09:00 to 10:00 A Hastings ([UC Davis])The dependence of the design of marine reserve networks on dispersal behaviourSession: Immunology, Ecology and Epidemiology (main themes) I will describe how the design of marine reserve networks depends on different descriptions of dispersal, focussing on designs based on fishing concerns and on sustatinability. The mathematical tools will be developed from integro-difference equations, and the sensivity and robustness of results to changes in the underlying assumptions will be emphasized. INI 1 10:00 to 11:00 HCJ Godfray ([Imperial])Age-structured models of insect natural-enemy interactionsSession: Immunology, Ecology and Epidemiology (main themes) INI 1 11:00 to 11:30 CoffeeSession: Immunology, Ecology and Epidemiology (main themes) 11:30 to 12:30 MA Lewis ([Utah])Territorial pattern formation through scent markingSession: Immunology, Ecology and Epidemiology (main themes) Social carnivores, such as wolves and coyotes, have distinct and well-defined home ranges. During the formation of these home ranges scent marks provide important cues regarding the use of space by familiar and foreign packs. In this talk I will propose a mechanism for territorial pattern formation through interactions with familiar scent marks. Rules for the behavior of individuals are translated to a partial differential equation (PDE) model. Analysis of this PDE model, through use application an energy method', shows the formation of distinct territories with abrupt edges. Connections will be made to earlier ecological models for aggregating populations (eg. Turchin 1989, Journal of Animal Ecology (58): 75-100). The mechanism proposed here differs from previous models for territorial pattern formation which have required a den site as the organizational center around which the territory is formed. Thus the model explains field observations of well-defined home ranges in the absence of den sites, and even in the absence of surrounding packs. INI 1 12:30 to 13:30 Lunch at the Centre for Mathematical ScienceSession: Immunology, Ecology and Epidemiology (main themes) 14:30 to 15:30 Masting of forest trees - intermittent and synchronisedSession: Immunology, Ecology and Epidemiology (main themes) 1. Many trees in mature forests, including beaches and oaks, show intermittent reproduction (masting). Intensive flowering and seed production occur only once in several years, often synchronized over a long distance. The reserve of a tree is affected by the flowering activity of other individuals in the same forest because successful fruit production requires pollen produced by other individuals. We study a coupled map model for the dynamics of energy reserve of individuals: a single tree grows in each site of a 2-dimensional finite lattice. 2. Without pollen limitation, trees in the forest show independent chaotic fluctuation. Coupling of trees via pollen exchange results in reproduction being synchronized partially or completely over the forest. When the coupling is global, we find perfectly synchronized periodic reproduction, synchronized reproduction with a chaotic time series, clustering phenomena, and chaotic reproduction of trees without synchronization over individuals. There are many parameter windows in which synchronized reproduction of trees show a stable periodic fluctuation. For perfectly synchronized forests, we can calculate all the Lyapunov exponents analytically. They shows that synchronized reproduction of trees can occur only if trees flower at low (but positive) levels in a significant fraction of years, resulting in small fruit sets due to the shortage of outcross pollen. 3. Next, we study a coupled map lattice in which the pollen availability for a tree is the average flowering intensity within its local neighborhood. Analysis of dynamic spatial covariance shows that strong synchronization of tree reproduction can develop over the whole forest that may be orders of magnitude larger than the distance of direct pollen exchange between trees. The fluctuation is close to a cycle of period 2. In addition, non-uniform spatial patterns are generated, but the enhanced spatial covariance caused by the spatial heterogeneity is restricted to a short range, only a few times larger than the spatial range of direct interaction. When pollen exchange occurs beyond the nearest neighbors, the local spatial pattern becomes proportionalily larger but the condition for synchronization of the whole forest and its magnitude are the same as the case with the nearest neighbor pollen exchange. When a fraction of seeds are sired by globally dispersed pollen and the rest are by local pollen, the long-range synchronization can occur for a wide parameter region, and trees may engage in a fluctuation with masting interval longer than 2. INI 1 15:30 to 16:00 TeaSession: Immunology, Ecology and Epidemiology (main themes) 19:00 to 00:00 Dinner at Wolfson Court (Residents only)Session: Immunology, Ecology and Epidemiology (main themes)
 10:00 to 11:00 Extensive MHC polymorphism requires frequency-dependent selection by coevolving pathogensSession: Immunology, Ecology and Epidemiology (main themes) There are ample examples of pathogens adapting towards evasion of immune responses. A well-known example commonly thought to reflect adaptation of hosts to pathogens is the polymorphism of major histocompatibility (MHC) molecules. MHC molecules play a key role in cellular immune responses. The population diversity of MHC molecules is extremely large: for some MHC loci, over one hundred different alleles have been identified. The mechanisms behind the selection for MHC polymorphism have been debated for over three decades. A commonly held view is that MHC polymorphism is due to selection favoring heterozygosity. It has been argued that selection for heterozygosity alone cannot explain the large MHC diversity observed in nature, and that frequency-dependent selection'' is required. We simulation evolution by developing a genetic algorithm in which hosts and pathogens co-evolve. The analysis demonstrates that selection involving rapid evolution of pathogens can account for a much larger MHC diversity than selection for heterozygosity alone can. INI 1 11:00 to 11:30 CoffeeSession: Immunology, Ecology and Epidemiology (main themes) 11:30 to 12:30 Genetic, dynamic and functional definition of the efficency of the anti-viral T cell responseSession: Immunology, Ecology and Epidemiology (main themes) In infection with the human T cell leukaemia virus (HTLV-I), there is a powerful T cell immune response to one of the viral proteins, called Tax. We have obtained evidence that the strength of this immune response determines the "set point" of HTLV-I load in the blood, which can vary between HTLV-I-infected people by more than 1000 times, but is constant in each infected person over time. Our evidence is derived from experimental data on genetic variation in the host and in HTLV-I, cellular immunology, and DNA expression microarrays. We have used dynamical approaches a) to reconcile the evidence of persistent HTLV-I replication with the observed conservation of HTLV-I sequence; b) to suggest a reason for the apparent threshold in HTLV-I load above which many people develop chronic inflammatory diseases; c) to explain the observed variation between individuals in the frequency of anti-HTLV-I T cells, and d) to test the consequences of HTLV-I-induced T cell death on the control of HTLV-I replication. The aims of this work are to define the concept of antiviral "T cell efficiency" in genetic, dynamical and functional terms, and to test experimentally whether this "efficiency" determines the outcome of HTLV-I infection. INI 1 12:30 to 13:30 Lunch at the Centre for Mathematical ScienceSession: Immunology, Ecology and Epidemiology (main themes) 14:30 to 15:30 Word frequency distribution under the restriction avoidanceSession: Immunology, Ecology and Epidemiology (main themes) Restriction enzymes of bacteria cut the unmodified recognition sites of DNA, thereby protect bacteria from the infection by phage. This imposes a strong selective pressure on the phage genome sequences. For example, the Bacillus phage phi1 genome has much fewer restriction sequences of Bacillus restriction enzymes than their random expectations. To answer the evolution of phage genome under the selection by bacteria restriction enzymes, a simple model for the evolution of binary or nucleotide sequences is proposed. The model shows that not only the frequency of the restricted sequence itself in the genome, but also that of the other subsequences (words) will be largely deviated from the random expectations. The pattern of word frequency distribution sensitively depends on the type of restricted sequence. If the restricted sequence is of the singlet repeat type (e.g. 000), the frequency of a 3-letter word is largely explained by its Hamming distance from the restricted sequence -- the farther is the Hamming distance of the word from the restriction sequence, the more is its abundance. However, quite unexpected word frequency distribution arises if the restricted sequence is of the other type (e.g. 001 or 010). The abundance of words is largely influenced by the vulnerability to restriction of partially overlapped adjacent words. For example, when 001 is the restriction sequence, both 000 and 100 become quite rare, whose frequencies approach to 0 as the genome size increases; whereas 101, which is only one-step distant from the restricted word, becomes quite common. A new theoretical framework is proposed to explain such peculiar distribution of words under restriction avoidance, which enable us to count the exact word frequency of any word in the 'feasible' sequences. A sequence is called feasible here if it contains no restriction site in any position (i.e. the feasible sequences are that survive under a strong selection). The fraction of feasible sequences in all random sequences exponentially decays towards zero as the genome size increases (e.g. if the restriction sequence is 001, the number of feasible sequences in all binary sequences of length n equals the (n+3)rd term of Fibonatti series minus 1, which gives the fraction of feasible sequences decaying with n as (0.81)^n). In the light of these results, I discuss the optimal recognition sequence of restriction enzyme to fight against phage, and the mutation and substitution loads and the fitness landscape of phage subject to such selection pressure imposed by a restriction enzyme. INI 1 15:30 to 16:00 TeaSession: Immunology, Ecology and Epidemiology (main themes) 16:00 to 17:00 Inequalitites during life and death of T cellsSession: Immunology, Ecology and Epidemiology (main themes) T cell selection during an immune response is being increasing observed with modern techniques, eg the (specific) T cell receptor (TCR) chain useage and its diversity alters throughout an immune response, and TCR avidity for the agonist ligands undergoes distinct focusing from a primary to secondary response. We explore physiologically structured models of T cell growth and T cell death to explain these observations. We demonstrate that significant selection of T cells can occur through heterogeneous expression of cytokine receptors and competition for growth/survival cytokines. INI 1 19:00 to 00:00 Dinner at Wolfson Court (Residents only)Session: Immunology, Ecology and Epidemiology (main themes)