Practice question

The variance-to-mean ratio, often called an index of dispersion, compares observed variation among equal sampling units with the Poisson expectation. Randomly and independently placed individuals yield a ratio near 1 because a Poisson distribution has equal mean and variance. A ratio greater than 1 indicates overdispersion: counts differ more among quadrats than chance alone predicts, with many low-count units and some high-count units. This is the statistical signature of clumping. Patchy resources, social attraction, restricted dispersal, and reproduction near parents can all generate it. Uniform spacing produces underdispersion and a ratio below 1 because counts are unusually even. Equilibrium is a demographic concept and cannot be inferred from this spatial index. The ratio’s interpretation depends on quadrat size, sampling design, and the number of samples; formal significance can be tested using the index multiplied by degrees of freedom. Nevertheless, a clearly elevated ratio provides direct evidence that individuals aggregate at the spatial scale represented by the sampling units.