Improving the Estimates from Inaccurate Censuses

Most eounts of animals are underestimates of the true total, beeause some animals are not seen during the eensus. This is partieularly true of an aerial eensus. A method is presented for esti- mating the nunlber of animals in an area from several eounts, eaeh of whieh underestimates the true total. It requires a mean and a varianee from sets of counts obtained at two levels of survey effieieney. An estimate of true numbers is obtained by solving a pair of simultaneous equations deseribing a para- bolic relationship between mean and variance. Computer simulations suggest that the estimate is stable whether sightabil*y is eonstant or variable between individuals and whether individual sightabilities re- main constant or vary between survey oecasions. A worked example utilizes eounts of blaek rhinoeeros (Dtceros bicounis). In this paper, we draw attention to a source of bias present in almost all enu- merations obtained by direct counting and suggest ways in which an estimate of true numbers can be obtained from these biased counts. As an illustration, we take the imaginary example of a population of elephants living on a lightly timbered island. The usual method of census in this case calls for fly- ing over all parts of the island and counting the elephants. But at any one time, a num- ber of elephants will be standing under trees and will therefore not be detected. If we carry out this census several times we will obtain a set of totals, but although we can present the highest of these as an estimate of minimum numbers, we have no way of knowing what proportion of the true total the estimate represents. This problem appears in almost all direct enu- merations.