"Timed Species Counts (TSCs) have been found to provide useful data for assessing the relative abundances of birds in conservation studies, particularly in species-rich areas, such as many tropical habitats. An index is conventionally based upon the mean TSC from a number of counts. In this paper, we develop a new statistic, lambda, which is based upon the assumption that the number of encounters with a species in unit time has a Poisson distribution. Using the same assumptions on detectability that underlie earlier analyses of TSC data, values of lambda, unlike the simple mean TSC, are directly proportional to abundance. However, TSC data are affected by detectability, so that comparisons of relative abundance for the same species between similar sites have greater validity than those between different species. Explicit formulae for calculating an estimate of lambda and its SE from sample data are described. Although lambda can be estimated from either TSC data or the simple proportion of counts in which the species was encountered, for the commonest species a simulation study shows that only data in full TSC form provide accurate estimates. The difference becomes negligible for scarcer species. The use of lambda in preference to mean TSC scores is recommended where it is important to compare values of relative abundance."
https://www.researchgate.net/publication/249437797_On_the_us...