Mechanical Inference in Dynamic Ecosystems
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Mechanical Inference in Dynamic Ecosystems by R. E. Langendorf B.S., Bates College, 2010 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Environmental Studies 2018 This thesis entitled: Mechanical Inference in Dynamic Ecosystems written by R. E. Langendorf has been approved for the Department of Environmental Studies Prof. Daniel F. Doak Prof. Sharon K. Collinge Prof. Aaron Clauset Prof. James A. Estes Prof. Mark Novak Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Langendorf, R. E. (Ph.D., Environmental Studies) Mechanical Inference in Dynamic Ecosystems Thesis directed by Prof. Daniel F. Doak Empirical studies of graphs have contributed enormously to our understanding of com- plex systems, growing into a more scientific exploration of communities spanning the physical, biological, and social called network science. As the quantity and types of networks have grown so has their heterogeneity in quality and specificity resulting in a wealth of datasets that are not matched by existing theoretical methods. This is especially true in ecology where the ma- jority of interactions are indirect and unobservable even in well-studied systems. As a result ecologists continue to grapple with three fundamental questions: Most basically, (i) ‘How do ecosystems function?’ I answered this question by comparing networks to each other such that poorly-studied systems can be understood through their similarity to well-understood ones and theoretical models. To do this I created the alignment algorithm netcom which recasts ecosystem processes as statistical dynamics of diffusion kernels originating from a network’s constituent nodes. Using netcom I constructed a supervised classifier which can distinguish processes in both synthetic and empirical network data. While this kind of inference works on currently available network data, I have shown how causality can serve as a more effective and unifying currency of ecological interaction. Measures of causality are even able to identify complex interactions across organizational scales of communities, answering the longstanding question (ii) ‘Can community structure causally determine dynamics of constituent species?’ Moreover, causal inference can be readily combined with existing modeling frameworks to quantify dynamic interactions at the same scale as the underlying data. In this way we can answer the question (iii) ‘Which species in an ecosystem cause which other species?’ These tools are part of a paradigm shift in ecology that offers the potential to make more reliable management decisions for dynamic ecosystems in real time using only observational data. Dedication For Camp Bear. v Acknowledgements Dan Doak Committee members Collaborators The Doak lab The University of Colorado Environmental Studies Program IQ Biology Program Family Friends Roommates Gilbert and Bear My mandolin Planet Bluegrass Bowers & Wilkins Weber 3821 Paseo Del Prado Funding generously provided by the National Science Foundation IGERT 1144807 GK-12 0841423 DGE-1144083 vi Contents Chapter 1 Overview 1 1.1 Can comparisons of communities infer underlying processes and their dynamics? .2 1.2 Can community structure causally determine dynamics of constituent species? . .2 1.3 Can we infer real-time ecological interactions using observational data? . .3 2 Aligning Statistical Dynamics Captures Biological Network Functioning 5 2.1 Introduction . .5 2.2 Methods . .7 2.2.1 Conceptual rationale . .7 2.2.2 Networks . .8 2.2.3 Alignment algorithm . .8 2.2.4 Analyses . 14 2.2.5 Data availability . 18 2.2.6 Code availability . 19 2.3 Results . 19 2.3.1 Comparison with other aligners . 19 2.3.2 Node centralities . 19 2.3.3 Tracking network dynamics . 20 2.3.4 Functional network classification . 20 2.4 Discussion . 27 vii 3 Can community structure causally determine dynamics of constituent species? A test using a host-parasite community 32 3.1 Introduction . 32 3.2 Methods . 35 3.2.1 Overview . 35 3.2.2 Causal Inference with CCM . 36 3.2.3 Data . 39 3.2.4 Community Properties . 40 3.3 Results . 40 3.3.1 Causal Community Matrix . 43 3.3.2 Cause vs Effect . 46 3.4 Discussion . 47 4 Understanding interspecific causation in multi-species systems: development of a gen- eral approach and application to dynamics of the endangered vernal pool plant Lasthenia conjugens 52 4.1 Introduction . 52 4.2 Methods . 55 4.2.1 Data . 55 4.2.2 S-maps . 56 4.2.3 Causality . 57 4.2.4 Causally-filtered S-maps . 59 4.3 Results . 61 4.3.1 Lolium multiflorium . 64 4.3.2 Eryngium vaseyi . 67 4.3.3 Water-Mediated Interactions . 69 4.4 Discussion . 69 viii 5 The future of causal community ecology 74 5.1 How do incomplete or aggregate community descriptions effect our ability to infer causal interactions? . 74 5.2 How does causality propagate through a community? . 75 5.3 Can we compare causality inferred in different systems? . 75 5.4 What is the relationship between causal strength and interaction strength? . 76 5.5 To what extent can we substitute spatial replication for temporal replication in inferring causality? . 76 5.6 Does the principle of nil causality result in a trade-off in sensitivity? . 77 5.7 What is the asymptotic behavior of causal inference? . 77 5.8 Can causal inference predict the effects of adding or removing a variable in a system? 78 5.9 What will convince people that causality can be inferred from observational data? . 78 Bibliography 79 Appendix A Chapter 1 Appendix 96 A.1 Supplemental Figures . 96 B Chapter 2 Appendix 106 B.1 Supplemental Methods . 106 B.1.1 Determining an Embedding Dimension . 106 B.1.2 Testing for Nonlinearity . 107 B.1.3 Applying CCM to Community Properties . 108 B.1.4 Real World Shadow Manifolds . 110 B.2 Supplemental Figures . 111 ix C Chapter 3 Appendix 117 C.1 Supplemental Figures . 117 x Tables Table 3.1 Community properties . 42 A.1 Theoretical models . 96 A.2 Induced Conserved Structure (ICS) scores . 97 A.3 Sources of networks in Fig. 2.6 . 105 xi Figures Figure 2.1 Example networks . .7 2.2 Network alignment algorithm . .9 2.3 Centrality comparisons . 21 2.4 Edge dynamics . 22 2.5 Network dynamics . 23 2.6 Biological network state-space . 25 2.7 Theoretical network classification . 26 2.8 Applied network classification . 28 3.1 Slovakia’s rodent-ectoparasite community . 41 3.2 Causal community matrix . 44 3.3 Cause vs effect . 48 4.1 Addressing multicollinearity in Pool 300 . 63 4.2 Interspecific effects on Lasthenia conjugens ......................... 65 4.3 Lolium multiflorium’s effects on Lasthenia conjugens .................... 66 4.4 Eryngium vaseyi’s effects on Lasthenia conjugens ...................... 68 4.5 Water-mediated interactions . 70 A.1 Ordination stress in Fig. 2.5 . 98 A.2 Ordination stress in Fig. 2.6 . 99 xii A.3 Alignment as a function of network size . 100 A.4 Ordination stress in Fig. 2.8 . 101 B.1 CCM assumptions . 111 B.2 Smoothness assumption . 112 B.3 Correlation vs causation . 113 B.4 Individual node effects on a community property . 114 B.5 Community detection without causality . ..