Measures of spatial heterogeneity for species occurrence or disease incidence with finite-counts

We propose two types of indices with finite-count correction to measure the spatial heterogeneity of binary characteristics of organisms, such as occurrence or non-occurrence of organisms and infected or non-infected plants. We consider the following two examples: plant occurrence in a grassland community, and yellow dwarf disease infection in a rice field. For the grassland community, N quadrats comprising n cells of equal area, were set at random sites in a grassland, and the occurrence of a given species A in each of n cells was recorded. For disease infection, N quadrats, each consisting of n rice plants, were set at random sites in a paddy field, and the number of plants infected with yellow dwarf virus in each quadrat were counted. In these examples, since the number of cells in a quadrat is finite, neither occurrence nor incidence increase infinitely, unlike the number of aphids on a maize leaf. The first category of index belongs to the mean : variance ratio type. The estimated index value for occurrence (or incidence) is the same as that for non-occurrence (or non-incidence). The second category belongs to the k-type of a negative binomial distribution. If some random plants die or recover from the disease then the expected value of the second type of index does not change. For n, the current indices approach the mean : variance ratio and the inverse of k in a negative binomial distribution, respectively. This indicates that these indices are suitable for binary data sets.