Practice question

The variance-to-mean relationship provides a simple index of spatial dispersion in counts from equal sampling units. A Poisson random distribution has variance approximately equal to its mean. Here the index of dispersion is 0.35/7.05 ≈ 0.05, far below 1, indicating that quadrat counts vary much less than expected under random placement. Such underdispersion corresponds to a uniform or regular spatial pattern. Regular spacing can arise through territorial behavior, interference, allelopathy, competition for resources, or deliberate spacing in managed systems. A clumped pattern would produce variance greater than the mean because many quadrats would contain few individuals while a few contain large aggregations. The inference assumes comparable quadrat sizes, adequate sampling, and counts taken at a spatial scale capable of detecting the pattern. Significance is ideally evaluated with an index-of-dispersion test rather than classification from the ratio alone. Nevertheless, the extreme underdispersion in these values strongly supports uniform spacing. The mean describes average density per unit, while the low variance reveals unusually consistent counts among units.