# Generates null models for network analysis by considering external abundances

### Description

An extension of r2dtable which rescales marginal totals according to independent data

### Usage

1 | ```
r2dexternal(N, web, abun.higher=NULL, abun.lower=NULL)
``` |

### Arguments

`N` |
number of null models to be generated. |

`web` |
Web is a matrix representing the interactions observed between higher level species (columns) and lower level species (rows). |

`abun.higher` |
Optional vector of externally measured abundances of the higher level. If missing (NULL) it will be replaced by column totals. |

`abun.lower` |
Optional vector of externally measured abundances of the lower level. If missing (NULL) it will be replaced by row totals. |

### Details

The underlying function is `r2dtable`

, which requires a vector of row and column totals, respectively. In function `nullmodel`

, these marginal totals are computed from the observed interaction matrix. Here, external abundances can be provided. These will be rescaled and combined with the observed marginal total to construct new row and column vectors for `r2dtable`

.

If neither row nor column abundances are provided this function will be identical to `r2dtable`

.

### Value

Returns a list of `N`

null model-generated networks. Species names are (obviously) dropped.

### Note

Since the function contains a rounding operation, it also has to include a re-distribution of 1s to keep all species in the system. That means, if one species has been observed in the external abundances extremely rarely (compared to the others), it will be overrepresented in this null model, because otherwise it would have to be dropped altogether! If you have a better solution, please let me know.

### Author(s)

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

### See Also

`nullmodel`

, `vaznull`

, `mgen`

, `vegan::simulate`

and `r2dtable`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 | ```
## Not run:
abun.lower <- c(15,5,2,7,4,8,6,0.01,6)
set.seed(2)
(abun.higher <- rpois(27, lambda=4))
abun.higher[1] <- 0.001
sum(ext.polls)
## note: external abundances do not sum up; this is intentional!!
r2dexternal(2, Safariland, abun.higher=abun.higher, abun.lower=abun.lower)
r2dexternal(2, Safariland, abun.higher=abun.higher)
## End(Not run)
``` |

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