42.1 10.8 6.0 26.3 6.1 15.0 4.3 24.4 24.3 13.1 17.3 6.8 11.1 8.2 22.4 4.3 5.3 13.5 47.6 63.6 2.0 Triangular 5.4 34.5 46.8 13.4 32.7 6.2 16.4 49.8 Generalized Exp. Polynomial 30.3 20.4 32.9 64.0 38.2 84.2 20.1 31.8 8.7 44.9 25.1 20.6 15.0 16.4 16.0 48.3 37.2 16.5 Fourier Series Kelker 2.18 55.5 29.7 10.3 15.6 31.0 32.9 28.9 20.6 19.3 36.6 27.0 53.2 9.0 43.1 3.2 3.2 14.6 58.0 47.9 30.4 10.2 43.2 Eberhardt-Cox 103 22.9 25.1 31.0 15.6 27.0 47.1 36.6 40 Splined . 11.6 42.3 44.7 18.1 13.3 10.1 45.5 34.7 22.8 Polynomial* Quadratic* Triangular* Hahn 6.2 33.8 39.8 11.0 17.3 22.6 45.3 18.7 19.2 18.6 11.9 30.8 14.0 16.6 56.2 16.2 13.8 41.4 24.9 26.4 9.7 21.8 # 18.5 5.7 11.2 14.0 6.9 26.3 15.7 24.4 25.7 68.4 22.8 16.8 30.0 15.9 13.2. Geometric 66.1- 50.3 20.9 4.4 18.8 31.2 20.7 10.1 35.9 14.7 15.3 15.9 Hayne Const. Rad. Modified Hayne Exponential** 32.1 51.7 48.3 30.8 28.2 26.0 23.6 27.5 21.2 13.8 31.7 13.9 11.9 16.1 43.1 16.8 13.5 11.2 * Based on grouped data. **Based on radial distances. # Not calculated for animals which flush. 104 .mumc osu anon» on moowum>uomoo .Nax woo mason» mo masses: a“ mum mmfiufimooc mo wanes: uooaofimmsmon m¢¢.c ~m~.m ~ec.q mec.c cam.c nmc.c c-.c Huc.c ~m~.c «ce.a n¢¢.~ wofix ccc.c ~m~.c cmq.m mmc.d cccuc cc~.c ¢-.c mm~.c mmc.c -~.~ ccm.m Hmauaooooxm mmc.~ ucq.q ncq.e mcc.~ cam.c nnc.c mmH.c cmc.c ec~.c u¢¢.~ c-.~ moan: ooHMfiooz mmm.~ ccc.m ch.m o>usm mcw3lxumo chad may Baum mousefiumo hufimcoc .om odome 105 .oumc moo osouw ou maoauo>uomoo 30m ecu mums ounces s N N a N o m m a N m waHe NH «H NH mH NH NH oH NH NH HH «H HmHucoaoaxm oN m oH NH oH a m N NH NH m maNmm umHNHuoz HN a «H NH NH oH N m «H oH m .cma .umcoo maNmm oH N a «H NH a s s OH N s oHHumaomu HHmHumac N H m H s m H N H N H can: Awowummoommficc a a NH a m NH HmHsmamHue N m HH N N oH UHsmHemao m s NH HH m a HmHaocNHoN N H m m m a umaHHam HH HH oH m N NH soouueumeumnm c a N c m a s a m a c noxaox some coosouc NH NH 0H SH SH HH m CH 0H NH nH new: aH NH NH NH NH NH a HH NH sH NH cmammozuccmammo H a N m a a N a a a N mmHHmm HoHusoa NH m NH 4 N m HH sH m m NH HmHaosNHoa «H N NH a a a a H NH s oN .axm amuHHmHmamo mH 4 NH n H H NH NH HH w OH HmHsmamHHH NH HH NH N aH N NH mH NH mH aH UHumHomso m OH 0 NH «H m m m mH a HH Hmauoz NmsmcHamm NH N mH N mH N o a a H N HaHuamaoaxm wmnuum3 303A 3039 woxwac wnwuc uamnm, Odommsm unmoo smog xuan pox Houmaaumm [comm Isaac m.aEHuc Imam nouns: Iuoum3 .uowfiz .3 xumm .ho>uSm oofizlxuoo cNmH Boom :wH: ou 30H Scum noumawumo mufimsoo mo mwofixcmm .nm odomH 106 These differences may have been a result either of small sample Sizes or of properties of the detection functions. Relative values of estimators The relative values of estimators reveal that there is more variability among density estimators for the park-wide survey than for the pooled data set (Table 26). Only the HemingwayéNormal and Geometric estimators always yield moderate estimates. As with the pooled data set, the Hahn estimator is always low and the Dasmann4Mossman, Webb and Exponential (r) estimators are always high. Other estimators, except the King and Modified Hayne, which are quite variable. There are sufficient observations to group the data for only 6 of the 11 species, and a complete evaluation of these is not possible therefore. It is noteworthy, however, that with the smaller sample Sizes of the.park—wide survey, these estimators are much leSS consistent. Goodness-of-fit tests Results of goodness-of-fit tests were Similar to those for the pooled data set except for the poor fits obtained for the quadratic and polynomial distributions (Table 27). The suprama for most species were rarely below the K—S criterion. As for the pooled data, estimators based on distributions which were not Significantly different from the assumed distribution yielded results which tended to be moderate in ranking. There were not enough observations to fit the cosine theta dis- tribution, but the tests for the sighting angles were not significant for any Species (Table 28), when determining if measured angles were significantly different from 32.7°. The test to determine whether the 107 z z z z z. x 21H 21H : zuH zuH wcHx H m m m H a H H m m H HmHuawaoaxm H z 2 ans. 2 z z. z z m z .cma bacoo oaNme m an: x m z z z z 2 an: 2 maNm: umHHHuoz z z z z z z z z z. z z oHuumaomo H H H H H H H. H H H H sea: 2 2 z z z z NmstamHHH z z z z z 2 33.395 2 A z z z z Hmaaochaom 2 H s H z z emaHHam 2 an: H H H z sounueumenmam z z z A z z meaox mu: m z m m m m m m m m HHmz mu: m m m m m m a m m : cmammozuaamsmmo H H z z x H H zuH zuH z z mmHNmm HmHusom m z z 2 H H m m H 2 H HmHaocNHoa an: m z z H H 2 H z z m .axm ooNHHmNmamo mu: mu: x 2 H H z m z z mu: NmHsmcmHHe m m z z m z m H m z m UHumHumao z z z z z z z z z z z Hmauoz NmawcHamm z m z z 2 H x H a H zuH HmHuaoaoaxm wonuum3 xoso xoao uoxfiac Hofiuc assoc. cammmsm umooo cmom soon pox Houmaaumm Icoom Iowan. m.aaauc loam nouns: lupus: .umwfiz .3 spam 6“ muoomomuu uoom new mumc ocfialxuoo cums one scum moumaaumo huamomc mo moSHm> o>wuoaom .cm odome 108 .Ho>oH ooooofioaoo Nmo moo um Homoaofiomams ocm. cow. HoH. «No. «moo. «ccc.H coo. “Homo. «HnN. Home. HmHaooxHom «cNm. «mmm. *wNm. 3o. «2:. «mooH «on. a oHN. ammN. xmoc. oHumuomoo Amuoumafiumm oauuoaoumouaozv moc. mNH. ooH. omH. mHH. mHN. mod. «NH. ch. coH. HHH. oHooHum> a assoc moc. ago. ooH. Ncc. «moo. ammo. mod. «3N. «coo. ammo. «2o. .oxm omuaaouoooc c2. «cccH NNN. « oom. «cccé «cccH 2N. «cccH «moo. « :o. aoom. c.~ a a assoc ammo. qu. Now. Now. NcH. oom. «NHc.H .mem.m chm. NmH. ammo. umaswamwue ooH. oNH. «Non. HcH. NoH. NcH. coH. cNN. ooH. ooH. coc. Hoauooloamm Aguascaoooouomv locc. cNN. :N. 2:. com. now. com. com. HoH. o3. :H. c.~ 1 d oaaoc oNc. omH. omH. HoH. NHH. oHN. cNN. omH. Hoc. NmH. mNc. oaomauw>.u.maawc HHmHemac mcoausoauumHa cmu. HNm. «cm. 1. Now. Now. cco. cmo. mom. cNN. mom. com. "coauoufiuo umoe wonuum3 xosn xooo uoxfiso «owuc Hanna canomsm umooo zoom xooo pox looom Iowan m.aEHHc imam swoon: nuouo3 .Hmez .3 spam a“ >o>uam oofialxuoo who. won scum mcouusoauumwo omuoodom cu mummy ugwlmOlmmooooow mo muaomom .NN manna 109 Table 28. Test statistics on angle measurements to determine the validity of radial estimators. Species E(O) = 32.70 E(sin Q) - 0.5 Kob 0.335* 0.116 Waterbuck 0.401* 0.470* Roan 0.383* 1.212* Hartebeest 0.237* 2.810* Buffalo 0.312* 1.137“ Elephant 0.354* 0.984* Oribi 0.529* 1.962* Grimm's duiker 0.282* 1.008* Bushbuck 0.431* 1.572* Reedbuck 0.550* 2.714* Warthog 0.535* 1.933* *Significant at the 95% confidence level 110 sin 9 equal 0.5, however, was significant for oribi, reedbuck and hartebeest, indicating that for those 3 Species in this study, radial estimators may not be appropriate. Comparisons of density estimates in the central study area Patterns in density estimates from the 1976, 1977 and 1978 surveys in the central study area were somewhat different to those for either the park-wide survey or pooled data set (Tables 29-31) Three esti- mators, the Quadratic, Triangular and Polynomial, gave estimates which were often considerably higher than other estimators, often by ten times or more. The Fourier Series estimator often gave results as low or lower than the Hahn estimator. The variability of these estimators with small sample Sizes was not surprising because a true detection function may not exist and consequently unbiased estimates of f(O) may not exist. Among the radial estimators, the sequential relationship was Similar to that of the pooled data set, but density estimates were moderate rather than high (Table 32). All estimators, however, generally followed the same ranking patterns as for the pooled data and park-wide survey. The relative values of estimators (Table 33) were fairly constant between the pooled data set, parkdwide survey and three surveys in the central Study area. The Geometric estimator was the only consistently moderate one, though the Hemingway-normal, Generalized Exponential, Fourier Series and Hayne estimators were usually moderate. Comparisons between years in the central Study area Comparisons of density estimates between the three annual surveys in the central study area (Tables 29-31) revealed that for most Species 111 emoNHm oaoaom Hanan >Ho> HOH oHonmoo no: mums muoumauumo Howeooodom vow oHumuoosc onu Boom nonmawumm « can. HNN.N HNN. «HH. NON. NNH. NNs.H oma.H maHx Nam. NNH.H oao.H NNN. son. HHs. NHN.N NHN.N HmHucmaoaxm Now. NNH.H NNN. NNH. soN. NoN. oss.H NNNeH .umm Sacco oaNmz HNN. NHN. mac. «NH. NNN. NHN. NNH.H HNN.H maNmm umHoHeoz Hoe. NNH.H HsN. NNH. NON. NNN. st.H NNN.H oHoumaomo NNN. «HN. HNN. NNH. NHN. NNH. NNN. NHN.H can: NNN.H NNo.N HoN.H sNN. NNs. NNN. NNN.H Hso.N Ham: NNN.H NNo.N NNH.H «NN. NNN. NNN. NHN.H «No.N amammoz-aamammn New. NHN.H sNN. oHH. NN.N sNN. NNN. NNN. mmHHom HmHuaoH soN.H . a . Has. NNN. NNN.N NNN.N HmHaoaNHoa NNo.H NHN.H NHN. NsN. NoN. sNN. NHN.H Noo.N .axm coNHHmHmcmu sHs.s NNN.N NNN. NHN.N NHN. NNo. NNN.NH oo.HN umHsmcmHHH . NNN.N Nmo.H . NNH.N NHN.N . « UHumHemao Hoo.H NoN.H NNN. ONN. NNN. aNN. NNN.H NHN.N HmaoozuNmamaHamm Hoo.H NNH.H NNN. NsH. HNN. NNN. NNN.H oao.N HmHusmcoaxm Nashua: ausaemam meHau HHHNo onoosm amoa soap Hos mumaHumm m.aaauc Iuoum3 .uomfiz .3 Juan ca mono ooaum Hmuucmo moo :N muosoo uommcmuu uOOm oNoH moo scum moumaaumo oufimooc .om manna 112 oumawumo so camuoo Ou Hanan OOH woman oHoamma ooc.c oNc.c omc.c ooc.c mo~.c ooo.c Hmwuo< NNN. mcc.m om~.~ mNo. coH. HcH. ch. coc. oom. moo. mom.H wcHM Nom. oHN.H ooo.m mH~.H «NH. cHH. mNH. QNH. Hmo. mmc.H mHo.N HoHuoooooxm NHm. mmo.H mmm.N ooh. omH. ooc. oNc. woc. NHm. ch.H woo.H .omm .umooc moon: Nmm. omo.N owc.m ooN. HoH. Hoc. ocH. mac. mom. Ncc.H ncm.H moon: ooHoHooz oom. omm.H mNm.o own. HoH. Hoc. ch. coc. NNN. occ.H moo.H OHuuosooc HHN. cc~.H cco.H moo. coH. omc. Noc. mnc. cHN. NNN. NNo. can: mmo. oco.m omm.m No~.H Hmm. HcH. ooH. HNc. moo. mNo.H oHo.~ ooo3 oom. coo.N coo.m wN~.H oom. ocH. mom. oNc. wan. «mo.H Hmo.m :mfimwoZuoomamoa Now. Noo. ooo.o oco. mmc. moc. omc. cmc. moH. coc.c oco. moauom Hoausom Noo. mom. coo.H~ NHH.N on.H mcH. Noo. NHN. coo. cNm.m moH.m Hmfisoooaom own. omm.m co~.N NoN. mcm. Noc. ooH. HNc. Now. mmo.H on.~ .oxm oouaaouoooc woN.H amouu o~.cH on.H ocm.o Hmm. oH~.H non. Nmm.H mHN.o omc.o uoaomcmaus coo.H omm.o mm.NH oo~.m « « oHc.H « me.m « « afiumuoosc oco. Nmo.n moo.H Now. ccm. ooc. oNH. omc. oom. Ncm.H moc.~ Hosnoz >m3w6NEo: mNo. ocH.m cNo.~ mmc.H Now. Noc. NoH. moc.. Hmo. ch.H wmm.~ Hofiuoooooxm woouuo3 xoao soon uoxH3o Hoauc Homnm. anmoam umooo omom xoao ooM HeumeHumm loomm Iowan Imam louuo: nuouo3 .uosz .3 mumm cH mono oosum Houusoo oou :H muosoo Hofiuom NNoH vow noomsmuu uOOo NNoH moo scum mmuoaaumo muamoon .cm manna 113 0&3“qu Gd GHQUn—O OH mGOHuG>H0m£O 30w OOH! ocN. Hoc.~ mwm.~ mNo.H Mam. mmH. omH. HcH. mam. oc~.~ omo.~ mcfix Hmm. Hum.m ocm.o cnc.m nun. cum. on. omH. Hon. Nm~.~ Noo.o HoHuoooooxm Hmo. cHN.N coo.o oo~.m mom. . oNH. ocH. NcH. Hmo.~ oo~.H cc~.m .omm .umooc moon: How. ocm.~ oco.m ooH.m mcm. mmH. oNH. ccc. Nmo.H How.“ ooo.~ moon: cofimfiooz omm. c-.~ cam.m oHH.N mum. moH. NoH. HcH. oHo. co~.H omo.~ Ofiuuoeooc ch. mmH.H cm~.~ NNn. cmN. NHH. Hoc. omc. oNH. mom. oNo.H com: moo. who.o mHo.m coo.N on. ooN. Hmm. NmH. Nco. nc~.~ cc.m ooo3 own. omo.m oom.o co~.m ooo. ocu. mum. omH. Noo. ooo.~ mnm.~ amamwozloomammc mmo. omo.H Hoo.N omm.H NHo. HmH. ocH. cmc. mmm. ooo. ccm.~ mmfiuom HOHusom oom.~ oNN.H cmc.- cmo.~ ocm.H cam. ocm. oNc. ooo. c-.m occ. Hoaaosoaom mom. Hon.~ Hoc.~ Noo.H mom. mNH. NcN. cua. Ncm. ch.~ mom.~ .oxw oosfiamumooc oco. HmH.N coH.m ooo.H mNo.o NoH. man. How. o~m.~ coo.c cmc. umasmomHuH omH.N NNH.m com.cH ooo.~ a ooo. * coN. con.~ « omo.m ONuouoosc ocm. -~.m mcc.m ocm. cmo. an. ooN. HNH. mam. ooo.~ umw.H Hmauoz omswoaao: mum. omm.m ~om.m mmo.~ ooo. How. ooN. NHH. cum. Hmm.m ~mn.~ HoHuomoooxm wozuum3 xooo xoso Hoxasc wowuc uooam. Oamwosm ammoo zoom soon ooM HoquHumm looom 1:95 m .guc loam Iouum: luoum3 .Hosz .3 xumm cH mono oosum Hmuucoo moo a“ oo>u=m uoomoouu uOOm cNoH moo aouo moumaaumo ouHmooc .Hm odomh 114 N N N H N o N N N N o N o N N N o N N N N N o o N N NIHN N N N NH N NH N OH N N cH HH HH HH nH NH cH N 6H NH N o NH NH HH oH HIHuadaosnu N N N N N NH HH N N N N o N o N o N NH N N cH HH 0 0H 6H N .vnn .ucaou canal HH N N N N o cH N N o N N N N N o H NH N c N o H o o N OUNII SOHHHNOI N N N N o N N o o N N N N N N N N o N N N N N N N N OHSuoloOo H H H N N N H H N N H H H N H N N H N N o N N H H N can: NH HH HH oH N N N HH HH N NH N NH cH NH HH N 0 NH HH NH 0. N NH NH NH 1403 NH NH NH NH «H H. N c. N. OH NH OH NH HH oH 6H N cH HH OH H. N. OH H. NH NH sols-ox N neon-On o N o N N o N N H H o N N H c H N o H N H H H N N H NOHuoN uoHNSON NH NH NH H H N. o. NH 0 0 9H NH HH N HH HH NH NH NH NH NH N o NH H-cheuHON o N N. N N. 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The range between the highest and lowest estimates for kob in 1978, for example was 0.030 to 5.634 /km2. This disparity between estimates was con- siderably greater than those of the park—wide survey and pooled data set. The apparent cause was small sample Sizes. The detection functions for small Samples were irregular and did not necessarily correspond to any of the assumed distributions. Fitting a polynomial or quadratic equation to a few Observations can lead to badly-biased and erratic density estimates. The rankings of estimators by species for the three annual censuses were relatively constant (see Table 32), though patterns were somewhat different than those found in larger data sets. Estimates of the Triangular and Quadratic estimators, for example, though much higher in ranking than in the pooled data set, were consistently high, not only between years, but between Species. Comparisons Of foot and aerial transect counts It was originally anticipated that aerial counts would provide standard for comparison with ground counts. The results indicate, however, that this may be true only for buffaloes and elephants. Den- sity estimates only of those two species were similar for aerial and foot transect counts (see Table 30). The aerial estimate of elephant groups fell midway between the Hahn and Dasmann-Mossman estimators, and was equal to the Hemingway-Normal, a consistently moderate estimator. 117 Aerial estimates for buffaloes also fell between the highest and lowest estimates, but was closer to the lowest one. Density estimates from aerial counts of hartebeests (see Table 30) were slightly below the Hahn estimate from the 1977 foot transect counts, but those of roans, waterbucks and kobs were considerably below it. From evidence presented earlier, it appeared that the Hahn estimator yielded underestimates Of density. Aerial counts too, therefore, underestimated densities Of the four antelope Species. The two Species for which foot and aerial estimates were Similar were the two largest and most visible from the air. It was possible, but unlikely that elephants, which mostly occurred in groups of 6 or more, were missed during aerial counts. Similarly, few buffaloes were probably missed Since they seldom occurred in cover with a dense canOpy and were mostly in groups. The four antelope Species, however, were more difficult to locate from the air, especially when they remained stationary as the aircraft passed over. It was possible that some animals were missed. The consistency between estimates from the three annual counts also may be Significant in comparing foot and aerial counts. Though variable, the lower range of ground estimates was considerably higher than the aerial counts. Thus it appears that aerial counts were useful mainly for buffaloes and elephants, but that foot transect counts were equally useful for those Species and served as a reliable general indicator Of animal density. Tests Of Assumptions An evaluationcfi the underlying assumptions Of the estimators gave a general indication of their reliability and usefulness. From this 118 study, assumptions ii and iii, the independence of individual Sightings and the avoidance Of duplicate counting appeared to have been met. Only rarely was a group of animals sighted as the result of the acti- vities of another group and those sightings could be and were excluded from the results. By plotting all observations on a map, it became apparent that no group had been counted more than once. This indicated that the minimum distance of 1 km between transects was adequate. Animals were not randomly distributed in the study area as re- quired in assumption 1, but it was felt that the systematic coverage of the Study area provided an accurate reflection of mean densities. The positioning of transects perpendicular to Streams and prOportional sampling in low and high density areas seemed to compensate for the tendency of animals to congregate near water. Those transects which were positioned parallel to Streams to obtain estimates of the riparian mammal Species, however, in all liklihOOd did not provide meaningful density estimates. They were not used for determining density estimates. Assumption iv, that each animal or group is seen in the exact position it occupied when startled, must have been violated to some degree for each species. By recording the activity of groups when first noticed, however, some measure of the validity of this assumption could be made. A large percentage of sightings of oribis, roans and Grimm's duikers was made only after groups had moved (Table 34). Only buffaloes and reedbucks tended to have all groups Spotted in their first positions. It is possible, nevertheless, that some buffalo and reedbuck groups moved away from the transect line prior to detection. The large per- centage of oribis running when first encountered reflected their wariness and the difficulty in Spotting them before they moved. Grimm's duikers, 119 om cm HH Nm cH oN No monuuo3 Ho m o No c m N xosocoom Ho m o Ho NH o NN Hosonmsm no N c No HN N cH uostc m.EEHuc cN HH NH mm mm oH cm HoHuc NN mm H o N NN NN HamnamHH NN oo oH NH O NH NN OHmmmsm oo mm NH c NH cm on umoooouum: mo oo NH o cH NN oo doom oN no N oH o co co Honououm3 no No cH cH m NH Ho ooM com Noam omme3 oOSHmamm c3ookwdeA wchoom wwaHm3 .onocmum moHooom oncomwom oouuomw oooa muH>Huo< .coom HmuOu moo mo mowmucoouoo :H mum moSHm> .uosz .3 Huwm cH who>uam uoomcmuu uoow HHo onuso :OHuoouoo Houwo monsoomou uHoou com couuoom umuHo con: mHoEHcm mo moHuH>Huo< .om oHomH 120 which usually flushed from thickets, were secretive and were observed attempting to sneak away undetected. These observations indicate not only that there were errors as a result Of movements in measurements of angles and radial distances, but also that some groups, which might have been Observable from the transect line, could have moved Off prior to detection. The high percentage of groups which ran after being encountered by an Observer also reflected the Shyness of many Species and the potential for not seeing groups (Table 34). Species which normally flushed (bushbuck, reedbuck and Grimm's duiker) characteristically sought hiding—cover after flushing. On two known occasions, bushbucks were flushed prior to being seen by the observer. They were heard moving through the brush and identified by their characteristic "bark". Undoubtedly, Other bushbucks were not detected and probably groups Of other species Similarly moved ahead Of or away from Observers prior to detection, especially when in dense cover. Because of their docile nature, it was unlikely that many kobs, waterbucks or buffaloes moved far enough to go undetected along transects. Complete accuracy in measurement, however, cannot be certain. Assumption v, that distance and angle measurements are made with- out bias, must have been violated at least to the degree that animals moved toward or away from transect lines prior to detection. For the oribis this was an important factor but for Other Species it was not believed Significant. Assumption v was also violated, however, where Observers tended to round measurements to the nearest five meters or five degrees. In this regard, the use Of rangefinders for recording distances presented difficulties in Obtaining exact readings, especially 121 where large animal groups were seen. It was not always possible to determine the center of a group when it was widely-scattered. Several other assumptions were implicit in all methods. Where animals occurred in groups of 2 or more, for example, it was assumed that the Size of the group had no effect on detection. To test this assumption, correlation coefficients were determined for relationships between group Size and distance measures (Table 35). None were found to be significant between group Size and Sighting, perpendicular or disappearing distances except for hartebeest, bushbuck and reedbuck. Significant correlations determined for bushbuck and reedbuck were caused by several Sightings Of groups Of 3 individuals at long distances. The latter correlations are not considered to be important because most individuals of these species occur singly or in groups of two. The correlation for hartebeest, too, was of questionable importance because of the small number of hartebeest groups encountered. In general, for this study it is believed that the asssumption that group Size has no effect on distance measures was met. Another assumption was that the countability or sightability of animals remained constant during the counting period. This implies that animal behavior Should not affect counts. Activity profiles for each Species, though showed that animal activity changed appreciably by time during the day (Fig. 25). During the early morning hours, most animals were active but, as temperatures increased, animals usually sought Shade or cover. Responses to rising temperatures varied from none and remaining in the Open to resting in thickets or seeking shelter in excavated holes, as with warthogs. Individuals Of some species including bushbuck, reedbuck and Grimm's duiker, normally 122 Table 35. Correlation coefficients for relationships between group Size and distance measures for the pooled foot transect data. Perpendicular Sighting Disappearing Species Distances Distances Distances Kob .011 .081 .077 Waterbuck .096 .023 .103 Roan .158 .101 .132 Hartebeest .365 4 .608* .742* Buffalo .041 .039 .068 Elephant .311 .192 . .231 Oribi .068 .115 .325 Grimm's duiker .403 .218 .057 Bushbuck .698* .592* .345 Reedbuck .485* .396 .187 Warthog .024 .054 .092 *Significant at the 95% level. 123 100 K00 WAYEIIUCK EGAN HAIYEIEESI’ :9 « " NW 0) H a: 3 IUFFALO t: m 2 H ‘5 m ELEPHANT u... 0 I 2’. cu OIIII u t: 0 U H 0 n. GRIMM'S DUIKEI IUSHIUCK REEDBUCK 100 WARYHOG 0 'ozoo |200 HOURS Figure 25. Percentages of animals active during 0700 and 1900 hours from January to February in Park W, Niger. 124 hid in dense cover duirng the day, Often as early as 0800 hours. During the course Of walking transects, therefore, the mode Of detection changed from that of spotting active animals to one Of detecting resting individuals, usually as a result of some response of an animal. The detection function certainly was altered, this may have adversely affected density estimates. For example, the mean Sighting and perpendicular distances of active bushbucks were 71.5 and 52.8 m respectively, whereas for inactive groups the respective mean distances were 22.3 and 12.0 m. Similar patterns were evident for reedbuck, Grimm's duikers and warthogs but was less evident for other Species. For any one Species, therefore, there can be at least two detection functions. Despite these uncertainties, animals were actually encountered at roughly the same rate throughout the counting period. Sighting rates per unit time walked were surprisingly constant for all species (Table 36). In this study, the assumption that all individuals of a Species are equally visible to the Observer throughout the course of . an animal census appears valid. It is acknowledged that the validity of this acceptance is Open to further review. Evaluation of Transect Locations Transects positions parallel to streams yielded higher density estimates for kob, bushbuck and reedbuck but lower estimates for water- bucks than those which were perpendicular tO streams. To help determine whether these differences were real or because Of differences in sighting distances, the number Of groups seen per kilometer walked were compared. For all species except kob, mean numbers Observed per kilometer of riparian transect were significantly different from those of per— pendicular transects at the 90% level (Table 37). Bushbuck and reedbuck 125 Table 36. Number of observations per unit time walked during the 1976, 1977 and 1978 foot transect counts in Park W, Niger. Time (am) Species 8-9 9-10 10-11 11-12 .12-1 Kob .16 .10 .09 .10 .15 Waterbuck ' .11 .06 .05 .06 .07 Roan ' .09 .13 .08 .08 .19 Hartebeest .00 .03 .02 .04 .04 Buffalo .08 .11 .11 .09 .06 Elephant Oribi .11 .13 .06 .12 .11 , Grimm's duiker .02 .09 .14 .15 .07 Bushbuck .09 .06 .09 .04 .19 Reedbuck .04 .00 .09 .12 .11 Warthog .11 .14 .16 .19 .19 126 Table 37. Comparisons between mean numbers of groups Observed per kilometer walked for transects positioned parallel and perpendicular to streams during the 1978 foot transect counts in Park W, Niger. Riparian Perpendicular1 Perpendicular2 Species Transects Transects Transects Kob 0.215 0.146* Waterbuck 0.062 0.188** Bushbuck 0.207 ' 0.038*** 0.076** Reedbuck 0.241 0.094*** 0.189* 1Mean density based on 1.0 km from streams 2Mean density based on 2.0 km from streams * Significant at the 60% level. ** Significant at the 90% level. ***Significant at the 952 level. 127 numbers were compared using both 1.0 km and 0.5 km as the maximum dis- tance at which all or most individuals were likely to be seen. The greatest discrepency occurred with bushbucks, which were usually found in or adjacent to riparian forests. Fewer waterbuck groups were Ob- served along riparian transects because that species ranges further into the savanna and usually avoids dense riparian vegetation. Differences in density estimates between riparian and perpendicular transects may be attributed to the distributions of riparian Species with reSpect to water. Concentrations of kobs, bushbucks and reed- bucks decreased as the distance from water increased (Fig. 26). Transects positions parallel to a stream therefore sample only a par— ticular density of any one Species. Results: Roadside Counts To provide a larger Sample for evaluation, data from the 1976, 1977 and 1978 roadside counts were combined into one pooled data set. Grimm's duikers, bushbucks and reedbucks were not included in the an- alyses. Because of their secretive diurnal habits, few Observations could be made on those Species from vehicles. AS compared to pooled foot transect data, sample Sizes for the pooled roadside counts are larger for each Species. The pooled angle and distance measures are comparable to those of foot transects, except for several Species where mean angles are somewhat larger (Table 38). Density estimates exhibit a wide range Of values, as did foot transect estimates, though ranges here are Slightly less extreme (Table 39). Patterns in relationships between roadside count estimators are Similar to those reported for foot transects, especially regarding those Numbers Of animals 128 IRANSECI Figure 2 6. J— Distance from water Diagramatic representation Of the decreasing concentrations of animals from a stream and the relative position of a transect positioned parallel to a stream. 129 Table 38. Basic measures of pooled data from roadside counts recorded during the 1976-1978 censuses in Park W, Niger. Mean per- Mean Mean Number of Mean pendicular Sighting disappearing Species observations angle distance*' distance distance Kob 121 39.2 39.7 68.1 90.6 Waterbuck 81 37.0 42.1 71.5 104.6 Roan 93 33.2 40.0 82.6 104.3 Hartebeest 61 37.8 38.9 67.9 100.2 Buffalo 52 43.3 45.1 71.3 102.1 Elephant 42 40.7 40.1 73.7 83.8 Oribi 78 36.7 40.7 70.9 .84.9 Warthog 79. 38.9 35.2 60.8 :82;3 *Distances are in meters. 130 NoHH NmH. occ. ooc. NNH. mNH. com. NN.H wcHI NNN. NHN. NNH. NHH. NHN. NHN. NNo.H NNN.N HmHuamcoaxm NHN. HNH. HNN. Nae. NHH. NHN. NNN. NHN.N .Nma .Hmcoo maNm: NNN. HNH. «we. was. NHH. NHN. NNN. NNN.H maNmm amHHHNoz NNN. HNH. mmo. NHH. NHH. NHH. NHN. soo.N oHNHmEOmo ooomumHo HmHomm ooH. NHH. ooc. cN. coc. HNH. mom. omm.H comm moawumHo mcHumooommHm NHN. NNN. HNH. SSH. NHN. oNN. HNN. HHN.N HHS: osN. HNN. NHH. HNH. HNN. NHN. NHN. Noo.N unease: a acmammo NNH. NHH. Nwo. NNo. ooH. NNH. NHN. NNN.H mmHHmN HmHHHoH HNH. HoH. Hmo. oHo. NNo. oNH. HoN. ooN.H HmHaoHNHoa NHH. NHH. ooH. HNo. ooH. HoH. NNN. HNH.H .axm aoNHHmHmamu HHH. HNH. Nae. Nmo. NNH. NHH. NNN. ooN.H HmHawamHHH NHH. NNH. omH. NNH. NNH. NNH. NNN. HNH.H UHHNHamso NNN. HNH. cHH. NoH. NNH. NNN. NNN. ooo.N HmauoanHmm oNN. NNH. NHo.. NHo. NNo. moo. NNN. NNN.H HmHuamcoaxm mucoumHo umHSOHosomuom Anuoc omosouwce wonuum3 HoHuc ucmsmon OHmmmam umoooouumm cmom Honoumum3 ooM uOumaHumm .uomHz .3 Iowa cH mucsoo oonomou mo mono ooHooo Scum mucuoaHumo NH oou scum mouoBHumo NuHmaoc .om oHomy 131 NNN. NHH. NNH. Nae. NHH. NNN. NNN. oNH.N umstcmHHH oNN. omH. ooc. occ. ooH. cNH. NHo. NoN.H OHumuomoc ocN. HNH. ooc. NNc. coH. ooc. Non. Noo.H HoHaochHom NoH. NNH. ooc. mcc. moH. moH. cHo. Nco.H oooHHom ocN. ooc. ch. ooc. NmH. mmc. moN. mNo.H xocluoumnuoom NoH. cNH. Noc. oNc. NoH. oHH. cHo. Nco.H uoxHoM ooomumHo umH30Hocmmuom Amado ooosoucv woouum3 HoHuc unonmon OHmmmsm umoooouumm zoom Honououo3 30M HOHmEHumm H.N.H:ooc .NN mHHmH 132 estimators which characteristically yield high or low estimates. The Webb, Dasmann-Mossman and Exponential (r) estimators are always high, while the Hahn estimator is always low (Table 40). Yet estimates of the Hahn estimator are seldom the lowest, however, because of the erratic nature of several other estimators which sometimes yield very low estimates which are out-Of—line with all others. The Exponential (x), Polynomial (ungrouped) and Eberhardt-Cox estimators, for example, are moderate in some cases but extremely low in others. A tight grouping of estimates based on grouped data, as found for foot transect data, is evident in roadside counts only for kobs, waterbucks, hartebeests and buffaloes. The large variability among density estimates for the other four species is caused mainly by extreme estimates from the Triangular and Eberhardt-Cox estimators, respectively. Among the radial estimators, the Exponential estimator is always the highest and the King always the lowest (Table 40). The sequential relationship between estimators in ascending order is King<=Geometric< Modified Hayne<=Hayne Constant Radius<=Exponential, which coincides with that for foot transect data. Only the Geometric estimator is always moderate (Table 41), though the King estimator is moderate for 6 of the 8 species, and never as low as the Hahn estimator. A comparison of sequential rankings (Table 40) between pooled foot and roadside transect data shows the Similar patterns between the two data sets. Two exceptions include the Fourier Series estimator, which is moderate for foot transects and low for roadside counts, and the King estimator, which is ranked much lower for foot transects. The relative values (Table 42) for estimators also are usually the Same for the two data sets. 133 NHH‘ OH NH NH HH OH NH NH OH HaHaNcmHHN ON HH N N N NH O OH HH OHHmuOmac ON N N N O OH N O N HNHaocNHON HN N OH HH N N HH O N OOOHHNN NO N H N N NH H OH O xooquHmHNmHN no N a N N N N N N HONHON NO N N N NH O N N OH NOHN ONH NH HN HN OH ON NH NH ON HmHHamaoaxm NNH OH NH OH OH NH NH OH NH .OmN .HNOOO ocNON NO NH NH O HH O NH NH NH OONNN OOHHHOoz ON NH NH NH OH HH OH NH NH OHHHOEONO NN N N a N N o N N seam NNH NH NH NH NH NH OH NH NH ONO: NOH NH ON ON NH NH NH OH NH assume: N ccmsmmO SN N N N N N N H N NOHHNN HNHNOON ON H O NH H H O N N HNHaocNHON HO O HH OH H o N N NH .OxN OONHHNHOONO ON o NH OH O. N O O O HmHawaaHNH oN m oH NH NH NH N N H OHumuvmsc NOH OH NH NH NH oH NH O NH HmauozuNmswcHaom Ho N N H N N N HH O HNHHamcoaxm Houoa wonuum3 HoHuc Hom£QOHm OHmmmsm umomoouumm doom Honououm3 pox HoumaHumm .uosz .3 Imam :« muoo Hoomamuu OonomOH oOHooo aouw mouoEHqu mo mchxamm .co OHQMH 134 z z z z z z z z NNHNNNNNNN N z z N z x z z ONNNHONOO z N. z N z N z z HNNaoaNHON z z z N z z z N NNNNHNN z N N N z N z z NOOINNHNNNNNN z A A A z A z z umwaM z z z z z z z an NNNN m m m m m m m m Amwusmcoaxm m z z z z z z z mnwvmm .umaoo oaks: 2 z z z z z z : NNNNN ONNNNOoz z z z z z z z 2 35253 N N N N N N N N NNNN N N Nu: N N N N N NNNN : m m = m m m z :mammozlacmamma N N z N :aN z N N NNNNNN uoNuaom N z z N N z z N HNNaoaNHom z z z N an zuN z z .NxN ONNNNNNNNNO zuN z z sz : z z N NNHNNNNNNN ZIA z m z z z z A oaumuvmao N z z z z z z z Hmauoz NmchNamN z z A A A A z z Amfiucmcoaxm wosuum3 Anwuo uamnmwAm kowmam umwmnouumm swam xusnumumz pox neumawumm .umwfiz .3 xumm :« mucnoo mwfimcmou vaooa Scum Nmumawumm mo mmsAm> m>fiumAmm .ficmAamH 135 Table 42. Rankings and relative values of the totals for all species for pooled foot and roadside transect data in Park W, Niger. Foot Roadside Estimator Rank Value Rank Value Exponential 9 I 4 I Hemingway Normal 15 MNH 16 MPH Quadratic 10 I 13 I Triangular 5 L-M 8 L-M Generalized Exponential 6 M 10 ‘ M Polynomial 2 L-M 3 I Fourier Series 12 _M 2 L-M Dasmann and Mbssman 19 H 20 H Webb 18 H 19 H Hahn. 1 L 1 L Geometric 10 M 14 M Mbdified Hayne 18 I 15 MPH Hayne Constant Radius 17 M-H 18 MFH Exponential 20 H 21 H King 3 L-M 9 M Kelker 4 M 5 L-M Eberhardt-Cox 8 M 6 L-M Splined 7 ‘M 11 M Polynomial 14 M 7 M Quadratic 13 M 12 M Triangular 16 M 17 MNH 136 The main differences are for estimators such as the Fourier Series and King in which a slight shift occurs from L to L-M or M to M-H. Hahn estimator The Hahn estimator has the lowest overall ranking (Table 42), but there is less discrepancy between the Hahn and moderate estimates than for foot transects. For several species, density estimates of the Hahn are only slightly below moderate values, and below estimates from the Dasmann—Mossman and Webb estimators by a factor of about two rather than three. Frequency histograms of perpendicular, sighting, and disappearing distances are very similar to those for pooled foot transect data, with the exception of more sightings made at longer distances (Figs. 27a and b). This may be because it is easier to concentrate on spotting animals while riding. Consequently, the discrepancy between estimates based on sighting and perpendicular distances and the Hahn estimator is reduced. Based on a comparison between perpendicular and disappearing distances, however, the Hahn estimator inaflJ.likelihood still under- estimates population density from roadside counts. Few animals were initially spotted at the points where they disappeared. This indicates that during roadside counts, observers can totally concentrate on spotting animals even though it is more difficult to locate animals than to follow them to the limits of visibility. Goodness-of-fit tests to detection functions Goodness-of-fit tests to detection functions follow patterns similar to those determined for foot transect data (Table 43). Radial dis- tances are nearly always distributed negative exponentially, with 137 [-_T K°b Roan h; m . mm c C Waterbuck Hartebeest I . W m ‘ Figure127a. Histograms of perpendicular (a), sighting (b) and disappearing (c) distances of the pooled roadside count data of kob, waterbuck, roan and hartebeest. .138 elephant warthog oribi buffalo Figure 27E: Histograms of perpendicular (a), sighting (b) and disappearing (c) distances of the pooled roadside count data of buffalo, elephant, oribi and warthog. 139 .Aw>mA mocqumcoo Nmm onu um Namowwficwfimx NNO. «NHN. «NNN. «NNN. «ONN. NNO. NONN. NNO. HmHaocNHON NNH. NNON. «ONN. «NNN. «NHN. NNO. «NNH. NNO. UHNNNNNOO NNO. NNO. NNO. NNO. NNH. NNO. NHH. NNO. NHNNNHN>.O.NaaNO «NNN. «NNN. «NNN. «NNN. «NNN. NNNN. NNO. «NNN. .NNN ONNHHNNmaNO «NNN. «NNN. «NNN. «NHN. «NNN. «NNN. NNH. NNN. O.N nHV.NeaNO NNON. ONO. «HON. NHH. NNO. «HNH. NNH. «NNN. NNHNNNNHNN HNO. NOH. NNH. NNH. NNH. NNNH. NNO. NNO. Hmauoz NHNN NOH. NNH. NNH. NNO. NHN. NNNH. HHH. HOH. O.N "HO.NaaNO NNO. ONO. NNO. NOH. NNO. NNO. NNH. NNO. NHNNHNN>HO.NaaNO aoHHONHHNmHO NNH. NNH. NHN. ONH. NNH. NNH. NNH. NNH. "OOHHNNHHU NuN wdnuumz “capo ucwzmmAm oAmmwsm umoonmuumm cmom xosauwumz AOM .NuNHz .3 NNNN NH mama ucsoo wvfimvmou wonon you NaoauanwuumAv vawfiooam ou mumou uwm-mo-mmm:uoow mo moaAm> .mq oAan 140 a = variable usually giving the best fit. Among the perpendicular distance distributions, consistently good fits are evident for both the half-normal and gamma distributions with a = variable. The suprama for the triangular, generalized exponential and gamma with a a variable distributions often exceed the critical value. Similarly, fits to the polynomial and quadratic distributions are significantly different for five of the eight species. As indicated earlier for foot transect data, poor fits to certain distributions may explain why estimates are unusually high or low. With roadside counts, this cause and effect is less evident. When suprama for the triangular distribution are significantly above the critical value, density estimates are still moderate. Only for the Quadratic and Polynomial estimators do goodness-of-fit tests aid in explaining erratic estimates. Frequency distributions The most obvious characteristic of frequency distributions of pooled roadside count data was the fewer observations in the first distance class as compared with the second (Fig. 28). The skewed distributions were likely caused by avoidance of roads by animals, presumably be— cause of vehicle disturbance. This avoidance of roads is more clearly illustrated by examining the detection functions between the transect line and 40 m, the point where most frequencies of sightings rapidly declined. For nearly every species, there were fewer observations in the first 10 m than the next three sighting classes (Fig. 28). For oribis, the detection function is the reverse of the expected shape. Despite the skewed distributions, the suprama for those species are 141 o no «a so no mo no no _. 23 WA'IIIUCI M I - Z - - 3 -0 10 no so to I00 . 2 2 Z I :N r——— IOAN ° to oo so to I00 ’0 "AIHIHSI _‘ —. m 0 m :0 no so I00 no IISHICE CUSSKS (I) Figure 28. F 20 I U"Al° o , 10 60 ‘0 .0 loo I30 1‘0 luvuaut ° 20 so to so I00 _D ’0 Oluo h 0 20 ‘0 .0, 80 no l20 _ 10 waltuoc 0 J E 20 so 60 80 "10 no I40 Frequency histograms of observed perpendicular distances for pooled roadside count data in Park W, Niger. 142 surprisingly low. With buffalo and oribi, for example, good fits are evident for the gamma and half normal distributions, though there were few observations in the first sighting class. But, as is the case for buffalo (Fig. 28), the poor fit at the origin is compensated for by a relatively good fit for the remainder of the frequency distribution. 1976-1978 roadside counts Results of the 1976-1978 roadside counts in the study area were evaluated in a manner similar to foot transect data. Sample sizes were considerably larger for roadside counts (Table 44), but data were too few to group except in a few cases, and evaluations of grouped data were omitted. Although angles, sighting and perpendicular distance measures vary considerably between species and between years (Table 45), patterns among density estimates are remarkably constant. These patterns, however, differ from those of the pooled roadside data set, probably because of smaller sample sizes. The rankings of estimators show that the Hahn estimator is always low, while the Dasmann-Mossman and Webb estimators are always high, as was the case for the pooled data set. The highest estimates, though, are from the Quadratic, Triangular, Polynomial and Exponential (r) estimators. Estimates from the first three are often considerably higher than the Webb and Dasmann-Mossman estimator, and in some cases, completely out-of-line. Values of the Fourier Series estimator range from very low, below those of the Hahn estimator, to moderate. Among estimators based on perpendicular distances, only the Hemingway—Normal and Generalized 143 c.0m w.mm m.mq o.mm m.Am m.wm m.~c w.Am m.oe w.~m m.on «.mm mm MA 0 wonuumz o.nm 5.5m o.mm A.mw m.mw o.om m.cm m.mo «.0m <.A¢ A.mm m.Am «A cm «A «capo m.on m.oq «.mc «.qm m.os O.Nm ~.¢m m.mc c.mm m.mq N.A¢ A.o~ mA m m ucmnaoAm «.mm m.Aq «.mc O.NAA m.NoA A.mm O.Nm ¢.A~ o.~o 0.0m m.n¢ A.uomno wcAumommmmAv cmoz. wawunwwm cams. umAaoAvsoauom saw: no Hogabz .muouoa :« mum moocmuman .uomfiz .3 xumm cw wmaA can .NmmA .omma :A noun xvzum ozu :A muczoo ocwwpmou mo mouammoa owmmm .cq oAnma 144 OOO. ONO. ONO. OOO. NON. OOO. .anu .O..OO OO.. .O.. OOO. NOO. NO.. ON.. OOO. NOO. ONO. NNO. NOO. NNO. ONO. OOO. NO.. ON.. OO.. ONO. OON. ONN. OOO. NNO.. .NO. ONN. OO.. NON. NO.. ONN. OO.. OON. OON. NO.. OOO. NO.. OOO. NOO. ON.. NO.. OO.. ONN. OON. NON. NN.. NON. NNO. OON. OOO.N N.O.. NON.. HO..OOOON.O OO.. ON.. NO.. .O.. OON. .NN. NO.. NOO. OOO. NNO. OOO. O... .NO. .NO. OO.. OO.. NN.. OOO. O.O.. .ON. NNO. NNN.. NNO.. .OO. .OO. ..OOOO OO..: ON.. NO.. ON.. NOO. ON.. ONN. OOO. NOO. ONO. NNO. ONO. NOO. OOO. NOO. NN.. OO.. NOO. NOO. NOO. NNN. OOO. ONN.. NNO. NOO. OON.: OO...O:: .N.. O... NN.. .OO. NN.. ..N. OOO. ONO. ONO. ONO. ONO. OOO. OOO. OOO. OO.. NN.. .O.. ONO. OON. NOO. NON. NNN.. OOO.. ONO. O.....u.e N.O.... .33. NO.. NNO. OOO. ONO. NN.. N... OOO. NOO. NNO. O.O. NNO. OOO. .NO. NNO. OOO. NO.. OO.. NOO. ONN. NON. HNN. OON. ONO. NON. OOOO N.O..O .O..-.0 OON. ON.. .N.. .O.. OON. N.N. NO.. NNO. NOO. ONO. OOO. OO.. NOO. OOO. ONN. ONN. OON. ON.. ONO. OOO. O.O. OON.. N.N.. NNN.. NOON OON. ON.. OO.. .O.. NNN. OON. NO.. ONO. OO.. NNO. .NO. NH.. .O.. NOO. ONN. OON. ..N. .O.. .NO. .NO. ONO. OON.. NNN.. O.N.. OO..-O: O OOO.-ON NO.. OOO. NNO. ONO. .N.. ON.. NO.. NNO. .OO. ONO. ONO. NOO. .OO. ONO. N... OO.. OO.. OOO. NNN. OON. ONN. .OO. ONO. ONO. ....ON ....ao. NO.. NOO. NOO. NNN. NN.. OOO.. NOO. .OO. OOO. ON.. NO.. NNN. OOO. NNO. N.O. NNO. NO.. O... OOO.N ONN.. ONO.. .NO.N OOO. OOO. .O.OOON.O. OO.. OOO. NNO. OOO. .O.. OON. OOO. NOO. NOO. ONO. ONO. OOO. NOO. ONO. ON.. NN.. O... OOO. NNO. NON. NNN. ONO.. OOO.. N.O. .OON O....O..O.O ON.. ONO. O.N. NNO. .NN. NON. ONO. NNN. O... O.N. O.O. NON. OON. .O.. ONO. OOO. ON.. NOO. ONN.. NNO. OOO. ONN.N ON..N OOO.. .O.OOOO..N NON. NON. ONO. OOO. OON. O.O. OON. OON. O.O. ON.. OON. NNN. NNN. ON.. NOO. OON. NON. ONO. NON.. OON.. .NO.. O.N.N NHN.N ONO.N .....OOOO OO.. .N.. OO.. OOO. OO.. OO.. .N.. NOO. N... ONO. OOO. OOO. NOO. OOO. NO.. OO.. N.N. N... .ON. OON. O.N. OOO.. .O.. NO.. .33.. .2658: N.O. OOO. ONO. O... OOO. N.N. NNO. ONO. O.O. NOO. O.O. NOO. OOO. ..O. ON.. O.O. O.O. O.O. .OO. ON.. OOO. NNN.. OOO. .OO. .O..¢.OOO.N NOoAauOchNo: ONO. NNO. ONO. ONO. NNO. ONO. ONO. NNO. ONO. NO. NNO. ONO. ONO. NNO. ONO. ONO. NNO. ONO. ONO. NNO.---NmmH. .-..----.NNuuNNNw flu...) Oar-o mooflo: 3oz... coo.- ..oOINoOo: and 3.0:: .3 Juan NO. 2: is. :0. .2: 3‘ no... his: 0... a. :55”. canteen IO: ION-I330 3.2.5: .NO. 0.....— 145 Exponential are consistently moderate (Table 46). Among the radial estimators, only the Geometric estimator is always moderate, though the Modified Hayne nearly always is. Comparisons of foot transect and roadside count estimates The patterns of relative values of estimators for all species and censuses are generally consistent between species (Table 47). The Hahn estimator is always low, Geometric always moderate, and the Dasmann- Mossman, Webb and Exponential estimators are always high. The Hemingway— Normal and Generalized Exponential are always moderate for roadside counts and usually for foot transects. Both the Fourier Series and King estimators range from low-to moderate, while the Modified Hayne and Hayne CR estimators are high to moderate. The remaining estimators, Exponential (x), Triangular, Quadratic and Polynomial, are less pre- dictable, and often give estimates which are extremely high or low. Comparisons of aerial, roadside and foot transect counts Comparisons between foot and roadside counts in the study area indicate that for each species, density estimates from roadside counts are nearly always lower than those of foot transects, usually be a factor of two or three. To illustrate these differences, comparisons are shown (Table 48) for three estimators, the Hahn, Geometric and Webb, which represent low, moderate and high estimates. Only in 1977, are density estimates similar for oribi, elephant, buffalo and harte- beest. In all other instances density estimates from roadside counts are lower than those of foot transects. Density estimates from roadside counts of the two riparian species, kob and waterbuck, are surprisingly 146 O N N N N N N N N N N O O N O N O O N N N O O N NOHN OH OH NH NH OH NH OH NH HH NH O NH NH NH NH NH NH NH OH H. N NH OH NH HNHOOOOOONN HH HH N N O. N N N N N NH OH N N N N N N NH NH HH O OH OH .OON .ONOOO OONON N N OH N N N N O N O N N N N N OH N N HH NH NH N N N OONNN NOHNHNoz N N N N N N N N N N N N N N N N N N N N N N N N OHNOOEOOO N N H N N N N O N N N H H N H O N N H N H N N N NOON NH NH N OH NH HH NH OH N OH OH N OH OH OH NH NH NH N N H OH NH NH ONO: NH NH H. H. N. OH NH HH OH HH HH HH H. H. HH OH OH OH N OH OH H. HH HH :NaNNoz N OONamNO N N N H N N O. H N N O N N N N N N N N O N H H O NOHNON NOHNOON N O OH N. N NH N N. N N. NH O. N. N. NH N NH OH NH O. N. N. H H HOHOOONHON N N O N O N N N OH N O N N O N N N N N N N N N N .OxN NONHHNOOOOO N N NH O. HH N. H N. NH OH H NH NH N. N. . N N. NH N NH OH NH O. NNHONOOHNO NH NH NH N. NH O. NH OH NH NH OH NH O. 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N1: Nu: Nu: z z .OON .OONOO ONNON z z z Nu: H Nu: H z zuN ONNON OOHNHOoz z z z z z z z z z OHNOONOOO N N N N N N N N N NNON N N N N N N N N N NOON N N N N N N N N N NONOOOz N NONOOOO NuN :uN zuN z N zuN zuN N zuN OOHNON NOHNNON zuN H H N an H H N N HOHNONNHON : z z z 2 N12 2 2 Nu: .NON OONHHONONOO 2 H H N sz N H N N NOHNNNOHNN H N N N N1: N N N N OHOONOONO z z z 2 Nu: z z 2 Nu: HOaNozuOHON N N N zuN N H Nu: Na: N HOHONONONNN OOHOON NNNH NNNH NNNH OOHOON «NNNH NNNH NNNH NNNH NOOONHOON mucaoo ocamvmom muoomcmua uoom .uomwz .3 xumm :A mucaoo ovfimvmou can Noom How mucumEAumo mo moaAm> o>Auonu AAmNo>o .NO oAan Table 48. 148 Comparisons of selected density estimates between foot and roadside counts in the study area from 1976-1978 in the study area in Park W, Niger. Densities are in numbers/km 1976 1977 1978 Estimator Foot Road Foot Road Foot Road Kob Hahn 1.316 0.505 0.877 0.654 1.429 0.759 Geometric 1.986 0.834 1.445 7.000 . 2.936 1.227 Webb 3.041 1.235 2.416 1.315 3.000 1.706 Waterbuck Hahn 0.877 0.253 0.772 0.205 0.124 0.102 Geometric 1.434 0.834 1.004 0.462 1.240 0.596 Webb 1.859 1.235 1.975 0.606 2.105 0.674 Roan Hahn 0.138 0.052 0.210 0.106 0.124 0.102 Geometric 0.255 0.078 0.177 0.161 0.414 0.137 Webb 0.362 0.125 0.485 0.284 0.402 0.239 Hartebeest Hahn 0.086 0.053 0.037 0.074 0.031 Geometric 0.166 0.068 0.064 0.101 0.064 Webb 0.238 0.071 0.080 0.157 0.095 Buffalo Hahn 0.215 0.049 0.062 0.032 0.061 0.018 Geometric 0.303 0.094 0.070 0.054 0.182 0.024 Webb 0.487 0.108 0.189 0.068 0.321 0.036 Eleghant Hahn 0.057 0.035 0.042 0.112 0.084 Geometric 0.076 0.061 0.056 0.168 0.098 Webb 0.083 0.101 0.072 0.269 0.157 Oribi Hahn 0.157 0.113 0.140 0.137 0.238 0.070 Geometric 0.157 0.211 0.181 0.177 0.328 0.091 Webb 0.284 0.312 0.321 0.250 0.526 0.141 Warthog Hahn 0.369 0.049 0.211 0.073 0.210 0.102 Geometric 0.741 0.127 0.264 0.114 0.359 0.171 Webb 1.333 0.121 0.321 0.158 0.526 0.248 149 lower than those of foot transect counts, since roads traverse areas of high kob and waterbuck densities. A comparison between aerial and roadside counts (see Table 45) shows that for hartebeest, buffalos and elephants density estimates are similar. For kobs, roans, and waterbucks, estimates from roadside counts are generally much lower than aerial counts. The same pattern is evident for foot transect counts, in that estimates for the large buffalos and elephants are comparable. There are mainly two factors which contribute to the lower density estimates from roadside counts. First, comparisons between the numbers of groups counted per kilometer of transect clearly shows that values from roadside counts are below those of foot transects in nearly every case (Table 49). Because roads poorly sampled the central portion of the study area, comparison counts were made only in the two high- animal-density areas where roads provide better coverage. Values from roadside counts, however, are still below those of foot transects in most cases, though discrepancies between values are considerably less for several species (Table 50). For roans, buffaloes, elephants and warthogs, numbers-perflinear-kilometer are quite close in at least one of the years. Large differences remain, however, for kobs, waterbucks, oribis, and in one or more years, for roans, harte- beests and warthogs. Second, the shape of the frequency distribution can contribute to lower density estimates. Burnham et al. (1980) found through simu— lation tests that density estimates may underestimate actual abundance by as much as 100% when fewer observations are made near the transect line than at longer distances. The frequency distributions in Figure 29 150 Table 49. Comparisons between numbers of groups recorded per kilometer of foot and roadside counts during the 1976, 1977 and 1978 censuses in the entire central study area in Park W, Niger. 1976 1977 1978 Species Foot Road Foot Road Foot Road Kob .286 .042 .200 .062 .333 .080 Waterbuck .200 .016 ..167 .051 .278 .080 Roan .032 .008 .026 .027 .029 .018 Hartebeest ' - .010 .009 .005 .029 .007 Buffalo .016 .012 .017 .019 .015 .011 Elephant - .006 .009 .005 .022 .023 Oribi .032 .021 .043 .025' .036 .013 Warthog .064 .006 .017 .016 .015 .020 151 Table 50. Comparisons of numbers of groups counted per kilometer of transect for foot and roadside counts in high animal- density areas within the central study area in Park W, Niger. Year 1976 1977 1978 Species Foot Roadside Foot Roadside Foot Roadside Kob .286 .092 .200 .113 .333 1.42 Waterbuck .200 .051 .167 .045 .278 .147' Roan .066 .012 .050 .023 .028 .020 Hartebeest .016 .008 .008 .022 .007 Buffalo .040 .009 .025 .007 .025 .004 Elephant .006 .017 .007 .023 .016 Oribi .026 .018 .050 .021 .039 .012 Warthog .053 .008 .042 .011 .028 .018 101 Frequency 152 ‘fll 10- >~. U c: m :3 U‘ a) H “I 5‘—‘ O 20 “O 69 80 100 0 20 40 60 80 100 Distance classes Figure 29. Frequency histograms of foot transects (top) and roadside counts (bottom) of kobs from the 1978 park- wide survey in Park W, Niger. (n=25). 153 represent observations from foot and roadside counts from the 1978 park-wide survey. The distribution of perpendicular distances from foot transects are approximately half—normal, while those of the road- side count are skewed (fewer observations in the first sighting class).' The corresponding density estimates from roadside counts are below those of foot transects for most estimators (Table 51). Goodness of fit tests Goodness of fit tests to distributions (Table 52) revealed that the detection functions were rarely triangular, and that good fits could seldom be obtained with the polynomial or quadratic distributions. Despite the skewed detection functions, however, they were seldom significantly different from the exponential or half-nromal distributions. The large values for the Generalized Exponential distribution were again believed the cause of program errors. Tests of assumptions For pooled data, tests of the validity of radial estimators re- vealed that for most species, the critical values have been exceeded (Table 53). Fits to the Cosine theta distribution were significantly different from expected distributions for all species except harte- beest. Similarly, 2 values are significant for most species. Despite these indications that radial estimators are not apprOpriate for road- side counts, the patterns and relative values of estimates from radial estimators remained constant, whether or not the tests were signifi- cant. Moreover, these patterns were similar to those for pooled foot transect data, most of which were not significant. 154 Table 51. Density estimates for a distribution which is approximately half normal and one which is skewed (fewer observations in the first sighting class). Estimator Half-Normal Skewed Difference Exponential 3.886 ' 3.270 -.616 Hemingway Normal 2.580 . 2.388 -.192 Quadratic 5.084 5.660 +.576 Triangular 5.317 6.066 +.749 Generalized Exp. 2.580 1.244 -1.366 Polynomial 5.211 3.154 -2.057 Fourier Series 1.250 1.244 -.006 Dasmann-Mossman 4.048 3.406 -.642 Webb 3.834 3.238 -.596 (Grouped data) Kelker 2.118 1.442 -.676 Eberhardt-Cox 2.294 .721 -1.573 Splined 2.118 2.163 +.045 Polynomial 2.384 2.232 -.152 Quadratic 2.124 1.754 -.370 Triangular 2.550 2.318 -.232 (Radial distances) Geometric 2.186 2.186 .000 Modified Hayne 2.451 2.114 -.337 Hayne Const. Rad. 2.464 2.464 .000 Exponential 3.857 3.869 +.012 King 1.967 1.967 .000 155 .02.. 03.03250 Man. a... ..o 233:5.3. .03. 52. ans. «moo. .NO.. :9. .8. an. . oz. .23. 33. one. «SQ. «98.. and. «:0 . cs . . n .n . mac. n... «3. 2... n2. n2. 0a... 00.. «.3. son. non. ooo. olllclol'l' ‘ lllul-"ll"|l.lu|ll||".-ll"l ,I"'1l 23. «man. one. «a... n2. «0:... «gen. 8... 1.3. .68.. «nan. .0... «sum. «08.. «can. on~. can. as. now. on... .I.!E:o.. came. «93. 09‘. «£3. «a. «$5.. «Nev . «.3. fiat. $~o. (ON.. «a... 83. .O..... 0.3“. 58. «$6. «a: . «nun. 0...: . u. Naval. na.. u... 2... a8. 0:. .2. 3.. nON. cg. n.~. ..O.. ..u. 2... nso. .nu. ¢-. 8.. 6:. :0. so... go. 0.30:3. .. a .clI-N 90.. n2. :9. oneo. 60.. .08. «can. 33. 3.. 8~. 193. 0:. «cam. 11*. «So. n3. qo~o. a... .8. 3'0. .x... .9... .53....53... 60.. .8. 8n. «8.... «on. 3. .OO.... .69... an. nan. a... 3n. «ooo.. OOO.—186.. nem. «:0. ~o~. a... 3.. 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Nuaats.-N sex .III111l11‘VIIOIV’I'o’1‘1'I'.l!;Ilutu. 9 1| .uou... .3 J»... a. qou< >3Nm .9320“. o... c. 3.50... 03.930.— oso. van :0. .20. 2.. no. 30:35.53... 3.302.: ca :3; a: .0 55553. .0 35.5. .3 9...: 156 Table 53. Test values from the goodness of fit test to the cosine theta distribution, whether 9 is significantly different from 32.7 and sin 9 is significantly different from 0.5 for the pooled data in Park W, Niger. Test Species Cos theta l. 12 Kob . 30.52* 3.32* 5.03* Waterbuck 17.59* 1.80 3.17* Roan 18.45* 0.22 1.49 Hartebeest 12.31 1.85 3.06* Buffalo 32.49* 3.55* 4.64* Elephant # 2.41* 3.42* Oribi 24.13* 1.64 2.99* Warthog 15.50* 2.56* 3.94* * Significant at the 95% level. # Observations too few to calculate cos theta distribution 157 The Z tests for 1976-1978 roadside counts are mostly non-significant though several values are only slightly below the critical value (Table 54). These results are in direct contrast to those of the pooled roadside count data (Table 53) despite the larger mean angles for several species. The non-significance though, is largely the result of smaller sample sizes. With buffaloes, for example, the mean angle and sample size in 1976 are 42.1 and 7, and the Z tests are both non-significant. If, however, the sample size had been 20, the test values would both be significant. Assumption 1, the random distribution of animals or transects was probably violated for roadside counts. As shown earlier, animal distributions were influenced by water availability, with a gradient of high to low density as distance from water increased. Much of the kilometerage of roads were parallel with rather than perpendicular to streams. An examination of animal sightings along roads revealed that sightings were clumped near water sources. In spite of the extensive road system, roadside counts did not appear to traverse a representa- tive sample of animal populations. As noted for foot transects positioned parallel to streams, roadside counts sampled, a particular density of each riparian species rather than an average density over the study area. An examination of field records showed that assumption ii, the independence of sightings and assumption iii, no animal counted more than once, was met. During roadside counts, the activities of one animal were not observed to influence the sighting of another except when other members of a group were detected. Movements of animals in response to observers were local, and did not result in duplicate counts on other roads. 158 Table 54. Test values to determine if 9 is significantly different from 32.7° and sin 9 - 0.5 for data from the 1976, 1977 and 1978 roadside counts in Park W, Niger. 1976 __. 1977 . 1978 Species Z1 .22 21 22 21 Z2 Kob .153 1.096 1.279 1.940 1.148 1.858 Waterbuck .485 .005 .209 .748 .593 1.213 Roan .209 .645 .245 .467 .273 .382 Hartebeest .675 1.205 1.701 2.174* .433 .860 Buffalo 1.154 1.558 1.128 1.568 .570 .917 Elephant 1.296 1.623 1.036 .1477 .849 1.516 Oribi .399 .954 1.183 1.970* .503 1.064 warthog 1.261 1.630 1.187 1.750 .718 1.426 * Significant at the 95% level. Z1 8 E(O) - 32.7° Z2 - Sin(0) - 0.5 159 Assumption iv, that all animals seen were in the exact position occupied as the observer approached, was violated to some degree for most species. Except for oribis and elephants, the percentages of animals running when first noticed were less for roadside counts than for foot transect counts. Approximately one-half of all oribis and elephants were in motion, either walking or running, when first spotted (Table 55). Many of those oribis, at full gallop when first seen, moved parallel to the road. In those instances, perpendicular dis- tances were not affected by movements. Most animals which were in motion when first seen, especially those which were close to the road, usually angled away from it on being disturbed. Bias from movement of animals which were walking when first noticed was believed to have been minimal. Nearly all movements of this type were natural movements, not induced by the vehicle. Though not quantified, observations indicated that animal movements toward and away from roads were approximately equal. One additional assumption is needed for roadside counts: the visibility of animals along roads remain constant during the counting period. An examination of the numbers of groups counted per hour reveals variability between morning and afternoon counts (Fig. 30) A comparison between counts made during the morning, mid-day and after- noon shows that only values for roan, buffalo and hartebeests are relatively constant (Table 56). Values for other species are quite variable, though these differences are significant only at the 90% and 80% levels. For kob and waterbuck, however, the larger values obtained during after- noon counts could translate into considerably higher density estimates. 160 «N am NH o w mm mm moguHmB me mm on c. mm oa we Hafiuo m cm on o m on 3 2232.... o he mq e. o o. mo oammmam um mo .. a. .. mm me ummwnouumm «N mm mm .. m mm mm swam 0 sq m: a 0 mm mm Noonuoumz c we we m N om me mom can Mean woxamz poowmamm asap wcfiwq wdwooom‘wonNHNS .wowvomuw mafioomm uncommom hww>auo< . .uowfiz .3 Much a. wmwasoma. Baum moaofino> ou uncommon .maficm mo mowmuoouuma pom muummomuu pmou macaw vo>uomao umufim can: mowuowoumo huH>Huom aw wo>ummao mamaaom mo mowmuoouuom .mm manna Numbers observed /hour 161 -- Waterbuck r-‘_‘ I l I A I l\ I \ I I \ I I l \ o “ i \ l a \ I ’r \ I \ l I, \\ I \ ‘ I’ \\ ’I ' I. \ I \ II V ‘ I ‘ , \ ,A ~ 7 ‘ ’I’ \~ ' \ 1' '~‘ \ X \ ,’ V’ 0800 0900 1000 1100 1200 1300 1900 1500 1600 1700 1800 Fig. 30. Numbers of kob and waterbucks observed along roads per hour driving between 0800 and 1800 hours during the 1976-1978 roadside counts in Park W, Niger. 162 Table 56. Mean numbers of groups counted per hour during the 1976-1978 roadside counts in Park W, Niger. Species 0800-1100 1100—1500 1500-1800 Kob .245 .215 .428** Waterbuck .148 .105 .378** Roan .123 .153 .188 Hartebeest .058 .040 .088 Buffalo .072 .060 .100 Elephant .058 ' .060 .003** Oribi .100 .070 .008** Warthog .190 .102* .102* * Significant at the 80% level from morning counts. ** Significant at the 90% level from morning counts. 163 The differences found for kobs and waterbucks were not surprising because those species were most active during mid-to—late afternoon, and actively sought water then. In many locations they had to traverse roads to reach water, and, in doing so, were more likely to be seen. Estimation of Population Size The estimation of population size for each species required choosing between density estimates from aerial, roadside or foot transect counts. Because aerial and roadside counts were not useful for some species, estimates from foot transects were adopted as the general basis for the calculating of population sizes. The transition from estimates of group density to population den- sity and pOpulation size required determinations of mean group sizes for each species and the total area surveyed. Both measures were easily obtainable, but may have been biased. Group means obtained from each survey were compared with group means from all observations made during the counting period. These included those data collected during foot transect counts, roadside counts and other activities. These pooled group means provided larger samples which in all liklihood more accurately reflected true mean group sizes. Among those species which occurred in small groups such as oribis and bushbucks, sample and pooled means were similar (Table 57). Howb ever, for roan, antelope, hartebeest and elephant, which occurred in large groups, there were substantial differences between means in some years. Few of these means were significantly different at the 95% confidence level, mainly because their variances were large. It was 164 cc.~ om.m o~.~ um.~ om.m .m.~ o~.m wozuum3 on.. on.. 00.N mm.. on.. c... Noonpmom mm.. mm.. on.. c... OO.. m~.. OO.. xoonnmsm NO.. 50.. .... wo.. ON.. om.. 00.. Hoxfisv m.aafiuu .m.. oo.. n..~ wo.. nc.. mm.. oo.N anfiuo NN.N Nm.m co.NN Na.h oo.m~ oo.N NamNNmNN om.. m..~ om.. .¢.N 00.N mm.~ mm.q onmwam mm.o m..o oo.m mm.m oc.o on.m ammonouumz ~<.N oe.¢ oo.m om.c mc.m mm.m om.m :mom m~.m o..m mm.~ no.m oo.m mm.~ oo.m Nonnumum3 mm.~ mm.~ mn.~ ao.~ m~.~ .m.~ oo.m cox opa3lxumm "mamamm pmaoom mamwmm poaoom oHQEMm voaoom mamamm moaoomm cum. .uowwz .3 xumm a. Nude aouou can mono hvaum Hmuuomo «no a. mmm>u=m Noomcmuu Noam mum. pom hum. .oma. onu wouusm couscous mowomnm no woman mooum ammz .nm oHan 165 Table 58. Estimated square kilometers occupied by species during the foot and roadside counts from 1976-1978 in the central study area and total park in Park W, Niger. Central Study Area Total Park Kob 57 181 Waterbuck 71 198 Roan 600 2100 Hartebeest 600 2100 Buffalo 600 2100 Elephant 600 1500 Oribi 500 1600 Grimm's duiker 600 2100 Bushbuck 47 172 Reedbuck 22 127 Warthog 600 2100 166 Table 59. Population estimates based on sample and total mean group sizes in the central study area from 1976-1978.- wOensity estimates are based on the Geometric mean estimator. 1976 1977 1978 Sample Total Sample Total Sample Total Species Mean Mean Mean Mean . Mean Mean Kob 396 358 327 319 293 275 Waterbuck 378 361 320 327 282 446 Roan 1847 725 813 1439 585 897 Hartebeest * * 212 206 363 448 Buffalo 1265 663 211 254 257 372 Elephant * * 952 328 986 483 Oribi 276 214 301 302 596 440 Grimm's duiker 515 773 635 572 1418 1428 Bushbuck 57 73 94 107 198 183 Reedbuck * * 179 159 142 92 Warthog 2037 1725 859 716 668 777 *None observed during survey. 167 DISCUSSION Methods 2£_surveying pepplations The best method to estimate animal density in Park W depends largely on the animal species studied and the kind of information desired. Each census method has both advantages and disadvantages. Aerial counts If elephants or buffaloes are the primary focus of a survey, aerial counts are perhaps the most useful. Both.species occur in large groups, and while accurate counts of group sizes usually are possible from.the air they often are difficult to obtain by ground surveys. Furthermore, the amount of information obtained in a few hours of flying could require several weeks on the ground. The use of aircraft for counting large mammals in Park W, however, had several major disadvantages. The Park's budgets were too small to permit such surveys, even on an occasional basis. If funds were made available, they would mean less money for such basic operations such as patrols and maintenance. Many international agencies and organizations have funded aerial counts, but these funds may not always be available when needed or for comparative follow-up counts. Even if funds were available, suitable aircraft and experienced pilots may not be. During this study, for instance, despite the availability of funds, a suitable aircraft could not be located during January or February, 1978. 168 Detailed studies have shown that aerial counts are less than 100% efficient (Caughley 1977), often yielding estimates considerably below true population sizes. In this study, too, the densities of most antelope species estimated from aerial surveys were much lower than those derived from foot transect counts. Where estimates of species other than buffaloes and elephants also are desired, the use of combined aerial and ground surveys would increase the total cost. Roadside Counts Based on results here and elsewhere in Africa, roadside counts appear to be of limited value for estimating densities of large mammals in wooded areas. Their value even as an index to animal abundance is questionable. In instances when both foot and roadside surveys have been used to estimate the same population, density values obtained from roadside counts often are either much higher or lower than those based on foot transects (Harris 1970; Sihvonen 1977; Van Lavieren and Bosch 1977; Barber 1980). In this study, most estimates from.roadside counts were lower than those derived from foot transects. Discrepencies between foot and roadside counts seem likely to occur especially because road transects do not traverse a representative sample of the study area. Norton—Griffith (1978) noted that roads tend to be built in good gamedviewing areas and along, rather than across contour lines. Much of the road transect followed in Park W was situated on well-drained sites perpendicular to streams and across-contours.. The total length of such road transects, moreover, was short in relation to the area sampled. Roads tended to be located on well-drained soils 169 characterized by low animal densities rather than traverse a represen- tative samples of the study area. In areas of high animal density, mainly along streams and near waterholes, roads followed mostly along contours. Inaccurate density estimates also resulted because animals tended to avoid roads. Even though some individuals seemed unafraid of vehicles, disturbance by tourist traffic was seen to cause others to move away. This was especially true when tourists exited their vehicles for a better view or to take photographs. Using roadside counts also was less desirable because estimates could be obtained for only 8 of the 11 species. Bushbucks, reedbucks and Grimm's duikers mostly were inactive during the day. Often they rested in dense vegetation and were unlikely to flush or be seen unless the vehicle stopped. The effects of tourist traffic and of small samples often prevented valid population estimates. Foot transect counts Foot transect counts are considered to have been the most useful in Park W. They were at least as accurate as aerial counts for buffaloes and elephants and could be used for all 11 common species. Their main disadvantage was that they were time-consuming. The number of skilled personnel in the park was too few to have carried out such a census without the outside assistance of several trained biologists. The 1978 park-wide survey, for example, required a full month to complete even though three and sometimes four walking teams were available. It would have required a party of two individuals nearly three months to 170 complete the same survey, and would have required time be spent away from other duties. As noted by Rogers (1975, unpublished paper), the near— universal shortage of trained personnel results in few ground counts undertaken in African parks and reserves. Recommendations on selecting estimators for foot transect counts Although foot transect counts can provide useful samples of large mammals, accurate estimates of population density are dependent on the selection of an estimator for each species which yields unbiased estimates. Estimators differ in that they are based on radial, perpendicular or disappearing distances. And, for each of these categories, there are choices regarding the collection and recording of data in the fields. It is desirable to identify those estimators which have been demonstrated consistently to be accurate. The selection process for the best or best set of estimators has been simplified somewhat in recent reviews of line transect methods (Eberhardt 1978; Gates 1979; Burnham et al. 1980). Burnham et al. (1979, 1980) have provided guidelines for asssessing the usefulness of density estimators on the basis of five desirable prOperties: 1. Model robustness. 2. Pooling robustness. 3. Shape criterion. 4. High efficiency. 5. Theoretical deve10pment. An estimator is Said to be model robust if it can be applied to a wide variety of habitats, observers and conditions under which counts 171 are made. Nonparametric estimators require no assumption about the pdf and generally meet the requirement of model robustness. These are in contrast to parametric estimators which involve assumptions about some known probability detection function (pdf). An estimator is pooling robust if it satisfies the condition that n f(O) . ni f(O) Data from strata or replicate samples involving several detection functions can be combined without causing bias. A robust estimator, for example, would give the same estimate of density whether an overall or weighted estimate was used. The shape criterion refers to the general shape of the detection function. The true detection curve g(x) should have a "shoulder" near x a 0 since, near the origin, the probability of detection should be 1.0 or nearly so. Estimator efficiency is also a desirable property. Not all estimators are equally efficient, and it is desirable that the sampling variance be as small as possible. Small sampling variance, of course, does not insure that an estimator is unbiased. Finally, the estimator should be theoretically sound, based on both logical and mathematical considerations. In the context of these desirable properties, the number of pro- spective estimators can be reduced. Burnham et a1. (1980), in fact, recommended only four estimators for general use in line transect studies (Table 60 . Those were all nonparametric estimators and generally met the five qualifications outlined above. The authors noted, however, that no single estimator is best for all data sets. 172 N N g N )4 K wcax .mwuomcomxm moavmm Nomumcoo mo3mm owuuoaoou Amooomumav .mavmm so woman. one: Amoocmumup moaumommmmav so pommmv echNam xooluvumnnonm HNNHmM noo3 emammozloomamma moauom uoauoom .maaoohaom .mfiucoooexm vouwamuocou HNHNwomaue uwumuvmoo Hmauoz hoswcwaom Hafiuoooomxm Amooomumwv umasoamooeuom so momma. fipnns Stun Aq papuammooag (6161) 59399 Kq papuammmoag (0861) '13 33 msquing Kq papuammooag 3U3191339 firearnetag uoraanrio adsqs ianna Burtood :anoa Iapon srssq Isornai -oaq3 punos pezrnbaz nuamaflpnf aarnoafqns poqnam Papom~1n0 muoumafiumm .mpOumaHumo you mowufiflmov poccoaaooou pom mowumauouomumno oHnmuwmon coo manmh 173 Gates (1979) followed a somewhat different approach in endorsing estimators for general use. For use with perpendicular distances, he advocated seven estimators (Table 59). His approach was to fit the esti- mator to the data. This was based on the premise that a parametric esti- mator whose assumed distribution was met provides the least biased estimate. For radial distances, he advocated the Hayne and Exponential estimators, and gave a blanket endorsement of nonparametric estimators. Gates also recognized that there is not necessarily any single best estimator for a given data set. Evidence from this study indicated that both approaches have merit. With.the exception of the Polynomial, those estimators recommended by Burnham et al. (1980) appeared promising in this study. Their recommended use of only two estimators for perpendicular distances, however, was found to be too restrictive, especially when sample sizes were small. Though several estimators he recommended did not perform well in this study Gates' more flexible approach has more appeal. Present recommendations gg_the use 2; estimators The Webb and Dasmann-Mbssman, were included in the calculations mainly as a basis of comparison because they have been shown to be biased (Robinette et al. 1974; Evans 1975). Neither has been proven to have sufficient mathematical development yet were of value in this study, because they proved to be consistently biased in a positive direction. 174 Methods based on Radial distances The King estimator has since been modified by Gates (1969), but it is believed that the original King estimator still has merit. It usually yielded estimates which were low in relation to others. The actual numerical differences, however, were small, and it was among the most consistent estimators. In field studies by Robinette et al. (1974), estimates from.the King model were consistently below true values, but only by small amounts. In certain cases, the King estimator may be the least biased radial estimator. Gates (1979) noted that radial estimators based on reciprocals of r are sensitive to short radial distances. Small r values have a disprOportionate effect on the harmonic mean, and can result in over- estimates. In a simulation test (Table 61), estimates were obtained for the King, Hayne and Geometric estimators where mean radial distances were constant but the number of short r values increased. When two or three short sighting distances were included, estimates from the King estimator remained constant whereas those of the other two were considerably higher. The Hayne estimator was the most seriously affected while the Geometric mean was affected to an intermediate degree. The Hayne and Modified Hayne estimators performed reasonably well in this study (Table 15) when there were few small r values. Modified Hayne estimates were usually slightly lower than those of the original Hayne estimator because of the correction factor. Burnham et al. (1980) recommended the modified estimator as a replacement for the Hayne. Gates (1979) advoacted the original Hayne estimator though he noted several drawbacks to this method. It is restrictive in that 9 is required to be 175 Table 61. Simulated effects of short sighting distances on radial distance estimators, where L = 10 km.and n - 10. The number of small r values increases from test 1 to 4. Test number Observation 1 2 3 4 1 5 16 26 15 2 ll 3 4 2 3 36 15 39 19 4 14 23 25 35 5 28 22 29 28 6 8 40 14 1 7 21 4 l 15 8 18 25 7 l 9 10 l 12 36 10 7 7 ' 1 3 Arithmetic mean: 15.8 15.6 15.8 15.5 Geometric mean: 13.23 10.0 9.0 5.1 Harmonic mean: 11.14 9.35 3.7 3.2 Density per square kilometer Estimator King .032 .032 .032 .032 Geometric .049 .056 .067 .098 Hayne .045 .102 .134 .156 176 about equal to 32.7°. In practice, 9 is often larger than this, especially when detection depends on the observer. The Geometric estimator was proposed by Gates (1969) to fill the void between the harmonic and arithmetic means of radial distances. It has not, however, been regarded as useful by most investigators. Later, Gates (1981) stated that it has no basis in reality because there is no evidence that logarithms of radial distances yield unbiased esti- mates. In a series of simulations, he found this estimator always to be negatively biased, yet the bias was small when the underlying distri- butions were triangular or half-normal rather than exponential. In con- trast, Robinette et al. (1974) found this estimator to be biased in a positive direction. The amount of bias, though, was relatively small, and they found it to be among the best estimators evaluated. When applied in connection with stratified data, they determined the amount of bias was quite small. In this study, the Geometric estimator yielded one of the most con- sistent set of results. Its estimates were always moderate in relation to those of other estimators, even when sample sizes were quite small. Its performance in this study indicated that perhaps its potential usefulness has not been fully explored. Its theoretical development seems sound, though its prOperties relative to robustness have not been investigated. Where sample sizes were too small for estimation by many other methods, this estimator always yielded moderate estimates, though of unknown accuracy. The Exponential estimator did not perform well in this study. De- rived estimates were consistently high in relation to other estimators, 177 whether or not the distribution of radial distances was exponential. It yielded estimates as high or higher than the Webb and DasmannNMossman estimators, which have been shown (Robinette et a1. 1974) to yield over- * estimates of density by more than 100% in several cases, and always to be at least 20% high. Under the assumption of a negative exponential distribution, Gates (1969) showed that the Exponential estimator performed well in simulation studies. Gates also showed, however, that when the underlying distribution was half normal or triangular, this estimator overestimated densities by significant amounts. Kovner and Patil (1974) also examined its pro- perties and found it to be an efficient estimator, but examined it only under the exponential distribution. The reason for the high estimates from the Exponential estimator in this study was not clear in view of Gates' simulation studies. Possibly, it is extremely sensitive even to small departuresfrom the assumed exponential distribution. Overall, this estimator was judged to have little use for estimating densities in Park W. Methods based on perpendicular distances The Polynomial, Quadratic and Triangular methods all yielded values close to those of more moderate estimators when sample sizes exceeded 40. As sample sizes decreased from.40, however, these estimators gave increasingly variable results for ungrouped data. Estimates were some- times completely out-of-line with those of other estimators. For sample sizes between 20 and 40, these estimators gave reasonable estimates only when operating on grouped, truncated data. Thus, it appeared that those 178 methods were only useful for relatively large sample sizes, and for grouped, truncated data sets. Burnham et al. (1980) recommended the Polynomial because it meets the 5 criteria outlined earlier. Robinette et al. (1974) found that the Polynomial estimator had relatively small bias and also recommended it as one of the better estimators. Gates (1974) recommended the Triangular estimator for use when the detection function is approximately linear. It appears that when data sets include over 40 observations each of these estimators may yield useful density estimates. Of the three, the Poly- nomial best meets the properties outlined earlier. Several other estimators, the Kelker, Eberhardt-Cox and Spline operate only with grouped data. When sample sizes are adequate (40 or more) their estimates were similar and appeared to be reasonable. An important drawback to the Kelker and Eberhardt—Cox estimators, however, was the subjective selection of w, the maximum distance at which all animals are presumed to be observed. In areas of open vegetation, these models are likely to be useful for large mammal counts because few individuals are likely to be missed. If sample sizes are large enough (eg. 50 or more), too, reliable decisions regarding w are more likely. In the wooded savannas of Park.W, however, gradual declines in observations and relatively small sample sizes commonly encountered increases the subjectivity in selecting w. Gatesé (1979) Spline method is a probable improvement on Kelker's method since subjectivity in selecting w is reduced. In Park W, esti- mates from the Spline and Kelker formulas yielded either the same density or the Spline showed only modest increases over the Kelker. 179 The performance of these estimators with respect to bias has been examined only for Kelker's method. It yielded good results in field tests on inanimate objects (Robinette et al. 1974) and on white-tailed deer (Evans 1975). Yet Hirst (1969) found that it yielded underestimates of large ungulate densities in southern Africa. Gates (1979) considered the Kelker estimator to be generally useful for perpendicular distances, but suggested that the Spline method was a better alternative. Gates also considered the Eberhardt-Cox estimator to be useful, but with the same reservations. He noted that estimates with both the Kelker and Eberhardt-Cox estimators can be quite variable, depending on ,which w is used. Eberhardt (1978) too, felt that the Eberhardt-Cox estimator should be employed only as a last resort. Burnham et al. (1980) recommended its use only as a rough guide to density because of the subjectivity factor discussed earlier. It appears that when data sets are large enough to group the data, the Kelker and Spline estimators give moderate estimates comparable to those of other estimators proven to have performed well in simulation and field tests. The Eberhardt-Cox estimator is more variable and is believed less useful than the Kelker or Spline, especially for sample sizes smaller than 40. The Exponential estimator has been found by most investigators to be too restrictive for general use. It is sensitive to departures from the negative exponential distribution, and has been found to give badly- biased estimates when the detection function is not exponential (Robinette 1974; Eberhardt 1978; Gates 1979). In this study too, values from the Exponential estimator were often very high or very low in relation to other estimators and not believed to be useful. 180 Among the parametric estimators, the Hemingway Normal yielded esti- mates which were consistent for a wide variety of species, detection functions and sample sizes. In some instances, estimates tended to be higher than others, but the method may be more generally useful than sometimes viewed. Burnham.et al. (1980) for instance, felt that this estimator was more desirable than the Exponential, but nevertheless was too restrictive for general use. The underlying detection function, of course, must be half-normal for estimates to be unbiased. Gates advocated its application only when the assumed distribution has been tested. In this study, detection functions were seldom significantly different from the half-normal except when sample sizes were small. Though estimator is neither model robust nor pooling rubust, it almost always provided a moderate estimate which was close in value to other estimators which were robust in those ways. The Generalized Exponential estimator, also a parametric estimator, was in performance similar to the Hemingway Normal. The Generalized Exponential should be more robust than other parametric estimators be- ‘cause it is based on a generalized exponential distribution which includes the negative exponential, half-normal and uniform distributions (Pollock 1978). This estimator has not been studied in simulation tests, and its prOperties are largely unknown. In this study, its performance relative to robust estimators was relatively good for sample sizes above 30. Below that level, the variability of estimates increased, but even with very small samples, it often yielded moderate estimates. Because of its involved computations, neither Gates (1979) nor Burnham et al. (1980) r econrnend ed this method . 181 The Fourier Series estimator was developed for line transect data by Burnham and Anderson (1976) and Crain et al. (1978). This estimator represents a most-significant advance in line transect theory. Its use over other estimators has been strongly recommended by Burnham et al. (1980) since this estimator meets all the desirable properties outlined earlier. They determined through simulation tests that it is often more accurate than parametric estimators even when the underlying parametric distributions have been met. It was especially useful in application to Park W data. It had the flexibility and robust properties for the variety of detection functions typically encountered when tallying multiple species. In consequence, it proved to be the single most useful esti— mator. For pooled data sets, estimates from the Fourier Series were reasonable and well within the range of moderate values. Its reliability for data sets smaller than 40, however, appeared to be questionable. Under those conditions it yielded estimates which were equal to or below those of the Hahn estimator and completely-out-of-line with those of other estimators. One plausable explanation is that frequently, the pdf de- clined rapidly from the transect line in the manner of an exponential distribution. In simulation studies (Burnham.et al. 1980), where the pdf was negative exponential, the Fourier Series estimator yielded negatively biased results which were as much as 20% low. In other simulation tests in which there were fewer observations near the transect line than at succeeding distances, this estimator underestimated densities by 20 to 90%. In Park W, the rapid falloff and skewed distributions often were due at least partly to movements of animals away from the transect line 182 and the detection of animals only after they were in motion. Though movements were not always directly away from the transect line, a relatively small number of such movements could bias the estimates. Another reason for low density estimates relates to sample sizes. It was found that sample sizes under 40 yielded estimates which were ranked much lower than those above 40. For sample sizes less than 30, estimates were sometimes lower even than those of the Hahn estimator, regardless of the shape of the pdf. From this study, the Fourier Series estimator appeared to be reliable when sample sizes exceeded 40 and when movements of animals prior to de- tection were minimal. In instances when the pdf was a approximately negative exponential or when observations nearest the transect line were fewer than longer distances, this estimator yielded lower estimates than the Hahn estimator. The present findings seemed to confirm.Burnham}s et al. (1980) observation that few if any estimators perform well when the pdf is skewed. Though widely used in Africa, the accuracy of the Hahn estimator could not be duplicated in this study with respect to bias has been examined in only one study. Hirst (1969) found success with this method in South Africa but there was strong evidence in Park W that this estimator yielded underestimates. PosSibly it is in more open habitat where visi- bility declines over longer distances that the Hahn method is most useful. The results of this study do not necessarily invalidate other methods of determining visibility profiles such as those employed by Lamprey (1964), Harris (1970) or Hahn (1949). From the experience gained in Park W, however, it appears unlikely that even where profiles have been 183 carefully determined by measuring disappearing distances of assistants at frequent intervals along the transect, this does not accurately re- present the area in which all individuals of a broad spectrum of animal species can be counted. Correction factors for very large and very small animals would appear to provide only crude estimates of density for species of extreme sizes. In the studies of Kranz (1973) and Evans (1975), the profile method underestimated the effective area, whereas in Park W, it was overestimated. Their conclusions were based on both simu-~ lation and field tests. The main differences between their studies and the present one apparently involves the interpretation and application of disappearing distances. In their approach, they measured the area visible at any one point along the center line and assumed that animals which were obscured” by vegetation at that point could not be detected further along the line. Possibly, in the vegetation encountered in their study area this was the case. In Park W, however, an animal might temporarily be obscured from view but as the observer continued along the transect, the animal came into view again from a second vantage point. Also in Park W, there was usually a gradual decline in visibility and the animals became increasingly more difficult to see as distances increased. In Evan's study the dis- appearance of animals was apparently more abrupt, as a shrub or hill caused them to disappear. One possible method of bringing the Hahn method as applied in this study into accord with estimates of other estimators would be to truncate observations at some distance beyond which most animals would not likely be detected. An examination of the Park W observations, however, re- vealed that a large number would have to be deleted for density estimates 184 to be reduced to the level moderate ones such as the Fourier Series. This truncation introduces an additional subjective variable into the formula and often would drastically reduce the sample size. Examining ‘frequency histograms of disappearing distances for a fall-off point where the data could be truncated was not helpful in most cases. No truncation points were obvious. The Hahn method is considered to be of limited usefulness. It can serve, perhaps, only as a rough index to animal abundance and as a minimum estimate for comparing the relative values of other estimators. Selection process for estimators Although several radial and perpendicular distance estimators have been recommended, further guidelines are desirable to narrow the array of choices. It is suggested that r and 9 routinely be measured in the field in addition to x, to enable a flexibility of choices should sample sizes be less than 40. The approach of examining the pdf, testing it against parametric distributions such as the negative exponential, and then selecting the parametric estimator whose assumed distribution has been most closely matched, is not recommended here. This is mainly because for any given pdf there are usually several distributions which are not significantly different from the observed distribution. Density estimates based on these parametric estimators are often quite variable and it is not clear which would likely be the most accurate. It has been noted (Gates 1979; Burnham.et al. 1980), too, that these parametric estimators can yield badly-biased estimates even when there are small departures from the assumed distributions. 185 A selection key (Figure 32) has been prepared in which the Fourier Series is recommended for data sets greater than 40 and where the pdf is not skewed. The Polynomial is recommended as a second choice. These estimators are believed to be the most applicable to a wide range of detection functions. Nevertheless, under certain circumstances, other estimators may be more appropriate. For sample sizes smaller than 40, the Generalized Exponential estimator is recommended where observations are based on perpendicular distances (Figure 32). This parametric estimator has been advocated be- cause it proved to be more flexible than other such estimators, and gave. consistent results even when sample sizes were quite small. Estimators based on radial distances were believed to be more reli- able for smaller sample sizes. They can be applied to larger data sets as well. For sample sizes smaller than 20, only the King, Geometric and Generalized Exponential estimators are recommended. As noted earlier, the King estimator is generally considered to be.an inaccurate.and out-of— data method. Based on field tests by Robinette et al. (1974) and results of this study, however, the King estimator proved to have merit, especially with.amall sample sizes. When small r values (flushing distances less than 5 m) were encountered, as with Grimm's duiker and bushbuck, and King estimator may be the most reliable radial estimator. Usefulness 25 density estimates As noted by Gates (1979), one of the most disturbing problems facing biologists in the application of line transect methods is the movement of animals prior to detection. The assumption that all animals are first seen in the position originally occupied is commonly violated to varying 186 .uomwz .3 Noam ow «.maama amps. mo moauamooo mouuoaaumo you AmvuoumEHumu no mo coauooaom onu ou hex .Hm ouowfim was: 33.206: 43.5253 llllllllllllllllll mm”...— uwuuoaoou ..oam ohm mooam> u no. _ _ llllllllll NMmMIM. awed. _ _ was. .1 l l. I and mood; .N No? lllll om v o llllllllll _ .mauoooofinm amazmuooou l I l l l l l l I I. mimlwlm llllll _ _ noxflox .HofiaoohHOA .owuuoaoooaoowm: _ _ BNNNBN . .33. 633238 8 A a 3 v a _ _ _ lllllll a mom x lllllll IIIIIIIIIIL .mmw wouHHNHoaoo .vooafimm commas .uom oq.nc Hoauooommxm oouwfimuooou coho: oouwavoz .moauom uoauoom_ I.I.I.I. oosoxm uoo .wom lllll oq.n: lllllllll NHoo x Nuouoaauuo oovsoaaooom muooaousmmoz 187 degrees with most species. The effect of this failure can be expected to cause underestimates, both due to missed animals and to depressed estimates caused by skewed distributions. There have been 110 field studies undertaken to measure this effect. For each species, too, there is potentially a unique pdf. The dis- tribution of perpendicular distances is influenced by activity patterns, response behavior, habitat preferences, animal size, protective coloration and herding and other behaviors. The effects of all these factors, often coupled with small sample sizes, results in a wide range of sighting and perpendicular distance distributions for a given census. These change 1 both by season and year and may be strongly influenced by the occurrence of burned vegetation. The search for a single best estimator for each animal species may lead to several radial and several perpendicular distance estimators for each census. Such a situation is less than desirable, eSpecially in the absence: of computers and with personnel untrained in quantitative methods. In consequence of the increased complexity of estimators, the broad array of choices and the questionable accuracy of many estimators, there may be a decrease in censusing efforts. Value of information from Line transect methods Despite the modest sample sizes and sampling design problems encountered in Park W, the line transect method appears to be a useful management and research tool. Density estimates that are carefully chosen and carefully computed may, in fact, be reasonably accurate. 188 Density estimates of line transect surveys, nevertheless, must be interpreted with caution, especially when small sample sizes are involved. As noted by Gates (1979) and Burnham et al. (1980), there may be no estimate which is accurate for small sample sizes. While sampling design can compensate for the clustered distributions of most species including kob and waterbuck, the usefulness of estimates of bushbuck and reedbuck is questionable. Because of their patchy dis- tributions and close association of these two species with riparian habi- tats, neither the perpendicular or riparian—transects are believed accurately to sample their densities. Also, because of their unknown distributions in the park, population estimates would seem especially unreliable. It is thought, therefore, that line transect methods are not well suited for estimating buskbuck or reedbuck densities. Sample counts 'along streams may, however, serve as indices of population trends. 1 The results of this study also indicate that small-scale line transect surveys are of little use for estimating densities or detecting popu- lation trends. Because of time limitations, replicate samples over the same area are impractable. Furthermore, it is not physically possible to saturate small areas with enough transects to achieve adequate sample sizes without risking duplicate counting of animals. Surveys therefore, should cover at least 50% of the park in order to obtain reasonably-large sample sizes. The future use of line transect methods in Park W, Niger is en— couraged with the precaution that the survey is carefully designed, accurate measurements are made and a large enough area is sampled to achieve meaningful sample sizes. 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