L'objectif de cette thèse est d'étudier les propriétés de variétés toriques particulières. La thèse est divisée en trois parties, les deux premières étant fortement liées. Dans la première partie, nous étudions des variétés algébriques associées aux processus de Markov sur les arbres. A chaque processus de Markov sur un arbre on peut associer une variété algébrique. Motivé par la biologie, nous nous concentrons sur les processus de Markov dé finis par une action de groupe. Nous étudions les conditions pour que la variété obtenue soit torique. Nous donnons un résultat où les variétés obtenues sont normales, ainsi que des exemples où elles ne le sont pas. L'une des principales méthodes que nous utilisons est la généralisation des notions de prises et de réseaux introduites dans [BW07] à des groupes abéliens arbitraires. Dans notre contexte, les réseaux forment un groupe qui agit sur la variété. Par ailleurs, l'espace ambiant de lavariété est la représentation régulière de ce groupe. Le principal problème ouvert que nous essayons de résoudre dans cette partie est une conjecture de Sturmfels et Sullivant [SS05, Conjecture 2] indiquant que le schéma a fine associé au modèle 3-Kimura estdé fini par un idéal engendré en degré 4. Notre meilleur résultat dit que le schéma projectif associé peut être dé fini par un idéal engendré en degré 4. Avec Maria Donten -Bury, nous proposons une méthode pour engendrer l'idéal associé à la variété pour tous les modèles. Nous montrons que notre méthode fonctionne pour de nombreux modèles ainsi que pour les arbres si et seulement si la conjecture de Sturmfels et Sullivant est vraie. Nous présentons quelques applications, par exemple au problème d'identi abilité en biologie. La deuxième partie concerne les variétés algébriques associées aux graphes trivalents pour le modèle de Jukes-Cantor binaire. Il s'agit d'un travail en commun avec Weronika Buczyńska, Jarosław Buczyński et Kaie Kubjas. La variété associée á un graphe peut être représentéevpar un semi-groupe gradué. Nous étudions les liens entre les propriétés du graphe et le semigroupe. Le théorème principal borne le degré en lequel le semi-groupe est engendré par le premier nombre de Betti du graphe, plus un. Dans la dernière partie, nous étudions la structure de la catégorie dérivée des faisceaux cohérents des variétés toriques lisses. Dans un travail commun avec Michał Lasoń [LM11], nous construisons une collection fortement exceptionnelle complète de fi brés en droites pour une grande classe de variétés toriques complètes lisses dont le nombre de Picard est égal á trois. De nombreuses questions concernant le type de collections auxquelles on peut s'attendre sur les variétés toriques de certains types sont encore ouvertes. A ce titre, nous prouvons que Pn éclaté en deux points ne possède pas de collection fortement exceptionnelle complète de fibrés en droites pour n assez grand. Ceci fournit une collection infi nie de contre-exemples à la conjecture de King. Le premier contre-exemple est dû à Hille et Perling [HP06]. Récemment, des contre-exemples ont également été trouvés par E mov [E ] dans le cadre des variétés de Fano. Nous allons travailler sur le corps des nombres complexes C. Toutes les variétés considérées sont des variétés algébriques dans le sens de [Har77]. / The aim of this thesis is to investigate the properties of special toric varieties. The thesis is divided into three parts. The first two of them are strongly related to each other.In the fi rst, main part we study algebraic varieties associated to Markov processes on trees. To each Markov process on a tree one can associate an algebraic variety. Motivated by biology, we focus on Markov processes de fined by a group action. We investigate underwhich conditions the obtained variety is toric. We provide conditions ensuring that the obtained varieties are normal, as well as give examples when they are not. One of the main tools we use is the generalization of the notions of sockets and networks introduced in [BW07] to arbitrary abelian groups. In our setting the networks form a group, that acts on the variety. Moreover the ambient space of the variety is the regular representation of this group. The main open problem that we address in this part is a conjecture of Sturmfels and Sullivant [SS05, Conjecture 2] stating that the afi ne scheme associated to the 3-Kimura model is de fined by an ideal generated in degree 4. Our strongest result states that the associated projective scheme can be generated in degree 4. Together with Maria Donten -Bury we also propose a method for generating the ideal defi ning the variety for any model. We prove that our method works for many models and trees if and only if the conjecture of Sturmfels and Sullivant holds. We present some applications, for example to theidenti ability problem in biology. The second part concerns algebraic varieties associated to trivalent graphs for the binary Jukes-Cantor model. It is a joint work with Weronika Buczyńska, Jarosław Buczyński and Kaie Kubjas. In case of the graph, the associated variety can be represented by a graded semigroup. We investigate the connections between properties of the graph and the semigroup. The main theorem bounds the degree in which the semigroup is generated by the first Betti number of the graph plus one. Due to connections with the first part much of the terminology that we use is either a specialization or generalization of previous de finitions. From the one hand, as we are working with graphs with possible loops the notions of leaves, nodes and valency are more subtile than for trees. From the other hand, as we are dealing only with the binary Jukes-Cantor model, sockets and networks have got a very special form. In the last part we study the structure of the derived category of coherent sheaves for smooth toric varieties. As a result of a joint work with Michał Lasoń [LM11] we construct a full, strongly exceptional collection of line bundles for a large class of smooth, complete toric varieties with Picard number three. Many questions concerning what kind of collections should be expected on toric varieties of certain types are still open. As a contribution we prove that Pn blown up in two points does not have a full, strongly exceptional collection of line bundles for n large enough. This provides an in finite collection of counterexamples to King's conjecture. The first such counterexample is due to Hille andPerling [HP06]. Recently also counterexamples in the Fano case were found by E mov [E ].

Adaptive radiations provide exceptional opportunities to examine the relationships between natural selection, adaptation, and speciation. Neotropical Adelpha butterflies may represent such a radiation, characterized by extraordinary breadth in host plant use and wing color patterns. In this study, we use genome-wide RAD markers to reconstruct the complex evolutionary history of Adelpha and the closely related temperate genus, Limenitis. Despite the presence of significant missing data, a variety of phylogenetic methods produce similar and highly supported trees. These well-resolved phylogenies allow for the identification of an ecologically important shift to a toxic host plant family, as well as the confirmation of rampant wing pattern mimicry throughout the genus. Taken together, our results support the hypothesis that the colonization of novel host plants represents a key evolutionary innovation that is fueling ongoing adaptive diversification within this large, phenotypically diverse butterfly radiation.

Sex and meiosis are ubiquitous in eukaryotes as the primary mode of reproduction. This suggests that despite the theoretical energetic advantages of asexual reproduction, organisms capable of sexual reproduction are at a much greater long-term evolutionary advantage. Rotifers, a group of microinvertebrates, offer unique opportunities to examine the evolution of sex due to their extensive proliferation, successful adaptation to a wide variety of ecological niches, and the diversity of reproductive modes represented in the group. The cyclically parthenogenetic monogonont rotifers have overcome constraints on the loss of sexual reproduction in order to frequently transition between sexual and asexual generations, making them a powerful system with which to address the maintenance of sex in animals. Obligately asexual bdelloid rotifers appear to have thrived without sex for tens of millions of years, a period of time much longer than expected given the hypothesized advantages of sexual reproduction. However, the molecular nature of sex and parthenogenesis is poorly understood in any rotifer species. To expand our knowledge of the molecular mechanisms of monogonont reproduction, we sequenced genomes of two distantly related species, Brachionus calyciflorus and Brachionus manjavacas and identified over 80 homologs for genes involved in meiotic processes. Several of these genes have undergone duplication events specific to the monogonont lineage, including genes with known roles in regulation of cell cycle transitions during meiosis. In addition, global gene expression patterns were determined using obligate parthenogenetic (OP) and cyclical parthenogenetic (CP) strains of B. calyciflorus. Quantitative comparison of expression between these strains revealed differentially expressed genes specific to sexual and asexual reproduction in this species, including genes related to dormancy/resting egg formation, meiosis, and hormone signaling pathways that are thought to be involved in the induction of sexual reproduction in monogononts. Finally, we analyzed gene expression in bdelloid rotifers for evidence of sexual reproduction or the utilization of meiotic genes under conditions inducing high levels of recombination. Through this work, we have established molecular markers for sexuality and asexuality in monogonont rotifers, and used these markers to evaluate reproduction in bdelloids. The data generated specifically allows for more informed analyses of the evolution of cyclical parthenogenesis and rotifer reproduction. Furthermore, this work extends the use of monogononts as a model system for addressing broader questions regarding the evolution of sexual reproduction.

The Fayúm Province of Egypt covers an almost continuous time span from the middle Eocene through the early Oligocene and has produced a number of vertebrate fossils important to evolutionary history. This area includes early crocodylids inaccurately assigned to crown-group Crocodylus, which has been shown through molecular and morphological phylogenetic analyses to have diverged during the Miocene. We reviewed two taxa from the early Oligocene Gebel Qatrani Formation, Crocodylus megarhinus Andrews 1905 and Crocodylus articeps Andrews 1905, which had previously been synonymized, with C. articeps thought to be based on a juvenile specimen of C. megarhinus. Crocodylus megarhinus outwardly resembles most living species of Crocodylus, however it is a basal crocodylid lacking diagnostic features for the crown genus. The holotype of C. articeps is now lost, but based on a cast and published images of the original material, it was a slender-snouted form that can be distinguished from smaller specimens of C. megarhinus. Although not synonymous with C. megarhinus, C. articeps cannot be diagnosed or scored for existing character matrices sufficiently to allow precise phylogenetic placement. Previous analyses of C. megarhinus included information from C. articeps; recoding C. megarhinus based only on material referable to that species does not change its phylogenetic position, but it forces a reconsideration of the polarity of character states in clades leading to the origin of crown-genus Crocodylus which, in turn, may inform efforts to resolve the relationships among living crocodylid lineages. Based on its confirmed phylogenetic position as a basal crocodylid, C. megarhinus provides insight into the ancestral conditions of all crocodylids and supports an African origin for Crocodylidae.

Alligatorines are a diverse clade of crocodylians whose history spans the entire Cenozoic. They are suited to answer a variety of questions with far‐reaching impacts due to their physiology and preservation potential, and have been the subject of several phylogenetic, biogeographic, and diversity analyses. However, prior phylogenetic analyses had poor resolution and several putative alligatorines have never been included, while other analyses would be more informative and accurate if viewed through the context of evolutionary history. Here, I analyze the phylogenetics, taxonomy, biogeography, ecomorphology, and diversity dynamics of alligatorines. An almost fully resolved phylogenetic hypothesis returns two major clades within Alligatorinae and includes several putative alligatorines not previously analyzed. The clade originated in North America and dispersed to Europe and Asia three to five times via at least three different corridors at high latitudes when climate—and potentially salinity—were favorable, likely including the recently discovered subaerial Lomonosov Ridge. The modern American alligator is a dietary generalist, but evolved from a durophagous specialist, contrary to the intuitive reasoning of the “Law of the Unspecialized”. It was able to do so by entering the generalist niche vacated by basal crocodyloids following their extirpation from mid‐latitude North America. Alligatorine diversity only weakly tracks climate change and does not track the rock record excepting swampy environments. Alligatorine diversity correlates with climate change. Climate change correlates with rocks, though in a more complicated pattern. Some diversity metrics correlate with some aspects of the rock record, but predominantly do not. There is more support for the common‐cause hypothesis than for rock record bias driving apparent alligatorine diversity. Overall, alligator evolution exhibits a pattern of being more diverse taxonomically and morphologically when the climate is warmer, and dispersing during the warmest and wettest of those times.

<p><i>Heterodrilus</i> is a marine group of small (3-25 mm) clitellates that occur interstitially in sandy sediments from the intertidal zone down to about 150 m depths. The taxon includes 42 valid species and has been recorded from localities in the Mediterranean Sea, the North-west Atlantic Ocean (including the Caribbean), the Galapagos Islands, and the Indo-Pacific Region. A majority of the species of <i>Heterodrilus</i> are characterized by having trifid anterior chaetae (i.e., chaetae with three teeth at the distal end). A few species have bifid chaetae, but these are regarded as having lost the third tooth secondarily. Within the taxon, species are distinguished by morphological characters in the internal organization of the male and female genitalia, but also by characters in the form and number of chaetae. In this thesis, two new taxa are introduced, <i>Heterodrilus tripartitus </i>and <i>H. ursulae</i>, both from the Mediterranean Sea. The ultrastructure of the cuticle in four species (<i>H. paucifascis, H. pentcheffi, H</i>. <i>flexuosus, H. minisetosus</i>) is studied and it is shown that there is interspecific variation in the morphology of the cuticle. One of the studied species, <i>H. paucifascis</i>, shows intraspecific variation, which is associated with sample locality. The systematic position of <i>Heterodrilus</i> within Tubificidae is studied with molecular markers, and the results support that <i>Heterodrilus </i>(earlier classified as a member of Rhyacodrilinae) is positioned within Phallodrilinae. Furthermore, the phylogenetic relationships within <i>Heterodrilus</i> are estimated based on molecular characters from mitochondrial COI, the 16S rRNA gene, and the nuclear 18S rRNA gene, and the result indicate that the two major clades in our tree corresponds to different geographical distributions. This thesis also includes a checklist, as well as a key, to the species of <i>Heterodrilus</i>.</p>

<p>This thesis concerns the evolution of African small carnivorans, with emphasis on East African Viverridae and Herpestidae (Carnivora, Mammalia). Viverridae and Herpestidae are two Old World feliform (belonging to the cat branch) carnivoran families with a confusing, and sometimes even misleading, taxonomic and systematic history, in addition to a scarce fossil record. </p><p>A new genus and species from Fort Ternan, western Kenya, dated to ca 14 Mya (million years ago), was described and tentatively assigned to the Viverridae. The excellent preservation of this material has the potential to shed much light on the evolution of feliform carnivorans from Africa. The fossil record of Carnivora from Laetoli, a Pliocene hominid-bearing site in northern Tanzania, was also described and placed in an evolutionary context. The age of the fossil fauna from Laetoli ranges from 4.3 Mya to 2.5 Mya. The fossil material from this site is remarkable for two reasons: it is extensive in both number of taxa represented and amount of fossil material, especially of small carnivorans, and it is fossilized and preserved under aeolian conditions. In addition to these paleontological studies, two studies concerning extant Viverridae and Herpestidae were conducted. First, the phylogeography of the white-tailed mongoose, <i>Ichneumia albicauda</i>, (Herpestidae), was examined, with the tentative conclusion that its origin is southern African. Second, the ecomorphology and biogeography of African and Eurasian Viverridae and Herpestidae was analysed in order to investigate if these features can be used to help assess their evolutionary history in the absence of fossils. The pattern that emerges in this study is that the species of Viverridae and Herpestidae do not generally overlap in ecomorphology where they overlap geographically, which indicates considerable competitive interactions between the families in both Africa and Eurasia.</p>

Heterodrilus is a marine group of small (3-25 mm) clitellates that occur interstitially in sandy sediments from the intertidal zone down to about 150 m depths. The taxon includes 42 valid species and has been recorded from localities in the Mediterranean Sea, the North-west Atlantic Ocean (including the Caribbean), the Galapagos Islands, and the Indo-Pacific Region. A majority of the species of Heterodrilus are characterized by having trifid anterior chaetae (i.e., chaetae with three teeth at the distal end). A few species have bifid chaetae, but these are regarded as having lost the third tooth secondarily. Within the taxon, species are distinguished by morphological characters in the internal organization of the male and female genitalia, but also by characters in the form and number of chaetae. In this thesis, two new taxa are introduced, Heterodrilus tripartitus and H. ursulae, both from the Mediterranean Sea. The ultrastructure of the cuticle in four species (H. paucifascis, H. pentcheffi, H. flexuosus, H. minisetosus) is studied and it is shown that there is interspecific variation in the morphology of the cuticle. One of the studied species, H. paucifascis, shows intraspecific variation, which is associated with sample locality. The systematic position of Heterodrilus within Tubificidae is studied with molecular markers, and the results support that Heterodrilus (earlier classified as a member of Rhyacodrilinae) is positioned within Phallodrilinae. Furthermore, the phylogenetic relationships within Heterodrilus are estimated based on molecular characters from mitochondrial COI, the 16S rRNA gene, and the nuclear 18S rRNA gene, and the result indicate that the two major clades in our tree corresponds to different geographical distributions. This thesis also includes a checklist, as well as a key, to the species of Heterodrilus.

This thesis concerns the evolution of African small carnivorans, with emphasis on East African Viverridae and Herpestidae (Carnivora, Mammalia). Viverridae and Herpestidae are two Old World feliform (belonging to the cat branch) carnivoran families with a confusing, and sometimes even misleading, taxonomic and systematic history, in addition to a scarce fossil record. A new genus and species from Fort Ternan, western Kenya, dated to ca 14 Mya (million years ago), was described and tentatively assigned to the Viverridae. The excellent preservation of this material has the potential to shed much light on the evolution of feliform carnivorans from Africa. The fossil record of Carnivora from Laetoli, a Pliocene hominid-bearing site in northern Tanzania, was also described and placed in an evolutionary context. The age of the fossil fauna from Laetoli ranges from 4.3 Mya to 2.5 Mya. The fossil material from this site is remarkable for two reasons: it is extensive in both number of taxa represented and amount of fossil material, especially of small carnivorans, and it is fossilized and preserved under aeolian conditions. In addition to these paleontological studies, two studies concerning extant Viverridae and Herpestidae were conducted. First, the phylogeography of the white-tailed mongoose, Ichneumia albicauda, (Herpestidae), was examined, with the tentative conclusion that its origin is southern African. Second, the ecomorphology and biogeography of African and Eurasian Viverridae and Herpestidae was analysed in order to investigate if these features can be used to help assess their evolutionary history in the absence of fossils. The pattern that emerges in this study is that the species of Viverridae and Herpestidae do not generally overlap in ecomorphology where they overlap geographically, which indicates considerable competitive interactions between the families in both Africa and Eurasia.

Mitochondria are eukaryotic cellular organelles responsible for power-generation, believed to have come into existence by an endo-symbiontic event where a bacterial cell was incorporated by an un-specified "proto-eukaryote". Phylogenetic analysis have shown that the mitochondrial ancestor was most related to present-day alpha-proteobacteria, although the exact nature of the mitochondrial progenitor remains disputed. In this work, I have used phylogenetic and other methods to investigate the identity of the organism giving rise to mitochondria, by analysing the evolutionary history of select proteins, the events where they have been transfered to the eukaryotic nucleus, and the time-point of mitochondrial establishment. In addition, a search for mitochondrially related organisms in the ocean metagenome was performed, in the hope that something more related to the mitochondrial progenitor than anything previously identified could be found. Previous analysis have shown that a large fraction of mitochondrial proteins does indeed trace their descent to the alpha-proteobacteria, but I found that the amino-acyl tRNA-synthetases display more general bacterial descent, making it likely that these proteins are of a different origin from the mitochondria themselves. While the synthetases are encoded on the nuclear genome, most mitochondria still posses most of the tRNA on their own genomes. In the cases where the tRNA has been lost from the mitochondrial genome, I found that the probability of loss correspond to the evolutionary history of their synthetase. The ocean metagenome represents an order of magnitude more data than previously available, making it suitable for improving the analyses dealing with mitochondrial placement. This large of amount of data was utilised to improve the phylogenetic analyses, showing that previous works might have suffered from artefacts inflating the support for placement of mitochondria with a specific alpha-proteobacterial group. Eukaryotic/mitochondrial radiation was shown to be as old, or older, than radiation of extant alpha-proteobacteria, casting doubt on previous analysis identifying a specific alpha-proteobacterial group as the mitochondrial ancestor.