Structure

Linking structure and function to ecological processes

Section Overview

• What do we mean by structure = a way in which we are ‘summarising’ the network (the architecture of the network).

• What do we mean by form? (probably nebulous and poorly articulated in general, or at least not explicitly backed by firm eco theory)

  • species vs system?

• But does form (structure) = function??

• Also does the form-function link differ when thinking of bipartite/unipartite systems? I’m inclined to think that many of the ways in which we measure form has been developed in the context of bipartite systems and is there really an ecological reason that they will hold in unipartite systems?

• See also Thompson et al. (2012) and Guimarães (2020)

Summarising networks

Delmas et al. (2019) gives a somewhat extensive overview of the different ways in which we can ‘summarise’ network properties (something akin to statistical moments) which is summarised in Table 1. Importantly we need to acknowledge that these summary statistics are ‘retrieved’ at different levels of organisation (scale) within the network. For example the in-degree is something that is determined on a by-species level (micro), but connectance is at the network (macro) level.

Table 1: Table with network summary statistics.

Summary Statistic (form)	What	Ref	Ecological interpretation (function)	Scale
Specificity	Related to number of links at the species level		Measure of (diet) specialisation	Micro
Generaility/vulnerability (In/out degree)	Number of prey/predators	Schoener (1989), Williams and Martinez (2000)	Position in food web e.g., top/basal species	Micro
Degree distribution	measures the probability (P(k)) that a species has k interactions within the network			Micro
Centrality		Estrada and Bodin (2008)	Position of species in network. The idea of hubs…	Macro
Motifs/graphlets	Smaller interacting units/patterns between 3 species	Milo et al. (2002), Stouffer and Bascompte (2010)		Meso
Shortest path	Shortest path from species a to a basal species		diameter, perturbation, food chain length	Meso
Links	Number of links in the network			Macro
Connectance	The number realised links compared to the number of potential links	Martinez (1992)		Macro
Nestedness	Interactions forming a subset of others - diets being subsets of others	Bastolla et al. (2009)		Macro
Clustering/modularity	Non-interacting units/clusters of species (opposite of nestedness?)	Watts and Strogatz (1998)		Macro
Intervaility	‘ordination’ of a network. How much can the network be described by a single trait	Eklöf and Stouffer (2016)		Macro
Complexity	A representation of links between species in a system	Strydom, Dalla Riva, and Poisot (2021), Riva et al. (2023)		Macro
\(\beta\)-diversity		Poisot et al. (2012)		Meta

What do we want to learn from networks?

This is probably just going to churn up thoughts of existential dread…

References

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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.

Eklöf, Anna, and Daniel B. Stouffer. 2016. “The Phylogenetic Component of Food Web Structure and Intervality.” Theoretical Ecology 9 (1): 107–15. https://doi.org/10.1007/s12080-015-0273-9.

Estrada, Ernesto, and Örjan Bodin. 2008. “Using Network Centrality Measures to Manage Landscape Connectivity.” Ecological Applications 18 (7): 1810–25. https://doi.org/10.1890/07-1419.1.

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Martinez, Neo D. 1992. “Constant Connectance in Community Food Webs.” The American Naturalist 139 (6): 1208–18. http://www.jstor.org/stable/2462337.

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.

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Riva, Federico, Caio Graco-Roza, Gergana N. Daskalova, Emma J. Hudgins, Jayme M. M. Lewthwaite, Erica A. Newman, Masahiro Ryo, and Stefano Mammola. 2023. “Toward a Cohesive Understanding of Ecological Complexity.” Science Advances 9 (25): eabq4207. https://doi.org/10.1126/sciadv.abq4207.

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