| Property | PCA 1 (30%) | PCA 2 (21%) | PCA 3 (17%) |
|---|---|---|---|
| richness | 0.29 | 0.82 | 0.35 |
| links | 0.63 | 0.68 | 0.1 |
| connectance | 0.5 | -0.5 | -0.61 |
| diameter | 0.55 | 0.47 | 0.35 |
| complexity | -0.48 | -0.08 | 0.46 |
| distance | 0.02 | 0.34 | -0.11 |
| basal | -0.46 | 0.45 | -0.69 |
| top | -0.56 | 0.17 | 0.28 |
| intermediate | 0.67 | -0.47 | 0.44 |
| predpreyRatio | -0.24 | 0.42 | -0.73 |
| herbivory | -0.5 | 0.24 | -0.06 |
| omnivory | 0.77 | -0.27 | 0.23 |
| cannibal | 0.73 | 0.12 | -0.29 |
| l_S | 0.83 | 0.5 | -0.13 |
| GenSD | -0.37 | 0.67 | -0.32 |
| VulSD | -0.4 | 0.52 | 0.38 |
| TL | 0.5 | -0.41 | 0.71 |
| ChLen | 0.48 | -0.54 | 0.53 |
| ChSD | 0.32 | 0.1 | 0.46 |
| ChNum | -0.19 | 0.74 | 0.48 |
| path | 0.28 | 0.34 | 0.41 |
| LinkSD | -0.25 | 0.68 | 0.4 |
| S1 | 0.92 | 0.02 | 0.01 |
| S2 | 0.85 | 0.01 | -0.35 |
| S4 | 0.62 | 0.53 | -0.19 |
| S5 | 0.67 | 0.49 | -0.42 |
| ρ | 0.56 | -0.3 | -0.55 |
| centrality | -0.23 | -0.63 | -0.35 |
| loops | 0.81 | 0.29 | -0.05 |
| robustness | 0.07 | 0.16 | -0.51 |
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)
| 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 | The degree to which the prey in a food web can be ordered so that all species can be placed along a single dimension | Daniel B. Stouffer, Camacho, and Amaral (2006) | |
| Prey:predator | Ratio of prey (basal + intermediate) to predators (top + intermediate) | A measure of food web ‘shape’. Values <1 imply an inverted structure and might indicate instability | |
| Robustness | Minimum level of secondary extinction that occurs in response to a particular perturbation | Jonsson et al. (2015) |
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.
Jonsson, Tomas, Sofia Berg, Alexander Pimenov, Catherine Palmer, and Mark Emmerson. 2015. “The Reliability of R50 as a Measure of Vulnerability of Food Webs to Sequential Species Deletions.” Oikos 124 (4): 446–57. https://doi.org/10.1111/oik.01588.
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.
Thompson, Ross M., Ulrich Brose, Jennifer Dunne, Robert O. Hall, Sally Hladyz, Roger L. Kitching, Neo D. Martinez, et al. 2012. “Food Webs: Reconciling the Structure and Function of Biodiversity.” Trends in Ecology & Evolution 27 (12): 689–97. https://doi.org/10.1016/j.tree.2012.08.005.
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.