class: center, middle, inverse, title-slide # Ecological networks ### Daijiang Li ### LSU --- class: left, middle class: left, center, inverse .font300[Announcements] + + + --- background-image: url('figs/network.jpg') background-position: 50% 50% background-size: contain class: center, top, inverse # .font200[.red[Networks are everywhere]] -- ### social network -- ### transportation network -- ### power grid network -- ### information network ??? 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 --- class: center, middle # Network & Graph .font200[ | Network Science | Graph Theory | |--|--| | Network | Graph | | Node (N) | Vertex (V) | | Link (L) | Edge (E) | ] --- background-image: url('figs/netTypes.png') background-position: 50% 50% background-size: contain class: center, top, inverse --- # [The rise of networks](http://networksciencebook.com/chapter/1#scientific-impact)  --- background-image: url('figs/econet.jpeg') background-position: 50% 50% background-size: contain class: left, top .font200[.red[Ecological Networks]] (Pocock et al. 2016) --- class: center, middle # .font150[Why ecological networks?] ??? 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 .pull-left[ .font150[ - unipartite + weighted? + directed? ] ] .pull-right[ .font150[ - bipartite + weighted? + directed? ] ]  .right[Delmas et al. 2019] --- # Unipartite networks ## Interactions between nodes of the .green[same class] .font200[ - 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) ] --- # Bipartite networks ## Interactions between .green[two classes] of nodes .font200[ - Host-parasite - Predator-prey - Plant-pollinator ] --- background-image: url('figs/diff_network.jpeg') background-position: 50% 50% background-size: contain class: left, top Different visualizations of the same network (Pocock et al. 2016) --- class: center, middle # Adjacency matrix  --- layout: true # Common measures of networks --- ### .green[Order (S)]: the total number of nodes -- ### .green[Size (L)]: the total number of links (interactions) -- ### .green[Linkage density]: L/S -- ### .green[Connectance (Co)]: L/m (m: possible number of interactions) ??? the connectance range: 0-1 --- ### .green[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 -- ### .green[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)_  --- ### .green[Clustering coefficient (CC)]: the degree to which the neighbors of a given node link to each other. `$$CC_i = \frac{2N_i}{K_i(K_i - 1)}$$` <br>  --- ### .green[Modularity]: how closely connected nodes are divided into modules  --- ### .green[Nestedness]: the tendency for species with fewer interactions to be a subset of those with more interactions <img src="figs/nestednes.png" width="90%" style="display: block; margin: auto;" /> --- layout: false background-image: url('figs/mod_nest.jpeg') background-position: 50% 50% background-size: contain class: right, bottom Pocock et al. 2016 --- layout: true # Common measures of networks --- ### .green[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) <img src="figs/central.png" width="55%" style="display: block; margin: auto;" /> ??? 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 --- ### .green[Contribution to network properties] .font130[ `$$C_{i}=\frac{P-\bar{P_{i}}}{\sigma_{\bar{P_{i}}}}$$` ] -- ### Error tolerance and attack tolerance  ??? 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 --- ### Compare different nodes and different networks .pull-left[ ### Nodes $$ J(A,B) = \frac{| A \cap B |}{| A \cup B|} $$ ] -- .pull-right[ ### Networks  .right[[Poisot et al. 2012](https://onlinelibrary.wiley.com/doi/abs/10.1111/ele.12002)] ] --- layout: false background-image: url('figs/econet.jpeg') background-position: 50% 50% background-size: contain class: center, top, inverse <br> <br> # .red[Network rewiring in a changing world]