Využití Giniho koeficientu pro analýzu prostorové distribuce společenstev v ekologii

This bachelor’s thesis examines the measurement of spatial inequality in bird distribution using the Gini coefficient. The goal is to analytically derive the natural bounds of this coefficient in discrete space and to quantify the behavior of its expected value as a function of the number of individuals n and the number of locations k. The research employs Monte Carlo simulations based on a null model uniform multinomial distribution. Five thousand simulation runs were performed for each of the twenty combinations of parameters n ∈ {10, 50, 100, 500, 1000}, k ∈ {5, 10, 20, 50}, which allowed for a systematic analysis of the behaviour of the Gini coefficient as a function of sample size. Based on the derived bounds, a rescaled coefficient is defined to ensure comparability of results across studies with different n and k. Furthermore, a parametric model is derived from the simulation data that allows for the approximation of the expected value of the Gini coefficient under the null model for any n and k without the need to rerun simulations. On this basis, a clustering simulation test is proposed that allows for a formal assessment of whether the observed spatial non-uniformity exceeds what would be expected by pure chance. The work also includes the development of a specialized R package providing tools for calculating, rescaling, and visualizing the Gini coefficient in monitoring data on animal species communities. These findings contribute to the interpretation of spatial patterns in the distribution of bird populations and provide a methodological foundation for working with limited field data.