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 2 Species1 691.3133454
#> 2 2 Species2 1096.2512131
#> 3 2 Species3 412.6304623
#> 4 2 Species4 710.4705820
#> 5 2 Species5 1963.8050546
#> 6 2 Species6 1101.5075599
#> 7 2 Species7 367.9637192
#> 8 2 Species8 723.8416417
#> 9 2 Species9 1069.7368973
#> 10 2 Species10 662.1893978
#> 11 2 Species11 316.5853082
#> 12 2 Species12 942.3847907
#> 13 2 Species13 742.1085669
#> 14 2 Species14 675.9023104
#> 15 2 Species15 527.5710984
#> 16 2 Species16 227.0991279
#> 17 2 Species17 1202.4261351
#> 18 2 Species18 925.0473763
#> 19 2 Species19 307.7180046
#> 20 2 Species20 177.3817961
#> 21 2 Species21 436.1779924
#> 22 2 Species22 608.1278588
#> 23 2 Species23 1947.3126985
#> 24 2 Species24 512.1929169
#> 25 2 Species25 560.4276251
#> 26 1 Species1 183.3278484
#> 27 1 Species2 1051.4573220
#> 28 1 Species3 1009.6815711
#> 29 1 Species4 536.3843150
#> 30 1 Species5 1194.3072004
#> 31 1 Species6 488.4302527
#> 32 1 Species7 1242.3913858
#> 33 1 Species8 1506.1928495
#> 34 1 Species9 676.9823831
#> 35 1 Species10 1606.9214943
#> 36 1 Species11 440.2892832
#> 37 1 Species12 269.4781531
#> 38 1 Species13 437.9754559
#> 39 1 Species14 913.8824323
#> 40 1 Species15 642.3366718
#> 41 1 Species16 595.4568834
#> 42 1 Species17 353.3680884
#> 43 1 Species18 1938.7264570
#> 44 1 Species19 1343.5323467
#> 45 1 Species20 87.6778193
#> 46 1 Species21 96.5192801
#> 47 1 Species22 1145.6882108
#> 48 1 Species23 1142.0084391
#> 49 1 Species24 517.8497341
#> 50 1 Species25 293.9785706
#> 51 3 Species1 0.3424674
#> 52 3 Species2 11.8636804
#> 53 3 Species3 190.4118992
#> 54 3 Species4 201.4804211
#> 55 3 Species5 341.6085246
#> 56 3 Species6 112.3809319
#> 57 3 Species7 9.0406793
#> 58 3 Species8 639.6173673
#> 59 3 Species9 212.0535988
#> 60 3 Species10 575.6975420
#> 61 3 Species11 64.2058096
#> 62 3 Species12 30.3083688
#> 63 3 Species13 579.1204538
#> 64 3 Species14 14.0411652
#> 65 3 Species15 -1.3698698
#> 66 3 Species16 166.6414981
#> 67 3 Species17 864.9095668
#> 68 3 Species18 278.5972662
#> 69 3 Species19 94.1723204
#> 70 3 Species20 257.7436212
#> 71 3 Species21 90.2468787
#> 72 3 Species22 78.3261041
#> 73 3 Species23 115.0690614
#> 74 3 Species24 251.0920600
#> 75 3 Species25 -1.2813958
# 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 6.704000e+03 71.36842 84.75000000 6.048474e+03
#> 2 1 Species2 1.571016e+04 181.15789 181.15789474 3.281818e+04
#> 3 1 Species3 8.989000e+03 95.42105 113.31250000 1.081240e+04
#> 4 1 Species4 1.006091e+04 92.31579 146.16666667 1.349349e+04
#> 5 1 Species5 2.572407e+04 288.10526 304.11111111 8.761601e+04
#> 6 1 Species6 1.278090e+04 139.52632 155.94117647 2.175790e+04
#> 7 1 Species7 1.178936e+04 132.52632 139.88888889 1.853896e+04
#> 8 1 Species8 2.028930e+04 233.68421 233.68421053 5.460831e+04
#> 9 1 Species9 1.231523e+04 134.47368 150.29411765 2.021060e+04
#> 10 1 Species10 1.613099e+04 181.00000 191.05555556 3.458106e+04
#> 11 1 Species11 5.466025e+03 60.15789 67.23529412 4.044734e+03
#> 12 1 Species12 9.469000e+03 100.47368 119.31250000 1.198777e+04
#> 13 1 Species13 1.217257e+04 140.57895 140.57894737 1.976244e+04
#> 14 1 Species14 8.834000e+03 93.78947 111.37500000 1.044580e+04
#> 15 1 Species15 7.939000e+03 84.36842 100.18750000 8.452661e+03
#> 16 1 Species16 7.061187e+03 81.94737 81.94736842 6.715371e+03
#> 17 1 Species17 1.698162e+04 185.10526 206.88235294 3.829501e+04
#> 18 1 Species18 2.289900e+04 241.84211 287.18750000 6.945403e+04
#> 19 1 Species19 1.269693e+04 130.15789 164.86666667 2.145870e+04
#> 20 1 Species20 3.103972e+03 31.26316 42.42857143 1.326451e+03
#> 21 1 Species21 4.627361e+03 46.26316 62.78571429 2.904665e+03
#> 22 1 Species22 1.313500e+04 143.36842 160.23529412 2.297268e+04
#> 23 1 Species23 2.412400e+04 254.73684 302.50000000 7.705789e+04
#> 24 1 Species24 9.011896e+03 98.63158 110.23529412 1.087268e+04
#> 25 1 Species25 6.460773e+03 64.31579 87.28571429 5.613850e+03
#> 26 2 Species1 2.523573e+00 3.00000 0.18750000 5.625000e-01
#> 27 2 Species2 1.200526e+02 115.00000 6.05263158 6.960526e+02
#> 28 2 Species3 6.104753e+02 533.00000 33.31250000 1.775556e+04
#> 29 2 Species4 1.237113e+02 94.00000 7.83333333 7.363333e+02
#> 30 2 Species5 5.201900e+01 49.00000 2.72222222 1.333889e+02
#> 31 2 Species6 -9.459053e-01 0.00000 0.00000000 0.000000e+00
#> 32 2 Species7 3.255243e+01 31.00000 1.72222222 5.338889e+01
#> 33 2 Species8 2.157895e+00 3.00000 0.15789474 4.736842e-01
#> 34 2 Species9 4.964890e+02 447.00000 26.29411765 1.175347e+04
#> 35 2 Species10 9.280147e+02 859.00000 47.72222222 4.099339e+04
#> 36 2 Species11 1.303680e+02 118.00000 6.94117647 8.190588e+02
#> 37 2 Species12 2.294157e-01 1.00000 0.06250000 6.250000e-02
#> 38 2 Species13 3.794737e+01 37.00000 1.94736842 7.205263e+01
#> 39 2 Species14 7.205948e+02 629.00000 39.31250000 2.472756e+04
#> 40 2 Species15 1.883503e+02 165.00000 10.31250000 1.701562e+03
#> 41 2 Species16 5.263158e-02 1.00000 0.05263158 5.263158e-02
#> 42 2 Species17 -9.459053e-01 0.00000 0.00000000 0.000000e+00
#> 43 2 Species18 -9.176629e-01 0.00000 0.00000000 0.000000e+00
#> 44 2 Species19 -8.885233e-01 0.00000 0.00000000 0.000000e+00
#> 45 2 Species20 9.601762e+01 79.00000 5.64285714 4.457857e+02
#> 46 2 Species21 -8.583951e-01 0.00000 0.00000000 0.000000e+00
#> 47 2 Species22 8.474199e+01 77.00000 4.52941176 3.487647e+02
#> 48 2 Species23 -9.176629e-01 0.00000 0.00000000 0.000000e+00
#> 49 2 Species24 4.579294e+01 42.00000 2.47058824 1.037647e+02
#> 50 2 Species25 6.499277e+00 6.00000 0.42857143 2.571429e+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 7 site 0.8368056 -0.5773503
#> 2 Site2 5 site 0.8088643 1.0690450
#> 3 Site3 3 site 0.8299320 1.0223973
#> 4 Site4 2 site 0.8144044 0.4677072
#> 5 Site5 1 site 0.8299320 NaN
#> 6 Site6 1 site 0.8199446 NaN
#> 7 Site7 7 site 0.8209877 -0.5773503
#> 8 Site8 5 site 0.8365651 1.0690450
#> 9 Site9 4 site 0.8350000 -0.3333333
#> 10 Site10 4 site 0.8347107 -0.3333333
#> 11 Site11 2 site 0.8209877 1.4031215
#> 12 Site12 4 site 0.8250000 -0.3333333
#> 13 Site13 4 site 0.8166090 -1.8333333
#> 14 Site14 3 site 0.8279773 1.7380754
#> 15 Site15 6 site 0.8347107 1.0690450
#> 16 Site16 6 site 0.8355388 1.0690450
#> 17 Site17 5 site 0.8388430 1.0690450
#> 18 Site18 4 site 0.8253968 -0.3333333
#> 19 Site19 6 site 0.8355388 1.0690450
#> 20 Site20 2 site 0.8347107 1.4031215
#> 21 Species1 6 species 0.8437500 -0.8017837
#> 22 Species2 5 species 0.8310249 -0.8017837
#> 23 Species3 5 species 0.8046875 -0.8017837
#> 24 Species4 2 species 0.8055556 -0.4677072
#> 25 Species5 2 species 0.8395062 -0.4677072
#> 26 Species6 6 species 0.8373702 -0.8017837
#> 27 Species7 4 species 0.8271605 1.1666667
#> 28 Species8 4 species 0.8365651 1.1666667
#> 29 Species9 3 species 0.8166090 -1.1246370
#> 30 Species10 5 species 0.8209877 -0.8017837
#> 31 Species11 2 species 0.8512111 -0.4677072
#> 32 Species12 5 species 0.8281250 -0.8017837
#> 33 Species13 2 species 0.8365651 -0.4677072
#> 34 Species15 1 species 0.8281250 NaN
#> 35 Species16 3 species 0.8365651 -0.4089589
#> 36 Species17 7 species 0.8235294 1.1547005
#> 37 Species18 4 species 0.8203125 1.1666667
#> 38 Species19 4 species 0.8355556 -0.3333333
#> 39 Species20 2 species 0.8469388 -1.4031215
#> 40 Species21 3 species 0.8571429 -0.4089589
#> 41 Species22 3 species 0.8442907 -0.4089589
#> 42 Species23 6 species 0.8203125 -0.8017837
#> 43 Species24 1 species 0.8442907 NaN
#> 44 Species25 6 species 0.8265306 -0.8017837
#> 45 Species14 3 species 0.8046875 -0.4089589