Wrapper function calling one, several or all currently implemented nestedness measures

1 |

`web` |
A matrix with elements of a set (e.g., plants) as rows, elements of a second set (e.g., pollinators) as columns and number of interactions as entries. |

`method` |
One or more of the following: discrepancy, discrepancy2, binmatnest, binmatnest2, NODF, NODF2, C.score, checker, weighted NODF, wine, ALL. See details for details on each method. |

`rescale` |
Should all measures be rescaled so that higher values mean higher nestedness? Defaults to FALSE, i.e. the standard interpretation of each measure is maintained. |

`normalised` |
Logical, defaulting to TRUE. Should C-scores be normalised to a value between 0 and 1? See |

There are five different measures currently available:

- 1
binmatnest calculates nestedness temperature following the function

`nestedness`

(0 = cold = highly nested; 100 = hot = not nested at all). It uses the original program of Miguel Rodriguez-Girones, only called from R; binmatnest2, in contrast, is the implementation in`nestedtemp`

of the same algorithm by Jari Oksanen. Because binmatnest sometimes (and to us unexplicably) invert the matrix, we prefer the binmatnest2 option.- 2
Discrepancy calculates the number of non-nested 0s and 1s. While

`discrepancy`

calls the function with the same name, discrepancy2 calls`nesteddisc`

, which handles ties differently. Most of the time, these two should deliver very, very similar results. Higher values indicate lower nestedness.- 3
NODF is the nestedness measure proposed by Almeida-Neto et al., correcting for matrix fill and matrix dimensions. Values of 0 indicate non-nestedness, those of 100 perfect nesting. NODF2 sorts the matrix before calculating the measure. NODF is, I understand, closer to the version presented in the paper, while NODF2 seems to make more sense for comparisons across different networks (because it is independent of the initial presentation of the matrix). Both call

`nestednodf`

in vegan. (Yes, I initially programmed NODF myself, only to find that it was there already. Luckily, there was a perfect agreement between my (depricated) version and nestednodf.) A weighted version is also now available (see point 6 below), following the paper of Almeida-Neto and Ulrich (2010).- 4
`C.score`

calculates the number of checkerboard pattern in the matrix. As default, it normalises this value between min and max, so that values of 0 indicate no checkerboards (i.e. nesting), while a value of 1 indicates a perfect checkerboard. checker is the non-normalised version, based on`nestedchecker`

.- 5
wine is one of two nestedness measure using the information on the weight of a link. See

`wine`

for details.- 6
weighted NODF is a version of 3, but now incorporating information on the weights of the link; it is the second quantitative nestedness measure, (chronologically) after wine. It uses the sorted matrix to compute NODF. If you want NODF of the unsorted, you have to directly use

`nestednodf`

in vegan.

A vector with values for each of the selected nestedness measures.

The idea behind this function is to encourage the comparison of different nestedness measures. That does not mean, we necessarily see much ecological sense in them (see, e.g., the paper by Blüthgen et al. 2008).

`nested`

uses one non-default setting for the `nestedness`

measures called: null.models=FALSE. This is simply to speed up the computation. Null models should be built for all nestedness measures, of course, not only for `nestedness`

!

Carsten F. Dormann carsten.dormann@biom.uni-freiburg.de

Almeida-Neto, M., Guimaraes, P., Guimaraes, P.R., Loyola, R.D. and Ulrich, W. 2008. A consistent metric for nestedness analysis in
ecological systems: reconciling concept and measurement. *Oikos* **117**, 1227–1239.

Almeida-Neto, M. and Ulrich, W. (2011) A straightforward computational approach for measuring nestedness using quantitative matrices. *Environmental Modelling & Software*, **26**, 173–178

Blüthgen, N., J. Fründ, D. P. Vazquez, and F. Menzel. 2008. What do interaction network metrics tell us about specialisation and biological traits? *Ecology* **89**, 3387–3399.

Brualdi, R.A. and Sanderson, J.G. 1999. Nested species subsets, gaps, and discrepancy. *Oecologia* **119**, 256–264.

Galeano, J., Pastor, J.M., Iriondo and J.M. 2008. Weighted-Interaction Nestedness Estimator (WINE): A new estimator to calculate over
frequency matrices. *arXiv* 0808.3397v2 [physics.bio-ph]

Rodríguez-Gironés, M.A. and Santamaría, L. 2006. A new algorithm to calculate the nestedness temperature of presence-absence
matrices. *J. Biogeogr.* **33**, 924–935.

Stone, L. and Roberts, A. 1990. The checkerboard score and species distributions. *Oecologia* **85**, 74–79.

Almeida-Neto, M. and Ulrich, W. 2010. A straightforward computational approach for measuring nestedness using quantitative matrices. Environmental Modelling & Software, in press.

`C.score`

, `wine`

, `nestedness`

, `discrepancy`

; and, within vegan: `nestedtemp`

,
`nestedchecker`

, `nesteddisc`

, `nestednodf`

1 2 3 4 5 6 7 8 | ```
## Not run:
data(Safariland)
nested(Safariland, "ALL")
nested(Safariland, "ALL", rescale=TRUE)
# illustration that non-normalised C.score and checker are the same:
nested(Safariland, c("C.score", "checker"), normalise=FALSE)
## End(Not run)
``` |

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