# Nestedness metric based on overlap and decreasing fill

### Description

The procedure calculates the “nestedness metric based on overlap and decreasing fill” (NODF) for a binary matrix following Almeida-Neto et al. (2008).

### Usage

1 |

### Arguments

`dataset` |
Object of class RInSp with data of type “double” or “integer”. |

`print.results` |
Define if results for NODF should be printed. Default is TRUE |

.

### Details

Nestedness is a feature of binary matrices (also called presence/absence or incidence matrices). The notion of nestedness is particularly relevant for studies focusing the patterns of species occurrence among a set of locations (e.g., islands) and the patterns of interacting species within ecological networks.

Almeida-Neto et al. (2008) propose a nestedness metric is based on two simple properties: decreasing fill (or DF) and paired overlap (or PO). Assuming that in a matrix with m rows and n columns, row i is located at an upper position from row j, and column k is located at a left position from column l. In addition, let MT be the marginal total (i.e. the sum of 1's) of any column or row. For any pair of rows/columns i and j, *DF_{ij}* will be equal to 100 if *MT_j* is lower than *MT_i*. Alternatively, *DF_{ij}* will be equal to 0 if *MT_j* is greater or equal to *MT_i*. For columns/rows, paired overlap (*PO_{kl}*) is simply the percentage of 1's in a given column/row l that are located at identical row/column positions to those in a column/row k. For any left-to-right column pair and, similarly, for any up-to-down row pair, there is a degree of paired nestedness (*N_{paired}*) as zero if *DF_{paired}* is zero, and PO if *DF_{paired}* is 100.

From the *n(n-1)/2* and *m(m-1)/2* paired degrees of nestedness for n columns and m rows, we can calculate a measure of nestedness among all columns (*N_{col}*) and among all rows (*N_{row}*) by simply averaging all paired values of columns and rows.

Finally, the measure of nestedness for the whole matrix is given by:

* NODF = \frac{∑{N_{paired}}}{(\frac{n(n-1)}{2})+(\frac{m(m-1)}{2})} *

In the context of studies of individual specialization, one form of diet variation arises when individuals differ in their niche breadth, such that some individuals diet is a subset of other individuals' diet. This is revealed by a nestedness metric, which may be large (indicating nesting) or small (indicating clustering).

### Value

The result is a list of class ‘RInSp’ composed of:

`NODF` |
Value of the index of nestedness. |

`Nrows` |
Value of the index of nestedness for rows. |

`Ncols` |
Value of the index of nestedness for columns. |

`R` |
Binary matrix with individuals as rows and resources as columns. This matrix can be imported into the software PAJEK (http://vlado.fmf.uni-lj.si/pub/networks/pajek/) to draw a binary bipartite network of diet connectance between individuals (one set of nodes) and resources (a second set of nodes). |

`NpR` |
The degree of nestedness observed for rows. |

`NpC` |
The degree of nestedness observed for columns. |

### Author(s)

Dr. Nicola ZACCARELLI

### References

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.

### See Also

For further indices see the R package “vegan”. Please consider that the NODF implementation lacks the ordering and weighting options of *nestednodf* available in “vegan”.

### Examples

1 2 3 4 5 6 7 | ```
# NODF example with stickleback data from Bolnick and Paull 2009
data(Stickleback)
# Select a single spatial sampling site (site D)
SiteD = import.RInSp(Stickleback, row.names = 1, info.cols = c(2:13),
subset.rows = c("Site", "D"))
Nesting = NODF(SiteD)
rm(list=ls(all=TRUE))
``` |

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