Practice question

Independent random placement of organisms is commonly modeled by a Poisson distribution. A defining property of the Poisson distribution is equality of its mean and variance, so the variance-to-mean ratio is expected to be 1. Values substantially below 1 indicate underdispersion or uniform spacing, because counts vary less than chance predicts. Values above 1 indicate overdispersion or clumping, because some units contain aggregations while others are nearly empty. An observed ratio will rarely equal exactly 1 in a finite sample; statistical tests evaluate whether the departure is greater than expected by sampling variation. The result also depends on quadrat size and spatial scale. A population may appear random at one grain even if it is clustered within smaller patches or regularly arranged at very short distances. Thus the ratio of 1 is a theoretical null expectation, not proof that no ecological processes operate. It means that, at the sampled scale, attraction and repulsion do not produce detectable departure from independent spatial placement.