Browsing by Subject "adaptive dynamics"
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(2020)The Hawk-Dove game has been used as a model of situations of conflict in diverse fields as sociology, politics, economics as well as animal behavior. The iterated Hawk-Dove game has several rounds with payoff in each round. The thesis is about a version of the iterated Hawk-Dove game with the additional new feature that each player can unilaterally decide when to quit playing. After quitting, both players return to the pool of temporally inactive players. New games can be initiated by random pairing of individuals from within the pool. The decision of quitting is based on a rule that takes into account the actions of oneself or one's opponent, or on the payoffs received during the last or previous rounds of the present game. In this thesis, the quitting rule is that a player quits if its opponent acts as a Hawk. The additional feature of quitting dramatically changes the game dynamics of the traditional iterated Hawk-Dove game. The aim of the thesis is to study these changes. To that end we use elements of dynamical systems theory as well as game theory and adaptive dynamics. Game theory and adaptive dynamics are briefly introduced as background information for the model I present, providing all the essential tools to analyze it. Game theory provides an understanding of the role of payoffs and the notion of the evolutionarily stable strategies, as well as the mechanics of iterated games. Adaptive dynamics provides the tools to analyze the behavior of the mutant strategy, and under what conditions it can invade the resident population. It focuses on the evolutionary success of the mutant in the environment set by the current resident. In the standard iterated Hawk-Dove game, always play Dove (all-Dove) is a losing strategy. The main result of my model is that strategies such as all-Dove and mixed strategy profiles that are also not considered as worthwhile strategies in the standard iterated Hawk-Dove game can be worthwhile when quitting and the pool are part of the dynamics. Depending on the relations between the payoffs, these strategies can be victorious.
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(2017)Recent biomathematical literature has suggested that, under the assumption of a trade-off between replication speed and fidelity, a pathogen can evolve to more than one optimal mutation rate. O'Fallon (2011) presents a particularly compelling case grounded in simulation. In this thesis, we treat the subject analytically, approaching it through the lens of adaptive dynamics. We formulate a within-host model of the pathogen load starting from assumptions at the genomic level, explicitly accounting for the fact that most mutations are deleterious and stunt growth. We single out the pathogen's mutation probability as the evolving trait that distinguishes strains from one another. Our between-host dynamics take the form of an SI model, first without superinfection and later with two types of non-smooth superinfection function. The pathogen's virulence and transmission rate are functions of the within-host equilibrium pathogen densities. In the case of our mechanistically defined superinfection function, we uncover evolutionary branching in conjunction with two transmission functions, one a caricatural (expansion) example, the other a more biologically realistic (logistic) one. Because of the non-smoothness of the mechanistic superinfection function, our branching points are actually one-sided ESSs à la Boldin and Diekmann (2014). When branching occurs, two strains with different mutation probabilities both ultimately persist on the evolutionary timescale.
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(2023)Pathogens are everywhere in nature, so organisms have developed various defense mechanisms in order to defend themselves against the pathogens. Two of the defense mechanisms are known as resistance and tolerance. Resistance describes the host's ability to avoid being infected by the pathogen, while tolerance describes the host's ability to reduce the fitness loss caused by the infection. We assume that investing into resistance reduces the transmission rate of the pathogens and investing into tolerance reduces the host's virulence. Developing the defense mechanisms is costly to the host. In this thesis, we assume that the resources invested into resistance and tolerance are taken away from the host's fecundity. The independent but simultaneous evolution of resistance and tolerance is modeled with an SIS model. The model is studied with the methods of adaptive dynamics. We concentrate on finding continuously stable strategies, which serve as the evolutionary end points for the population. We study the varying ecological parameters to determine which strategies are optimal for the host in different environments. We find that for low values of transmission rate, the hosts favor resistance over tolerance. When the transmission rate increases, resistance is traded for tolerance and the host benefits more from high tolerance. Low values of virulence result in tolerance being favored over resistance. Increasing virulence leads to a change in the defense mechanism as for high values of virulence investing into resistance is more beneficial to the host. The same holds for recovery rate, as tolerance is favored for low values of recovery rate and changed for resistance when the recovery rate increases. Patterns and associations between resistance and tolerance are also studied. Positive correlation between resistance and tolerance is found with low values of transmission rate, low and high values of virulence and high values of recovery rate. Resistance and tolerance correlate negatively with high values of transmission rate, intermediate values of virulence and low values of recovery rate.
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(2020)Within the last century humanity has grown significantly more numerous and more globally connected than ever before in its history. Together with the increased risks of climate change, we are more susceptible than ever to major epidemics and pandemics caused by novel zoonotic diseases. For these reasons it is not only important understand under which conditions novel pathogens are able to invade and spread in a host population but also to understand how these pathogens can be eradicated following an invasion event. In this thesis we present and study the demographic and evolutionary dynamics of a compartmental epidemiological model that includes a compartment for asymptomatic individuals, who require a second infection to become symptomatic and infectious. We show that the model exhibits a wide variety of demographic dynamical behaviour, all of which can be evolutionarily attracting configurations under simple evolutionary considerations. The model is an extreme simplification of the real world and excludes relevant information such as age and spatial structures of the population at hand. The aim of this thesis is to obtain a general understanding of how varying certain parameters on one hand allows a pathogen to invade a host population and, on the other hand, allows the host to eradicate an established pathogen, in particular, through the process of evolution.
Now showing items 1-4 of 4