Darwinian Evolutionary system - a system satisfying the abstract conditions: reproduction with heritable variation, in a finite world, giving rise to Natural Selection encompasses a complex and subtle system of interrelated theories, whose substantive transplantation to any artificial medium let it be mathematical model or computational model - will be very far from easy. There are two motives in bringing Darwinian evolution into computational frameworks: one to understand the Darwinian evolution, and the other is to view Darwinian evolution - that carries out controlled adaptive-stochastic search in the space of all possible DNA-sequences for emergence and improvement of the living beings on our planet - as an optimization process, which can be simulated in appropriate frameworks to solve some intractable problems. The first motive led to emerging field of study commonly referred to as Artificial Life, and other gave way to emergence of Evolutionary Computation, which is speculated to be the only practical path to the development of ontogenetic machine intelligence. In this thesis we touch upon all the above aspects. Natural selection is the central concept of Darwinian evolution and hence capturing natural selection in computational frameworks which maintains the spirit of Darwinian evolution in the sense of conventional, terrestrial and biological perspectives is essential. Naive models of evolution define natural selection as a process which brings in differential reproductive capabilities in organisms of a population, and hence, most of the evolutionary simulations in Artificial Life and Evolutionary Computation implement selection by differential reproduction: the Attest members of the population are reproduced preferentially at the expense of the less fit members of the population. Formal models in evolutionary biology often subdivide selection into components called 'episodes of selection' to capture the different complex mechanisms of nature by which Darwinian evolution can occur. In this thesis we introduce the concept of 'episodes of selection' into computational frameworks of Darwinian evolution by means of A Conceptual Evolutionary model (ACE-model). ACE-model is proposed to be simple and yet it captures the essential features of modern evolutionary perspectives in evolutionary computation framework. ACE-model is rich enough to offer abstract and structural framework for evolutionary computation and can serve as a basic model for evolutionary algorithms. It captures selection in two episodes in two phases of evolutionary cycle and it offers various parameters by which evolutionary algorithms can control selection mechanisms. In this thesis we propose two evolutionary algorithms namely Malthus evolutionary algorithms and Malthus Spencer evolutionary algorithms based on the ACE-model and we discuss the relevance of parameters offered by ACE-model by simulation studies. As an application of ACE-model to artificial life we study misconceptions involved in defining fitness in evolutionary biology, and we also discuss the importance of introducing fitness landscape in the theories of Darwinian evolution. Another important and independent contribution of this thesis is: A Mathematical Abstraction of Evolutionary process. Evolutionary process is characterized by Evolutionary Criteria and Evolutionary Mechanism which are formalized by classical mathematical tools. Even though the model is in its premature stage to develop any theory based on it, we develop convergence criteria of evolutionary process based on this model.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Computational molecular evolution is a field that attempts to characterize how genetic sequences evolve over phylogenetic trees – the branching processes that describe the patterns of genetic inheritance in living organisms. It has a long history of developing progressively more sophisticated stochastic models of evolution. Through a probabilist’s lens, this can be seen as a search for more appropriate ways to parameterize discrete state continuous time Markov chains to better encode biological reality, matching the historical processes that created empirical data sets, and creating useful tools that allow biologists to test specific hypotheses about the evolution of the organisms or the genes that interest them. This dissertation is an attempt to fill some of the gaps that persist in the literature, solving what we see as existing open problems. The overarching theme of this work is how to better model variation in the action of natural selection at multiple levels: across genes, between sites, and over time. Through four published journal articles and a fifth in preparation, we present amino acid and codon models that improve upon existing approaches, providing better descriptions of the process of natural selection and better tools to detect adaptive evolution. / AFRIKAANSE OPSOMMING: Komputasionele molekulêre evolusie is ’n navorsingsarea wat poog om die evolusie van genetiese sekwensies oor filogenetiese bome – die vertakkende prosesse wat die patrone van genetiese oorerwing in lewende organismes beskryf – te karakteriseer. Dit het ’n lang geskiedenis waartydens al hoe meer gesofistikeerde waarskynlikheidsmodelle van evolusie ontwikkel is. Deur die lens van waarskynlikheidsleer kan hierdie proses gesien word as ’n soektog na meer gepasde metodes om diskrete-toestand kontinuë-tyd Markov kettings te parametriseer ten einde biologiese realiteit beter te enkodeer – op so ’n manier dat die historiese prosesse wat tot die vorming van biologiese sekwensies gelei het nageboots word, en dat nuttige metodes geskep word wat bioloë toelaat om spesifieke hipotesisse met betrekking tot die evolusie van belanghebbende organismes of gene te toets. Hierdie proefskrif is ’n poging om sommige van die gapings wat in die literatuur bestaan in te vul en bestaande oop probleme op te los. Die oorkoepelende tema is verbeterde modellering van variasie in die werking van natuurlike seleksie op verskeie vlakke: variasie van geen tot geen, variasie tussen posisies in gene en variasie oor tyd. Deur middel van vier gepubliseerde joernaalartikels en ’n vyfde artikel in voorbereiding, bied ons aminosuur- en kodon-modelle aan wat verbeter op bestaande benaderings – hierdie modelle verskaf beter beskrywings van die proses van natuurlike seleksie sowel as beter metodes om gevalle van aanpassing in evolusie te vind.

Un des buts principaux de la biologie évolutive et de la médecine moléculaire consiste à reconstruire les relations phylogénétiques entre organismes à partir de leurs séquences moléculaires. En littérature, cette question est connue sous le nom d’inférence phylogénétique et a d'importantes applications dans la recherche médicale et pharmaceutique, ainsi que dans l’immunologie, l’épidémiologie, et la dynamique des populations. L’accumulation récente de données de séquences d’ADN dans les bases de données publiques, ainsi que la facilité relative avec laquelle des données nouvelles peuvent être obtenues, rend l’inférence phylogénétique particulièrement difficile (l'inférence phylogénétique est un problème NP-Hard sous tous les critères d’optimalité connus), de telle manière que des nouveaux critères et des algorithmes efficaces doivent être développés. Cette thèse a pour but: (i) d’analyser les limites mathématiques et biologiques des critères utilisés en inférence phylogénétique, (ii) de développer de nouveaux algorithmes efficaces permettant d’analyser de plus grands jeux de données. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished