Richard B. HARRIS Kenneth P. BU RN HAM

Transcription

1 48 (6) : , 2002 A cta Zoologica S inica Richard B. HARRIS Kenneth P. BU RN HAM ( Wildlife Biology Program University of Montana, Missoula, MT 59812, USA) ( Colorado State University, Fort Collins, CO 80523, USA),, DISTANCE, DISTANCE,,, (1992), (Southwell, 1994 ; Harris, 1996),, (, 1993 ;, 1997),,,, ( Anderson et, ( Fourier series, al., 1979 ; Burnham et al., 1980 ; Buckland et al., 1993) : (1) 110, ( ) ; (2) ;, (3),, ( ) ; Burnham et al., 1980) (4) ; ( Thomas et al., 1998) (5) ; (6) (,, ), (Burnham et al., 1998) ) ; (7) ( ( Eberhardt, 1968 ; Gates et ) al., 1968 ; 1) : ( half2nor2 mal Buckland et al., 1993), DISTANCE, g ( x) = e ( - ax) ( 1), ( ), Burnham et al. (1980) g ( x) = ( ) x 40), , Robert M. Lee Richard B. Harris, 48,, Research Associate. :, E2mail : com

2 813 6 Richard B. HARRIS : a = x = 1 Beta, (,, 1) Table 1 Mean percent relative bias of the negative exponential function ( Eq. 1) and the more flexible, Fourier series, when applied to simulated data (, 1992 ; 2) using underlying negative exponential, half2 D = ns/ 2 L W ( 2) normal, and modif ied beta detection functions : D = ( ) n = ( ) s = L = W =, 2 (Negative exponential) ( ), 2 2 ( 1), ,, (Moderately truncated) 1 2,, (Untrunctated) Buckland et al. (1993), (Shoulder) ( 2) 57 % al., Burnham et (1980) 1, (Spiked), 25 ( Values in each case are, means from 25 simulations) ; 100, 12 % 16 %,,, 10 %, 66 %,, Burnham et al. ( 1980),, Robinette et al. (1974) Underlying detection function Model used in calculation (Negative exponential) ( Fourier series) (Severely truncated) (Moderately truncated) (Untruncated) ( Half2normal) (Severely truncated) Beta (Modified beta) (Linear) ( The sample size of distances in each simulation was 100) ; Burn2 ham et al. (1980 : 158) [ Data taken from Burnham et al. (1980 : 158) ] 2 19 % 89 %, 48 %, Parmenter et al. (1989)

3 Fig. 1 Histograms and f itted detection functions for an example of distance data A., 4215 / hm 2 (A. The Fourier series detection function, which yielded an esti2 mate of 4215 stakes/ hm 2 ) B., 2, 6719 / hm 2, 3715/ hm 2 (B. The negative exponential detection function, which is assumed when using Eq. 2, which yielded an estimate of 6719 stakes/ hm 2. The true density of stakes as 3715 hm 2 ) (Burnham et al., 1980 : 62) [Data are from wooden stakes placed in the ground at a known density (Burnham et al., 1980 : 62) ], Laake (1978),,, g (0) = 0182 [ g (0) = 110 ] 1A 3715 / hm 2,,

4 815 6 Richard B. HARRIS : DISTANCE ( 2), 4215 / hm 2, 13 %, 2 ( 1B), 6719 / hm 2 ( 81 %),,, Anderson et ( 2A) al1 (2001) ( ) 327 m, 380 m, 12,, 0153 / km 2 12, 7 % 0141 / km 2, 13 % ( 4 %, 2) ( 2B) 0182 / km 2, 2, 62 % 93 %, 0154 / km 2 2, 70 % ( 2) 2 2 ( Burnham et al. 1980) 12 Table 2 Abundance estimates of artif icial tortoises using Eq. 2 and the Fourier series method ( Burnham et al. 1980) from 12 different survey teams 2 Team N Eq. 2 Percent Bias Fourier Percent Bias % 74-3 % % % % 75-1 % % % % 73-4 % % 71-7 % % % % % % 75-1 % % % % % % 72-5 % (Mean) % 73-4 % Anderson et al. ( ), [ Data are taken from Anderson et al. ( submitted). The true abundance of tortoises in all 12 cases was 76 ] 112 2, Fig. 2 Histograms of perpendicular distances,, (1997) ( Ovis am mon) , [ 2 ( ), 9 14, 40 (Burnham et al., 1980) (1997), 2 ( 1997) of argali ( Ovis ammon) observed during line transect surveys conducted by Gao Xing2Yi et al. ( 1997) A. [ 1 (1997) ], [ A. Surveys in Hami ( Table 1 from X. Y. Gao et al., 1997, fitted with the negative exponential function) ] B. (1997) ], 1 [B. Surveys in Mulei ( Table 2 from X. Y. Gao et al., 1997), fitted with the negative exponential distribu2 tion. Compare the shape of histograms from those in Fig. 1 ]

5 Fig. 3 Fourier series detection functions superimposed on histograms of perpendicular distances from a survey of Tibetan gazelles in Qinghai Province DISTANCE (Using program DISTANCE) n = 64 2, DISTANCE ( ) DISTANCE,,,,,, DISTANCE, 2, Harris ( 1996) Harris et al. (1995, 1996),,, ( Procapra picticauda2, DISTANCE ta), ( n = 64 ), 10 % (An2 ( 3) derson et al., 1995),,,,,,, (1997) 3 (http :/ / ruwpa. st2and. ac. uk/ distance), ( n = 1), 2 2,,, 2,,,, ( Thomas et al., 1998) ( (Burnham et al., 1980 ; Buckland et al., ), 1993) (DISTANCE ) ( ), (Buckland et al., 1993)

6 817 6 Richard B. HARRIS :,,,,,,,, DISTANCE, S. T. Buckland J. L. Laake,,, ( References) Anderson, D. R., J. L. Laake, B. R. Crain and K. P. Burnham 1979 Guidelines for line transect sampling of biological populations. Journal of Wil dlif e Management 43 : Anderson, D. R. and C. Southwell 1995 Estimates of macropod density from line transect surveys relative to analyst expertise. Journal of Wil dlif e Management 59 : Anderson, D. R., K. P. Burnham, B. C. Lubow, L. Thomas, P. S. Corn, P. A. Medica and R. W. Marlow 2001 Field trials of line transect methods applied to estimation of desert tortoise abundance. Journal of Wil dlif e Management 65 : Buckland, S. T., D. R. Anderson, K. P. Burnham and J. L. Laake 1993 Distance Sampling : Estimating Abundance of Biological Populations. London : Chapman and Hall, 446. Available from http :/ / ruwpa. st2and. ac. uk/ distance. Burnham, K. P. and D. R. Anderson 1998 Model Selection and Inference : A Practical Information2theoretical Approach. New York : Springer2 Verlag. Burnham, K. P., D. R. Anderson and J. L. Laake 1980 Estimation of density from line transect sampling of biological populations. Wil dlif e Monographs 72 : Eberhardt, L. L A preliminary appraisal of line transects. Journal of Wil dlif e Management 32 : Gao, X. Y. and J. Yao Argali of the eastern Tianshan, Xinjiang. Chi nese Wil dlif e 18 (4) : [, (4) : ] Gates, C. E., W. H. Marshall and D. P. Olson 1968 Line transect method of estimating grouse population densities. Biomet rics 24 (1) : Harris, R. B., D. J. Miller, Cai G. Q. and D. H. Pletscher 1996 Wildlife status and conservation in Yeniugou, Qinghai. Si nica 16 : : ] Acta Theriologica [ Harris, R. B., D. J. Miller,, D. H. Pletscher Harris, R. B Wild ungulate surveys in grassland habitats : satisfying methodological assumptions. Chi nese Journal of Zoology 31 (2) : [ Harris, R. B (2) : ] Harris, R. B. and D. J. Miller 1995 Overlap in summer habitats and diets of Tibetan plateau ungulates. Mam malia 59 : Laake, J. L Line Transect Estimators Robust to Animal Movement. M. S. Thesis. Logan : Utah State University, 55. Liu, W. L. and B. G. Yi 1993 Wildlife Protection in Tibet. Beijing : China Forestry Press, 219. [, :, 219. ] Parmenter, R. R., J. A. MacMahon and D. R. Anderson 1989 Animal density estimation using a trapping web design : field validation experi2 ments. Robinette, W. L., C. 96. Ecology 70 : M. Loveless and D. A. Jones, 1974 Field tests of strip census methods. Journal of Wil dlif e Management 38 : 81 Sheng, H. L. and H. F. Xu 1992 Field Research Methods for Mammals. Beijing : China Forestry Press, 379. [, :, 379. ] Southwell, C Evaluation of walked line transect counts for estimating macropod density. Journal of Wil dlif e Management 58 : Thomas, L., J. L. Laake, J. F. Durry, S. T. Buckland, D. L. Borchers, D. R. Anderson, K. P. Burnham, S. Stringberg, S. L. Hedley, M. L. Burt, F. Marques, J. H. Pollard and R. M. Fewster 1998 Program DISTANCE 315. Research Unit for Wildlife Population Assessment. University of St. Andrews, U. K. Available from http :/ / ruwpa. st2and. ac. uk/ distance.

7 ( Abstract) ON ESTIMATING WILDL IFE DENSITIES FROM L INE TRANSECT DATA 3 Richard B. HARRIS 33 Kenneth P. BURN HAM ( U niversity of Montana, Missoula, M T 59812, USA ) ( Colorado State U niversity, Fort Colli ns, CO 80523, USA ) Line t ransect s are one of t he best ways to estimate density of wildlife populations over large areas. Howev2 er, density estimates will be unreliable if using mathematical procedures that, although simple and easy to use, do not correspond with reality. We provide theoretical and empirical evidence that using a simple mean dis2 tances approach (e. g., Sheng et al., 1992 ; Gao et al., 1997) in which the mean of observed perpendicular distances is equated with the effective strip width (i. e., D = ns/ 2 L W, in which D = estimated density of ani2 mals, n = number of animals seen, s = mean group size, L = length of transect line, and W = mean perpendicu2 lar distance of animals seen) is unlikely to yield reliable results. This mean distances approach will be approxi2 mately t rue only when t he t rue ( underlying) detection probability follows a negative exponential dist ribution (and even then, does not allow calculation of variance). However, if the half2normal detection function is true, this mean distances approach can be expected to be positively biased by 57 %. In empirical tests of line transect estimators, the mean distances approach overestimated true density by 41 % to 81 %. Alternative mathemati2 cal formulations to this mean distances approach, incorporated into program D ISTANCE, are much less likely to be seriously biased. Using t hese alternative approaches also forces investigators to consider seriously issues of sample size (whereas the mean distances approach will produce an estimate even when n = 1, in which case t he researcher really has no data on how detection varies wit h distance). We urge researchers to familiarize t hemselves wit h t he line2t ransect t heory (Buckland et al., 1993), and to use program D ISTANCE. Equally importantly, we urge researchers to minimize assumption violations of distance sampling, and to follow rigorous random sampling protocols. Key words Density estimation, Detection function, Fourier series, Line transect, Negative exponential distri2 bution, Program D ISTANCE 3 Work in China was funded by the Robert M. Lee Foundation and the Liu Guo Lit Charitable Trust. 33 Corresponding author. com