# Nestedness Indices for Communities of Islands or Patches

### Description

Patches or local communities are regarded as nested if they all could be subsets of the same community. In general, species poor communities should be subsets of species rich communities, and rare species should only occur in species rich communities.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 | ```
nestedchecker(comm)
nestedn0(comm)
nesteddisc(comm, niter = 200)
nestedtemp(comm, ...)
nestednodf(comm, order = TRUE, weighted = FALSE, wbinary = FALSE)
nestedbetasor(comm)
nestedbetajac(comm)
## S3 method for class 'nestedtemp'
plot(x, kind = c("temperature", "incidence"),
col=rev(heat.colors(100)), names = FALSE, ...)
## S3 method for class 'nestednodf'
plot(x, col = "red", names = FALSE, ...)
``` |

### Arguments

`comm` |
Community data. |

`niter` |
Number of iterations to reorder tied columns. |

`x` |
Result object for a |

`col` |
Colour scheme for matrix temperatures. |

`kind` |
The kind of plot produced. |

`names` |
Label columns and rows in the plot using names in |

`order` |
Order rows and columns by frequencies. |

`weighted` |
Use species abundances as weights of interactions. |

`wbinary` |
Modify original method so that binary data give the same result in weighted and and unweighted analysis. |

`...` |
Other arguments to functions. |

### Details

The nestedness functions evaluate alternative indices of nestedness.
The functions are intended to be used together with Null model
communities and used as an argument in `oecosimu`

to analyse
the non-randomness of results.

Function `nestedchecker`

gives the number of checkerboard units,
or 2x2 submatrices where both species occur once but on different
sites (Stone & Roberts 1990).

Function `nestedn0`

implements
nestedness measure N0 which is the number of absences from the sites
which are richer than the most pauperate site species occurs
(Patterson & Atmar 1986).

Function `nesteddisc`

implements discrepancy index which is the
number of ones that should be shifted to fill a row with ones in a
table arranged by species frequencies (Brualdi & Sanderson
1999). The original definition arranges species (columns) by their
frequencies, but did not have any method of handling tied
frequencies. The `nesteddisc`

function tries to order tied
columns to minimize the discrepancy statistic but this is rather
slow, and with a large number of tied columns there is no guarantee
that the best ordering was found (argument `niter`

gives the
maximum number of tried orders). In that case a warning of tied
columns will be issued.

Function `nestedtemp`

finds the matrix temperature which is
defined as the sum of “surprises” in arranged matrix. In
arranged unsurprising matrix all species within proportion given by
matrix fill are in the upper left corner of the matrix, and the
surprise of the absence or presences is the diagonal distance from the
fill line (Atmar & Patterson 1993). Function tries to pack species and
sites to a low temperature (Rodríguez-Gironés
& Santamaria 2006), but this is an iterative procedure, and the
temperatures usually vary among runs. Function `nestedtemp`

also
has a `plot`

method which can display either incidences or
temperatures of the surprises. Matrix temperature was rather vaguely
described (Atmar & Patterson 1993), but
Rodríguez-Gironés & Santamaria (2006) are
more explicit and their description is used here. However, the results
probably differ from other implementations, and users should be
cautious in interpreting the results. The details of calculations are
explained in the `vignette`

*Design decisions and
implementation* that you can read using functions
`browseVignettes`

. Function
`nestedness`

in the bipartite package is
a direct port of the BINMATNEST programme of
Rodríguez-Gironés & Santamaria (2006).

Function `nestednodf`

implements a nestedness metric based on
overlap and decreasing fill (Almeida-Neto et al., 2008). Two basic
properties are required for a matrix to have the maximum degree of
nestedness according to this metric: (1) complete overlap of 1's
from right to left columns and from down to up rows, and (2)
decreasing marginal totals between all pairs of columns and all
pairs of rows. The nestedness statistic is evaluated separately for
columns (`N columns`

) for rows (`N rows`

) and combined for
the whole matrix (`NODF`

). If you set `order = FALSE`

,
the statistic is evaluated with the current matrix ordering allowing
tests of other meaningful hypothesis of matrix structure than
default ordering by row and column totals (breaking ties by total
abundances when `weighted = TRUE`

) (see Almeida-Neto et
al. 2008). With `weighted = TRUE`

, the function finds the
weighted version of the index (Almeida-Neto & Ulrich,
2011). However, this requires quantitative null models for adequate
testing. Almeida-Neto & Ulrich (2011) say that you have positive
nestedness if values in the first row/column are higher than in the
second. With this condition, weighted analysis of binary data will
always give zero nestedness. With argument `wbinary = TRUE`

,
equality of rows/colums also indicates nestedness, and binary data
will give identical results in weighted and unweighted analysis.
However, this can also influence the results of weighted analysis so
that the results may differ from Almeida-Neto & Ulrich (2011).

Functions `nestedbetasor`

and `nestedbetajac`

find
multiple-site dissimilarities and decompose these into components of
turnover and nestedness following Baselga (2012); the pairwise
dissimilarities can be found with `designdist`

. This can
be seen as a decomposition of beta diversity (see
`betadiver`

). Function `nestedbetasor`

uses
Sørensen dissimilarity and the turnover component is
Simpson dissimilarity (Baselga 2012), and `nestedbetajac`

uses
analogous methods with the Jaccard index. The functions return a
vector of three items: turnover, nestedness and their sum which is
the multiple Sørensen or Jaccard dissimilarity. The
last one is the total beta diversity (Baselga 2012). The functions
will treat data as presence/absence (binary) and they can be used
with binary `nullmodel`

). The overall dissimilarity is
constant in all `nullmodel`

s that fix species (column)
frequencies (`"c0"`

), and all components are constant if row
columns are also fixed (e.g., model `"quasiswap"`

), and the
functions are not meaningful with these null models.

### Value

The result returned by a nestedness function contains an item called
`statistic`

, but the other components differ among functions. The
functions are constructed so that they can be handled by
`oecosimu`

.

### Author(s)

Jari Oksanen and Gustavo Carvalho (`nestednodf`

).

### References

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

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

Atmar, W. & Patterson, B.D. (1993). The measurement of order and
disorder in the distribution of species in fragmented
habitat. *Oecologia* 96, 373–382.

Baselga, A. (2012). The relationship between species replacement,
dissimilarity derived from nestedness, and nestedness. *Global
Ecol. Biogeog.* 21, 1223–1232.

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

Patterson, B.D. & Atmar, W. (1986). Nested subsets and the structure
of insular mammalian faunas and archipelagos. *Biol. J. Linnean
Soc.* 28, 65–82.

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

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

Wright, D.H., Patterson, B.D., Mikkelson, G.M., Cutler, A. & Atmar,
W. (1998). A comparative analysis of nested subset patterns of species
composition. *Oecologia* 113, 1–20.

### See Also

In general, the functions should be used with `oecosimu`

which generates Null model communities to assess the non-randomness of
nestedness patterns.

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
data(sipoo)
## Matrix temperature
out <- nestedtemp(sipoo)
out
plot(out)
plot(out, kind="incid")
## Use oecosimu to assess the non-randomness of checker board units
nestedchecker(sipoo)
oecosimu(sipoo, nestedchecker, "quasiswap")
## Another Null model and standardized checkerboard score
oecosimu(sipoo, nestedchecker, "r00", statistic = "C.score")
``` |