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Finally Projected Over the Landscape Topology to Infer Upon Regional-Specific Population Interactions and to Detect Population ''Hot Spots''

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Finally Projected Over the Landscape Topology to Infer Upon Regional-Specific Population Interactions and to Detect Population ''Hot Spots'' Aristotle University of Thessaloniki Faculty of Sciences Mathematics Department Pest-Insect time series analysis and the Development of Population Causal networks Petros Damos Dissertation for the fulfilment of the M.Sc. Degree in Web Science and Bio-Networks Veroia 2012 Population Networks Petros Damos The dissertation was completed in the Department of Mathematics at Aristotle University of Thessaloniki, defended before and approved by the following members of the scientific committee: Dimitris Kugiumtzis (Thesis Advisor) Mathematics Department, Faculty of Science Aristotle University of Thessaloniki Stefanos Sgardellis (Member) Biology Department Faculty of Science Aristotle University of Thessaloniki John Halley (Member) Biological applications and Technology Department University of Ioannina 2 _______________________________ ______________________________ Population Networks Petros Damos Contents Preface ....................................................................................................................... 5 Abstract ..................................................................................................................... 6 Περίληψη ................................................................................................................... 7 1. Introduction ........................................................................................................... 8 1.1 Graph theory and ecological networks ........................................................... 8 1.2 Structural and Causal networks .................................................................... 14 1.3 Transforming Time Series into Complex Networks ..................................... 18 1.3.1 Cycle networks ......................................................................................... 18 1.3.2 Recurrence networks ................................................................................ 19 1.3.3. Correlation and causal networks ............................................................ 19 1.4 Principal concepts of Population dynamics .................................................. 20 1.4.1 Deterministic population models ............................................................. 21 1.4.2 Stochastic population models .................................................................. 24 1.4.3 Population emergence and spatial synchronisation ................................ 27 1.5 Scope of the dissertation ............................................................................... 28 2. Study system and moth population dynamics .................................................... 31 2.1 Species ........................................................................................................... 31 2.2.1 The summer fruit totrix Adoxophyes orana ............................................. 31 2.1.2 The peach twig borer Anarsia lineatella .................................................. 31 2.1.3 The oriental fruit moth Grapholitha molesta ........................................... 32 2.2 Sampling sites ................................................................................................ 33 2.3 Species monitoring and data registration ..................................................... 33 2.4. Moth population and weather data time series ........................................... 34 3. Stochastic modelling of insect population cycling and seasonality.................... 36 3.1 Problem setting and solving algorithm ......................................................... 36 3.2 Basic background on univariate time series analysis ................................... 38 3.2.1 Moth populations dynamics regarded as stochastic process .................... 38 3.2.2 Autocorrelation and partial autocorrelation ........................................... 39 3.2.3 Autocorelation in the frequency domain and Power spectrums .............. 40 3.2.4 Autoregressive models ............................................................................. 41 3.2.5 Model comparison and validation ............................................................ 42 3 _______________________________ ______________________________ Population Networks Petros Damos 3.5 Results ............................................................................................................ 43 3.5.1 Seasonality and population feedbacks ..................................................... 43 3.5.2 Spectral analysis ...................................................................................... 47 3.5.3 Parameter optimisation ........................................................................... 48 3.5.4 Diagnostic checking and residual error analysis ..................................... 52 3.5.5 Model validation ...................................................................................... 56 3.6 Discussion ...................................................................................................... 58 4. Multivariate moth population analysis and causal networks ............................ 61 4.1 Ecological networks and state of the art ....................................................... 61 4.2 Weighed and binary causal network construction algorithm............................. 62 4.2 Basic background on multivariate time series analysis ............................... 64 4.2.1 Cross correlations .................................................................................... 64 4.2.2 Partial correlations .................................................................................. 65 4.2.3 Granger causality measures - preliminaries............................................ 66 4.2.4 The Granger Causality Index (GCI) ........................................................... 67 4.2.5 The Causal Granger Causality Index (CGCI) ............................................. 67 4.3 Time series networks .................................................................................... 68 4.3.1 Correlation networks and undirected links .............................................. 68 4.3.2 Causality networks and directed links ....................................................... 71 4. 3. 3 Graph theoretic network measures ........................................................ 72 4.3.3 Ecological network analysis and standard graph metrics .......................... 73 4.6 Results ............................................................................................................ 75 4.6.1 Cross and partial cross correlation networks .......................................... 75 4.6.2 Granger causality and conditional Granger causal networks .................. 77 4.6.3 Causal force directed network layouts ..................................................... 80 4.6.4 Graph theoretic metrics ........................................................................... 81 4.6.5 Landscape topology of moth population networks .................................. 83 4.7 Discussion ...................................................................................................... 86 5. Concluding Remarks ............................................................................................. 89 5.1 Population cycling and seasonality ............................................................... 89 5.2 Moth population causal networks ................................................................. 91 5.3 Population networks in advancement of pest information systems ............ 96 References ............................................................................................................. 100 4 _______________________________ ______________________________ Population Networks Petros Damos Preface In this dissertation we use multivariate time series analysis combined with graph theory to describe moth population dynamics and their causal relations. From a phenomenological perspective the insect spatiotemporal structure is addressed as dynamical (physical) system and efforts are made to elucidate the mechanism which could explain how its elements are functioning and are arranged in a particular network form. From a population ecologically perspective, efforts are made to infer upon the experimental result to provide information utile in pest management and improve web-based information systems. The author would like to express his most sincere thanks to the persons who helped to go through the above topics and especially Assoc. Prof. D. Kugiumtzis who was instrumental in enabling this work and in particular for the introduction of several topics of multivariate time series analysis, such as the concept of causality which exploits the natural ordering of variables. Prof S. Sgardellis for the interesting discussions we hade concerning some current issues of ecological networks and Prof. J. Halley for being member of the advisory board and evaluating the current work. The author also likes to thank Prof. I. Antoniou, director of the Post Graduate Web Science Program of the Mathematics Department at Aristotle University of Thessaloniki, for his inspirational lectures and discussions upon the phenomenological perspectives of network functioning in complex systems. The author acknowledges also the help provided by the Agronomists of the public confederation ALMME®, in collecting part of the data that were used to illustrate some representative region specific ecological networks. Any errors that remain throughout the current work are my sole
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