Finding the mjor descriptors of species networks

Blah blah blah Vermaat, Dunne, and Gilbert (2009)

“It is incumbent on network ecologists to establish clearly the independence and uniqueness of the descriptive metrics used.” - Lau et al. (2017)

Table 1: An informative caption about the different network properties

Label	Definition	“Function”	Reference (for maths), can make footnotes probs
Basal	Percentage of basal taxa, defined as species who have a vulnerability of zero
Connectance	\(L/S^2\), where \(S\) is the number of species and \(L\) the number of links
Cannibal	Percentage of species that are cannibals
ChLen	Mean food chain length, averaged over all species (where a food chain is defined as a continuous path from a ‘basal’ to a ‘top’ species)
ChSD	Standard deviation of ChLen
ChNum	log number of food chains
Clust	mean clustering coefficient (probability that two taxa linked to the same taxon are also linked)		TODO
GenSD	Normalized standard deviation of generality of a species standardized by \(L/S\)		Williams and Martinez (2008)
Herbivore	Percentage of herbivores plus detritivores (taxa that feed only on basal taxa)
Intermediate	Percentage of intermediate taxa (with both consumers and resources)
LinkSD	Normalized standard deviation of links (number of consumers plus resources per taxon)
Loop	Percentage of taxa in loops (food chains in which a taxon occurs twice)
L/S	links per species
MaxSim	Mean of the maximum trophic similarity of each taxon to other taxa, the number of predators and prey shared by a pair of species divided by their total number of predators and prey		TODO
Omnivory	Percentage of omnivores (taxa that feed on \(\geq\) 2 taxa with different trophic levels)
Path	characteristic path length, the mean shortest food chain length between species pairs
Richness	Number of nodes in the network
TL	Prey-weighted trophic level averaged across taxa		Williams and Martinez (2004)
Top	Percentage of top taxa (taxa without consumers)
VulSD	Normalized standard deviation of vulnerability of a species standardized by \(L/S\)
Links	The number of links in the network
Diameter	Diameter can also be measured as the average of the distances between each pair of nodes in the network		Delmas et al. (2019)
\(\rho\)	Spectral radius is a a conceptual analog to nestedness (and more appropriate for unipartite networks). It is defined as the absolute value of the largest real part of the eigenvalues of the undirected adjacency matrix		Staniczenko, Kopp, and Allesina (2013)
Complexity	SVD complexity of a network, defined as the Pielou entropy of its singular values	Something about structural v behavioural complexity being captured	Strydom, Dalla Riva, and Poisot (2021)
Centrality	Centrality is a measure of how ‘influential’ a species is, under various definitions of ‘influence’…	Centrality can help in quantifying the importance of species in a network
S1	Number of linear chains		Daniel B. Stouffer et al. (2007) Milo et al. (2002)
S2	Number of omnivory motifs		Daniel B. Stouffer et al. (2007) Milo et al. (2002)
S4	Number of apparent competition motifs		Daniel B. Stouffer et al. (2007) Milo et al. (2002)
S5	Number of direct competition motifs		Daniel B. Stouffer et al. (2007) Milo et al. (2002)
Intervality			TODO Daniel B. Stouffer, Camacho, and Amaral (2006)

In [1]:

library(knitr)
library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   3.5.1     ✔ tibble    3.2.1
✔ lubridate 1.9.3     ✔ tidyr     1.3.1
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

dat = readr::read_csv("tables/allNetworks_corr_complete.csv")

Rows: 28 Columns: 4
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (3): Property, PCA 1 (27%), PCA 2 (24%)
dbl (1): PCA 3 (11%)

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

kable(dat)

In [2]:

Table 2: Here is a table showing the correlation of the different network properties with the first three dimensions of the PCA

Property	PCA 1 (27%)	PCA 2 (24%)	PCA 3 (11%)
richness	0.8	0.46	-0.11
links	0.89	0.14	-0.16
connectance	0.05	-0.9	0.02
diameter	0.81	-0.06	0.14
complexity	-0.28	0.48	0.41
distance	0.41	0.13	-0.03
basal	-0.29	0.38	-0.73
top	-0.24	0.59	0.55
intermediate	0.4	-0.68	0.32
herbivory	-0.29	0.51	0.13
omnivory	0.52	-0.71	0.18
cannibal	0.29	-0.72	-0.19
l_S	0.78	-0.33	-0.18
GenSD	-0.1	0.42	-0.80
VulSD	-0.05	0.76	0.31
TL	0.59	-0.13	0.39
ChLen	0.17	0.45	0.30
ChSD	0.42	0.05	0.15
ChNum	0.19	0.69	0.42
path	0.66	0.09	0.17
LinkSD	0.04	0.63	-0.54
S1	0.82	0.29	0.00
S2	0.84	0.12	-0.06
S4	0.74	0.43	-0.13
S5	0.76	0.39	-0.22
ρ	0.14	-0.82	-0.24
centrality	-0.49	-0.29	0.21
loops	0.45	0.12	0.07

VERMAAT networks only

All networks. Vermaat subset = using only the structural measures from Vermaat

References

Delmas, Eva, Mathilde Besson, Marie-Hélène Brice, Laura A. Burkle, Giulio V. Dalla Riva, Marie-Josée Fortin, Dominique Gravel, et al. 2019. “Analysing Ecological Networks of Species Interactions.” Biological Reviews 94 (1): 16–36. https://doi.org/10.1111/brv.12433.

Lau, Matthew K., Stuart R. Borrett, Benjamin Baiser, Nicholas J. Gotelli, and Aaron M. Ellison. 2017. “Ecological Network Metrics: Opportunities for Synthesis.” Ecosphere 8 (8): e01900. https://doi.org/10.1002/ecs2.1900.

Milo, R., S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon. 2002. “Network Motifs: Simple Building Blocks of Complex Networks.” Science 298 (5594): 824–27. https://doi.org/10.1126/science.298.5594.824.

Staniczenko, Phillip P. A., Jason C. Kopp, and Stefano Allesina. 2013. “The Ghost of Nestedness in Ecological Networks.” Nature Communications 4 (1): 1391. https://doi.org/10.1038/ncomms2422.

Stouffer, Daniel B., Juan Camacho, and Luís A. Nunes Amaral. 2006. “A Robust Measure of Food Web Intervality.” Proceedings of the National Academy of Sciences 103 (50): 19015–20. https://doi.org/10.1073/pnas.0603844103.

Stouffer, Daniel B, Juan Camacho, Wenxin Jiang, and Luís A Nunes Amaral. 2007. “Evidence for the Existence of a Robust Pattern of Prey Selection in Food Webs.” Proceedings of the Royal Society B: Biological Sciences 274 (1621): 1931–40. https://doi.org/10.1098/rspb.2007.0571.

Strydom, Tanya, Giulio V. Dalla Riva, and Timothée Poisot. 2021. “SVD Entropy Reveals the High Complexity of Ecological Networks.” Frontiers in Ecology and Evolution 9. https://doi.org/10.3389/fevo.2021.623141.

Vermaat, Jan E., Jennifer A. Dunne, and Alison J. Gilbert. 2009. “Major Dimensions in Food-Web Structure Properties.” Ecology 90 (1): 278–82. https://doi.org/10.1890/07-0978.1.

Williams, Richard J., and Neo D. Martinez. 2004. “Limits to Trophic Levels and Omnivory in Complex Food Webs: Theory and Data.” The American Naturalist 163 (3): 458–68. https://doi.org/10.1086/381964.

———. 2008. “Success and Its Limits Among Structural Models of Complex Food Webs.” The Journal of Animal Ecology 77 (3): 512–19. https://doi.org/10.1111/j.1365-2656.2008.01362.x.