Probabilistic Reconciliation Analysis for Genes and Pseudogenes M OWAIS MAHMUDI Doctoral Thesis Stockholm, Sweden 2015 TRITA-CSC-A 2015:03 ISSN-1653-5723 ISRN-KTH/CSC/A-15:03 ISBN 978-91-7595-488-2 KTH School of Computer Science and Communication SE-100 44 Stockholm SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen i datalogi onsdagen den 15 april 2015 klockan 09.00 i Air, SciLifeLab, Tomtebodavägen 23A, Stockholm. © M Owais Mahmudi, March 2015 Tryck: Universitetsservice US AB To my family iii iv Abstract Phylogeneticists have studied the evolution of life from single celled organisms to the astonishing biodiversity around us for a long time now. The relationship between species is often expressed as a binary tree - the tree of life. Availability of fully sequenced genomes across species provides us the opportunity to investigate and understand the evolutionary processes, and to reconstruct the gene and species phylogeny in greater detail and more accurately. However, the effect of interacting evolutionary processes, such as gene duplications, gene losses, pseudogenizations, and lateral gene transfers, makes the inference of gene phylogenies challenging. In this thesis, probabilistic Bayesian methods are introduced to infer gene phylogenies in the guidance of species phylogeny. The distinguishing feature of this work from the earlier reconciliation-based methods is that evolutionary events are mapped to detailed time intervals on the evolutionary time-scale. The proposed probabilistic approach reconciles the evolutionary events to the species phylogeny by integrating gene duplications, gene losses, lateral gene transfers and sequence evolution under a relaxed molecular clock. Genomewide gene families for vertebrates and prokaryotes are analyzed using this approach that provides interesting insight into the evolutionary processes. Finally, a probabilistic model is introduced that models evolution of genes and pseudogenes simultaneously. The model incorporates birth-death process according to which genes are duplicated, pseudogenized and lost under a sequence evolution model with a relaxed molecular clock. To model the evolutionary scenarios realistically, the model employs two different sequence evolution models for the evolution of genes and pseudogenes. The reconciliation of evolutionary events to the species phylogenies enable us to infer the evolutionary scenario with a higher resolution. Some subfamilies of two interesting gene superfamilies, i.e. olfactory receptors and zinc fingers, are analyzed using this approach, which provides interesting insights. v Sammanfattning Biologer har under en lång tid studerat livets utveckling från encelliga organismer till den häpnadsväckande mångfalden omkring oss. Förhållandet mellan arter uttrycks ofta som ett träd. Tillgång till fullt sekvenserade genom ger oss idag möjlighet att undersöka och förstå evolutionära processer bättre, samt att rekonstruera gen- och artträd i mer detalj. Men evolutionära processer, såsom genduplikationer, genförluster, pseudogenbildning och lateral genöverföringar, gör rekonstruktion av genträd utmanande. Denna avhandling handlar delvis om två probabilistiska Bayesianska metoder som är utvidgningar av metoder för att hitta genträd med ledning av artträd. Det utmärkande för dessa, jämfört med tidigare metoder, är att de är probabilistiska samt att de evolutionära händelserna avbildas på artträdet. Den modell som används är en integrerad probabilistisk modell som innehåller genduplikationer, genförluster, laterala genöverföringar samt sekvensevolution utan molekylär klocka. Med hjälp av denna metod analyseras genfamiljer från ryggradsdjur och prokaryoter, vilket ger intressant inblickar i var, i arträden, genduplikationer och laterala genöverföringar har skett. Slutligen presenterar vi en probabilistisk modell som både beskriver evolution av gener och pseudogener. Modellen innehåller en födelse-döds liknande process enligt vilken gener dupliceras, förloras, eller blir pseudogener samt två modeller av sekvensevolution utan molekylär klocka. För att modellera de evolutionära scenarierna realistiskt, innehåller modellen två olika modeller för sekvensevolution, en för evolution av gener och en för pseudogener. Vi analyserar flera underfamiljer av två intressanta stora generfamiljer, dels luktreceptorer dels zinkfingrar, med hjälp av denna metod. Resultaten indikerar att visa pseudogener kan ha funktion, exempelvis som RNA kodande gener. Contents Contents vi Acknowledgements 1 List of Publications 3 1 Introduction 1.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Current Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 5 2 Evolutionary Events 2.1 Historical Perspective . . . 2.2 Micro-Evolutionary Events 2.3 Macro-Evolutionary Events 2.4 Interesting Gene Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7 9 11 15 3 Modeling Evolution 3.1 Models of Sequence Evolution . . . . . 3.2 Distance-Based Methods . . . . . . . . 3.3 Parsimony-Based Methods . . . . . . . 3.4 Maximum-Likelihood-Based Methods . 3.5 Bayesian Methods . . . . . . . . . . . 3.6 Reconciliation-based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 21 23 25 25 26 27 . . . . . . . . . . . . . . . . . . . . 4 Present Investigations 39 5 Discussion & Conclusion 41 Bibliography 45 vi Acknowledgements A journey filled with reflection, excitement, memories, and a few stressful periods finally comes to an end. This journey enabled me to learn new scientific fields as well as provided me with opportunities to reflect upon many other aspects of life. I am grateful to all those who supported me during this period. Jens Lagergren, my supervisor, supported me the most during this period. He is a brilliant researcher and a true inspiration for me. His ingenious ideas and lively personality made this journey very interesting. Jens, I am grateful for both the personal and professional support that you have extended throughout this period. I am also thankful to my co-supervisor Lars Arvestad, who is an exceptionally good teacher and a researcher, for helping me to explore the exciting area of bioinformatics. I am also grateful to Bengt Sennblad, my co-supervisor, whose elaborate explanations made this journey very exciting. His clarity of thinking and ability to explain complex ideas in an easy way always impressed me. I was fortunate enough to start this journey in the presence of guys like Hossein - cancer & opera specialist, and Joel - my most recent ancestor in the group. I must mention all the comrades of our alliance; it was a pleasure working with them. I would like to thank Mehmood - a companion all the way from Pakistan, Hashim - a true family man, and Auwn - a self-made man, for all the valuable discussions and collaborations. Mattias and Kristoffer, my desk and gym fellows, I will always envy their physical and mental fitness. I should also thank Pekka for all interesting puzzles, explanations, and interesting table hockey games. I will always remember Erik for his ever-smiling personality, technical help and folk music discussions. Lumi and Viktor, my desk neighbors, thanks for all the fun stories and sci-fi discussions! I must mention all other friends at Scilifelab, which I was able to meet during this period. This includes, but is not limited to Linus, Lukas, Jose, Samuel, Ilgar, Arman, Karolis, Ino, Jorrit, Matthews, Wenjing, and Yrin. This PhD would have been much harder without Ikram - my brother in arms, whose discussions, jokes, ideas and suggestions made this period really enjoyable. It was an amazing friendship all the way from the first lecture of ‘Introduction to Computing’ till this time! Finally, I would like to thank all my family, specially my parents for providing such a strong support throughout my life. I love you! I would like to thank my wife Lubaina, for bearing all my stress and providing the critical support throughout this period. Life would have been much boring without you! 1 List of Publications I: Mahmudi O, Sjöstrand J, Sennblad B, & Lagergren J. Genome-wide probabilistic reconciliation analysis across vertebrates. BMC Bioinformatics 2013; 14(Suppl 15):S10. II: Mahmudi O., Sennblad B., Arvestad L., Nowick K., & Lagergren J. Evolution of Pseudogenes: A probabilistic approach. Manuscript. III: Khan MA.∗ , Mahmudi O.∗ , Ullah I., Arvestad L., & Lagergren J. Probabilistic inference of lateral gene transfer events. Manuscript. ∗ Contributed equally to this manuscript. 3 Chapter 1 Introduction 1.1 Fundamentals Life propagates itself by the process of reproduction. This process is, however, not perfect, which leads to a variety of forms of life. Thus the forms of life that are best suited to its environment, and able to reproduce faster are more likely to survive in the long term. The suitability of a life form to its environment is also dependent on the suitability of other life forms interacting with its environment. The “survival of the fittest” is therefore, a central idea of the process of natural selection. This simple but powerful idea has enabled life consisting of single cells to evolve into this amazing variety of forms of life today. Evolution takes place in every reproductive cycle of an organism, but in terms of the evolution of new species, it typically takes millions of years. The first life on earth is estimated to have evolved around 3.6 billion years ago, while the first multicellular organisms are estimated to have evolved around 2.1 billion years ago. Around 540 million years ago, complex multicellular organisms evolved. This followed Cambrian Explosion that resulted in appearance of most major animal phyla that resembles today’s forms of life. Evolution of life is central to all aspects of modern biology. As the evolutionary biologist Theodosius Dobzhansky summarized it in 1973, “nothing in biology makes sense except in the light of evolution”. Studying evolutionary relationships between genomes across the species helps us developing a better understanding of the human genome. 1.2 Current Work This thesis is an attempt to further extend computational methods to reconstruct the evolutionary history using the major evolutionary processes. In the methods proposed in this thesis, genomic information of extant species is combined with the information available about the evolution of species from other sources to get a clearer picture of the evolution of life. The studies included in this thesis mainly 5 6 CHAPTER 1. INTRODUCTION attempts to model microevolutionary events such as nucleotide/amino-acid substitutions and macroevolutionary events such as gene duplications, pseudogenizations, gene losses, and lateral gene transfers. The methods proposed in this thesis are focused on obtaining a detailed picture of evolution in the sense that the evolutionary events of gene families are reconciled to the evolutionary events of species along the evolutionary history. The methods proposed are Bayesian and employ Markov Chain Monte Carlobased framework for analyses. The distinguishing feature of this work from earlier reconciliation-based methods is that evolutionary events of gene tree are mapped to the species tree on the evolutionary time-scale. We present a probabilistic approach that reconciles the evolutionary events to the species phylogeny by integrating gene duplications, gene losses, lateral gene transfers and sequence evolution under a relaxed molecular clock. The method proposed in paper I considered only gene duplications and gene losses as evolutionary events. Its extension (paper III) is a more comprehensive method that considers lateral gene transfers as well and is therefore, more biologically realistic and also applicable when analyzing prokaryotes. Using these methods we analyzed genome-wide gene families for vertebrates and prokaryotes that provided interesting insights into the evolutionary processes. The approaches enable us to develop a better understanding of evolutionary processes and can be further used to analyze possible interaction of evolutionary and ecological processes. Paper II proposes a probabilistic model that models evolution of genes and pseudogenes simultaneously. The model incorporates birth-death process according to which genes are duplicated, pseudogenized and lost under a sequence evolution model with a relaxed molecular clock. To model the evolutionary scenarios realistically, the model employs two different sequence evolution models for the evolution of genes and pseudogenes. The reconciliation of evolutionary events to the species phylogenies enable us to infer the evolutionary scenario with a higher resolution. Some interesting subfamilies of two interesting gene superfamilies, i.e. olfactory receptors and zinc fingers, are analyzed using this approach, which provides interesting insights. The rest of the thesis is organized as follows. A historical perspective of evolution and a brief introduction to the current understanding of evolutionary processes is provided in chapter 2. The introduction to the evolutionary processes includes basic introduction to microevolutionary events as well as macroevolutionary events followed by introduction to some interesting gene families. Chapter 3 provides a brief discussion about some of the current methods used to model the evolutionary processes. Present investigations/studies are described in Chapter 4. Conclusion and future directions are given in Chapter 5. Chapter 2 Evolutionary Events Genes are thought to be the basic functional unit of evolution, which evolve through various evolutionary processes. Genes with similar characteristics that are believed to have evolved from a single ancestral gene, are grouped into gene families. Gene families mostly evolve through microevolutionary events, such as mutations, and macroevolutionary events, such as gene duplications, gene losses, and lateral gene transfers. This chapter provides an introduction to the evolutionary processes that shape genomes. In the following, section 2.1 provides a historical perspective of the theory of evolution and genetics, which is followed by section 2.2, which contains a brief description of the microevolutionary processes that shapes the genome of a species. Macroevolutionary processes that are responsible for the evolution of genomes will be discussed in the following section (2.3). These macroevolutionary events include gene duplication events, gene loss events, gene pseudogenization events and lateral gene transfer events. The last section (2.4) provides introduction to some interesting gene families that are used in some of the studies of this thesis. 2.1 Historical Perspective The theory of evolution was popularized mainly by Charles Darwin, but it can be dated back even further. In attempts to survey the coast of lower South America, he embarked on HMS beagle in 1831. He spent most of the time investigating geology and collecting natural history collections. The voyage ended in 1836 but it was not until 1859 when he published his book, ‘On the origin of species’ . The book received much attention at that time attracting both positive and negative criticism. In his later work, Darwin also explained his Pangenesis theory, according to which cells in organisms shed tiny particles called gemmules, that circulate throughout the body and reach the gonads. The acquired fitness of the parents during their life time is therefore inherited by the offsprings. Francis Galton conducted a wide range 7 8 CHAPTER 2. EVOLUTIONARY EVENTS of experiments from 1869-1871 in consultation with Darwin to see if gemmules were circulated in blood. He found no evidence of the characters transmitted through the transfused blood between dissimilar breeds of rabbits . The inheritance from parents to offsprings was further investigated by Gregor Mendel, when he conducted a detailed study on peas between 1856-1863, and studied seven characteristics of pea plant, i.e. plant height, pod shape and color, seed shape and color, and flower position and color. He concluded that traits were inherited in a predictable manner through independent assortment and segregation of elements. Mendel’s laws of inheritance later on replaced the pangenesis theory proposed by Darwin . He used the term gene for the first time, when he noticed that the biological variations are inherited from parents to offspring as specific discrete traits . In 1880s, August Weismann, conducted a set of experiments on mice, removing the tails of 68 white mice repeatedly for five generations. He reported that no mice were born in consequence without a tail or even with a shorter tail . His main contribution was the germ-plasm theory, according to which inheritance only takes place through germ cells, such as egg cells and sperm cells. Other cells of the body do not have any role in inheritance. Hugo de Vries made the work of Gregor Mendel well known, and suggested that Mendelian traits are the heritable elements transferring along the germ line. He also reconciled the Darwin’s pangenesis theory with Weismann’s germ-soma cells distinction, by saying that pangenes according to Darwin theory are located in the nucleus of cell, which when expressed can move into cytoplasm to change cell structure. By conducting careful studies of wild variants of Oenothera lamarckiana, Hugo de Vries showed in 1901 that distinct new forms can suddenly arise in nature, that can last for several generations without dissipation . These big changes or small changes that suddenly arise in the offspring, and propagate in the future generations were called ‘mutations’. In the beginning of twentieth century, genes were discovered as the basic functional units of heredity that resides on chromosomes, a discovery that was awarded with Nobel Prize in 1933. In the 1930s, Haldane  and Muller  hypothesized that new gene functions may emerge from refashioned copies of old genes based on cytological observations of chromosomal duplications. This highlighted, for the first time, the importance of gene duplication in the evolution of genomes. Later in 1944, Avery et al.  showed through experiments that the genetic information was contained in the DNA of chromosomes. At the end of twentieth century, J. B. S. Haldane, Sewall Wright, and Ronald Fisher set robust foundations for modern statistical science, and population genetics. Modern evolutionary synthesis (also referred to as neo-Darwinian synthesis) was introduced between 1936-1947, integrating all the previous theories. It basically connected natural selection, mutation theory, Mendelian inheritance to explain patterns observed across the tree of life using fossils information. 2.2. MICRO-EVOLUTIONARY EVENTS 9 Later on the discovery of DNA structure by James Watson and Francis Crick in 1953  revolutionized the field. Deoxyribonucleic Acid (DNA) is a molecule that is composed of simpler units called nucleotides. There are four types of nucleotides in DNA. All the genetic information that is used in the development and functioning of living organisms is encoded by the sequences of these four nucleotides. The central dogma of molecular biology was introduced by Francis Crick [23, 24], according to it information flows from DNA to mRNA, to protein but never from protein to nucleic acid. The messenger RNA (mRNA) is a ribonucleic acid molecule that transfers genetic information from DNA to the ribosome, where the triplets of nucleotides specify the amino-acid sequence for the protein products. This paved the way for studying hereditary changes from one generation to another. Discovery of the accurate model of DNA inspired molecular biologists to study the sequence of DNA, however, it was not possible until 1970s when first Ray Wu and his colleagues , and later Frederick Sanger and Charles Coulson  described methods for determining the sequence of DNA. This opened a new field of molecular phylogenetics. Sequencing technologies became more and more sophisticated with the passage of time. Complete genome sequencing projects followed, and the first complete genome of a free living organism (bacterium) was sequenced in 1995. Human genome was sequenced by the Human Genome Project in 2003 . This was followed by the sequencing of around 1092 genomes of different individuals by the 1000 Genomes Project to study human genetic variation . Genomes of other species from different clades of the tree of life were also sequenced in the meanwhile. The development of faster and cheaper sequencing technologies made it possible to launch projects like Genome 10K Project  and 1000 Plant Genomes Project . The availability of genomic sequences provided the opportunity to discover the functional as well as non-functional elements of genomes, and it became possible to compare entire genomes and study the relationships between them. Understanding how inheritance works at molecular level significantly improved our knowledge about the relationship of the genetic code to that of physical characteristics. Sequencing the genomes of different species provides the opportunity to reconstruct the evolutionary history based on the sequence data along with the fossils information. The disjoint facts of our natural history, that were earlier difficult to understand without the concept of evolution, are now a coherent explanation of how life evolved on this planet. 2.2 Micro-Evolutionary Events One of the most basic process of all genetic processes that produce genetic diversity is a spontaneous point mutation in the germ cells lineage. Mutations in the germ cells are passed on to the offsprings, while the mutations in somatic cells are specific 10 CHAPTER 2. EVOLUTIONARY EVENTS to the individual. A point mutation is typically caused by a change of DNA sequence. In a protein-coding DNA sequence, triplets of nucleotides (codons) encode for a specific amino-acid. A mutation in any of the nucleotides may or may not result in the change of encoding amino-acid. The mutation may result in a silent mutation (synonymous mutation), change of amino-acid (non-synonymous mutation), or a frame shift in a sequence (which may be caused by deletion or addition of a nucleotide). There are many potential causes due to which a DNA sequence can undergo a point mutation. Errors during DNA replication is one of the causes of a point mutation. Another cause is exposure to ultraviolet or high-frequency light ionizing electrons which in turn may lead to a point mutation. Similarly, reactive oxygen molecules with free radicals (a byproduct of cell metabolism) can also be harmful for the DNA. Bonds in DNA also degrade in some cases, due to which keeping the integrity of DNA becomes difficult. Spontaneous mutations are context-dependent, i.e. its occurrence depends on the neighboring nucleotides. Drake et al. found that the mutation rates are different in germline cells and somatic cells, and the mutation rate in somatic cells was higher than germline cells for murine . The mutation rate also depends on the size of the genome and number of germline cell division per generation [87, 35]. A DNA sequence consists of functional as well as non-functional regions. Around 2% of the human genome encodes proteins , while around 10 percent of the genome consists of non-protein coding functional regions such as regulatory sequences and others, that are under significant selective pressure . Much more is known about the protein coding regions of the human genome than the non-protein coding functional regions. However, ENCODE was able to associate 80% of the human genome with at least one biochemical function . Deleterious mutations are those that make the organism less fit in its environment and are eventually eliminated from the population over the time. Advantageous mutations contributes towards the fitness of the organism, and are much more likely to prevail in the species in the long run. If the number of synonymous mutations per synonymous site (dN ) is larger than the number of non-synonymous mutations per non-synonymous site (dS), i.e. (dN/dS < 1), it is believed that the sequence has underwent negative selection or purifying selection. Higher rate ratio of nonsynonymous to synonymous mutations (dN/dS > 1) implies that the sequence has been under positive selection or diversifying selection. A sequence is thought to have been evolving neutrally, if the the ratio between the two types of mutations is approximately equal to one (dN/dS ≈ 1). If a nucleotide changes from a purine (adenine and guanine) to purine, or from a pyrimidine (cytosine and thymine) to pyrimidine, it is called a transition. On the other hand, if a nucleotide changes from a purine to pyrimidine or vice versa, it is called transversion. Transversion involves much greater change in the structure as compared to transition and are 2.3. MACRO-EVOLUTIONARY EVENTS 11 therefore not as common as transitions. Mutations in any functional part, e.g., the regulatory regions of the genome can also make an organism less or more fit in its environment, depending on the change it brings in the gene function. In the majority of cases living organisms invest heavily in preventing mutations, e.g. they develop mechanisms, to export or destroy substances causing mutations, and to repair damaged DNA. In certain environments, such as stress environments, a higher mutation rate may bring advantageous mutations necessary for the survival of the species . However, deleterious mutations gained become a fitness cost for the species in the long run, when the stress period is over . Therefore, a balance between deleterious mutations, and rare advantageous mutations increases the long-term fitness . Extreme environmental changes, and mass extinctions are also closely associated with the genetic diversity leading to appearance of phenotypic novelties [70, 57, 152]. Although the exact mechanism of how stress-induced variation occurs in the genome is not clear, it is known that stress plays an important role in the evolution of genomes . 2.3 Macro-Evolutionary Events In 1970, Susumu Ohno published his famous monograph, in which he suggested that gene duplication is a mechanism responsible for the origin of most novel genes. He also introduced two possible fates for the genes originated from a gene duplication. After a gene duplication, one of the two copies of genes can carry out the ancestral function, while the other gene is free to evolve a new gene function, socalled neo-functionalization. The ancestral gene is more likely to keep the original function, while the duplicated copy may evolve a new gene function. However, the most probable fate of a duplicated gene copy is pseudogenization and consequently, majority of the duplicate genes are lost during evolution. A third possible fate of a gene duplication, sub-functionalization, was introduced by Stoltzfus  and Force et al. . In this case, both of the child genes keeps on performing the ancestral function for a while, and eventually specializes in a subset of the functions performed by the ancestral gene. The three fates of gene duplication are also discussed in article published by Lynch et al. , where they conclude that in most cases gene duplication experience a short period of relaxed selective pressure which ends with a silencing mutation. In a few cases, the duplicated gene survive long enough to develop a new function, which is subsequently put under selective pressure. Estimated rates of gains and losses varies across different clades in the tree of life. Anciently diverged group of species such as yeasts, mammals and flies have similar average duplication/loss rates . In mammals the rate of gain and loss of genes per million year is around 0.0016, in flies the rate is around 0.0012, while in yeast the rate is around 0.0020 [30, 61]. The rate is higher in the primates where the rate of gain/loss of genes per million year is 0.0024 . In great apes this rate is even higher, i.e. 0.0039 gain/loss of genes per million years . Other lineages such as 12 CHAPTER 2. EVOLUTIONARY EVENTS dog, mouse and rate have low rates (like the overall trend of mammals) i.e. 0.0014 gain/loss of genes per million years. In drosophila the rate of gain/loss of genes per million years varies between 0.0006-0.0193. However, low coverage of genomes in some cases is a source of error in the gain/loss estimates. The highest rates are estimated for genomes having low coverage , and consequently those genomes should be treated with caution. Gene Duplication A number of mechanisms may cause a gene to duplicate. These mechanisms include unequal crossing-over, segmental duplication, whole genome duplication, and retro-transposition. Unequal crossing-over only happens in diploid cells. During meiosis, the duplicated chromosomes attach to each other at the centromere region. Reciprocal or non-reciprocal recombination may take place during this time. In the case of unequal crossing-over during recombination, one chromatid receives a longer segment, while the other receives a shorter one. If there are similar regions, such as repetitive elements, on the chromosomes, unequal crossing over is more likely to occur. This may result in loss of some genes from one chromosome and addition of those genes to the other chromosome. Similar genes on one of the chromosomes may subsequently induce further unequal crossovers. Loss or gain of genes may result in change of gene dosage. Gene dosage is the number of copies of a gene present in a cell or nucleus. Increase or decrease in gene dosage may result in higher or lower levels of gene products provided that it is not regulated elsewise. Around 30% of all recent human segmental duplication are reported to be caused by recombination-like mechanism, and more or less similar figure has been observed for rodents genome . Segmental duplications are found to be large and highly identical in humans. This has also been observed for the chimpanzee genomes . The high identity of segmental duplications makes the genome unstable and more vulnerable to the rearrangements through recombination events. Using wholegenome shotgun sequence detection method, segmental duplications for human were observed to be 5.32%, chimpanzee 3.78%, orangutan 1.18%, rhesus macaque 1.55%, mouse 6.13%, dog 0.82%, cow 5.63%, and opossum 2.7% . Also whole genome duplications may happen during evolution, in which the entire genome is duplicated in the offspring. Ohno hypothesized that the early vertebrates went through two rounds of whole genome duplications . The lineage of ray-finned fishes is also believed to have undergone a third round of whole genome duplication . Flowering plants are believed to have frequent whole genome duplications that enabled them to evolve into such an astounding variety . Whole genome duplication may result in duplication of all genes, which follows a substantial relaxation of selective pressure. Although most of the duplicated genes are destined to get pseudogenized and lost from the genome ultimately, some of the 2.3. MACRO-EVOLUTIONARY EVENTS 13 genes develop new functionality thus creating diversity in the gene function and ultimately new phenotypes. Barbara McClintock, while studying various mutation patterns in maize discovered that some segments of DNA had the ability to move around in the genome . The ‘jumping genes’ were later on known as transposons (a.k.a. mobile elements or transposable elements). Transposons have the ability copy themselves to another location of the genome, or cut-and-paste themselves to the target location. In bacteria, DNA-only transposons are common, which cut-and-paste themselves to the new genomic location using a transposase enzyme without the involvement of an RNA intermediate. In the process of retrotransposition (common in eukaryotic cells), genes are transcribed to RNA (mRNA) and then retrotranscribed back to DNA (cDNA) using a reverse transcriptase and are then inserted back into some random positions in the genome. The enzyme necessary for this process, reverse transcriptase, are encoded by different retrotransposable elements in different species, for example LINE-1 retrotransposons provide the required enzymes in mammals. The resulting retrotransposon have no introns, and generally reside on a different chromosome. If the retrotransposon lands in an intron of another gene, it is transcribed with that gene, if it, in contrast, lands outside the existing genes, the most probable fate is pseudogenization, as it lacks regulatory sequence. In the case a regulatory sequence is evolved by chance, this may result in addition of a new gene to the genome also known as retrogenes. Retrogenes which are eventually transcribed are much more likely to adapt a new gene function compared to what genes duplicated by other mechanisms are. Detailed analyses of some hominoid young retrogenes suggest that they have contributed to brain evolution . Sometimes retrogenes, such as Rps23, evolve a completely new gene function by simply being transcribed in reverse direction in the new genomic location . Some striking phenotypic changes were also associated to a retrogene derived from a growth factor gene (FGF4). It was reported that the conserved, expressed retrogene fgf4 contributed towards a morphological change i.e. short-legged phenotype of several common dog breeds . In this case the change of phenotypic characteristic is more likely to be associated with only the change of gene dosage. That is, a gene duplication has the potential to innovate new phenotypic characteristics by manipulating gene dosage . Lateral Gene Transfer Lateral gene transfer (LGT) or horizontal gene transfer is the transfer of a gene from one organism to another organism such that neither of them is ancestor of the other. Lateral gene transfer is common in bacteria and archae and can be mediated by viruses, plasmids and transposons . LGT is also believed to be a primary reason for the evolution of resistance in bacteria against antibiotics . The role of LGT seems to be limited in the case of metazoans, although some cases have 14 CHAPTER 2. EVOLUTIONARY EVENTS been reported [161, 84]. Among bacterial genomes, LGT is often observed between distantly related species . The key mechanisms for LGT are transformation, conjugation and transduction. Transformation is the direct uptake of foreign genetic material through the cell, conjugation is the transfer of genetic material through a bridge-like structure between the two cells, while transduction is the insertion of foreign genetic material through bacteriophages. Various types of mobile elements are also among the important forces that drives the genomic re-arrangements. Lateral gene transfers challenges the classical definition of species, and the assumption of tree-like evolution of the species. Since the LGTs are observed between distant bacterial species, they are a confounding factor in the inference of phylogenetic trees that are based on the gene sequences. Process of Pseudogenization One of the three possible fates of a duplicated gene is pseudogenization. As mentioned in the earlier section, after a gene duplicates, one of the two genes evolves under relaxed selective pressure for a while, and in most cases it gets ‘pseudogenized’. The pseudogenized genes were initially thought to be nonfunctional genes and often termed as ‘junk DNA’. Jacq and his colleagues used the term pseudogene for the first time, when they discovered a version of the gene coding 5S rRNA that was truncated but retained the homology with the active gene in Xenopus laevis . They are also frequently referred as ‘genomic fossils’, as they are thought to be evolving neutrally . Pseudogenes are present in a wide range of species including prokaryotes , plants , insects , nematode worms , but they are particularly numerous in mammals . A gene may get transformed into a pseudogene in many ways. After a gene duplicates, the selective pressure on the resulting genes is relaxed for sometime and one of the genes may, therefore, accumulate non-sense mutations. This may result in a frameshift (deletion or addition of a single nucleotide), thus resulting in disruption of the open reading frame of a gene. A gene might also gain a pre-mature stop codon thus preventing it from either transcription or translation. Pseudogenes may exist in a genome in form of a processed pseudogene that results from the process of retrotransposition. In this case, the transcribed mRNA is reverse transcribed to cDNA and integrated into a new genomic location. If this newly integrated sequence lacks its own regulatory sequence, it may be ‘dead on arrival’. This processed pseudogene also lacks intron. A non-processed pseudogene is a gene that pseudogenizes as a result of accumulating non-sense mutations. Recent studies have, however, shown that pseudogenes in some cases are still performing some function. For instance it was found that synonymous mutations were far more frequent than the nonsynonymous mutations in the Drosophila Est-6 pseudogene suggesting a selective pressure . In some of the pseudogenes present in chicken, i.e. IglV and IghV, and in mouse i.e. VH, the number of stop codons in the coding sequence region is far lower than expected under neutral evolution [121, 124]. It has also been observed 2.4. INTERESTING GENE FAMILIES 15 that some pseudogenes retain conservation across species, for example, during the analysis of major histocompatibility complex extended class II, two pseudogenes were found to be homologous to human HIV TAT-specific factor-1-like and zincfinger-like pseudogenes . Svensson et al.  identified ancient pseudogenes common to human and mouse that originated before the speciation split and were still highly conserved. Another study identified 48 conserved pseudogenes in human, mouse, rate and dog suggesting a potential function . Therefore, in order to understand how the genome functions, it is important to understand the process of pseudogenization and the potential role of pseudogenes across organisms. 2.4 Interesting Gene Families A gene family is a set of genes that shares similar characteristics such as similar sequence, structure or function. The genes in a gene family are thought to have duplicated and evolved from a single ancestral gene. Such a gene family is called a homologous gene family A gene family evolve by undergoing processes such as duplications, losses, pseudogenization, and lateral gene transfers. During evolution some genes may change significantly in their characteristics from the existing members of the gene family, e.g., by obtaining a different function. The evolution is also affecting gene families through large segmental duplications and whole genome duplications that replicates some or all of the existing genes in the genome. As discussed earlier, duplicate copies of genes relax the selective pressure, and results in neo-functionalization or sub-functionalization of the gene function of the parental gene. Rate of evolution varies across the gene families. Some gene families evolve faster than others and develop new gene functions. Evolution of new gene families is expected to contribute towards the fitness of an organism in its surroundings. Sensing the environment is one of the critical requirement for the survival of a species. The genomes of different species have developed sophisticated senses to sense the surrounding environment during the course of evolution. One such gene family is Olfactory Receptors - the largest gene family in vertebrates, that is targeted towards sensing odors. Regulation of expression of other genes is another important genome function. It has been shown that paralogs mostly sub-functionalizes at regulation level and less frequently through changes in their cellular component, biological process or molecular interactions, and rarely in biochemical function . The Zinc Finger gene family, the second largest gene family in vertebrates, regulates other genes by up- or down-regulating their expression. In the following, I will briefly describe the above-mentioned gene families, i.e. Zinc Fingers and Olfactory Receptors, that have had higher rates of duplications, losses, and pseudogenization in some lineages in the tree of life. 16 CHAPTER 2. EVOLUTIONARY EVENTS C2H2 - ZINC FINGER The C2H2 Zinc-Finger (ZNF) family is one of the largest gene families in mammals. It is the second largest gene family in the human genome, and the largest class of transcription factors. The ZNF genes encode transcription factors that regulate gene expression by binding to DNA and RNA using the ZNF motifs. Each ZNF gene typically encodes a number of ZNF motifs, each consisting of 28 amino-acids. ZNF genes are grouped into multiple subfamilies based on the presence or absence of N-terminal effector domain such as Kruppel-associated box (KRAB). Mammalian genomes have expanded a lot by duplicated these genes (see Figure 2.1) . In the 800 700 600 500 400 300 200 100 0 Human Mouse Chicken Fly Worm Yeast Plant Figure 2.1: Distribution of the C2H2-ZNF genes in different genomes. The total number of C2H2-ZNF genes in different genomes is shown. There has been a massive expansion in the number of C2H2-ZNF genes over the course of evolution . Humans (Homo sapiens [140, 33]) have the highest number of genes as compared to the other species for instance Mouse (Mus musculus ), Chicken (Gallus gallus ), Fly (Drosophila melanogaster), Worm (Caenorhabditis elegans), Yeast (Saccharomyces cerevisiae) and Plant (Arabidopsis thaliana ). human genome, a large proportion of all the C2H2-ZNF genes (more than 70%) are found in tandemly clustered gene families, whereas the remaining exist as singleton genes. These clusters have on average six ZNF genes . Detailed studies of these clusters show that except from duplication of single genes, duplication of partial and whole clusters are also responsible for the rapid evolution of C2H2-ZNF gene family [140, 74, 64]. These genes are thought to be a result of unequal crossing over or DNA slippage during replication, favored by highly identical repetitive motifs . The unstable genomic location of these clusters is also thought to be one of the potential reasons for making this gene family prone to duplications and losses . Recent studies have reported evidence of positive selection for KRAB-ZNF genes, which suggest a strong drive for neo-functionalization after gene duplication 2.4. INTERESTING GENE FAMILIES 17 in this family [105, 42, 110]. Pseudogenes are mostly produced by partial gene duplications, whereas they comprise of approximately half of the KRAB-ZNF loci . OLFACTORY RECEPTORS Sensing the environment through different types of odors constituted a big advantage for tetrapods during the process of terrestrial adaptation. The ability to identify odors was evolved by expansion of a gene family known as Olfactory Receptors (OR). The number of olfactory receptor genes vary from species to species, but they form the largest gene family in vertebrates. The high frequency of OR genes in mammals suggests that detecting and identifying odors was one of the basic requirement for the survival of these species. Species that have other sources of sensing the environment have lower number of OR genes, e.g. primates have trichromatic vision and less number of OR genes as compared to the dichromatic mammalian species. Humans have a higher rate of pseudogenization (around 50%) and consequently a lower number of functional genes (800) in the OR gene family, while mice have a lower rate of pseudogenization and consequently a higher number of total functional genes (1400) with (around 20-25%) . The number of functional functional OR genes in mice is 2.7 times higher than humans. Species such as toothed whales have had an extremely high rate of pseudogenization of OR genes and have completely lost the olfactory system. The development of echolocation system, as well as, the adaptation to the aquatic environment might be the possible reasons for the loss of olfactory system . Platypus have a semi-aquatic life style and using a sophisticated bill sense they can find prey with their eyes, ears, and nostrils closed. The number of OR genes (718) in platypus is also comparatively low with a higher rate of pseudogenization (around 50%). In paper II, we study a model of evolution that also incorporates pseudogenization and analyze some sub-families of this interesting gene family. Chapter 3 Modeling Evolution In this chapter, I will discuss some traditional as well as recent methods developed in order to model key biological processes involved in the evolution of gene families. The evolutionary relationships of gene families and species are called gene phylogenies, and species phylogenies, respectively. Phylogenetics is the sub-field of biology, in which phylogenies are studied by taking into account the molecular sequences, as well as information from other sources such as morphological data and fossils records. The molecular sequences may be in the form of DNA sequences or protein sequences. Phylogenomics refers to the use of phylogenetic methods using large stretches of genomes across the species to infer the gene function and evolutionary relationships in multi-gene families [127, 88]. The evolutionary relationships among the genes, species and their populations are usually represented by binary trees. Two basic phylogeny problems are resolving gene phylogeny and resolving species phylogeny. A brief introduction about species phylogeny, and its reconstruction methods is given below, which is followed by the introduction of key concepts of the gene phylogeny and the methods used to construct gene families. The first five sections of this chapter contains introduction to classical approaches that attempts to resolve gene phylogenies. It includes an introduction to substitution models, distance-based methods, parsimony-based methods, maximum likelihoodbased methods, and Bayesian methods. The last section describes some of the recent methods used to reconcile gene phylogenies and species phylogenies. Species Phylogeny Problem Attempts to resolve species phylogeny have been made since Darwin first proposed the tree-like nature of the evolution of species. Phenotypic evidence was initially used to resolve the evolutionary relationships among species before the availability of molecular sequences. However, with the discovery of DNA, it became possible to compare the molecular sequences of two species to study their evolutionary 19 20 CHAPTER 3. MODELING EVOLUTION relationship. This revolutionized the field, and later on with the availability of ever increasing computational resources, it became possible to develop sophisticated algorithms to address phylogeny problems. Many algorithms have been proposed to study species phylogeny using molecular sequences and to approximate times associated with the speciation events. The species phylogeny is usually represented as a binary tree. The ancestor of all the species in the tree is represented by the root of the tree, while leaves of the tree represent extant species. Least common ancestor (LCA) of a set of leaves in a tree is the internal vertex of the tree, which have no additional leaves as its descendants, except than the set itself, . The internal vertices of a species tree represent speciation events. A speciation event is an event in the evolutionary history of a species after which a part of the population of the species evolve so differently from the rest, such that the two groups are typically no longer able to interbreed and produce fertile offsprings. However, the distinction between species is sometimes not very clear as Charles Darwin wrote in his book, “I was much struck how entirely vague and arbitrary is the distinction between species and varieties” . A speciation event may happen for several reasons, some of which are: geographic isolation leading to different selective pressures and genetic drifts, isolation of the population due to other reasons, or even without isolation merely due to the genetic drift. Fossils of ancestral species may provide important information for accurate estimation of the age of a specific lineage in the tree of life; however, fossils records are not readily available throughout the evolutionary history. Genomes of the extant species on the other hand provides molecular sequences that can be used to resolve the species phylogeny and date the tree of life. A number of methods have been proposed to reconstruct the species phylogeny from the molecular sequence data. Some of the methods involves the use of a ‘super-gene’ that is formed by concatenating many genes of different gene families (typically having one-to-one relationship of genes across species). These supergenes are then used to reconstruct the species phylogeny. However, since the gene families usually do not have the same number of genes across species, it is difficult to create such representative super-genes. Recently, methods based on summary statistics that account for coalescence variance have shown promise to reconstruct species tree . Gene coalescence has also been modeled in ML and Bayesian methods recently to infer the most likely species tree. Some recent methods that attempt to solve this problem are STAR , STEAC, BEST , and BEAST . Gene Phylogeny Problem Another interesting and challenging problem is resolving the gene family phylogeny. The gene family phylogeny is typically represented by a binary tree, where the leaves represent extant genes and the root represents the ancestral gene from which all 3.1. MODELS OF SEQUENCE EVOLUTION 21 genes originated mainly through duplications. A group of genes, which are similar in gene sequence and gene function, evolving from the same ancestral gene forms a homologous gene family. The term homology was coined by Owen  for the first time by referring to the “the same organ in different animals under every variety of form and function". With the advent of molecular sequences, homology is now also defined as the existence of shared ancestry between a pair of sequences, genes or their products such as protein sequences. A homologous relationship may be orthologous, paralogous, or xenologous as defined by Walter Fitch in his seminal article . Two extant genes in two species are orthologous if both of them evolved from a common gene in the least common ancestral species (i.e. least common ancestor occurs due to a speciation event). Alternatively two genes are paralogous, if they exist within the same species or arise from different genes in the most recent common ancestral species. Two genes belonging to two different species are xenologs if they emerge from a lateral gene transfer event. Paralogous genes that arise from a whole genome duplication event are termed as ohnologs. A gene tree represents all the evolutionary events (such as duplications, losses, speciations, and lateral gene transfers) as internal vertices and all the extant genes as leaves of the tree. Any lineage of the gene tree that is lost during the process, is usually pruned from the tree. A gene family phylogeny is sometimes represented by structures other than trees as well, e.g. phylogenetic networks/graphs are also used to represent the evolutionary relationships involving lateral gene transfers in certain gene families . Identifying homologous gene families is often the first step in a phylogenomic analysis. This is however, a non-trivial task. Several methods have been proposed to construct a homologous gene family. These methods usually use one or many of the three kinds of information: sequence information, copy-number of gene across extant species, and location of genes on the corresponding genomes (synteny). Synteny is the condition where a block of genes is found in the same relative position in the genomes of the two species. These methods usually make use of one or more of the following techniques: similarity-based searches such as BLAST, gene clustering techniques, gene-function-based searches, and/or gene synteny . For a given gene family, the gene tree is usually inferred from the gene sequences. There are a number of traditional approaches to estimate the gene tree from the gene sequences. A brief introduction to each of the broad categories is given below. 3.1 Models of Sequence Evolution Genomes of species experience constant molecular evolution through random mutations. Genetic drift and selective pressure are two major forces that shape genomes of two species differently. A number of molecular/sequence evolution models for nucleotides as well as amino-acids have been proposed. These models are usually based on a Markov chain model of nucleotide/amino-acids substitution. The 22 CHAPTER 3. MODELING EVOLUTION parameters used to define the rates at which one nucleotide/amino-acid replaces another during evolution, differentiate one substitution model from the other. The sequence evolution models are used to compute the likelihood of a phylogenetic tree (see 3.4, 3.5). A brief description of commonly used nucleotide substitution models, amino-acid substitution models, and codon substitution models is given below. First I discuss four commonly used Markov models for nucleotide substitutions. JC69 (proposed by Jukes and Cantor ) is the simplest of all substitution models, having equal substitution rates between all nucleotides. Motoo Kimura  proposed the assumption of different rates for transitions (nucleotide substitutions that changes purines to pyrimidines or vice versa) and transversions (nucleotide substitutions between purines or between pyrimidines) in 1980. The model is known as K80. Later on in 1981, Felsenstein proposed a nucleotide substitution model, F81, in which the assumption of equal nucleotide frequencies was relaxed and the substitution rate corresponds to the equilibrium frequency of the target nucleotide. In 1985, Hasegawa et al. introduced a model(HKY85) that allowed unequal nucleotide frequencies as well as proposed different rates for transition and transversions. Sequence evolution can also be modeled in protein sequences. Protein sequences consists of amino-acids; in the DNA sequence of the corresponding gene, each amino-acid is encoded by a codon comprising three nucleotides. The genetic code in case of protein sequences is degenerate, where 20 amino-acids are encoded by 64 codons. Point mutation in any of the nucleotides of a codon may result either in a synonymous mutation, in which the encoded protein does not change, or in a non-synonymous mutation, in which the encoded protein is changed. Because of the lower selection pressure on synonymous substitutions, they are likely to occur at a higher rate than non-synonymous substitutions. For distant species, nucleotide sequences are therefore, more likely to become saturated (i.e. showing reverse substitutions) as compared to the amino-acid sequences. Thus evolutionary pressures at the level of protein sequences cannot be modeled appropriately by nucleotide substitution models. The amino-acid based substitution models not only model the evolutionary pressures at protein level, but they are also more realistic at longer evolutionary distances. They typically are based on 20x20 exchangeability matrix between the 20 possible amino-acids. Different amino-acids have different biological, chemical, and physical properties, due to which they have different rates of substitution with other amino-acids . For example, isoleucine and valine are two amino-acids that have a higher rate of substitution between each other as compared to arginine and aspartate. The amino-acid based substitution models are traditionally empirical models [28, 79]. The substitution rates in these models are typically estimated from large collections of molecular sequences. Studying sequence evolution in the amino-acid sequences hides the details of synonymous substitutions (transitions between codons encoding same amino-acid). 3.2. DISTANCE-BASED METHODS 23 Codon-based models, in the contrast, can better model evolutionary pressures at different codon positions. Codon-based substitution models enable us to study the relative rate of synonymous substitutions to that of non-synonymous substitutions, which is an unambiguous indicator of positive natural selection at molecular level . The codon-based substitution matrices are usually 61x61 (without stop codons), or 64x64 including three stop codons. This matrix consists of the transition probabilities from any codon to any other codon. Typical codon-based substitution models take advantage of the nucleotide position in a codon by incorporating ratio between non-synonymous mutations and synonymous mutations. The ratio of non-synonymous to synonymous rates ω = dN/dS is used to determine if a gene is going through positive/adaptive selection, negative/purifying selection or neutral selection. The transitions to transversion rate ratio is also usually incorporated in the codon-substitution model. Transversions (substitutions of purine to pyrimidine or vice versa) are usually not as common as transitions (substitution of purine to purine or pyrimidine to pyrimidine), because transversions involve much greater change in the structure. The exchangeability matrix between codons is determined by different configurations of parameters such as non-synonymous to synonymous rate ratio, transition to transversion rate ratio, and equilibrium frequencies of codons. One of the commonly used codon substitution models was proposed by Bielawski et al. . The instantaneous substitution rate matrix between codon i to codon j in this case is given as: 0, if i and j differ at more than one position in a codon triplet µπ , differ by a synonymous transversion j qij = µκπj , differ by a synonymous transition µωπj , differ by a nonsynonymous transversion µκωπ , differ by a nonsynonymous transition j where πj is the equilibrium frequency of codon j, µ is the normalizing factor, κ is the transition/transversion ratio, and ω is non-synonymous to synonymous (dN/dS) ratio. In paper II, we use the above-mentioned codon substitution matrix modeling pseudogene evolution, where ω is equal to 1 and transition to stop codon has a nonzero probability. To model gene evolution we use the standard codon substitution matrix described above, where transition to stop codon is not possible. The codon equilibrium frequencies are estimated from the genes/pseudogenes sequences. 3.2 Distance-Based Methods Distance-based methods use the dissimilarity of gene sequences to identify phylogenetic relationship among the genes. Using the pairwise distances between all the sequences as input, distance-based methods attempts to reconstruct a phylogenetic tree with branch lengths. Pairwise-distances between two sequences can 24 CHAPTER 3. MODELING EVOLUTION be computed using pairwise alignment methods. A brief description of the pairwise alignment methods and multiple sequence alignment methods is given later in this section. The pairwise-distances are typically used in one of the agglomerative clustering methods to construct an estimate of the gene tree. One of the most widely used distance-based methods is neighbor joining (NJ) . This method start with a starlike tree, and the pair of taxa having minimum pairwise-distance is successively joined together, until a fully resolved tree is obtained. It is a fast and efficient method, which makes it possible to obtain confidence estimates using bootstrapping. Neighbor joining has been implemented in a variety of settings with some minor improvements (such as BIONJ , RapidNJ , and FNJ  etc.), improving its efficiency or its accuracy. Pairwise alignment methods usually belong to one of the two broad categories, i.e. Dynamic-Programming-based methods (such as Needleman-Wunsch , SmithWaterman ) or Word-Search Methods (such as BLAST ). Dynamic programming (DP)-based methods usually uses a scoring scheme for a match, a missmatch, opening a gap and extending a gap. DP-based methods are guaranteed to find the optimal alignment given a scoring function. A good scoring function in practice is usually based on empirical observations. Word-search-based methods such as BLAST are not guaranteed to give optimal alignment, but are much more efficient than DP-based methods. A gapped BLAST first identifies all matching words between the sequences, then identifies high-scoring segments above the given threshold, occurring within the allowed distance from another high-scoring segments, on the same diagonal. A limited use of DP follows to join the high scoring segments. Word-search-based methods are very useful in searching large-scale databases. Pairwise methods can be used to obtain a phylogenetic tree. Such a phylogenetic tree can be then used in aligning multiple sequences (more than two sequences). A brief introduction to the multiple sequence alignments is given in the following. Multiple sequence alignment (MSA) methods attempts to align more than two gene sequences at a time. This is often the first step in the phylogenetic studies, which can potentially effect the quality of a study. Getting MSA is computationally challenging and the common variations of MSA are shown to be NP-hard . The technique of DP-based alignment is applicable to more than two sequences, but is rarely used in practice since it is computationally expensive both in terms of time and space. Progressive alignment methods is another class of MSA, that aligns the query sequences based on an initial tree such that most similar sequences are aligned first, followed by less similar sequences until all the sequences have been aligned. The initial tree is based on pairwise alignments of the gene sequences. T-Coffee  and Clustal  are some of the examples of progressive alignment methods. Another class of MSAs is iterative methods, which work similarly to the progressive methods, except that it realigns the sequences in each iteration, by aligning a chosen sequence against the profile of remaining aligned sequences. This 3.3. PARSIMONY-BASED METHODS 25 process is repeated until the there is no further increase in the overall alignment score. There are a number of other MSA methods that uses different heuristics to efficiently generate MSA. Some other interesting MSA methods use Hidden Markov Models (e.g. HMMER ), genetic algorthims and simulated annealing. 3.3 Parsimony-Based Methods Parsimony methods are based on the assumption that evolutionary events are rare and, hence, the tree with minimum number of evolutionary events is the most likely scenario. Parsimony was originally developed for use in analyzing discrete morphological characters, but the same principle was later on extended in the phylogenetics. The evolutionary events are typically gene duplications, gene losses and gene transfers, or in the form of substitutions in the gene sequence . Maximum parsimony has, however, been debated since long. The relative efficiency of parsimony-based methods over probabilistic methods made it a tool of choice. Parsimony-based methods should be used with caution as it has been shown that they can be misleading in some scenarios . They have been widely used in the biological community in different settings. Some of the commonly used tools include MEGA5  and PAUP . 3.4 Maximum-Likelihood-Based Methods Maximum Likelihood (ML)-based approaches were first advocated and popularized by R. A. Fisher around 1920, but were used in estimation of evolutionary trees for the first time by Edwards and Cavalli-Sforza . Joseph Felsenstein published an algorithm for computing the likelihood P (D|T ) for discrete and continuous characters in 1973 [43, 44], where D is the gene sequence information, and T is the topology and branch-lengths of the gene tree. Given the topology of gene tree and the branch lengths, the likelihood of the sequences is computed starting from the leaves by marginalizing all possible character assignments of the internal vertices. Finding the optimal ML tree, however, still remains a problem as it is NP-complete . ML-based methods are found to be more accurate in majority of cases in comparison with distance-based methods . Getting the ML-tree usually involves many iterations of tree and branch lengths optimization. The tree optimization is done by methods such as branch swapping (e.g., nearest neighbor interchange and subtree pruning and re-grafting). One may also use bootstrapping to estimate the confidence intervals of the inferred parameters. Some of the popular programs that implement ML-based methods include RAxML , PhyML , PAML , and PLL . 26 3.5 CHAPTER 3. MODELING EVOLUTION Bayesian Methods Bayesian inference methods are based on Bayes’ rule which states that P r(θ|D) = P r(D|θ)P r(θ) P r(D) where P r(θ|D) is the posterior distribution about the set of hypotheses, P r(θ) is the prior belief about the parameters θ, P r(D|θ) is the likelihood of the data D given the parameters θ, and P r(D) is the probability of data (which acts as a normalization constant). The posterior distribution is directly proportional to the product of the likelihood of the data and the prior. When the normalization constant (P r(D)) involves high-dimensional integrals over all possible values of parameters θ, the posterior distribution is hard to compute directly. In order to obtain posterior distribution using Bayesian methods, phylogenetic methods usually relies on MCMC-based approaches (MCMC-based methods are discussed later in this section). The use of priors is, however, controversial and has been debated in phylogenetics. The subjective nature of prior makes the Bayesian inference subjective. This is, however, also an advantage of Bayesian inference as it allows the researcher to incorporate prior biological knowledge and underlying assumptions in the form of an appropriate prior. It may be difficult, due to practical reasons, to provide appropriate prior in terms of a probability distribution representing existing information about the data. It has been shown that under certain conditions more and more similar posterior distributions are obtained with increasing amount of data , therefore, priors do not always have strong influence on results. Non-informative priors are argued as an objective choice, when there is lack of knowledge about the prior. The posterior density may still be sensitive to the boundary conditions. Markov Chain Monte Carlo (MCMC) Markov Chain Monte Carlo (MCMC)-based inference in phylogenetics is used to find the relative probabilities of the possible evolutionary scenarios. MCMC is typically used in cases where one has to search high dimensional spaces and analytical solutions are not easily available. This method sets up a Markov Chain, where every state are points in the parameter space and only depends on the previous state. The parameter space is sampled by a random walk in which the frequency of state visits, in the limit, equals the posterior distribution. The posterior distribution is then summarized to get the estimates of the marginal distribution for the quantities of interest. Metropolis-Hastings is a sampling method used in cases where direct sampling from posterior distribution is hard. In every iteration, a new state x0 is proposed by perturbing one or many parameters of the current state x. The new state is then accepted with a probability that is determined by comparing the likelihoods of the current state and the proposed state with respect to the desired distribution assuming the forward/backward proposal probabilities between any 3.6. RECONCILIATION-BASED APPROACHES 27 two states are the same. If the forward/backward proposal probabilities between the two states are not the same, then the acceptance probability of any proposed state is given by: ) ( T (x0 , x) P (x0 ) 0 A(x, x ) = 1, T (x, x0 ) P (x) where T (x, x0 ) is the transition probability given by the proposal function from state x to state x0 . Although the random walk process eventually converges to the desired stationary distribution, the initial samples may follow a different distribution. These initial samples, also known as the burnin period, are therefore conventionally discarded. As more and more states are sampled, the distribution of sampled states becomes an increasingly better approximation of the desired distribution. This method has theoretical guaranties on convergence to the posterior distribution and is used frequently in phylogenetics, as well as in other fields. MCMC-based methods are computationally demanding but the availability of improved computational power and parallelization are making them increasingly feasible. In the particular case of gene tree reconstruction, proposal functions such as branch swapping are used to sample the search space. Some Bayesian phylogenetic tools that employ MCMC framework to reconstruct the gene trees are MrBayes , PrIME , BAliPhy , PhyloBayes , BEAST , and JPrIME . In this thesis, I will discuss some novel methods that use the MCMC framework to reconstruct gene trees and reconcile those gene trees with the corresponding species tree, which enables us to get the precise time estimates of the events (e.g., duplications, losses, LGT or speciations) represented by gene tree vertices. 3.6 Reconciliation-based Approaches Reconciliation-based approaches maps the evolutionary events of a gene tree to that of the species tree. Depending on the model, evolutionary events of a gene tree are typically duplications, losses, or lateral gene transfers. As discussed earlier, the evolutionary history of a gene family is represented by a gene tree, while its internal vertices represents the evolutionary events. The internal vertices of the gene tree are mapped to the edges or vertices of the species tree, thereby determining the evolutionary events. The reconciliation-based approaches expects the species phylogeny and the mapping of extant genes to the leaves of species tree as input in addition to the MSA of the gene family, and are treated as reality. Two genes are orthologous if their least common ancestor happens to be due to a speciation event. In all other cases, where the least common ancestor happens on an edge of the species tree, the two gene lineages are paralogous to each other. An internal vertex of the gene tree may also be a transfer event, in which case it is usually mapped to any two edges of the species tree. Similarly, an internal vertex may also be a pseudogenization event in the gene tree. Pseudogenization vertices are degreetwo vertices and have only one descendant lineage, representing pseudogenization of the gene lineage (See Paper II). 28 CHAPTER 3. MODELING EVOLUTION Reconciling the evolutionary history of genes with that of species is not a trivial task. Gene-species tree discordance can arise, e.g., because that genes usually do not have one to one correspondence with the species. The process of reconciliation is complicated by evolutionary events such as gene duplications and gene losses. Moreover, the lateral gene transfers is another phenomenon that adds to the genespecies tree discordance specially in the prokaryotes. Some other such processes are hybridization of species, gene fusion/fission that makes the process of reconciliation even harder. Hybridization of species is common in plants, but also found in animals, which sometimes can result in multiple sets of homologous chromosomes. last decade (see, for instance, [138–142]). In parsimony, LGT adds a level of In gene fusion two gene lineages merge into one, which cannot be appropriately complexity compared to structures. gene duplication and on loss, because multiple modeled by tree-like Gene fission, thepartly other hand, splits a gene MPR two coexist. or more parts. Incomplete sorting such (ILS) as also makesapplicable the processonly on optimasinto often Initially having lineage limitations being of reconciliation further complicated. ILS happens when a species lineage, having monocopy families allowing time,speciation there are today population withor more than oneLGT alleles,backwards goes throughinseveral events, andefficient than one alleles survives in loss the descendent lineages. sound In such LGT cases, the allele for inmethodsmore that model duplication, and temporally events, tree might be different from the gene tree, and therefore has the potential to cause stance the work by Tofigh and Lagergren , David and Alm , Bansal et discordance. al. [145,146], Daubin et al. [28,147], and Doyon et al. [148,149]. A major shortparsimony has been used for reconciling the evolutionary history of reconcomingTraditionally, of many combinatorial frameworks is that sequence evolution and genes with that of species. Methods based on the parsimony principle are quick and ciliationefficient constraints not taken into scenarios account[45, simultaneously. LGT from but can are be misleading in some 95]. Probabilistic Also, approaches aimed at reconciling possible gene trees with the given species tree have been species not included in the analysis can complicate gene family analysis,ineither by troduced in the last decade. These approaches are biologically more realistic, and introducing homologs alongside those stemming from the most recent common mathematically robust. They are typically Bayesian-based and as discussed earlier ancestorthey of provide the studied species, or by giving to the ofentire family. a posterior distribution over therise parameters the model. I will briefly discuss both of the approaches in the following: Figure 3.1: Two ways to reconcile a gene tree with species tree  Figure 10. Shows two ways to reconcile the same gene tree topology. The non-MPR solution induces two implicit losses (note that most methods work with the pruned topology only). Not surprisingly, there is a twilight zone between purely combinatorial and probabilistic approaches. For example, sampling among equally optimal solutions in LGT-enabled parsimony to achieve better estimates was suggested recently . Another approach is to let duplication-loss reconciliations guide improvements of an a priori estimated tree inferred using sequence data [150–152]. 3.6. RECONCILIATION-BASED APPROACHES 29 Parsimony-Based Approaches Goodman et al  pioneered the field by introducing the concept of reconciliation. They used a parsimony-based approach and proposed an algorithm that finds the most parsimonious reconciliation (MPR). The MPR is a reconciliation that uniquely maps the vertices of a gene tree to the vertices or edges of a species tree such that the number of inferred evolutionary events (such as duplications and losses) is minimized. Many variations of this algorithm has been proposed since then. In figure 3.1, the reconciliation on the left minimizes the number of evolutionary events and is therefore, MPR. The reconciliation on the right have two additional gene losses, a gene duplication, and speciation event (six events in total) while the reconciliation on the left has only two evolutionary events. MPR works under the assumption that evolutionary events are rare and therefore, parsimonious scenarios are the most likely scenarios. The MPR-based methods are faster but are less realistic than probabilistic methods. A number of parsimony-based methods have been introduced that reconciles the gene tree with the species tree. These methods take into account one or more of evolutionary events such as gene duplications, gene losses, lateral gene transfers, and hybridization of species. In the following I will briefly discuss some recent parsimony-based methods that takes into account 1) duplication and loss events only, 2) lateral gene transfers, 3) incomplete lineage sorting and 4) hybridization events. Many parsimony-based reconciliation methods, proposed in the past decade, take into account gene duplications and gene losses while reconciling a given gene tree with a given species tree. One such approach was proposed by Durand et al. . This method reconstructs the gene tree by any sequence evolution model of choice in the first stage. In the second stage, the gene tree is refined by rearranging regions of the tree that do not have strong support, in order to minimize the cost of duplication and losses. Some commonly used parsimony-based reconciliation methods are SYNERGY  and NOTUNG . Hallet et al. [63, 144] proposed one of the first parsimony methods that take into account lateral gene transfers. They proposed fixed parameter tractable algorithms that count the minimum number of gene duplications and lateral gene transfer events required by any reconciliation. Recently, Doyon et al.  proposed a combinatorial parsimony-based approach (Mowgli) for reconciling a gene tree and a species tree that computes a time-consistent (i.e. lateral gene transfers can happen in the same time slice) most parsimonious reconciliation. Other methods addressing lateral gene transfers along with gene duplications and gene losses as evolutionary events include AnGST  and RANGER-DTL . Incomplete Lineage Sorting is another evolutionary scenario that contributes to the discordance between gene trees and species trees. Wu et al.  recently proposed 30 CHAPTER 3. MODELING EVOLUTION an algorithm (DLCpar) to incorporate deep coalescence that uses an additional allele tree to find the most parsimonious reconciliation in the presence of coalescent and duplication-loss history. Each duplication creates an additional locus that is not linked with the original locus. DLCpar uses a data-structure of three nested trees, i.e., the allele tree evolving inside the gene tree (called locus tree by Wu et al.), which evolves inside the species tree, together with a dynamic programming approach, and efficiently explores the entire search space of reconciliations, and provide the most parsimonious reconciliation as output. Hybridization of species is yet another factor that contributes to the discordance between gene/allele tree and species tree. A parsimony-based approach for reconciling gene trees within the branches of a phylogenetic network was recently proposed by Yu et al. , where they considered speciation, hybridization and incomplete lineage sorting as the evolutionary events affecting the gene tree evolution. The species tree is first converted into a multi-labeled tree (introduced in ), which makes it easier to apply all existing tree-based phylogenetic methods in the context of hybridization. A phylogenetic network is converted into a multi-labeled tree by going in a bottom-up fashion and replicating the subtrees at all the reticulation nodes. This results in a rooted binary tree, whose leaves are not necessarily uniquely labeled. Probabilistic Approaches A number of generative models have been proposed for the evolution of genes inside a species tree. The Duplication-Loss model is one such model, which models the evolution of gene tree inside the species tree. Gene lineages are duplicated and lost during the evolution according to an underlying birth-death process. The Duplication-Loss model has been frequently used to model evolutionary events (e.g., speciation, duplications, LGT) in trees. The gene duplications and gene losses were first modeled probabilistically by a Duplication-Loss model. DuplicationLoss models typically employ a birth-death process that models the genes evolving inside a species tree. The generalized birth-death process was introduced by David G. Kendall . A birth-death process is initiated at the root of the species tree that undergoes births (gene duplications) and deaths (gene losses). A birth in a lineage cause duplication, which bifurcates a gene lineage. A loss of a gene lineage is modeled by a death in the birth-death process. Gene lineages passing through speciation vertices in the species tree always bifurcate. At the end of the birth-death process, all the gene lineages having no descendants in extant species are pruned. Duplication-loss models resolve the discordance caused due to duplications and losses of genes in the evolutionary history, and do not consider the population level processes that cause discordance, such as incomplete lineage sorting. Some recent methods using Duplication-Loss models in different settings will be discussed later in this section. 3.6. RECONCILIATION-BASED APPROACHES 31 Coalescent models are another type of generative models, that are used for tracing back the genealogical history of alleles. These models are retrospective models for population genetics that model the evolution of alleles backwards in time. For a given locus in the genome, at any given time there may be several alleles due to mutations in some of the gene copies across individuals of the population. The evolutionary history of the alleles can be represented as an allele tree. Once the speciation happens, the alleles are sorted randomly, and as a result the resulting populations of species receives all or a subset of the parental species’ alleles. Successive speciation events over a brief interval of time may result in the difference in the topology between the alleles tree and the species tree . Use of coalescent models for resolving this problem has became the method of choice. Coalescent models builds on the Wright-Fisher model, which was independently developed by Sewall Wright and Ronald Fisher during 1929-31. This model considers a population that is equally likely to mate with each other, with the same reproductive success, and evolving in the same conditions. The alleles may be haploid - having one parent, or diploid - having two parents. The population of N genes evolves in discrete generations. The process runs backwards in time, and each gene randomly chooses its parent from the parental generation independently from other genes in the same generation. An alternative model for the problem was introduced by Patrick Moran in 1958. The generations of alleles are allowed to overlap in this model, and population size remains constant. At discrete time intervals, two individuals of population are randomly chosen for reproduction and death. Some recent methods using the coalescent models will be discussed later in this section. In the following I will discuss some recent probabilistic models that are used to resolve gene-species inconsistencies by taking into account evolutionary events such as gene duplications, gene losses, incomplete lineage sorting and hybridization. Duplication-Loss Models The first probabilistic model that modeled duplications and losses was proposed by Arvestad et al. in 2003 , and modeled how a gene family evolves inside a species tree by undergoing evolutionary events such as gene duplications and gene losses. In 2004, the same group introduced a gene sequence evolution model, that integrated probabilistic model (DLRS) for gene duplications, gene losses and sequence evolution under a molecular clock . The assumption of molecular clock was later relaxed . Figure 3.2 illustrates the basic components of the model, a more detiled description are given in paper I. The approach takes an alignment of gene sequences, a dated species tree, and a mapping of the genes to the species as input. A Bayesian method (MCMC-based framework) is then used to obtain a posterior distribution over all gene trees, edge lengths over the gene trees, and 32 CHAPTER 3. MODELING EVOLUTION Figure 3.2: An illustration of DLRS Model, where A) illustrates the evolution of a gene lineage modeled according to the Duplication-Loss model that undergoes duplications and losses. B). Illustrates the clock relaxation according to the Rate model, C) Illustrates the Sequence evolution model other parameters. The probability density in this case is given as follows: p(G, l, θ|D, S) = P (D|G, l)p(G, l|θ, S)p(θ) P (D|S) whereas G is the gene tree, l are edge lengths over gene tree, D is the multiple sequence alignment of gene sequences, S is the dated species tree, and θ denotes the parameters of Duplication-Loss model and substitution rate model. The first factor P (D|G, l) can be computed using the standard DP algorithm by Felsenstein . The second factor p(G, l|θ, S) is the probability of a gene tree (along with the branch-lengths) evolving inside a species tree given all the parameters of the model. This factor can be computed using the dynamic programming algorithm introduced in . The priors p(θ) are chosen so that they can be easily computed. The denominator P (D|S) cancels during the estimation of posterior probabilities in in any ratio between two such probabilities. Instead of searching the entire search space, some methods restrict the search space to near-MPR gene trees. This reduces the required computation and accuracy appears not to be compromised in a majority of the cases [117, 116]. Both of the above-mentioned methods assume that the correct species tree is known. Recently, Boussau et al.  proposed a probabilistic method that estimates the species tree and gene tree at the same time. The input to this method are a multiple sequence 3.6. RECONCILIATION-BASED APPROACHES 33 alignment of gene sequences, species names and a mapping between genes and species, while the method infers gene trees, species tree and branch-wise numbers of duplications and losses. The following equation is maximized for gene tree G and species tree S: Y L(Gi ) L(G, S, N |A) = Gi ∈G whereas G is the set of all gene families, and the N is the branch-wise expected numbers of duplications and losses. The likelihood for a gene family is given as: L(Gi ) = L(S, N |Gi )L(Gi |Ai ) where Gi and Ai are the gene tree and alignment for a gene family G, respectively. The likelihood L(Gi |Ai ) can be computed using any probabilistic model of sequence evolution . The factor L(S, N |Gi ) is the likelihood of the reconciliation of a gene tree with a species tree according to duplication loss rates. This factor is computed in a similar way to Åkerborg et al. , but the gene families share the parameters of duplication and loss events that are branch-specific on the species tree. The method does not take into account the branch-lengths on the gene trees while reconciling a gene tree with a species tree, and instead only reconciles the topologies. This reduces the number of global parameters and therefore helps in faster computation. But since the hierarchical model also includes sequence evolution for joint inference of gene trees and species trees, branch lengths are essential to estimate. LGT Models Horizontal gene transfer or lateral gene transfer is another evolutionary event that can create discordance between gene trees and species trees. Sjöstrand et al. [143, 128] introduced one of the first probabilistic models, DLTRS (Duplication, Loss, Transfer, substitution Rate variation over gene tree, and Sequence evolution), that integrates duplication-loss events, lateral gene transfer events along with sequence evolution in a single comprehensive model. A modified version of the birthdeath process is used in this case, which models lateral gene transfers as well as gene duplications and gene losses. The probability of a gene tree, its edge lengths and other parameters are computed similarly to what is done in Åkerborg et al. . In this case, the gene tree lineages are allowed to jump across the species tree lineages in the same time (see Figure 3.3). The present work extends this method and propose a dynamic programming algorithm for sampling reconciliations and computing most-likely reconciliations. Further details about this method are given in chapter 4, and in Paper III. Another method was proposed by Suchard , where he proposed a hierarchy of stochastic models to investigate LGTs using multiple orthologous gene alignments. The models works in a hierarchical manner, in which the top layer builds a joint distribution over multiple gene trees and an unknown species tree through a random walk in the ‘trees space’. In the bottom layer, gene 34 CHAPTER 3. MODELING EVOLUTION Figure 3.3: PrIME-DLTRS  trees are reconstructed given the multiple sequence alignments conditional on the random walk process. This hierarchical distribution provides likelihoods of gene trees given an unknown species tree and unknown number of LGTs. Szollosi et al.  integrated the processes of originations (from ‘scratch’ or from extinct species), duplications, losses and lateral gene transfers into single model, ODT (Origination, Duplication, Transfer, and Loss) to reconstruct a chronologically ordered species tree by explicitly modeling the evolution of genes in their genomes. The birthdeath process in this case consists of two types of births, i.e. duplication, or lateral gene transfer. Moreover, in this model lateral gene transfer can also occur from the species that have gone extinct (or not present in the species under consideration). The probability of a gene tree G given a species tree S, with probabilities of origination, duplication, transfer and losses denoted by M is computed as follows: ! X X ~ p(G|S, M) = PO (x)P (R, x) ~ R∈R x∈N (S) where R is the set of all possible roots of G, N (S) denotes all positions across species tree, and pO (x) corresponds to the origination probability at position x along S. Under the assumption that the gene families G evolved independently, the likelihood of S and M is computed as: Y LODT (S, M|G) = p(G|S, M) G∈G In the context of prokaryotes, models that take into account lateral gene transfer along with gene duplications and losses are biologically more realistic than the Duplication-Loss models. However, the addition of lateral gene transfer to the Duplication-Loss models usually comes at the cost of increase in the amount of required computation. ILS Models The probabilistic methods discussed above do not account for Incomplete Lineage Sorting (ILS) of alleles. Different coalescent models have been developed that 3.6. RECONCILIATION-BASED APPROACHES 35 account for variation of population sizes, divergence times, and migration rates [91, 115, 69]. Incomplete lineage sorting has recently been addressed by using Figure 3.4: Duplication and loss events within a multispecies coalescent. (A) A duplication occurs in one chromosome and creates a new locus, “locus 2”, in the genome. At locus 2, the Wright-Fisher model dictates how the frequency p of the child duplicate (black dots) competes with the null allele (white dots) until it eventually fixes (p = 1). A allele tree is therefore a “traceback” in this combined process. (B) A new duplicate can undergo hemiplasy, and fixes in some lineages and goes extinct in others. (C ) Similar to duplication, a gene loss (deletion) starts in one chromosome and drifts until it fixes or goes extinct.  coalescent models along with Duplication-Loss models. Rasmussen et al.  proposed a probabilistic model DLCoalRecon, that integrates the Duplication-Loss model with coalescence model. DLCoalRecon expects a dated species tree S, an estimated population size N , gene duplication-loss rates (λ and µ), and allele tree topology T A as input (Note that I use different terminology for allele tree and gene tree than ). The gene tree T G is generated by a birth-death process similar to . For each duplication node in the gene tree, one of the children is randomly denoted as a child and the other as the parent. Each new gene (child) corresponds to a new chromosomal location. The allele tree T A is generated bottom-up using a multilocus coalescent within the gene tree T G (see Figure 3.4). A hill-climbing search is used to estimate the maximum a posteriori reconciliation between the three trees. It returns as output the reconciliation R, which is defined as tuple, R = (T G , RA , RG , δ G ), where RA is a mapping of the allele tree to the gene tree, RG is a mapping from the gene tree to the species tree S, and δ G is the set of child nodes. The probability of a gene tree T G and the reconciliation R given the dated species tree (S, tS ), population sizes and and duplication-loss rates is given as follows: P (T A , R) = P (δ G |T G , RG , S)P (T G , RG |S, θ)× Z P (T A , RA |T G , tG , σ G , N G )P (tG |T G , RG , S, θ)dtG G G (3.1) The first factor P (δ G |T G , RG , S) = 2−|dup(T ,R ,S)| where dup(T G , RG , S) gives the number of duplications in the gene tree. Second factor, P (T G , RG |S, θ) is com- 36 CHAPTER 3. MODELING EVOLUTION puted similar to , and the integration of the last factor is the main contribution of this method. Hybridization Models As discussed earlier, hybridization of species may result in a non-tree like structure or cause discordance between the gene/allele tree and the species tree [125, 14]. Several methods have attempted to resolve the discordance/non-tree like evolution caused by hybridization by using a species network, where an allele in the hybrid species is assumed to originate from one of the two parental species with some probability. Meng and Kubatko  in 2009 proposed a method that estimates the role of hybridization using a likelihood as well as bayesian framework, both in case of hybridization and coalescence. The model assumes that in the case of hybridization of species, a randomly selected gene from one of the two parental species is inherited. A usual coalescence process is employed for the alleles, where a parent for hybridized allele is chosen according to the probability γ, which is inferred based on a likelihood function. Yu et al.  recently proposed another approach for addressing hybridization of species in the presence of incomplete lineage sorting. The phylogenetic network W is first converted into a multi-labeled species tree T , (a tree whose leaves are not uniquely labelled by a set of taxa) by going in a bottomup fashion and replicating the subtrees at all the reticulation nodes. This results in a rooted binary tree, whose leaves are not necessarily uniquely labeled. Alleles of the tips of gene tree G are mapped in every valid way to the tips of T , and finally the probability of G is computed as the sum, over all valid allele mappings, of the probabilities of G given T . P (G|W, l, γ) = X P (G|T, l0 , γ 0 , f ) f ∈F where edge lengths of the gene tree are denoted by the vector l, of hybridization probabilities (which indicates for each allele in a hybrid population its probability of inheritance from each of the two parent populations) are denoted by γ, and all valid allele mappings are denoted by F. Given a collection (G) of gene tree topologies, one per locus, in a set of sampled loci, where pg is the sum of posterior probabilities associated with the gene tree g, the likelihood function is given by: L(W, l, γ|G) = Y [P (G = g|W, l, γ)]pg g∈G Like other coalescent models, population size is assumed constant and it is assumed that no recombination takes place. 3.6. RECONCILIATION-BASED APPROACHES 37 Pseudogenization Models Gene losses is also a factor that contributes towards the discordance in the reconciliation of gene trees and the species tree. The process of pseudogenization has been regarded as the most likely fate for the newly duplicated genes. Interestingly, some pseudogenes remain conserved over long period of time and are even attributed a potential function. The conservation of pseudogenes over long period of time and their potential function highlights the importance of the studying pseudogenes. Svensson et al.  conducted a genome-wide survey for and analysis of human pseudogenes, in which they used a BLAST-based pipeline augmented by maximum-likelihood phylogeny estimations. Their results suggested that functional pseudogenes are rarely found in the evolutionary timescale, but they still exists. A comprehensive model that models pseudogenization events, gene duplications, gene losses, and sequence evolution under a relaxed molecular clock is introduced in paper II. The model is based on a birth-death process, where a gene family starts with a gene at the root, and may pseudogenized during evolution. A pseudogene lineage may duplicate or get lost just like a gene lineage. Conversion of a pseudogene to gene is however not allowed in the model. A neutral codon substitution model is used for the sequence evolution of pseudogenes. Paper II provides the details of this model. Chapter 4 Present Investigations Paper I: In this study, we extend the DLRS framework introduced by Åkerborg et al. . The proposed method samples reconciliations as well as compute the most likely reconciliation from the posterior distribution over gene trees and other parameters. The method is used to analyze genome-wide gene families of OPTIC dataset consisting of nine vertebrate species. The species tree is augmented by a heatmap for each edge, illustrating how frequently duplications occur on the edges, across the gene families. We also compare the obtained reconciliations with the most parsimonious reconciliations (MPR) and conclude that MPR leads to an incorrect reconciliation in 19% of all reconciliations. Finally, we propose algorithms for sampling and computing the most likely realizations (a finer reconciliation, that maps vertices of the gene tree to specific time points on the species tree). Paper II: In order to facilitate the proper analysis of gene families including the process of pseudogenization, we introduce PDLRS by introducing the possibility of pseudogenization of gene lineages. The model integrates sequence evolution (under a relaxed molecular clock for substitution rates) with evolution of genes and pseudogenes that may undergo duplication/loss events, gene-to-pseudogene conversions according to a birth-death process. We devise MCMC-based methods that allows data analysis with respect to this model, and apply it on synthetic as well as biological datasets. The biological datasets consists of genes and pseudogenes from two largest gene families in vertebrates, i.e. Olfactory Receptors and Zinc Fingers. Olfactory receptors are studied across human, dog, opossum, and platypus, while zinc fingers are studied across the four primate species human, chimpanzee, rhesus monkey, and orangutan. Paper III: This study extends the model introduced by Sjöstrand et al. . The proposed method provides algorithms for sampling reconciliations as well 39 40 CHAPTER 4. PRESENT INVESTIGATIONS as computing most likely reconciliations from the posterior distribution over gene trees, edge lengths and other parameters of the model. By conducting a simulation study, we observe that the method is able to infer the true LGT events on gene tree and reconcile it to the correct edges of the species tree in most cases. Chapter 5 Discussion & Conclusion The increasing number of fully sequenced genomes have expanded our understanding about the evolutionary process. Identifying the regulatory, functional and nonfunctional regions of the genomes is an important step in understanding genomes. This valuable insight is provided by comparing genomes or large part of genomes across the species. Phylogenomics is the field in which we compare genomes to reconstruct their evolutionary history. It also helps us understand when and how different genes evolved inside different species. This enable us to study the origins of genetic diseases that are incurable at the moment. Furthermore, phylogenomics also open up new avenues to understand diseases like cancer, alzheimer etc. and other natural processes at the level of our genome such as aging, by comparing genomes across different species. In this thesis, two methods are proposed to estimate the age of evolutionary events. In the first project, age of the gene duplications are estimated on evolutionary scale, while in the last project we estimate age of the gene duplication events as well as gene transfer events. Mapping the gene duplication events to the evolutionary time-scale give us interesting insights into the evolutionary history and the ecology of earth. Heatmap of the gene duplications across genefamilies for the selected species of vertebrates is given in figure 5.1. The heatmap provides an overall picture of the rate of gene duplications across different lineages. We observed the high- Figure 5.1: Heatmap of gene dupliest rate of duplication during the Cambrian pe- cation events across gene families riod, followed by the Ordovician period. Most of the major animal phyla resembling current day life forms appeared during the Cambrian period. 41 42 CHAPTER 5. DISCUSSION & CONCLUSION The ordovician period, which is associated with a mass extinction, also had a high rate of gene duplication according to our analysis. High duplication rates were also observed for the edges corresponding to the Carboniferous period, which is associated with highest levels of oxygen on earth, and Permian period, which is associated with mass extinction and plummeting oxygen levels . Moreover, a high rate of duplication was also observed for the common ancestral edge of human, mouse and dog (Boreoeutheria). This edge corresponds to the Cretaceous period which is also associated with a mass extinction . The role of extinctions in shaping evolution has been under debate [119, 76]. It would be interesting to investigate further if a higher rate of duplication on certain vertebrate lineages is related to the mass extinctions or not. Comprehensive probabilistic methods that model most of the evolutionary events can give us further insight into the evolutionary history of the species and their ecology. Modeling pseudogenization events was the second project of this thesis. Pseudogenes were initially thought to be the ‘junk DNA’ but recently many studies have reported their potential functionality. Some have even called them ‘potogenes’ suggestive of the potential functionality they might have . A model that can take into account the process of pseudogenization realistically can be very helpful in correctly determining the evolutionary history of pseudogenes. Pseudogenes that have remained conserved across large evolutionary distance are more likely to be functionally active. Identifying such pseudogenes is obviously important to understand the functioning of genomes. In this project we introduce a probabilistic method that estimates the age of the gene-to-pseudogene conversion points along with the gene duplication events on the evolutionary scale. Two gene families were studied using this method and some ancient pseudogenes in the selected subfamilies of olfactory receptors and zinc-finger-gene superfamilies were identified. Further analysis of more gene families can be helpful to reconstruct the evolutionary history of genes and pseudogenes more precisely. Taking into account the ecology of species, it can be further investigated how much the genomes of different species have been shaped by the ecology. The methods presented in this thesis have the room for improvement, as they do not take into account all the evolutionary processes. Evolutionary processes such as incomplete lineage sorting and hybridization are two important evolutionary processes that plays an important role in the evolution of a genome. Population-based phylogenomics will become more and more feasible with the increasing number of sequenced genomes per species. Hybridization of genes is also an important confounding factor while reconstructing the gene phylogenies. There are also evolutionary processes acting at sub-gene level. Some genes are composed of multiple protein domains. The evolutionary processes on the domain level, might also play an important role in the evolution of a gene family. Having a comprehensive model that takes into account most of the evolutionary mechanisms is therefore, an obvious future direction. However, the models that take into account more and more evo- 43 lutionary processes have the possibility to suffer from over-parameterization. This makes the computational aspect of this interesting problem even more challenging. With the availability of computational resources and sequenced genomes with better coverage, it is relatively easier to do the phylogenomic analysis. However, at the same time there is a need for comprehensive probabilistic methods that can efficiently use the genomic information to reconstruct the evolutionary history. This thesis adds new methods to estimate the approximate times for the evolutionary events to the existing existing literature. 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