Nestedness Indices for Communities of Islands or Patches

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

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 plot.
col: Colour scheme for matrix temperatures.
kind: The kind of plot produced.
names: Label columns and rows in the plot using names in comm. If it is a logical vector of length 2, row and column labels are returned accordingly.
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/columns 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 nullmodels 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.

References

Almeida-Neto, M., Guimarães, P., Guimarães, 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. Biogeogr. 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.

Author

Jari Oksanen and Gustavo Carvalho (nestednodf).

Examples

data(sipoo)
## Matrix temperature
out <- nestedtemp(sipoo)
out
#> nestedness temperature: 10.23506 
#> with matrix fill 0.2233333 
plot(out)

plot(out, kind="incid")

## Use oecosimu to assess the non-randomness of checker board units
nestedchecker(sipoo)
#> Checkerboard Units    : 2767 
#> C-score (species mean): 2.258776 
oecosimu(sipoo, nestedchecker, "quasiswap")
#> oecosimu object
#> 
#> Call: oecosimu(comm = sipoo, nestfun = nestedchecker, method =
#> "quasiswap")
#> 
#> nullmodel method ‘quasiswap’ with 99 simulations
#> 
#> alternative hypothesis: statistic is less or greater than simulated values
#> 
#> Checkerboard Units    : 2767 
#> C-score (species mean): 2.258776 
#> 
#>               statistic     SES   mean   2.5%    50%  97.5% Pr(sim.)
#> checkerboards      2767 0.55254 2715.3 2564.9 2713.0 2911.2     0.57
## Another Null model and standardized checkerboard score
oecosimu(sipoo, nestedchecker, "r00", statistic = "C.score")
#> oecosimu object
#> 
#> Call: oecosimu(comm = sipoo, nestfun = nestedchecker, method = "r00",
#> statistic = "C.score")
#> 
#> nullmodel method ‘r00’ with 99 simulations
#> 
#> alternative hypothesis: statistic is less or greater than simulated values
#> 
#> Checkerboard Units    : 2767 
#> C-score (species mean): 2.258776 
#> 
#>         statistic     SES   mean   2.5%    50%  97.5% Pr(sim.)   
#> C.score    2.2588 -28.215 9.2285 8.7036 9.2294 9.6735     0.01 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1