Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODF
Nestedness is a concept employed to describe a particular pattern of organization in species interaction networks and in site-by-species incidence matrices. Currently the most widely used nestedness index is the NODF (Nestedness metric based on Overlap and Decreasing Fill), initially presented for b...
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2016-01-01
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| Series: | Biomath |
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| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/476 |
| _version_ | 1827852688432300032 |
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| author | Nicholas Britton Mario Almeida Neto Gilberto Corso |
| author_facet | Nicholas Britton Mario Almeida Neto Gilberto Corso |
| author_sort | Nicholas Britton |
| collection | DOAJ |
| description | Nestedness is a concept employed to describe a particular pattern of organization in species interaction networks and in site-by-species incidence matrices. Currently the most widely used nestedness index is the NODF (Nestedness metric based on Overlap and Decreasing Fill), initially presented for binary data and later extended to quantitative data, WNODF. In this manuscript we present a rigorous formulation of this index for both cases, NODF and WNODF. In addition, we characterize the matrices corresponding to the two extreme cases, (W)NODF=1 and (W)NODF=0, representing a perfectly nested pattern andthe absence of nestedness respectively. After permutations of rows and columns if necessary, the perfectly nested pattern is a full triangular matrix, which must of course besquare, with additional inequalities between the elements for WNODF. On the other hand there are many patterns characterized by the total absence of nestedness. Indeed, any binary matrix (whether square or rectangular) with uniform row and column sums (or marginals) satisfies this condition: the chessboard and a pattern reflecting an underlying annular ecological gradient, which we shall call gradient-like, are symmetrical or nearly symmetrical examples from this class. |
| first_indexed | 2024-03-12T10:53:50Z |
| format | Article |
| id | doaj.art-c13edbaa4d0048aca41df8a930ee5f1d |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T10:53:50Z |
| publishDate | 2016-01-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-c13edbaa4d0048aca41df8a930ee5f1d2023-09-02T06:41:28ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182016-01-014210.11145/j.biomath.2015.12.171388Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODFNicholas Britton0Mario Almeida Neto1Gilberto Corso2Department of Mathematical Sciences and Centre for Mathematical Biology University of Bath, Bath BA2 7AY, UKDepartmento de Ecologia, Universidade Federal de Goias, 74001-970 Goiania-GO, Brazil,Universidade Federal do Rio Grande do NorteNestedness is a concept employed to describe a particular pattern of organization in species interaction networks and in site-by-species incidence matrices. Currently the most widely used nestedness index is the NODF (Nestedness metric based on Overlap and Decreasing Fill), initially presented for binary data and later extended to quantitative data, WNODF. In this manuscript we present a rigorous formulation of this index for both cases, NODF and WNODF. In addition, we characterize the matrices corresponding to the two extreme cases, (W)NODF=1 and (W)NODF=0, representing a perfectly nested pattern andthe absence of nestedness respectively. After permutations of rows and columns if necessary, the perfectly nested pattern is a full triangular matrix, which must of course besquare, with additional inequalities between the elements for WNODF. On the other hand there are many patterns characterized by the total absence of nestedness. Indeed, any binary matrix (whether square or rectangular) with uniform row and column sums (or marginals) satisfies this condition: the chessboard and a pattern reflecting an underlying annular ecological gradient, which we shall call gradient-like, are symmetrical or nearly symmetrical examples from this class.http://www.biomathforum.org/biomath/index.php/biomath/article/view/476biogeography, interaction networks, nestedness, bipartite networks |
| spellingShingle | Nicholas Britton Mario Almeida Neto Gilberto Corso Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODF Biomath biogeography, interaction networks, nestedness, bipartite networks |
| title | Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODF |
| title_full | Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODF |
| title_fullStr | Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODF |
| title_full_unstemmed | Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODF |
| title_short | Which Matrices Show Perfect Nestedness or the Absence of Nestedness? An Analytical Study on the Performance of NODF and WNODF |
| title_sort | which matrices show perfect nestedness or the absence of nestedness an analytical study on the performance of nodf and wnodf |
| topic | biogeography, interaction networks, nestedness, bipartite networks |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/476 |
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