Nestedness

Nestedness is a measure of structure in an ecological system, usually applied to species-sites systems (describing the distribution of species across locations), or species-species interaction networks (describing the interactions between species, usually as bipartite networks such as hosts-parasites, plants-pollinators, etc.).

A system (usually represented as a matrix) is said to be nested when the elements that have a few items in them (locations with few species, species with few interactions) have a subset of the items of elements with more items. Imagine a series of islands that are ordered by their distance from the mainland. If the mainland has all species, the first island has a subset of mainland's species, the second island has a subset of the first island's species, and so forth, then this system is perfectly nested.

Measures of nestedness

One measurement unit for nestedness is a system's 'temperature' offered by Atmar and Patterson in 1993.[1] This measures the order in which species' extinctions would occur in the system (or from the other side - the order of colonizing a system). The 'colder' the system is, the more fixed the order of extinction would be. In a warmer system, extinctions will take a more random order. Temperatures go from 0°, coldest and absolutely fixed, to 100° absolutely random.

For various reasons, the Nestedness Temperature Calculator is not mathematically satisfying (no unique solution, not conservative enough).[2][3] A software (BINMATNEST) is available from the authors on request and from the Journal of Biogeography to correct these deficits [4] In addition, ANINHADO solves problems of large matrix size and processing of a large number of randomized matrices; in addition it implements several null models to estimate the significance of nestedness.[5][6]

Bastolla et al. introduced a simple measure of nestedness based on the number of common neighbours for each pair of nodes.[7] They argue that this can help reduce the effective competition between nodes in certain situations. For instance, two insect species might "help" each other by pollinating the same subset of plants, thereby reducing the extent to which they are harmful to each other. The authors suggest that this effect is behind a correlation between nestedness and diversity in plant-pollinator ecosystems. However, Johnson et al. have shown that this measure does not, in fact, properly account for the desired effect.[8] These authors propose a refined version of the measure, and go on to show how certain network properties affect nestedness.

gollark: The gradient descent thing is basically moving down hills by going in whichever direction is slightly lower, except it's not hills it's higher-up regions in several million-dimensional abstract spaces of some kind.
gollark: (Apparently you can maybe get somewhat better performance from image recognition neural networks by feeding them "DCT" things which also conveniently happen to be what JPEG images contain, but almost nobody does this?)
gollark: Also that.
gollark: The image is just 3 matrices of R/G/B values.
gollark: There are 129057189471894718247141491807401825701892912 random details and things but that's the gist of it.

References
  1. Patterson and Atmar; Patterson, Bruce D. (1993). "The measure of order and disorder in the distribution of species in fragmented habitat". Oecologia. 96 (3): 373–382. Bibcode:1993Oecol..96..373A. doi:10.1007/BF00317508. PMID 28313653.
  2. Rodríguez-Gironés MA, Santamaría L (2006). "A new algorithm to calculate the nestedness temperature of presence–absence matrices". Journal of Biogeography. 33 (5): 924–935. doi:10.1111/j.1365-2699.2006.01444.x.
  3. Guimarães, P. R. , P. Guimarães (2006). "Improving the analyses of nestedness for large sets of matrices". Environmental Modelling and Software. 21 (10): 1512–1513. doi:10.1016/j.envsoft.2006.04.002.CS1 maint: multiple names: authors list (link)
  4. Rodriguez-Girones, Miguel A.; Santamaria, Luis (2006). "A new algorithm to calculate the nestedness temperature of presence-absence matrices". Journal of Biogeography. 33 (5): 924–935. doi:10.1111/j.1365-2699.2006.01444.x.
  5. Guimaraesjr, P.; Guimaraes, P. (2006). "Improving the analyses of nestedness for large sets of matrices". Environmental Modelling. 21 (10): 1512–1513. doi:10.1016/j.envsoft.2006.04.002.
  6. http://www.iemss.org/shortcom/software/software.php?aid=201%5B%5D
  7. Bastolla U, Fortuna MA, Pascual-García A, Ferrera A, Luque B, Bascompte J (2009). "The architecture of mutualistic networks minimizes competition and increases biodiversity". Nature. 458 (7241): 1018–1020. Bibcode:2009Natur.458.1018B. doi:10.1038/nature07950. PMID 19396144.
  8. Johnson S, Domínguez-García V, Muñoz MA (2013). "Factors Determining Nestedness in Complex Networks". PLOS ONE. 8 (9): e74025. arXiv:1307.4685. Bibcode:2013PLoSO...874025J. doi:10.1371/journal.pone.0074025. PMC 3777946. PMID 24069264.

Software
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