This thesis focuses a mathematical model from statistical mechanics called the Arboreal gas. The Arboreal gas on a graph $G$ is Bernoulli bond percolation on $G$ with the conditioning that there are no ``loops". This model is related to other models such as the random cluster measure. We mainly study the Arboreal gas and a related model on the $d$-ary wired tree which is simply the $d$-ary wired tree with the leaves identified as a single vertex. Our first result is finding a distribution on the infinite $d$-ary tree that is the weak limit in height $n$ of the Arboreal gas on the $d$-ary wired tree of height $n$. We then study a similar model on the infinite $d$-ary wired tree which is Bernoulli bond percolation with the conditioning that there is at most one loop. In this model, we only have a partial result which proves that the ratio of the partition function of the one loop model in the wired tree of height $n$ and the Arboreal gas model in the wired tree of height $n$ goes to $0$ as $n \rightarrow \infty$. This allows us to prove certain key quantities of this model is actually the same as analogues of that quantity in the Arboreal gas on the $d$-ary wired tree, under an additional assumption. / Graduate / 10000-01-01

Lemur fulvus, the brown lemur, is a cat-sized arboreal prosimian, native to Madagascar and the island of Mayotte, in the Comoro Archipelago. A social prosimian, ~ fulvus typically forms cohesive troops of from 5-15 individuals. Troop composition is usually reported to be at, or near, a 1:1 sex ratio. The problems examined in this thesis were chosen in order to address aspects of L. fulvus social dynamics that are unclear, given the depiction of L. fulvus social behaviour presented in the primate literature. What are adult males doing, in the reported absence of agonistically-determined dominance hierarchies, to gain and maintain access to estrus females? Given the breeding season behavioural changes and fluctuations exhibited by adult males (a behavioural complex here termed, "fall-fever"), how do these changes and fluctuations contribute to male L. fulvus breeding opportunities, and potential reproductive success? These questions were investigated in the study of a semi-free-ranging ~ fulvus troop during the 1984 (Northern Hemisphere) breeding season. Utilizing an extensive ethogram it was found that, contrary to previous literature on the species, hierarchical social dominance relationships are indeed present in L. fulvus social groups. Additionally, it was found that these relationships play a crucial role in the reproductive behaviour of adult males. Statistically significant variation in the behaviour of the focal males is presented for seven inclusive behavioural categories. The picture of male L. fulvus reproductive behaviour that emerges from these considerations is then compared to the view derived from previous research on the species. Several amendments to our understanding of ~ fulvus social behaviour are suggested. An attempt is also made to place ~ fulvus in the socioecological categorizations of several authors. / Thesis / Master of Arts (MA)

This study was carried out in a woodland on the campus of University of Western Sydney at Richmond, Australia to investigate seasonal effects and recovery speed of arboreal arthropods after disturbance. Twenty one pairs of Melaleuca linariifolia Sm. trees were sampled using insecticide spraying in a log2 nine period sequence (1-32) of weeks supplemented by additional samples to incorporate seasonal (weeks 24 and 48) and annual (week 52) samples. Using species accumulation curves, it was found that four collectors provided a reasonable representation of a tree's fauna and that a single tree does not provide a representative sample of the arthropod fauna found on trees of this species in the study area. The application of richness and evenness indices in different seasons showed significant changes in diversity. It was clear from the findings of the study that careful attention needs to be paid to experimental design. Under replication is the normal situation in previous studies and the effects of location, season and disturbance are all critical factors affecting the estimation of diversity. / Doctor of Philosophy (PhD)

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Gap crossing is a regular locomotor activity for arboreal animals. The distance between branches likely plays a role in determining whether an animal is capable of crossing a given gap, and what locomotor behavior it uses to do so. Yet, despite the importance of gap distance as a physical parameter influencing gap crossing behavior, the precise relationships between gap distance and movement kinematics have been explored in only a very small number of species. One particularly interesting group of arboreal inhabitants are the flying snakes (Chrysopelea). This species is able to use a dynamic "J-loop" movement to launch its glides, but it is not known whether it is also capable of using such jumps to cross smaller gaps between tree branches. This dissertation addresses this knowledge gap, and investigates the influence of gap distance on crossing behavior and kinematics in three closely-related species of snake: Chrysopelea paradisi, a species of flying snake, and two species from the sister genus, Dendrelaphis, neither of which can glide. Chapter 2 is a literature review of the biomechanics of gap crossing, specifically focusing on the role played by gap distance, and establishes the context for the rest of the work. Chapter 3 presents a detailed study of how increasing gap size influences the behavior and kinematics of gap crossing in C. paradisi, showing that this species uses increasingly dynamic movements to cross gaps of increasing size. Chapter 4 explores the same relationships between gap size and kinematics in D. punctulatus and D. calligastra, revealing remarkable similarities between the three species, suggesting the possibility that dynamic gap crossing may have evolved prior to gliding in this clade. Finally, chapter 5 addresses the role played by gap distance in limiting the non-dynamic, cantilever movements used by these species to cross small gaps, comparing observed stopping distances to those predicted by various torque-related limitations. / Doctor of Philosophy / To successfully cross a gap, an animal must be able to reach or jump from one side to the other. Animals who live in trees must do this quite frequently, as they live among the branches and there are often not connected paths from one place to another. But we don't know very much about how the distance between two structures (the "gap distance") affects the ways an animal moves between them. In this dissertation, I explore how gap distance changes the way a few special species of snakes cross a gap. The species I am studying are special because one species, the paradise tree snake, can glide. Because this 'flying' snake launches its glides by doing a big jump, it is possible that the snake can also jump between tree branches, but this question has never been examined before. We also don't know how the ability to do big jumps evolved, so I studied how distance affects the way two very closely related species of snake, the common tree snake and the northern tree snake, cross gaps. By looking at all of these species, we can understand more about what kinds of behavior are specific to the flying snakes, and which are present in related species. Finally, I also explore how gap distance limits the way the snakes cross gaps when they are not jumping. When the snakes do not jump, they have to hold themselves out straight off the end of a branch. This requires a lot of muscular effort, which means they can't go as far. The fact that the non-jumping behavior is distance-limited might help explain why the snakes need to jump. Altogether, the projects in this study help us understand how gap distance influences what behavior an animal chooses to cross the gap, and increases our knowledge of how flying snakes and their relatives cross gaps in particular.

Avant la fondation de Rome, le chêne, le figuier et le cornouiller faisaient partie des essences d’arbres qui poussaient sur le territoire de la cité. Dans l’histoire des origines de Rome, le chêne d’Enée présageait déjà des destinées de la ville auxquelles donnera corps le figuier du Lupercal et celui du Comitium. Cependant, ce fut le cornouiller qui singularisa la création et l’élection de Rome, investie d’une mission civilisatrice universelle. La Cornus fut un des signes matériels des significations politique, sociale et religieuse des actes de Romulus, pourvoyeur de richesses, guerrier, et organisateur qui avait su transformer un lieu à demi forestier en une ville. Ces rôles, assumés par Romulus, répondent au schéma ternaire dégagé par G. Dumézil. Trois symboliques communes aux trois arbres se croisent : la notion de la constitution d’un peuple particulier dont les origines résultaient de la combinaison de peuples grecs et/ou italiques ; l’idée que ces arbres légendaires avaient été impliqués dans des actes de fondation ; enfin le rapport étroit entre une Rome mythique et la Rome des temps historiques que les arbres créent. La tradition sur la fondation de Rome qui a subi l’influence de la Grèce, s’est approprié cette ascendance pour en faire une histoire proprement romaine. Du chêne qui signifiait pour le Troyen Enée le terme de son voyage, puis du figuier, qui avait contribué à sauver Romulus en abritant la louve, jusqu’au cornouiller, poussé en haut du Palatin, les trois arbres mythiques ont symbolisé le lieu de la naissance de Rome et sont restés aux temps historiques des acteurs d’une civilisation urbanisée, regroupée en un seul peuple romain. / Before the founding of Rome by Romulus, oak, fig tree and dogwood were part of various tree species growing on the territory of Rome. In the history of the origins of the city, the oak of Aeneas already presaged the destinies of Rome to whom the lupercal fig tree will give body, it was the dogwood which illustrated the creation and election of Rome. The tree, or rather the shrub, was a material sign for political, social and religious meanings of the acts of Romulus in his threefold role as provider of wealth by the gathering of heterogeneous people, warrior who was given a place surrounded by forests, a veritable territory centered on a city, Rome, and deified King. Three symbolic notions common to the three founding trees crosses : the notion of an origin of the territory and the people that was based on an ancient pre-Roman, Greek and/or Italic ; the idea that these legendary trees had been involved in acts of fundation and creation of a people ; finally the close relationship between a mythical Rome and that of historical times, according to the tripartite scheme established by G. Dumézil. The Tradition on the founding of Rome was not exempt from Greek influence but had appropriated this Greek ancestry to make a proper Roman history. The oak, which meant the end of Trojan Aeneas journey, the fig tree which, with the wolf, had helped to save Romulus and the dogwood, pushed at the top of the Palatine Hill, in the middle of Roma Quadrata, the three trees symbolized the place of the birth of Rome, a city that gave a town and a civilization to a grouping of diverse populations before scattered in the woods.

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