The Poisson distribution is obtained as the limit as k -> o At the other end of the scale, as k -> 0, we approach the logarithmic series [6]. If we have' several sets of counts on the same species of insect, from different districts or after different treatments, we may find that the mean m varies between the sets, but k remains approximately the same. To analyse such data statistically, we need to obtain a pooled estimate of k from all sets of counts and estimate the mean m separately for each set. There is some theoretical evidence [7] to show that k depends on the intrinsic power of the species to reproduce itself, while m depends on external factors. To try to fit negative binomial distributions with a common value of k to sets of counts on the same species is therefore a reasonable procedure.
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