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On the Interaction of Function, Constraint and Complexity in Evolutionary Systems UNIVERSITY OF SOUTHAMPTON FACULTY OF PHYSICAL SCIENCES AND ENGINEERING ELECTRONICS AND COMPUTER SCIENCE Volume 1 of 1 On The Interaction Of Function, Constraint And Complexity In Evolutionary Systems by Adam Paul Davies Thesis for the degree of Doctor of Philosophy April 2014 UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF PHYSICAL SCIENCES AND ENGINEERING Electronics and Computer Science Doctor of Philosophy ON THE INTERACTION OF FUNCTION, CONSTRAINT AND COMPLEXITY IN EVOLUTIONARY SYSTEMS by Adam Paul Davies Biological evolution contains a general trend of increasing complexity of the most complex organisms. But artificial evolution experiments based on the mechanisms described in the current theory generally fail to reproduce this trend; instead, they commonly show systematic trends of complexity minimisation. In this dissertation we seek evolutionary mechanisms that can explain these apparently conflicting observations. To achieve this we use a reverse engineering approach by building computational simulations of evolution. One highlighted problem is that even if complexity is beneficial, evolutionary simulations struggle with apparent roadblocks that prevent them from scaling to complexity. Another is that even without roadblocks, it is not clear what drives evolution to become more complex at all. With respect to the former, a key roadblock is how to evolve ‘irreducibly complex’ or ‘non- decomposable’ functions. Evidence from biological evolution suggests a common way to achieve this is by combining existing functions – termed ‘tinkering’ or ‘building block evolution’. But in simulation this approach generally fails to scale across multiple levels of organisation in a recursive manner. We provide a model that identifies the problem hindering recursive evolution as increasing ‘burden’ in the form of ‘internal selection’ as joined functions become more complex. We show how having an ontological development process that occurs by local growth, as present in most complex biological organisms, resolves this problem, enabling evolution to occur recursively. Meanwhile, to understand what drives complexity in evolution we provide a model showing that under certain conditions a well-studied concept from the computational study of algorithms – complexity lower bounds – applies in evolution. The model shows how the ‘difference’ between the conditions required by an organism’s replicator and its external environment results in a minimum complexity floor that varies as the external environment changes. We find that selection in such a system produces a system-wide, overall trend of increasing complexity of the most complex organisms (as environments are colonised), coupled with local trends of complexity minimisation in individual environments (as evolution seeks to minimise its cost of resources) –thereby resolving the tension between biological observations and theoretical outcomes. Our simulations and analytic results demonstrate (a) how evolution can, when complexity is beneficial, scale to complexity over multiple organisational levels, and (b) the conditions in which complexity is beneficial in evolution. These models describe a set of phenotypic, ontogenetic and environmental conditions that are generally present in biological evolution, in which evolution consistently generates an overall trend of increasing complexity of the most complex organisms. Table of Contents ABSTRACT ............................................................................................................... i Table of Contents ....................................................................................................... i List of tables .............................................................................................................. v List of figures ............................................................................................................ vii DECLARATION OF AUTHORSHIP ......................................................................... xi Acknowledgements ............................................................................................... xiii Chapter 1: Introduction and literature review ........................................ 1 1.1 Motivation ................................................................................. 1 1.2 Theoretical perspective .............................................................. 5 1.3 Approach and previous work ..................................................... 7 1.3.1 Complexity roadblocks ..................................................... 9 1.3.2 Complexity drivers ......................................................... 18 1.3.3 Complexity lower bounds ............................................... 21 1.3.4 The origins of complexity lower bounds in evolution ...... 23 1.3.5 Homeogenesis ................................................................ 26 1.4 Summary of major topics of this dissertation ........................... 31 1.5 Implications ............................................................................. 32 1.6 Models and approach .............................................................. 34 1.6.1 Modelling approach ........................................................ 34 1.6.2 Model 1: Combinatorial Exaptation – exaptation by joining functions ...................................................................... 35 1.6.3 Model 2: Metabolic evolution by homeogenesis .............. 36 1.6.4 Model 3: Complexity trends of evolution in a system of complexity lower bounds ............................................. 38 1.6.5 Model 4: Complexity lower bounds in NAND circuit calculations .................................................................. 39 i 1.7 Claims 40 1.8 Contributions .......................................................................... 41 1.9 Scope ................................................................................... 42 1.10 Structure of this dissertation ................................................... 43 Chapter 2: Combinatorial Exaptation ........................................................ 45 2.1 Introduction ............................................................................ 45 2.2 Previous work .......................................................................... 47 2.2.1 Exaptation ...................................................................... 47 2.2.2 Tinkering ....................................................................... 48 2.2.3 Building Block Mechanisms ............................................. 48 2.2.4 Recursive evolution and encapsulation ........................... 51 2.3 Theoretical analysis ................................................................. 53 2.4 Results and Discussion ............................................................ 58 2.4.1 S1 Simulation results ...................................................... 61 2.4.2 C1 simulation results ..................................................... 65 2.4.3 A recursive mechanism of combinatorial exaptation ....... 66 2.4.4 S2 Simulation results ...................................................... 71 2.4.5 The effect of genotype-phenotype map evolution on the fitness landscape .......................................................... 74 2.4.6 Supplementary results .................................................... 76 2.5 Conclusions ............................................................................. 78 2.5.1 Key Results .................................................................... 79 2.6 Methods .................................................................................. 80 Chapter 3: Homeogenesis .............................................................................. 87 3.1 Introduction ............................................................................ 87 3.2 Background ............................................................................. 87 3.3 An extreme and simple example of homeogenesis .................. 89 ii 3.4 A biological example of homeogenesis .................................... 92 3.5 A model of metabolic evolution ............................................... 94 3.5.1 Aim ................................................................................ 94 3.5.2 Methods ......................................................................... 95 3.5.3 Results and discussion ................................................... 99 3.5.4 Wider implications of homeogenesis ............................ 106 3.6 Conclusions ........................................................................... 107 3.6.1 Key Results .................................................................. 109 Chapter 4: Complexity lower bounds ..................................................... 111 4.1 Introduction .......................................................................... 111 4.2 Structure of this chapter ........................................................ 112 4.3 Generating a hypothesis for a complexity trend generation mechanism ............................................................................ 113 4.3.1 Exploratory modelling .................................................. 113 4.3.2 Summary of exploratory modelling ............................... 125 4.4 A hypothesis for a novel complexity generation mechanism in evolution: Environmental dissociation complexity .................. 126 4.4.1 The Environmental Dissociation Hypothesis .................. 130 4.5 Testing the environmental
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