Practice question

Counts from a random Poisson distribution have variance approximately equal to their mean. When variance is smaller than the mean, sampling units contain more similar numbers of individuals than random placement would produce, indicating a uniform or regular pattern. Organisms may become regularly spaced through territorial exclusion, direct competition, allelopathy, or local depletion around each individual. In contrast, clumped or patchy distributions usually give variance greater than the mean because occupied units contain aggregations while many units contain few organisms. The variance-to-mean ratio formalizes the comparison: values below 1 indicate underdispersion, around 1 indicate randomness, and above 1 indicate aggregation. This classification depends on the spatial scale and size of sampling units; the same population can appear clumped at one scale and regular at another. Statistical testing is also preferable when the ratio lies close to unity. Nonetheless, variance below the mean captures the central signature of uniform spacing: abundance is distributed among quadrats more evenly than expected by chance.