compute_div: compute network diversity indices

In MarcOhlmann/metanetwork: Handling and Representing Trophic Networks in Space and Time

compute network diversity indices

Description

Function to compute network diversity indices based on Hill numbers following the method described in Ohlmann et al. 2019

Usage

compute_div(metanetwork, q = 1, res = NULL)

Arguments

metanetwork	object of class 'metanetwork'
q	viewpoint parameter controlling the weight given to abundant species/groups and links, default is 1
res	a vector containing the resolutions at which the diversities are computed

Details

This function compute diversity indices using Hill numbers on node and link abundances. Importantly, a viewpoint parameters q allows giving more weigth to abundant nodes/links. Given a network, we note p_q the abundance of node q (stored as node attribute ab) and \pi_{ql} interaction probability between nodes q and l (stored as edge attribute weight). The link abundance L_{ql} between nodes q and l is then:

L_{ql} = \pi_{ql}p_q p_l

Node diversity (for q = 1) is then computed as:

D(p) = \exp (\sum_q - p_q \log p_q)

Link diversity is computed as:

D(L) = \exp (\sum_{ql} - \frac{L_{ql}}{C} \log L_{ql}{C})

where C is the weighted connectance

C = \sum_{ql} \pi_{ql}p_q p_l

The overall \alpha-diversity in node abundances is (for q = 1):

A_{P} = \exp(\sum_{q=1}^{Q} \sum_{k} - \frac{P_{qk}}{P_{++}} \log(\frac{P_{qk}}{P_{++}}) - \log(K))

The overall \alpha-diversity in node abundances is (for q = 1):

A_{P} = exp(\sum_{q=1}^{Q} \sum_{k=1}^{K} - \frac{P_{qk}}{P_{++}} log ( \frac{P_{qk}}{P_{++}}) - log(K) )

where P_{++}=\sum_{k} \sum_{q} P_{qk} The overall \alpha-diversities in link abundances and link probabilities are equal to:

A_{L} = exp (\sum_{q,l=1}^{Q} \sum_{k=1}^{K} - \frac{L_{qlk}}{L_{+++}} \log (\frac{L_{qlk}}{L_{+++}}) - log(K))

where L_{+++}=\sum_{k} \sum_{q,l} L_{qlk}. The \gamma-diversity in node and link abundances are (for q = 1):

G_{P}=exp(\sum_{q=1}^{Q} -\frac{P_{q+}}{P_{++}} log (\frac{P_{q+}}{P_{++}}))

G_{L}=exp(\sum_{q,l=1}^{Q} -\frac{L_{ql+}}{L_{+++}} log(\frac{L_{ql+}}{L_{+++}}))

The \beta-diversity is then defined in a multiplicative way:

B_{P}=\frac{G_P}{A_P}

B_{L}=\frac{G_P}{A_L}

For more details on \alpha-,\beta- and \gamma-diversity, see Ohlmann et al. 2019.

Value

a data.frame

References

Ohlmann, M., Miele, V., Dray, S., Chalmandrier, L., O'connor, L., & Thuiller, W. (2019). Diversity indices for ecological networks: a unifying framework using Hill numbers. Ecology letters, 22(4), 737-747.

See Also

compute_dis()

Examples

library(metanetwork)
library(igraph)

#on angola dataset
data("meta_angola")
compute_div(meta_angola,q = 1)

#computing diversities only at Phylum level
compute_div(meta_angola,q = 1,res = "Phylum")

MarcOhlmann/metanetwork documentation built on July 1, 2023, 6:27 a.m.