tailieunhanh - Niche Modeling: Predictions From Statistical Distributions - Chapter 4

Các trọng tâm của cấu trúc liên kết ở đây là nghiên cứu về cấu trúc tập hợp con của tập hợp trong không gian toán học. Cấu trúc liên kết có thể được sử dụng để mô tả và liên quan các không gian khác nhau được sử dụng trong mô hình thích hợp. Topology là một cấu trúc nội bộ tự nhiên, xác định chính xác định nhóm toàn bộ các tập con được sản xuất bởi các hoạt động tiêu chuẩn của công đoàn và ngã tư. Đặc biệt quan trọng là những tập con, gọi bộ. | Chapter 4 Topology The focus of topology here is the study of the subset structure of sets in the mathematical spaces. Topology can be used to describe and relate the different spaces used in niche modeling. A topology is a natural internal structure precisely defining the entire group of subsets produced by standard operations of union and intersection. Of particular importance are those subsets referred to as open sets where every element has a neighborhood also in the set. More than one topology in X may be possible for a given set X. Examples of subsets in niche modeling that could form topologies are the geographic areas potentially occupied by a species regions in environmental space groups of species and so on. Application of topological set theory helps to identify the basic assumptions underlying niche modeling and the relationships and constraints between these assumptions. The chapter shows the standard definition of the niche as environmental envelopes around all ecologically relevant variables is equivalent to a box topology. A proof is offered that the Hutchinsonian environmental envelope definition of a niche when extended to large or infinite dimensions of environmental variables loses desirable topological properties. This argues for the necessity of careful selection of a small set of environmental variables. Formalism The three main entities in niche modeling are S the species N the niche of environment variables and B geographic space where the environmental variables are defined. . 45 2007 by Taylor and Francis Group LLC 46 Niche Modeling The relationships between these entities constitute whole fields of study in themselves. Most applications of niche modeling fall into one of the categories in Table . TABLE Links between geographic environmental and species spaces. S N B S interspecies relationships N habitat suitability correlations B range predictions geographic information autocorrelation Niche modeling operates on the .