Foundations for Sustainability Brian D. Fath & Dan Fiscus Fulbright Distinguished Chair, Masaryk University, Brno, Czech Republic Professor, Towson University, Maryland, USA Senior Research Scholar, International Institute for Applied Systems Analysis, Austria Chapter 6: Life science lessons from ecological networks and systems ecology •Your reaction 1)What do you think is a main conclusion from using network analysis? Why? 2) 2)What questions do you have? Ecological Network Analysis provides holistic tools 1)Discrete versus sustained life 2)Developmental tendencies of ecosystems are complementary 3)Indirect impacts are often greater than direct ones 4)All Life is connected—via ENA, we can quantify the connections 5)Ecosystems show mutualism between species 6)Ecosystems and networks naturally balance order and flexibility 7)A hypothetical new formalism prohibits fragmentation of life from environment and of life from life Knowing what we know Life’s great advance as a complex adaptive system was to emerge as differentiations from and using the stuff of the background and simultaneously develop ways to interact and make sense of this background. Rosen’s (1991) modeling relation: An elegant representation of the scientific process as heavily entangled with the real world it seeks to understand Network Primer Networks are everywhere! http://www.analytictech.com/networks/pitts1.jpg http://www-personal.umich.edu/~mejn/networks/contagion.gif Communicable disease http://www.orgnet.com/19hijackers_nolabels.gif Terrorism network http://www-personal.umich.edu/~mejn/networks/school.gif High School Friendship http://www-personal.umich.edu/~mejn/networks/addhealth.gif High School Dating http://www.cheswick.com/ches/map/gallery/wired.gif The Internet F:\MEDIA\1793\179302.JPG Ecological Food Web Oyster Reef Model Dame and Patten 1981 – flow is in kcal/(day m2), storage in kcal/m2 x1 x2 x3 How to measure structure and indirectness Example – digraph to adjacency matrix x1 x2 x3 Matrix multiplication gives Higher Order (Indirect) Pathways Am, where m > 1 Powers of a matrix!! The matrix Am gives exactly the number of paths between two nodes of length m. A1 are the direct paths. A2 are the paths that take two steps A3 are the paths that take three steps, etc. Notice that some elements which were zero originally get filled in. In other words we have a way to identify the indirect, i.e., m>1, walks in the matrix, and hence in the graph. Food web model Gulf of Mexico ecosystem Very many pathways as path length increases As m increases, the number of paths typically increases greatly The outflow (time forward, input driven) fractions are given by gij where x1 x2 x3 100 80 2 20 18 2 Flow Analysis Inter-compartmental flows outputs inputs Adjacency matrix Total flow through each compartment Just as powers of A gave higher order pathways, Powers of G give flow transfers along higher order pathways. G2 gives the fraction of flow leaving j that took 2 steps to reach i. x1 x2 x3 100 80 2 20 18 2 Continuing: G3 gives the fraction of flow leaving j that took 3 steps to reach i. x1 x2 x3 100 80 2 20 18 2 Summarizing: G2 gives transfers over pathways of length 2 G3 gives transfers over pathways of length 3, etc., i.e., Gm gives transfers over pathways of length m Summing over m=1→∞ gives powers over all pathways where represent indirect transfers Unlike like powers of A, powers of G get smaller and the series converges N is the INTEGRAL output flow matrix since it includes direct and all indirect flows Flow: N = I + G + G2 + G3 + G4 +… integral = initial + direct + indirect input Key findings: •Quantify input and output flow •Indirect flows > direct flows •Flows are well mixed •Mutualistic relations dominate Propagation of network indirect effects L1: Coupled Complementary Life has Discrete and Sustained Aspects https://upload.wikimedia.org/wikipedia/commons/f/f9/Loxodonta_africana_-_old_bull_%28Ngorongoro,_20 09%29.jpg A single organism possesses all the necessary aspects to be alive http://www.bostonbakesforbreastcancer.org/wp-content/uploads/2012/03/sun.jpg Rain Cloud Clip Art http://www.cityfarmer.info/wp-content/uploads/2008/08/soil.jpg Environment and ecological interactions http://t0.gstatic.com/images?q=tbn:ANd9GcRJjKUkHB6gIOngBao_fcpDbgu_RIESE5qVbRcAMNPToWb6yep-bRiTohCA jg Interacting ecological community and its environment is an ecosystem An ecosystem possesses all the necessary aspects to sustain life Life and environment are best understood and modeled as unified as a single “life–environment” system. Fiscus D, Fath BD, Goerner S. 2012. E:CO 14(3), 44–88. Bounty of the Commons Humans win, environment improves “Biologists have rather been in the habit of reflecting upon the evolution of individual species. This point of view does not bear the promise of success, if our aim is to find expression for the fundamental law of evolution. We shall probably fare better if we constantly recall that the physical object before us is an undivided system, that the divisions we make therein are more or less arbitrary importations, psychological rather than physical, and as such, are likely to introduce complications into the expression of natural laws operating upon the system as a whole.” (Lotka p. 158) And later: “. . . the concept of evolution, to serve us in its full utility, must be applied, not to an individual species, but to groups of species which evolve in mutual interdependence; and further to the system as a whole, of which such groups form inseparable part.” (Lotka p. 277) Evolution of an undifferentiated whole L2: Complementarity of Ecological Goal Functions •Ecological Goal Functions are assumed to measure given properties or tendencies of ecosystems, emerging as a result of self-organization processes in their development (Marques 1998). • Examples of Goal functions from the literature 1 Minimize specific entropy production (Prigogine 1947). Decrease in the respiration to biomass ratio. 2 Maximize energy throughflow (Odum 1983). Increase in the internal energy flow. 3 Maximize exergy degradation (Kay 1984). As the amount of exergy captured increases, so does the amount dissipated. 4 Maximize exergy storage (Jørgensen & Mejer 1977). Exergy storage (biomass) and information increase due to shift to more complex species composition. 5 Maximize retention time (Cheslak & Lamarra 1981). Biological components develop mechanisms to increase time lags to maintain the energy stores longer. mode 3 dissipation mode 2 recycle mode 1 1st passage system H1 input environ- influencing output environ- influenced mode 0 – boundary input mode 4 – boundary output Hi Hi Hi Hj Hj Hj Environs form a partition of the system. FLOW pair-wise interactions STORAGE pair-wise interactions mode 1 (first passage) mode 2 (cyclic) mode 3 (dissipative) Network representation of flow and storage partitioning for any (i,j) pair in the system. Goal Function Ecological Representation Network Parameter Network Analysis Formulation max power max(TST) TST = f(1) + f(2) TST =∑∑ (nij)zj max exergy storage max(TSS) TSS = x(1)+x(2) TSS = ∑∑τi(nij)zj max dissipation max(TSE) TSE = f(3) TSE = ∑ ∑ (nij/nii)zj max cycling max(TSC) TSC = f(2) TSC =∑ ∑ (nij/nii)(nii−1)zj min specific dissipation min(TSE/TSS) TSE/TSS = f(3)/(x(1)+x(2)) TSE/TSS = ∑ ∑ ((nij/nii)zj)/xij = ∑∑1/(τinii) max residence time max(TSRT) TSRT = τ TSRT = ∑∑xi/(nij)zj = ∑τi Conclusion Goal functions 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). L3: Dominance of Indirect Effects Measuring indirect flows G = 0 0 0 0 0 0 0.3808 0 0 0.5000 0.7600 0.4758 0 0.3670 0 0 0 0 0 0.3267 0.1476 0 0 0 0 0.0289 0.1476 0.0779 0 0 0.0124 0 0 0 0.0686 0 G2 = 0 0 0 0 0 0 0.0059 0.1853 0.1859 0.0592 0.0326 0 0.1398 0 0 0.1835 0.2789 0.1746 0.1244 0.0542 0 0.1634 0.2483 0.1554 0.0110 0.0796 0.0115 0.0144 0.0220 0.0137 0 0.0020 0.0101 0.0053 0 0 G3 = 0 0 0 0 0 0 0.0706 0.0885 0.0136 0.0952 0.1408 0.0882 0.0022 0.0680 0.0682 0.0217 0.0120 0 0.0226 0.0605 0.0608 0.0464 0.0518 0.0258 0.0305 0.0096 0.0054 0.0415 0.0615 0.0379 0.0008 0.0055 0.0008 0.0010 0.0015 0.0009 G4= 0 0 0 0 0 0 0.0348 0.0401 0.0348 0.0552 0.0733 0.0421 0.0259 0.0325 0.0050 0.0349 0.0517 0.0324 0.0234 0.0390 0.0145 0.0343 0.0478 0.0288 0.0041 0.0173 0.0152 0.0096 0.0099 0.0046 0.0021 0.0007 0.0004 0.0028 0.0042 0.0026 N = 1.0000 0 0 0 0 0 0.5369 1.3885 0.2775 0.7800 1.1006 0.6606 0.1971 0.5096 1.1019 0.2863 0.4039 0.2425 0.2045 0.5288 0.2533 1.2971 0.4192 0.2516 0.0605 0.1565 0.1904 0.1659 1.1241 0.0745 0.0165 0.0107 0.0131 0.0114 0.0771 1.0051 N-I-G = 0 0 0 0 0 0 0.1561 0.3885 0.2775 0.2800 0.3406 0.1848 0.1971 0.1426 0.1019 0.2863 0.4039 0.2425 0.2045 0.2021 0.1057 0.2971 0.4192 0.2516 0.0605 0.1276 0.0428 0.0879 0.1241 0.0745 0.0042 0.0107 0.0131 0.0114 0.0085 0.0051 Indirect/direct= sum(sum(N–I–G))/sum(sum(G)) = 5.0523 3.2932 =1.5341 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. L4: All Life is Physically and Relationally Connected Relation – qualitative, value-oriented, direct or indirect interaction types. Nine possible interaction types Transaction – transfer of energy or matter between two directly connected components —determines relationship types —demonstrates network synergism and mutualism • — •Let — — —Normalized net flow between components — Utility Analysis Three compartment food chain Network utility analysis uses net flow between components x1 x2 x3 20 2 100 80 2 18 Direct Sign Matrix (sd21,sd12) = (+, –) → predation (sd32,sd23) = (+, –) → predation (sd31,sd13) = (0, 0) → neutralism Direct relations – from comparing terms across the main diagonal: x1 x2 x3 20 2 100 80 2 18 Integral Utility: Utility: U = I + D + D2 + D3 + D4 + … integral = initial + direct + indirect input All terms are non-zero indicating relational connectivity Direct interaction matrix, shows null (0,0) relations Integral (direct + indirect) relations are all non-zero, indicating everything affects everything, at least indirectly L5: Mutualism is Common and Crucial Integral Utility: Utility: U = I + D + D2 + D3 + D4 + … integral = initial + direct + indirect input (sd21,sd12) = (+, –) → predation (sd32,sd23) = (+, –) → predation (sd31,sd13) = (+, +) → mutualism What is indirect relation between X1 and X3? Community-level relations are more positive than the direct relations that produced them: This is network mutualism. 43 are positive and 38 are negative Oyster Reef Model Oyster Reef Model L6: Ecosystems Balance Efficiency and Adaptability Information-based Ecological Network Analysis Robustness as a trade-off between efficiency and diversity Efficiency Total system capacity Degree of order Diversity Robustness Two example networks 54 Fully connected Minimally connected Degree of order (a) untitled2.jpg Robustness combines both efficiency and redundancy Greater efficiency Greater redundancy Toward stagnation (too little efficiency) Toward brittleness (too little redundancy) Degree of order Optimal balance “Window of Vitality” Data from ecosystems Ulanowicz 2009 A Third Window L7: A Hyperset Formalism of Life Prohibits Fragmentation of Life from Environment 1) 1)A hyperset equation explicitly and formally prohibits fragmentation of life from environment Recursive nature of nature Fiscus D, Fath BD, Goerner S. 2012. E:CO 14(3), 44–88. life–environment = {environment{ecosystems{organisms{environment}}}} n Bounty of the Commons Humans win, environment improves Summary of the six principles •Network insight and tools can give new understanding and contribute to a new holistic, interconnected, reflective science • •“With an eco-mind, we move from ‘fixing something’ outside ourselves to realigning our relationships within our ecological home.” (Lappe 2011, p. 16) Discussion questions •could a plant exist alone with a “very slow working cycle” • •What if all organisms incorporated chloroplast cells? Is it sufficient? • Discussion questions •How can the hyperset formulation help us think like an ecosystem? –Practical implementations of it? – •