5.3 Contribution

Pierre Denelle, Boris Leroy and Maxime Lenormand

2024-10-17

In this vignette, we aim at evaluating the contribution of individual species to each bioregion, using the function contribution().

Data

We use the vegetation dataset that comes with bioregion.

data("vegedf")
data("vegemat")

# Calculation of (dis)similarity matrices
vegedissim <- dissimilarity(vegemat, metric = c("Simpson"))
vegesim <- dissimilarity_to_similarity(vegedissim)

Bioregionalization

We use the same three bioregionalization algorithms as in the visualization vignette, i.e. a non-hierarchical, hierarchical and network bioregionalizations.
We chose 3 bioregions for the non-hierarchical and hierarchical bioregionalizations.

# Non hierarchical bioregionalization
vege_nhclu_kmeans <- nhclu_kmeans(vegedissim, n_clust = 3, index = "Simpson")
vege_nhclu_kmeans$cluster_info # 3

##     partition_name n_clust
## K_3            K_3       3

# Hierarchical bioregionalization
set.seed(1)
vege_hclu_hierarclust <- hclu_hierarclust(dissimilarity = vegedissim,
                                          index = names(vegedissim)[3],
                                          method = "mcquitty", n_clust = 3)
vege_hclu_hierarclust$cluster_info # 3

##   partition_name n_clust requested_n_clust output_cut_height
## 1            K_3       3                 3             0.625

# Network bioregionalization
set.seed(1)
vege_netclu_walktrap <- netclu_walktrap(vegesim,
                                        index = names(vegesim)[3])
vege_netclu_walktrap$cluster_info # 3

##     partition_name n_clust
## K_3            K_3       3

Indices

The contribution index $\rho$ is calculated for each species x bioregion combination, following (Lenormand et al., 2019).
Its formula is the following:

$$\rho_{ij} = \frac{n_{ij} - \frac{n_i n_j}{n}}{\sqrt{\frac{n - n_j}{n-1} (1-\frac{n_j}{n}) \frac{n_i n_j}{n}}}$$ with $n$ the number of sites, $n_i$ the number of sites in which species $i$ is present, $n_j$ the number of sites belonging to the bioregion $j$, $n_ij$ the number of occurrences of species $i$ in sites belonging to the bioregion $j$.

Contribution

We can now run the function contribution().

contrib_kmeans <- contribution(vege_nhclu_kmeans, vegemat,
                               indices = "contribution")
contrib_hclu <- contribution(vege_hclu_hierarclust, vegemat,
                             indices = "contribution")
contrib_netclu <- contribution(vege_netclu_walktrap, vegemat,
                               indices = "contribution")

contribution() produces a single data.frame output.

Lenormand, M., Papuga, G., Argagnon, O., Soubeyrand, M., Alleaume, S., & Luque, S. (2019). Biogeographical network analysis of plant species distribution in the mediterranean region. Ecology and Evolution, 9, 237–250.