Size Bias in Line Transect Sampling

SUMMARY Line transect sampling is used to estimate the number of individuals in a study area. It is usually assumed that the detections of individuals constitute independent events, and that the probability of detecting an item is a function of its perpendicular distance from the transect. However, certain species of plants/animals tend to aggregate, or cluster, thus possibly violating the assumption of independence. Also, larger clusters may tend to have a higher probability of detection, thus distorting the observed probability distribution of cluster sizes. This can cause overestimation of the true population size. A similar problem occurs if the experimenter is using line transect data to estimate the mean and total amount of some attribute of the items, and this attribute influences the item's probability of detection. Bivariate detection functions that incorporate the cluster size, or another attribute, as a covariate are proposed. Estimators of total population size and of the moments of the additional variate are derived using the theory of weighted distributions. An application of the method to a shipboard survey of minke whales is provided. Line transect sampling is traditionally used to estimate the total number of items in a study area. It is usually assumed that the probability of detecting an item is a function of its perpendicular distance from the transect. See Burnham, Anderson, and Laake (1980) for a comprehensive review of line transect estimation procedures. The primary application of the proposed procedure is for the case when the population consists of groups, or clusters, of individuals. In order to estimate the density of individuals per unit area, the experimenter will need an estimate of mean group size. However, if group size influences delectability, the observed mean group size is a biased estimator of the mean. Also, an experimenter may desire to use line transect surveys to estimate some attribute of the items other than their density (number) per unit area. For example, if the item under study is a particular shrub species, the experimenter may require an estimate of the mean height of the plants in the study area. If larger plants have a greater chance of being detected from the transect, then these data are size-biased toward larger plants. Thus, the observed mean height may be a poor estimate of the true mean. The line transect estimator of density that is based solely on the observed distances from the transect to the items may also be biased. It is important to determine whether the additional variable(s) of interest influences an item's probability of detection. If this is the case, then estimates of the characteristics of this variable must be adjusted for the size-biased sampling phenomenon.