Calculate contribution metrics of sites and species
Source:R/site_species_metrics.R
site_species_metrics.RdThis function calculates metrics to assess the contribution of a given species or site to its bioregion.
Usage
site_species_metrics(
bioregionalization,
comat,
indices = c("rho"),
net = NULL,
site_col = 1,
species_col = 2
)Arguments
- bioregionalization
A
bioregion.clustersobject.- comat
A co-occurrence
matrixwith sites as rows and species as columns.- indices
A
characterspecifying the contribution metric to compute. Available options arerho,affinity,fidelity,indicator_valueandCz.- net
NULLby default. Required forCzindices. Adata.framewhere each row represents an interaction between two nodes and an optional third column indicating the interaction's weight.- site_col
A number indicating the position of the column containing the sites in
net. 1 by default.- species_col
A number indicating the position of the column containing the species in
net. 2 by default.
Value
A data.frame with columns Bioregion, Species, and the desired summary
statistics, or a list of data.frames if Cz and other indices are
selected.
Details
The \(\rho\) metric is derived from Lenormand et al. (2019) with the following formula:
\(\rho_{ij} = \frac{n_{ij} - \frac{n_i n_j}{n}}{\sqrt{\left(\frac{n - n_j}{ n-1}\right) \left(1-\frac{n_j}{n}\right) \frac{n_i n_j}{n}}}\)
where \(n\) is the number of sites, \(n_i\) is the number of sites in which species \(i\) is present, \(n_j\) is the number of sites in bioregion \(j\), and \(n_{ij}\) is the number of occurrences of species \(i\) in sites of bioregion \(j\).
Affinity \(A\), fidelity \(F\), and individual contributions \(IndVal\) describe how species are linked to their bioregions. These metrics are described in Bernardo-Madrid et al. (2019):
Affinity of species to their region: \(A_i = \frac{R_i}{Z}\), where \(R_i\) is the occurrence/range size of species \(i\) in its associated bioregion, and \(Z\) is the total size (number of sites) of the bioregion. High affinity indicates that the species occupies most sites in its bioregion.
Fidelity of species to their region: \(F_i = \frac{R_i}{D_i}\), where \(R_i\) is the occurrence/range size of species \(i\) in its bioregion, and \(D_i\) is its total range size. High fidelity indicates that the species is not present in other regions.
Indicator Value of species: \(IndVal = F_i \cdot A_i\).
Cz metrics are derived from Guimerà & Amaral (2005):
Participation coefficient: \(C_i = 1 - \sum_{s=1}^{N_M}{\left(\frac{k_{is}}{k_i}\right)^2}\), where \(k_{is}\) is the number of links of node \(i\) to nodes in bioregion \(s\), and \(k_i\) is the total degree of node \(i\). A high value means links are uniformly distributed; a low value means links are within the node's bioregion.
Within-bioregion degree z-score: \(z_i = \frac{k_i - \overline{k_{si}}}{\sigma_{k_{si}}}\), where \(k_i\) is the number of links of node \(i\) to nodes in its bioregion \(s_i\), \(\overline{k_{si}}\) is the average degree of nodes in \(s_i\), and \(\sigma_{k_{si}}\) is the standard deviation of degrees in \(s_i\).
References
Bernardo-Madrid R, Calatayud J, González‐Suárez M, Rosvall M, Lucas P, Antonelli A & Revilla E (2019) Human activity is altering the world’s zoogeographical regions. Ecology Letters 22, 1297–1305.
Guimerà R & Amaral LAN (2005) Functional cartography of complex metabolic networks. Nature 433, 895–900.
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.
See also
For more details illustrated with a practical example, see the vignette: https://biorgeo.github.io/bioregion/articles/a5_3_summary_metrics.html.
Associated functions: bioregion_metrics bioregionalization_metrics
Author
Pierre Denelle (pierre.denelle@gmail.com)
Boris Leroy (leroy.boris@gmail.com)
Maxime Lenormand (maxime.lenormand@inrae.fr)
Examples
comat <- matrix(sample(0:1000, size = 500, replace = TRUE, prob = 1/1:1001),
20, 25)
rownames(comat) <- paste0("Site",1:20)
colnames(comat) <- paste0("Species",1:25)
dissim <- dissimilarity(comat, metric = "Simpson")
clust1 <- nhclu_kmeans(dissim, n_clust = 3, index = "Simpson")
net <- similarity(comat, metric = "Simpson")
com <- netclu_greedy(net)
site_species_metrics(bioregionalization = clust1, comat = comat,
indices = "rho")
#> Bioregion Species rho
#> 1 1 Species1 1515.511843
#> 2 1 Species2 364.794029
#> 3 1 Species3 171.937257
#> 4 1 Species4 714.327872
#> 5 1 Species5 453.213412
#> 6 1 Species6 450.241223
#> 7 1 Species7 660.588567
#> 8 1 Species8 834.441913
#> 9 1 Species9 285.287785
#> 10 1 Species10 1110.387912
#> 11 1 Species11 1791.976471
#> 12 1 Species12 1155.609692
#> 13 1 Species13 1107.664249
#> 14 1 Species14 482.090909
#> 15 1 Species15 840.849114
#> 16 1 Species16 773.914158
#> 17 1 Species17 314.177135
#> 18 1 Species18 614.034174
#> 19 1 Species19 712.064360
#> 20 1 Species20 816.170805
#> 21 1 Species21 1043.316688
#> 22 1 Species22 791.513661
#> 23 1 Species23 673.000000
#> 24 1 Species24 1133.842077
#> 25 1 Species25 739.426209
#> 26 2 Species1 174.724740
#> 27 2 Species2 741.049144
#> 28 2 Species3 652.263823
#> 29 2 Species4 86.970784
#> 30 2 Species5 754.613568
#> 31 2 Species6 100.418459
#> 32 2 Species7 775.715529
#> 33 2 Species8 482.091959
#> 34 2 Species9 427.633703
#> 35 2 Species10 791.389856
#> 36 2 Species11 416.199603
#> 37 2 Species12 393.430261
#> 38 2 Species13 5.153062
#> 39 2 Species14 718.691955
#> 40 2 Species15 1067.828448
#> 41 2 Species16 331.114167
#> 42 2 Species17 113.386253
#> 43 2 Species18 197.239056
#> 44 2 Species19 884.092160
#> 45 2 Species20 575.291145
#> 46 2 Species21 51.729780
#> 47 2 Species22 258.895528
#> 48 2 Species23 493.572183
#> 49 2 Species24 467.249282
#> 50 2 Species25 63.405401
#> 51 3 Species1 974.991715
#> 52 3 Species2 466.957908
#> 53 3 Species3 165.633736
#> 54 3 Species4 59.224257
#> 55 3 Species5 324.490831
#> 56 3 Species6 438.671957
#> 57 3 Species7 7.045180
#> 58 3 Species8 896.250294
#> 59 3 Species9 287.397031
#> 60 3 Species10 -2.431278
#> 61 3 Species11 809.583130
#> 62 3 Species12 100.776712
#> 63 3 Species13 1036.254154
#> 64 3 Species14 1207.029494
#> 65 3 Species15 477.044072
#> 66 3 Species16 563.920750
#> 67 3 Species17 115.202913
#> 68 3 Species18 775.846703
#> 69 3 Species19 182.023754
#> 70 3 Species20 129.307472
#> 71 3 Species21 77.379795
#> 72 3 Species22 695.157385
#> 73 3 Species23 518.916842
#> 74 3 Species24 1371.049071
#> 75 3 Species25 23.259566
# Contribution metrics
site_species_metrics(bioregionalization = com, comat = comat,
indices = c("rho", "affinity", "fidelity", "indicator_value"))
#> Bioregion Species rho affinity fidelity indval
#> 1 1 Species1 20350.0617580 228.10526 240.77777778 5.492268e+04
#> 2 1 Species2 12189.1129075 133.10526 148.76470588 1.980137e+04
#> 3 1 Species3 4151.4822937 45.89474 51.29411765 2.354130e+03
#> 4 1 Species4 6112.8587148 63.05263 79.86666667 5.035804e+03
#> 5 1 Species5 11825.3094699 129.15789 144.35294118 1.864432e+04
#> 6 1 Species6 7299.9735616 72.57895 98.50000000 7.149026e+03
#> 7 1 Species7 11152.9595574 125.42105 132.38888889 1.660435e+04
#> 8 1 Species8 16928.2590207 184.52632 206.23529412 3.805584e+04
#> 9 1 Species9 6582.7806941 67.84211 85.93333333 5.829898e+03
#> 10 1 Species10 13634.0649949 134.94737 183.14285714 2.471465e+04
#> 11 1 Species11 21071.3106748 236.15789 249.27777778 5.886892e+04
#> 12 1 Species12 12279.6163621 138.00000 145.66666667 2.010200e+04
#> 13 1 Species13 16399.6918738 184.00000 194.22222222 3.573689e+04
#> 14 1 Species14 15076.9726142 173.89474 173.89473684 3.023938e+04
#> 15 1 Species15 18441.6813209 200.94737 224.58823529 4.513041e+04
#> 16 1 Species16 11369.8056370 127.84211 134.94444444 1.725158e+04
#> 17 1 Species17 4136.9301562 45.73684 51.11764706 2.337960e+03
#> 18 1 Species18 12174.5607699 132.94737 148.58823529 1.975441e+04
#> 19 1 Species19 10219.7236322 111.73684 124.88235294 1.395396e+04
#> 20 1 Species20 11614.0000000 123.05263 146.12500000 1.798107e+04
#> 21 1 Species21 8905.1805445 97.47368 108.94117647 1.061890e+04
#> 22 1 Species22 12761.4969825 139.31579 155.70588235 2.169229e+04
#> 23 1 Species23 12346.9253812 142.57895 142.57894737 2.032876e+04
#> 24 1 Species24 22814.0000000 240.94737 286.12500000 6.894107e+04
#> 25 1 Species25 6279.2615277 57.84211 91.58333333 5.297373e+03
#> 26 2 Species1 0.1081476 1.00000 0.05555556 5.555556e-02
#> 27 2 Species2 -0.9459053 0.00000 0.00000000 0.000000e+00
#> 28 2 Species3 815.8711445 734.00000 43.17647059 3.169153e+04
#> 29 2 Species4 99.8107859 85.00000 5.66666667 4.816667e+02
#> 30 2 Species5 9.0695626 9.00000 0.52941176 4.764706e+00
#> 31 2 Species6 62.9080962 52.00000 3.71428571 1.931429e+02
#> 32 2 Species7 1.1896238 2.00000 0.11111111 2.222222e-01
#> 33 2 Species8 17.9722008 17.00000 1.00000000 1.700000e+01
#> 34 2 Species9 264.4837739 224.00000 14.93333333 3.345067e+03
#> 35 2 Species10 224.7768819 184.00000 13.14285714 2.418286e+03
#> 36 2 Species11 458.6540313 425.00000 23.61111111 1.003472e+04
#> 37 2 Species12 77.9744298 73.00000 4.05555556 2.960556e+02
#> 38 2 Species13 0.1081476 1.00000 0.05555556 5.555556e-02
#> 39 2 Species14 806.3684211 767.00000 40.36842105 3.096258e+04
#> 40 2 Species15 -0.9459053 0.00000 0.00000000 0.000000e+00
#> 41 2 Species16 328.8768944 305.00000 16.94444444 5.168056e+03
#> 42 2 Species17 4.6182435 5.00000 0.29411765 1.470588e+00
#> 43 2 Species18 -0.9459053 0.00000 0.00000000 0.000000e+00
#> 44 2 Species19 809.1941659 728.00000 42.82352941 3.117553e+04
#> 45 2 Species20 19.7297531 18.00000 1.12500000 2.025000e+01
#> 46 2 Species21 -0.9459053 0.00000 0.00000000 0.000000e+00
#> 47 2 Species22 141.4963050 128.00000 7.52941176 9.637647e+02
#> 48 2 Species23 143.2105263 137.00000 7.21052632 9.878421e+02
#> 49 2 Species24 -0.9176629 0.00000 0.00000000 0.000000e+00
#> 50 2 Species25 -0.7947194 0.00000 0.00000000 0.000000e+00
# Cz indices
net_bip <- mat_to_net(comat, weight = TRUE)
clust_bip <- netclu_greedy(net_bip, bipartite = TRUE)
site_species_metrics(bioregionalization = clust_bip, comat = comat,
net = net_bip, indices = "Cz")
#> Node Bioregion Category C z
#> 1 Site1 1 site 0.8204159 0.5720776
#> 2 Site2 3 site 0.8254848 0.2070197
#> 3 Site3 1 site 0.8223140 0.5720776
#> 4 Site4 1 site 0.8254848 -0.8581163
#> 5 Site5 4 site 0.8223140 -0.7302967
#> 6 Site6 6 site 0.8264463 0.6437963
#> 7 Site7 6 site 0.8140496 0.6437963
#> 8 Site8 6 site 0.8027211 1.5021914
#> 9 Site9 1 site 0.8223140 0.5720776
#> 10 Site10 2 site 0.8204159 1.4031215
#> 11 Site11 2 site 0.8181818 1.4031215
#> 12 Site12 5 site 0.8204159 1.6561573
#> 13 Site13 3 site 0.8117914 1.6561573
#> 14 Site14 2 site 0.8223140 0.4677072
#> 15 Site15 5 site 0.8100000 0.2070197
#> 16 Site16 4 site 0.8033241 -0.7302967
#> 17 Site17 4 site 0.8150000 -0.7302967
#> 18 Site18 5 site 0.7977839 0.2070197
#> 19 Site19 3 site 0.8235294 0.2070197
#> 20 Site20 1 site 0.8200000 -0.8581163
#> 21 Species1 6 species 0.8333333 -0.2145988
#> 22 Species2 2 species 0.8096886 -1.4031215
#> 23 Species3 3 species 0.8096886 -1.2421180
#> 24 Species4 2 species 0.8266667 -0.4677072
#> 25 Species5 5 species 0.8096886 0.2070197
#> 26 Species6 6 species 0.8061224 -1.9313889
#> 27 Species7 3 species 0.8271605 0.2070197
#> 28 Species8 6 species 0.8027682 -0.2145988
#> 29 Species9 5 species 0.8000000 0.2070197
#> 30 Species11 2 species 0.8086420 -0.4677072
#> 31 Species12 6 species 0.8271605 -0.2145988
#> 32 Species13 1 species 0.8148148 0.5720776
#> 33 Species14 1 species 0.8199446 0.5720776
#> 34 Species15 3 species 0.8096886 -1.2421180
#> 35 Species16 1 species 0.8148148 0.5720776
#> 36 Species18 6 species 0.8235294 -0.2145988
#> 37 Species19 3 species 0.8027682 0.2070197
#> 38 Species20 4 species 0.7890625 1.0954451
#> 39 Species21 2 species 0.8166090 -0.4677072
#> 40 Species22 5 species 0.8096886 -1.2421180
#> 41 Species23 4 species 0.8199446 1.0954451
#> 42 Species24 1 species 0.7968750 0.5720776
#> 43 Species25 1 species 0.8194444 -2.2883102
#> 44 Species10 5 species 0.8163265 -1.2421180
#> 45 Species17 2 species 0.8304498 -0.4677072