Nestedness and τ-temperature in ecological networks |
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| Institution: | 1. Department of Ecology & Environmental Sciences, Pondicherry University, Kalapet, Pondicherry 605014, India;2. Université Grenoble Alpes, Laboratoire d''Écologie Alpine, 38000 Grenoble, France;3. French Institute of Pondicherry, 11 St Louis Street, Pondicherry 605001, India;4. Sigur Nature Trust, Mavinhalla PO, Nilgiris 643223, Tamil Nadu, India;5. Centre for Environmental Studies, Amrita Vishwa Vidyapeetham, Ettimadai, Coimbatore 641112, India;1. Department of Biological Sciences, University of Arkansas, Fayetteville, AR, United States;2. Illinois Natural History Survey, Prairie Research Institute, University of Illinois at Urbana-Champaign, Champaign, IL, United States |
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| Abstract: | The τ-temperature is a measure of disorder of bipartite networks that is based on the total Manhattan distance of the adjacency matrix. Two properties of this measure are that it does not depend on permutations of lines or columns that have the same connectivity and it is completely determined by connectivities of lines and columns. The normalisation of τ is done by an uniform random matrix whose elements were previously sorted. τ shows no bias against uniform random matrices of several occupations, ρ, sizes, L, and shapes. The scaling of the total Manhattan distance of a random matrix is Drand ∝ L3ρ while the same scaling for a full nested matrix is Dnest ∝ L3ρ3/2. We test τ for a large set of empirical matrices to verify these scalings. The index τ correlates better with the temperature of Atmar than with the NODF index of nestedness. We conclude this work by discussing differences between nestedness indices and order/disorder indices. |
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