Population ecology of the single species. Growth of single population. Application of Leslie Matrices to change in population composition. Tree demography; leaf demography. Interaction of two species. k- species interaction. Spatial patterns in 1-species population: aggregation. Diffusion, patterns of ecological maps. Spatial patterns of two or more species. Association between pairs of species. Segregation between 2 species; segregation among many species (n-phase mosaics); patterns in zoned communities. Many species populations: species abundance; species diversity, stability and resilience; ecological diversity; classification of communities; ordination of continuously varying communities; canonical variate analysis and multiple discriminant analysis. Population and habitat vibrant analysis (Lacy: see Species 25:1) Problems of mathematical bioeconomics: optimal management of renewable resources (Clark).