Frequency distribution models for spatial patterns of vegetation abundance

In a plant community, measurements of the number of plant individuals, the number of binary occurrences, plant cover, and biomass per unit area have frequently been used to explain species composition and spatial variation. Studies have shown that frequency distribution can be expressed in several ways: the number of individuals can be expressed using the negative binomial distribution, the number of binary occurrences can be expressed using the beta-binomial distribution, plant cover can be expressed by the beta distribution, and biomass by the gamma distribution. In this study, we have mathematically clarified the relationships between these distributions and their biological relevance. We have also defined a spatial heterogeneity index for each of the above four methods of measurement. For each of these four distribution patterns, several-fitted examples of plant populations or communities, obtained from grassland surveys, are provided.