---
title: "Finding the mjor descriptors of species networks"
author:
  - name: Tanya Strydom
    id: ts
    orcid: 0000-0001-6067-1349
    corresponding: true
    email: t.strydom@sheffield.ac.uk
    role: 
    - conceptualization: lead
    - methodology: supporting
    affiliation:
      - id: sheffield
        name: School of Biosciences, University of Sheffield, Sheffield, UK
  - name: Andrew P. Beckerman
    id: apb
    orcid: 0000-0002-7859-8394
    corresponding: false
    role: 
    - conceptualization: lead
    - methodology: supporting
    affiliations:
      - ref: sheffield
funding: "The author(s) received no specific funding for this work. Well they did I just haven't done the homework"
keywords:
  - food web
  - structure
  - dimensionality reduction
abstract: |
  TODO
date: last-modified
bibliography: references.bib
number-sections: true
---

Blah blah blah @vermaatMajorDimensionsFoodweb2009

*"It is incumbent on network ecologists to establish clearly the independence and uniqueness of the descriptive metrics used."* - @lauEcologicalNetworkMetrics2017

| 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 $L/S$ |  | @williamsSuccessItsLimits2008a |
| 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 |  | @williamsLimitsTrophicLevels2004 |
| 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 |  | @delmasAnalysingEcologicalNetworks2019 |
| $\rho$ | 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 |  | @staniczenkoGhostNestednessEcological2013 |
| Complexity | SVD complexity of a network, defined as the Pielou entropy of its singular values | Something about structural v behavioural complexity being captured | @strydomSVDEntropyReveals2021 |
| 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 |  | @stoufferEvidenceExistenceRobust2007 @miloNetworkMotifsSimple2002 |
| S2 | Number of omnivory motifs |  | @stoufferEvidenceExistenceRobust2007 @miloNetworkMotifsSimple2002 |
| S4 | Number of apparent competition motifs |  | @stoufferEvidenceExistenceRobust2007 @miloNetworkMotifsSimple2002 |
| S5 | Number of direct competition motifs |  | @stoufferEvidenceExistenceRobust2007 @miloNetworkMotifsSimple2002 |
| Intervality |  |  | **TODO** @stoufferRobustMeasureFood2006a |

: An informative caption about the different network properties {#tbl-properties}

```{r}
#| label: tbl-corr
#| tbl-cap: "Here is a table showing the correlation of the different network properties with the first three dimensions of the PCA"
library(knitr)
library(tidyverse)

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

kable(dat)
```

![VERMAAT networks only](figures/pca_vermaat.png)

![All networks. Vermaat subset = using only the structural measures from Vermaat](figures/pca_allNetworks.png)

# References {.unnumbered}

::: {#refs}
:::