|
Abstract:
|
Upon any matrix representation of a binary bipartite network, a coupling geometry is computed to approximate the system's minimum energy macrostate. Such a macrostate contains intrinsic structures of the system. The coupling geometry is taken as information contents, or the nonparametric minimum sufficient statistics of the network data. It is argued that pertinent null and alternative hypotheses, such as nestedness, are to be formulated according to the macrostate, while any sufficient testing statistic needs to be a function of this coupling geometry. These conceptual mechanisms are still missing in Community Ecology literature. Our algorithmically computed coupling geometry provides a series of ensembles of a binary matrix that are subject to constraints of row and column sums sequences. Based on such a series of ensembles, a profile of distributions becomes a natural device of checking the validity. In this paper, we also propose an energy-based index that is used for testing whether network data indeed contains structural geometry and a new block-based nestedness index. Their validities are checked and compared with the existing ones.
|
