Network analysis: social, ecological, and social-ecological approaches FSS:ENSb1315 (Spring 2024) Yanhua Shi & Harald Waxenecker Social Network Analysis (SNA) Ecological Network Analysis (ENA) Social-Ecological Network Analysis (SENA) Ecological networks [Fiscus & Fath, 2018] [including slides from the course “Framework for Sustainablity”, Masaryk University, Dr. Brian Fath, 2022] Ecological Food Web Deposited Detritus x2 = 1000.00 Filter Feeders x1 = 2000.00 Meiofauna x4 = 24.12140 Microbiota x3 = 2.4121 Deposit Feeders x5 = 16.2740 Predators x6 = 69.2367 z1 = 41.4697 y4 = 3.5794 y5 = 0.4303 y6 = 0.3594 y3 = 5.7600 y2 = 6.1759 y1 = 25.1646 f26 = 0.3262 f21 = 15.7915 f61 = 0.5135 f25 = 1.9076 f32 = 8.1721 f65 = 0.1721 f52 = 0.6431 f42 = 7.2745 f54 = 0.6609 f24 = 4.2403 f53 = 1.2060 f43 = 1.2060 Oyster Reef Model Dame and Patten 1981 – flow is in kcal/(day m2), storage in kcal/m2 Ecosystem tendencies are consistent and mutually implicating Three common properties: 1) First passage flow 2) Cycling 3) Retention time Get as much as it can (maximize first passage flow); Hold on to it for as long as it can (maximize retention time); and If it must let it go, then try to get it back (maximize cycling). Deposited Detritus x2 = 1000.00 Filter Feeders x1 = 2000.00 Meiofauna x4 = 24.12140 Microbiota x3 = 2.4121 Deposit Feeders x5 = 16.2740 Predators x6 = 69.2367 z1 = 41.4697 y4 = 3.5794 y5 = 0.4303 y6 = 0.3594 y3 = 5.7600 y2 = 6.1759 y1 = 25.1646 f26 = 0.3262 f21 = 15.7915 f61 = 0.5135 f25 = 1.9076 f32 = 8.1721 f65 = 0.1721 f52 = 0.6431 f42 = 7.2745 f54 = 0.6609 f24 = 4.2403 f53 = 1.2060 f43 = 1.2060 How can we analize ecological networks? x1 x2x3 How to measure structure and indirectness Example – digraph to adjacency matrix ú ú ú û ù ê ê ê ë é = 011 001 100 A ú ú ú û ù ê ê ê ë é = 101 100 011 2 A x1 x2x3 Matrix multiplication gives Higher Order (Indirect) Pathways Am, where m > 1 ú ú ú û ù ê ê ê ë é = 011 001 100 A ú ú ú û ù ê ê ê ë é = 212 111 112 5 A ú ú ú û ù ê ê ê ë é = 111 011 101 3 A ú ú ú û ù ê ê ê ë é = 112 101 111 4 A Powers of a matrix!! A1 are the direct paths. A2 are the paths that take two steps A3 are the paths that take three steps, etc. = Dominance of Indirect Effects Dominance of Indirectness occurs when indirect contribution is greater than direct. This occurs in the majority of food web models studied so far and is one of the key results of ecological network analysis and insights into understanding the role of networks on system organization. Indirectness increases with increasing: connectivity cycling system order direct effects Make the direct observation, but analyze the whole system. Direct observations give less than half the story. ú ú ú û ù ê ê ê ë é = 212 111 112 5 A Notice that elements which were zero originally get filled in… = All Life is Physically and Relationally Connected Transaction – transfer of energy or matter between two directly connected components x1 x2 x3 20 2100 80 218 Relation – qualitative, value-oriented, direct or indirect interaction types. Nine possible interaction types + + + + + + + - - - + - - - 0 0 0 0 0 0 0 0 ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) (0, 0) → neutralism (–, –) → competition (+, –) → predation (+, +) → mutualism + + + + + + + - - - + - - - 0 0 0 0 0 0 0 0 ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) Oyster Reef Model Deposited Detritus x2 = 1000.00 Filter Feeders x1 = 2000.00 Meiofauna x4 = 24.12140 Microbiota x3 = 2.4121 Deposit Feeders x5 = 16.2740 Predators x6 = 69.2367 z1 = 41.4697 y4 = 3.5794 y5 = 0.4303 y6 = 0.3594 y3 = 5.7600 y2 = 6.1759 y1 = 25.1646 f26 = 0.3262 f21 = 15.7915 f61 = 0.5135 f25 = 1.9076 f32 = 8.1721 f65 = 0.1721 f52 = 0.6431 f42 = 7.2745 f54 = 0.6609 f24 = 4.2403 f53 = 1.2060 f43 = 1.2060 neutralism mutualism mutualism predation ú ú ú ú ú ú ú ú û ù ê ê ê ê ê ê ê ê ë é +-+ -++- -++ --+ ++--+ -- = 000 00 000 000 0 0000 sD ú ú ú ú ú ú ú ú û ù ê ê ê ê ê ê ê ê ë é ++++-+ -+++++ +-++++ +--+++ -+--++ --++-+ =sU ú ú ú ú ú ú ú ú û ù ê ê ê ê ê ê ê ê ë é ++++-+ -+++++ +-++++ +--+++ -+--++ --++-+ =sU ú ú ú ú ú ú ú ú û ù ê ê ê ê ê ê ê ê ë é +-+ -++- -++ --+ ++--+ -- = 000 00 000 000 0 0000 sD Oyster Reef Model Deposited Detritus x2 = 1000.00 Filter Feeders x1 = 2000.00 Meiofauna x4 = 24.12140 Microbiota x3 = 2.4121 Deposit Feeders x5 = 16.2740 Predators x6 = 69.2367 z1 = 41.4697 y4 = 3.5794 y5 = 0.4303 y6 = 0.3594 y3 = 5.7600 y2 = 6.1759 y1 = 25.1646 f26 = 0.3262 f21 = 15.7915 f61 = 0.5135 f25 = 1.9076 f32 = 8.1721 f65 = 0.1721 f52 = 0.6431 f42 = 7.2745 f54 = 0.6609 f24 = 4.2403 f53 = 1.2060 f43 = 1.2060 predation mutualism predation com petition Two relations “flipped” Community-level relations are more positive than the direct relations that produced them: This is network mutualism. Two example networks Fully connected Minimally connected Robustness Degree of order (a) Robustness combines both efficiency and redundancy = network balance Greater efficiency Greater redundancy Toward stagna;on (too li