Ecological networksDaijiang LiLSU1 / 23

Announcements

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Networks are everywhere3 / 23

Networks are everywheresocial network3 / 23

Networks are everywheresocial networktransportation network3 / 23

Networks are everywheresocial networktransportation networkpower grid network3 / 23

Networks are everywheresocial networktransportation networkpower grid networkinformation network3 / 23

Internet Routers Internet connections Undirected 192,244 609,066 6.34 WWW Webpages Links Directed 325,729 1,497,134 4.60 Power Grid Power plants, transformers Cables Undirected 4,941 6,594 2.67 Mobile-Phone Calls Subscribers Calls Directed 36,595 91,826 2.51 Email Email addresses Emails Directed 57,194 103,731 1.81 Science Collaboration Scientists Co-authorships Undirected 23,133 93,437 8.08 Actor Network Actors Co-acting Undirected 702,388 29,397,908 83.71 Citation Network Papers Citations Directed 449,673 4,689,479 10.43 E. Coli Metabolism Metabolites Chemical reactions Directed 1,039 5,802 5.58 Protein Interactions Proteins Binding interactions Undirected 2,018 2,930 2.90

Network & Graph

Network Science
Graph Theory

Network
Graph

Node (N)
Vertex (V)

Link (L)
Edge (E)

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Network Science	Graph Theory
Network	Graph
Node (N)	Vertex (V)
Link (L)	Edge (E)

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The rise of networks

rise of networks

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Ecological Networks

(Pocock et al. 2016)

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Why ecological networks?8 / 23

what is ecology? networks as a natural way to connect interactive species be able to handle complex systems analytical tools to detect system level structure and species level contributions

Network types

unipartite
- weighted?
- directed?

bipartite
- weighted?
- directed?

network types Delmas et al. 2019

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Unipartite networks

Interactions between nodes of the same class

social contact network (e.g., contact tracing, target vaccination)
species co-occurrence network (e.g., metapopulations, community assembly/disassembly)
www (e.g., information flow, fraud prevention)

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Bipartite networks

Interactions between two classes of nodes

Host-parasite
Predator-prey
Plant-pollinator

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Different

visualizations

of the same

network

(Pocock et al.
2016)

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Adjacency matrix

adjacency matrix

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Common measures of networksOrder (S): the total number of nodes14 / 23

Common measures of networksOrder (S): the total number of nodesSize (L): the total number of links (interactions)14 / 23

Common measures of networksOrder (S): the total number of nodesSize (L): the total number of links (interactions)Linkage density: L/S14 / 23

Common measures of networksOrder (S): the total number of nodesSize (L): the total number of links (interactions)Linkage density: L/SConnectance (Co): L/m (m: possible number of interactions)14 / 23

the connectance range: 0-1

Common measures of networksDegree: the number of links a node has to other nodes; kiki to be the degree of the i th node in the network15 / 23

Common measures of networks

Degree: the number of links a node has to other nodes; $k_{i}$ to be the degree of the i th node in the network

Degree distribution P(k): the probability that a species has k interactions within the network. P(k) = N(k)/S.

The degree distribution plays a central role in network theory with the calculation of most network properties requires us to know P(k)

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Common measures of networks

Clustering coefficient (CC): the degree to which the neighbors of a given node link to each other.

$C C_{i} = \frac{2 N_{i}}{K_{i} (K_{i} - 1)}$

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Common measures of networks

Modularity: how closely connected nodes are divided into modules

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Common measures of networks

Nestedness: the tendency for species with fewer interactions to be a subset of those with more interactions

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Pocock et al. 2016

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Common measures of networks

Centrality: the importance of a node in the network; many different types to measure centrality: degree, closeness, betweenness, eigenvector, and Katz’s covered in Delmas et al. (2019)

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degree: just number of interactions closeness: global scale, the proximity of a species to all other species in the network, account the structure of the whole network

Common measures of networks

Contribution to network properties

$C_{i} = \frac{P - \bar{P_{i}}}{σ_{\bar{P_{i}}}}$

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Common measures of networks

Contribution to network properties

$C_{i} = \frac{P - \bar{P_{i}}}{σ_{\bar{P_{i}}}}$

Error tolerance and attack tolerance

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Error tolerance refers to the ability of a network to recover from the loss of a node

attack tolerance: the robustness of a network to a targeted attack

negative relationships between them

Common measures of networks

Compare different nodes and different networks

Nodes

$J (A, B) = \frac{| A \cap B |}{| A \cup B |}$

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Common measures of networks

Compare different nodes and different networks

Nodes

$J (A, B) = \frac{| A \cap B |}{| A \cup B |}$

Networks

Poisot et al. 2012

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Network rewiring in a changing world

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