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Thematic program: Mathematical Biology
March 4 - June 14, 2013 Lyon, France |
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Evolutionary biology > Posters
Abstracts of the posters
Title : "Evolutionary rescue of a viral population via drug resistance"
Abstract : “Evolutionary rescue” is a term coined in the context of conservation biology, to describe the situation in which genetic adaptation prevents extinction of a population in a novel or changing environment. The emergence of drug resistance in pathogens has been recognized as an example of evolutionary rescue, but research in conservation and medical applications has been largely disconnected. The relationships between mathematical models developed on each side have thus hardly been explored. Here, we briefly compare theoretical approaches to scenarios in which extinction or rescue may occur. We go into a more detailed description of a model of viral dynamics within a host undergoing drug treatment (Alexander & Bonhoeffer 2012, Epidemics 4:187-202). The probability of emergence of resistance (i.e. rescue), from either standing genetic variation (existing before treatment begins) or de novo mutation (occurring after treatment begins), is derived. We compare these results to those obtained under a population genetics model more closely connected to the conservation literature (Martin et al. 2012, Phil. Trans. R. Soc. B 368:20120088). The key results turn out to fit within a common mathematical formulation, highlighting the similarities between models derived with different applications in mind. We suggest that this case is indicative of the potential for fruitful exchange between conservation biological and medical communities tackling similar, challenging theoretical problems.
Title : "Front blocking and propagation in cylinders with varying cross section"
Abstract : We consider a bistable reaction diffusion equation in an infinite cylinder with varying cross section and we investigate the existence of propagation phenomena (possibly partial propagation) or on the contrary of blocking phenomena depending on the geometry of the domain. These problems are of interest in different fields of study such as population dynamics and medicine, to model for instance the existence of Cortical Spreading Depression in the brain. We consider here three different cases, one when the diameter of the cross section decreases, another when the diameter increases and lastly the case of a progressive change in the geometry and prove in each case the existence of a propagation or blocking phenomenon.
Title : "A kinetic Fisher-KPP equation : traveling waves and front acceleration"
Abstract : We analyze a kinetic model which describes the same situation as the Fisher-KPP equation. Thus, this model describes particles moving according to a velocity-jump process, and proliferating thanks to a kinetic reaction term of monostable type. We study existence and stability of traveling wave solutions. It turns out that we exhibit a critical speed for this existence, when the velocity space is bounded. Moreover, we recover the standard Fisher-KPP speed in the parabolic limit. The constructed fronts of minimal speed are linearly stable in suitable weighted L2 spaces. We also investigate the case of an unbounded velocity space and we are able to conclude that not only traveling waves can not exist, but also the equation induces an accelerated propagation behavior according to a scaling law, which depends on the stationnary Maxwellian.
Title : "An age-structured within-host model for multi-strain malaria infections"
Abstract : In this paper we propose an age-structured malaria within-host model taking into account multi-strains interaction. We provide a global analysis of the model depending upon some threshold T_0. When T_0<=1, then the disease free equilibrium is globally asymptotically stable and the parasites are cleared. On the contrary if T_0>1, the model exhibits the competition exclusion principle. Roughly speaking, only the strongest strain, according to a suitable order, survives while the other strains go to extinct. Under some additional parameter conditions we prove that the endemic equilibrium corresponding to the strongest strain is globally asymptotically stable.
Title : "Consequences of heterogeneity for Wolbachia invasion"
Abstract : The maternally transmitted bacterial symbiont Wolbachia is known to modulate many life- history traits of its hosts, such as lifespan, fecundity, cytoplasmic incompatibility (CI) and resistance to pathogens. Wolbachia invasion of a resident population without Wolbachia requires a threshold initial frequency, determined by fitness costs and the advantages of CI. When Wolbachia-mediated effects include resistance to pathogens, this threshold is reduced, making invasion easier. In this study we model invasion by Wolbachia when symbiont- mediated effects are heterogeneously distributed. We link invasion thresholds derived from deterministic models with stochastic simulations of invasion. We explore systematically consequences of heterogeneity for the threshold of invasion, its speed and the equilibrium population size.
Title : "Front dynamics in a two-species competition model driven by Lévy flights"
Abstract : A number of recent studies suggest that many biological species follow a Lévy random walk in their search for food. Such a strategy has been shown to be more efficient than classical Brownian motion when resources are scarce. However, current diffusion-reaction models used to describe many ecological systems do not account for the superdiffusive spread of populations due to Lévy flights. We have developed a model to simulate the spatial spread of two species competing for the same resources and driven by Lévy flights. The model is based on the Lotka-Volterra equations and has been obtained by replacing the second-order diffusion operator by a fractional-order one. Theoretical developments and numerical simulations show that fractional-order diffusion leads to an exponential acceleration of the population fronts and a power-law decay of the fronts’ leading tail. Depending on the skewness of the fractional derivative, we derive catch-up conditions for different types of fronts. Our results indicate that second-order diffusion-reaction models are not well-suited to simulate the spatial spread of biological species that follow a Lévy random walk as they are inclined to underestimate the speed at which these species propagate.
References:
Title : "Quantifying outbreak thresholds, and effect of susceptible depletion on pathogen emergence"
Abstract : The evolutionary emergence and invasion of new pathogens causes a considerable health risk to human populations, and is a major focus of current research. We first outline criteria to determine how many infected individuals are needed to guarantee emergence in a fully susceptible population (what we call the outbreak threshold). We find that, if the pathogen has a reproductive ratio R0, on the order of 1/Log(R0) infected individuals are needed to prevent stochastic fade-out. Secondly, we investigate the case where an initial strain spreading, with R0 close to one, can mutate into a faster-spreading strain. We show how to formulate results for the probability of emergence of the mutated strain, which take into account the ongoing depletion of the susceptible population by the first strain. Even if the first strain's R0 is close to one, ongoing susceptible depletion has a drastic effect on subsequent pathogen emergence. We highlight this fact by applying our model to the re-emergence of Chikungunya virus on La Réunion island.
Title : "Clonal evolution in the hematopoietic system"
joint work with Anthony D. Ho (Medical Clinic V, University of Heidelberg) and Anna Marciniak-Czochra (Interdisciplinary Center for Scientific Computing and Bioquant Center, University of Heidelberg)
Abstract : The hematopoietic (blood forming) system is maintained by a small population of hematopoietic stem cells (HSCs) giving rise to all types of mature blood cells. Over the last decade evidence has accumulated that the HSC compartment is heterogeneous and that its composition might change over time. Similar phenomena hold for some clonal hematological malignancies.
Based on models of blood formation and leukemias we propose a cell population model of the hematopoietic system that is structured by crucial cell traits and regulated by nonlinear negative feedback. This model allows to investigate the impact of cellular properties such as proliferation and differentiation behavior on dynamics of clonal evolution and selection.
Since the model is built based on biologically motivated parameters, modeling results can be easily interpreted in the biomedical context.
Title : "Sympatric speciation by optimal specialisation".
Abstract : Sympatric speciation is one of the most controversial and intriguing concepts in evolutionary biology, because in contrast to allopatric speciation it happens without geographic isolation (Via:2001, Bolnick:2007, Bird:2012). Sympatric speciation can reduce resource competition (Bolnick:2007) via niche partitioning. It stimulates disruptive selection and assortative mating, leading to reproductive isolation, e.g., by divergent mate timing or habitat choice (Bolnick:2007). However, a concrete mechanism which allows sympatric speciation has been difficult to pin down. Here we show that specialisation can lead to sympatric speciation, provided that sufficient ability is retained to eat the less-preferred prey. We define a specialisation trade-off between the improved ability to eat the preferred prey (gain) and reduced ability to eat the less-preferred prey (cost). We find that the degree of specialisation, and hence interaction strength (Emmerson:2004), strongly depends on specialisation cost and that high costs can prevent speciation. Low and intermediate specialisation costs show disruptive selection and create two niches via resource partitioning. Our model can generate a wide range of specialisation strengths, from generalists to specialists, and associated interaction strengths (Emmerson:2004).
Title : "Phenotypic evolution of hermaphrodites"
Abstract : We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes mating process of individuals with or without self-fertilization phenomena. By increasing the number of individuals to infinity we obtain a non-linear transport equation, which describes the evolution of distribution densities of phenotype. Existence of one-dimensional attractor is proved and the formula for the density of phenotype in the limiting (asymptotic) population is derived in some particular case. |
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