Summary
In the field, animals, birds and fishes are often distributed inhomogeneously. In such situations, the variance of sightings of strip or line transect survey would be larger than when they are independently distributed one another. We formulate in this paper the structure of the patchy configuration, and deduce the variance of sightings of strip or line transect survey. From this, we see that it is larger when the patch size (the expected number of objects in each patch) is larger and the patch radius is smaller.
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References
Anscombe, F. J. (1950). Sampling theory of the negative binomial and logarithmic series distributions,Biometrika,37, 358–382.
Bliss, C. I. and Fisher, R. A. (1953). Fitting the negative binomial distribution to biological data,Biometrics,9, 176–200.
Buckland, S. T. (1985). Perpendicular distance models for line transect samplings,Biometrics,41, 177–195.
Buckland, S. T. (1986). Estimation of minke whale numbers from the 1984/85 Antarctic sightings data, paper SC/38/Mi12 presented to the IWC Scientific Committee, May 1986.
Buckland, S. T. (1986). An assessment of the performance of line transect models on modelling IDCR cruise data, 1978/79 to 1984/85, paper SC/38/Mi22 presented to the IWC Scientific Committee, May 1986.
Burnham, K. P., Anderson, D. R. and Laake, J. (1980). Estimation of density from line transect sampling of biological populations,Wildlife Monographs, No. 72, The Wildlife Society.
Butterworth, D. S. (1982). A possible basis for choosing a function form for the distribution of sightings with right-angle distance: some preliminary ideas,Rep. Int. Whal. Commn.,32, 555–558.
Butterworth, D. S. (1982a). On the functional form used forg(y) for minke whale sightings, and bias in its estimation due to measurement inaccuracies,Rep. Int. Whal. Commn.,32, 883–888.
Butterworth, D. S., Best, P. B. and Hembree, D. (1984). Analysis of experiments carried out during the 1981/82 IWC/IDCR Antarctic minke whale assessment cruise in area II,Rep. Int. Whal. Commn.,34, 365–392.
Butterworth, D. S. and McQuaid, L. H. (1986). An initial analysis of experiments carried out on the 1984/85 IWC/IDCR Antarctic minke whale assessment cruise to compare closing and passing mode procedures in respect of minke whale density estimation, paper SC/38/Mi13 presented to the IWC Scientific Committee, May 1986.
Cooke, J. G. (1984). Some considerations for the design and analysis of sightings surveys for estimating whale stocks, document IWC/IDCR/7thSHMi/SM8 submitted to the IDCR Specialists' Meeting, Tokyo, October 1984.
Daley, D. J. and Vere-Jones, D. (1972). A summary of the theory of point processes, inStochastic Point Processes (ed. P. A. W. Lewis), Wiley.
Hayes, R. J. and Buckland, S. T. (1983). Radial distance models for the line transect method,Biometrics,39, 29–42.
Hiby, A. R. and Ward, A. J. (1986). Analysis of cue-counting and blow rate estimation experiments carried out during the 1984/85 IDCR minke whale assessment cruise,Rep. Int. Whal. Commn.,36, 473–475.
Kasamatsu, F. and Kishino, H. (1986). Preliminary investigation on effects of sighting condition, paper SC/38/Mi14 presented to the IWC Scientific Committee, May 1986.
Kishino, H. (1986). On parallel ship experiments and the line transect method,Rep. Int. Whal. Commn.,36, 491–495.
Kishino, H. and Kasamatsu, F. (1986). Comparison of closing and passing mode, paper SC/38/Mi7 presented to the IWC Scientific Committee, May 1986.
Matthes, K., Kersten, J. and Mecke, J. (1978)Infinitely Divisible Point Processes, Wiley, New York.
Ward, A. J. and Hiby, A. R. (1986). Analysis of cue-counting and blow rate estimation experiments carried out during the 1985/86 IDCR minke whale assessment cruise, paper SC/38/Mi10 presented to the IWC Scientific Committee, May 1986.
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Kishino, H. Variance of sightings in the survey of patchily distributed objects. Ann Inst Stat Math 39, 275–287 (1987). https://doi.org/10.1007/BF02491467
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DOI: https://doi.org/10.1007/BF02491467