In ecology, the Shannon diversity of a community is defined by \[H=-\sum_{i}^R p_i\log p_i,\] where \(R\) is the number of distinct species and \(p_i\) is the proportion of species \(i\). The Shannon diversity measures richness (i.e. the number of distinct species in a community) and evenness (i.e. how evenly the proportions of species are spread). In the following illustration, each dot represents a mock community: the horizontal coordinate shows the number of distinct species (richness) and the color shows the various distributions of proportions given the number of distinct species. Even distribution means that the proportions are evenly distributed (thus giving the maximum possible Shannon diversity). Proportion of most dominant species of 0.7, for example, means that the community is dominated by a single species which takes up 70%, and the remaining species are evenly distributed.