Wildl. Soc. Bull. 19:117-118. 1991

WILDLIFE SOFTWARE

                     SIZETRAN: ANALYSIS OF SIZE-BIASED
                            LINE TRANSECT DATA
                                     
THOMAS D. DRUMMER, Department of Mathematical Sciences, Michigan Technological
     University, Houghton, MI  49931

     Line transect sampling is 1 method that can be used to estimate the density of
a biological population (Seber 1982). Burnham et al. (1980) provide an overview of
the line transect sampling procedure and mathematical aspects of the estimation
procedures. The computer program TRANSECT (Laake et al. 1979) is available for the
analysis of such data. In some line transect surveys, however, observations consist
of groups of items rather than individuals. In addition to measuring the perpendicular
distance to the center of the group, group size is also recorded. The experimenter
must estimate group density and mean group size to estimate the density of
individuals.
     Size-biased density estimates may occur when the probability of detecting a
group is a function of the group size. In particular, if the chance of detection
increases with group size, the observed mean group size will tend to overestimate the
true mean group size and hence overestimate the true density. Drummer and McDonald
(1987) proposed a family of bivariate detection functions incorporating both
perpendicular distance and group size. These detection functions employ a size-bias
parameter that reflects the degree of influence of group size on detectability. Based
on the estimated detection function parameters, estimates of group density, mean group
size, and individual density are adjusted for size-bias. Drummer and McDonald (1987)
provide derivations of these bivariate estimators and their variances. A test for
significant size-bias can be performed as well as goodness-of-fit tests for the
detection functions.
The software package SIZETRAN consists of 2 programs, SIZTRANU and SIZTRANG. The
program SIZTRANU is used when the perpendicular distance data are ungrouped, whereas
SIZTRANG is used for the grouped distance data case. Both programs fit the bivariate
and distance-only versions of the negative exponential (Gates et al. 1968),
half-normal (Quinn 1977), general exponential (Quinn and Gallucci 1980), and reversed
logistic models (Eberhardt 1978).
 Both programs are written in ANS FORTRAN-77. The PC version was compiled using MS-DOS
with the Microsoft Fortran (version 3.13) compiler for use on IBM PC's and
compatibles. A copy of the source code, PC executable code, user documentation, and
test data are available on the southeastern software and message exchange (SESAME),
or can be obtained from the author.
     Acknowledgments. - The author thanks 2 referees for taking the time to review
the program code and making many helpful suggestion.~

                             LITERATURE CITED
                                     
BURNHAM, K. P., D. R. ANDERSON, AND J. L. LAAKE. 1980. Estimation of density from line
     transect sampling of biological populations. Wildl. Monogr. 72. 202pp.

DRUMMER, T. D., AND L. L. MCDONALD. 1987. Size-bias in line transect sampling.
     Biometrics 43:13

EBERHARDT, L. L. 1978. Transect methods for population studies. J. Wildl. Manage.
     42:1-31.

ATES, C. E., W. H. MARSHALL, AND D. P. OLSON. 1968. Line transect method of estimating
     grouse densities. Biometrics 24:135-145.

LAAKE, J. L., K. P. BURNHAM, AND D. R. ANDERSON. 1979. User's manual for program
     TRANSECT. Utah State Univ. Press, Logan. 26pp.

QUINN, T. J. 1977. The effects of aggregation on linetransect estimators of population
     abundance with application to marine mammal populations. M.S. Thesis, Univ.
     Washington, Seattle. 116pp.

-----, AND V. F. GALLUCCI. 1980. Parametric models for line transect estimators of
     abundance. Ecology 61:293-302.

SEBER, G. A. F. 1982. The estimation of animal abundance. MacMillan Publ. Co., New
     York, N.Y. 654pp.

Received 3 October 1990.
Accepted 6 October 1990