Evolutionary games on graphs and the speed of the evolutionary process

In this paper, we investigate evolutionary games with the invasion process updating rules on three simple non-directed graphs: the star, the circle and the complete graph. Here, we present an analytical approach and derive the exact solutions of the stochastic evolutionary game dynamics. We present formulae for the fixation probability and also for the speed of the evolutionary process, namely for the mean time to absorption (either mutant fixation or extinction) and then the mean time to mutant fixation. Through numerical examples, we compare the different impact of the population size and the fitness of each type of individual on the above quantities on the three different structures. We do this comparison in two specific cases. Firstly, we consider the case where mutants have fixed fitness r and resident individuals have fitness 1. Then, we consider the case where the fitness is not constant but depends on games played among the individuals, and we introduce a ‘hawk–dove’ game as an example

Models of kleptoparasitism on networks: the effect of population structure on food stealing behaviour

The behaviour of populations consisting of animals that interact with each other for their survival and reproduction is usually investigated assuming homogeneity amongst the animals. However, real populations are non-homogeneous. We focus on an established model of kleptoparasitism and investigate whether and how much population heterogeneities can affect the behaviour of kleptoparasitic populations. We consider a situation where animals can either discover food items by themselves or attempt to steal the food already discovered by other animals through aggressive interactions. Representing the likely interactions between animals by a network, we develop pairwise and individual-based models to describe heterogeneities in both the population structure and other individual characteristics, including searching and fighting abilities. For each of the models developed we derive analytic solutions at the steady state. The high accuracy of the solutions is shown in various examples of populations with different degrees of heterogeneity. We observe that highly heterogeneous structures can significantly affect the food intake rate and therefore the fitness of animals. In particular, the more highly connected animals engage in more conflicts, and have a reduced food consumption rate compared to poorly connected animals. Further, for equivalent average level of connectedness, the average consumption rate of a population with heterogeneous structure can be higher

Evolutionary models in structured populations

Evolutionary dynamics have been traditionally studied in infinitely large homogeneous populations where each individual is equally likely to interact with every other individual. However, real populations are finite and characterised by complex interactions among individuals. In this work, the influence of the population structure on the outcome of the evolutionary process is explored. Through an analytic approach, this study first examines the stochastic evolutionary game dynamics following the update rules of the invasion process, an adaptation of the Moran process, on finite populations represented by three simple graphs; the complete graph, the circle and the star graph. The exact formulae for the fixation probability and the speed of the evolutionary process under different conditions are derived, and the effect of the population structure on each of these quantities is studied. The research then considers to what extent the change of the strategy update rules of the evolutionary dynamics can affect the evolutionary process in structured populations compared to the process in homogeneous well-mixed populations. As an example, the evolutionary game dynamics on the extreme heterogeneous structure of the star graph is studied analytically under different update rules. It is shown that in contrast to homogeneous populations, the choice of the update rules might be crucial for the evolution of a non-homogeneous population. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. This work introduces an effective method for the approximation of the evolutionary process in populations with a complex structure. Another component of this research work involves the use of game theory for the modelling of a very common phenomenon in the natural world. The models developed examine the evolution of kleptoparasitic populations, foraging populations in which animals can steal the prey from other animals for their survival. A basic game-theoretical model of kleptoparasitism in an infinite homogeneous well-mixed population is extended to structured populations represented by different graphs. The features of the population structure that might favour the appearance of kleptoparasitic behaviour among animals are addressed. In addition, a game-theoretical model is proposed for the investigation of the ecological conditions that encourage foraging animals to share their prey, a very common behaviour occurring in a wide range of animal species

Evolutionary models in structured populations

Evolutionary dynamics have been traditionally studied in infinitely large homogeneous populations where each individual is equally likely to interact with every other individual. However, real populations are finite and characterised by complex interactions among individuals. In this work, the influence of the population structure on the outcome of the evolutionary process is explored. Through an analytic approach, this study first examines the stochastic evolutionary game dynamics following the update rules of the invasion process, an adaptation of the Moran process, on finite populations represented by three simple graphs; the complete graph, the circle and the star graph. The exact formulae for the fixation probability and the speed of the evolutionary process under different conditions are derived, and the effect of the population structure on each of these quantities is studied. The research then considers to what extent the change of the strategy update rules of the evolutionary dynamics can affect the evolutionary process in structured populations compared to the process in homogeneous well-mixed populations. As an example, the evolutionary game dynamics on the extreme heterogeneous structure of the star graph is studied analytically under different update rules. It is shown that in contrast to homogeneous populations, the choice of the update rules might be crucial for the evolution of a non-homogeneous population. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. This work introduces an effective method for the approximation of the evolutionary process in populations with a complex structure. Another component of this research work involves the use of game theory for the modelling of a very common phenomenon in the natural world. The models developed examine the evolution of kleptoparasitic populations, foraging populations in which animals can steal the prey from other animals for their survival. A basic game-theoretical model of kleptoparasitism in an infinite homogeneous well-mixed population is extended to structured populations represented by different graphs. The features of the population structure that might favour the appearance of kleptoparasitic behaviour among animals are addressed. In addition, a game-theoretical model is proposed for the investigation of the ecological conditions that encourage foraging animals to share their prey, a very common behaviour occurring in a wide range of animal species.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

How Can Viral Dynamics Models Inform Endpoint Measures in Clinical Trials of Therapies for Acute Viral Infections?

Acute viral infections pose many practical challenges for the accurate assessment of the impact of novel therapies on viral growth and decay. Using the example of influenza A, we illustrate how the measurement of infection-related quantities that determine the dynamics of viral load within the human host, can inform investigators on the course and severity of infection and the efficacy of a novel treatment. We estimated the values of key infection-related quantities that determine the course of natural infection from viral load data, using Markov Chain Monte Carlo methods. The data were placebo group viral load measurements collected during volunteer challenge studies, conducted by Roche, as part of the oseltamivir trials. We calculated the values of the quantities for each patient and the correlations between the quantities, symptom severity and body temperature. The greatest variation among individuals occurred in the viral load peak and area under the viral load curve. Total symptom severity correlated positively with the basic reproductive number. The most sensitive endpoint for therapeutic trials with the goal to cure patients is the duration of infection. We suggest laboratory experiments to obtain more precise estimates of virological quantities that can supplement clinical endpoint measurements

Methods for approximating stochastic evolutionary dynamics on graphs

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the evolutionary process. However, for more complicated heterogeneous structures, computationally intensive methods are required such as individual-based stochastic simulations. By adapting methods from statistical physics, including moment closure techniques, we first show how to derive existing homogenised pair approximation models and the exact neutral drift model. We then develop node-level approximations to stochastic evolutionary processes on arbitrarily complex structured populations represented by finite graphs, which can capture the different dynamics for individual nodes in the population. Using these approximations, we evaluate the fixation probability of invading mutants for given initial conditions, where the dynamics follow standard evolutionary processes such as the invasion process. Comparisons with the output of stochastic simulations reveal the effectiveness of our approximations in describing the stochastic processes and in predicting the probability of fixation of mutants on a wide range of graphs. Construction of these models facilitates a systematic analysis and is valuable for a greater understanding of the influence of population structure on evolutionary processes

The development of a stochastic mathematical model of Alzheimer's disease to help improve the design of clinical trials of potential treatments

Alzheimer’s disease (AD) is a neurodegenerativ e disorder characterised by a slow progres- sive deterioration of cognitive capacity. Drugs are urgently needed for the treatment of AD and unfortunately almost all clinical trials of AD drug candidates have failed or been discon- tinued to date. Mathematical, computational and statistical tools can be employed in the construction of clinical trial simulators to assist in the improvement of trial design and enhance the chances of success of potential new therapies. Based on the analysis of a set of clinical data provided by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) we developed a simple stochastic mathematical model to simulate the development and pro- gression of Alzheimer’s in a longitudinal cohort study. We show how this modelling frame- work could be used to assess the effect and the chances of success of hypothetical treatments that are administered at different stages and delay disease development. We demonstrate that the detection of the true efficacy of an AD treatment can be very challeng- ing, even if the treatment is highly effective. An important reason behind the inability to detect signals of efficacy in a clinical trial in this therapy area could be the high between- and within-individual variability in the measuremen t of diagnostic markers and endpoints, which consequently results in the misdiagno sis of an individual’s disease state

Using Clinical Trial Simulators to Analyse the Sources of Variance in Clinical Trials of Novel Therapies for Acute Viral Infections.

BACKGROUND:About 90% of drugs fail in clinical development. The question is whether trials fail because of insufficient efficacy of the new treatment, or rather because of poor trial design that is unable to detect the true efficacy. The variance of the measured endpoints is a major, largely underestimated source of uncertainty in clinical trial design, particularly in acute viral infections. We use a clinical trial simulator to demonstrate how a thorough consideration of the variability inherent in clinical trials of novel therapies for acute viral infections can improve trial design. METHODS AND FINDINGS:We developed a clinical trial simulator to analyse the impact of three different types of variation on the outcome of a challenge study of influenza treatments for infected patients, including individual patient variability in the response to the drug, the variance of the measurement procedure, and the variance of the lower limit of quantification of endpoint measurements. In addition, we investigated the impact of protocol variation on clinical trial outcome. We found that the greatest source of variance was inter-individual variability in the natural course of infection. Running a larger phase II study can save up to $38 million, if an unlikely to succeed phase III trial is avoided. In addition, low-sensitivity viral load assays can lead to falsely negative trial outcomes. CONCLUSIONS:Due to high inter-individual variability in natural infection, the most important variable in clinical trial design for challenge studies of potential novel influenza treatments is the number of participants. 100 participants are preferable over 50. Using more sensitive viral load assays increases the probability of a positive trial outcome, but may in some circumstances lead to false positive outcomes. Clinical trial simulations are powerful tools to identify the most important sources of variance in clinical trials and thereby help improve trial design

The importance of endpoint selection: how effective does a drug need to be for success in a clinical trial of a possible Alzheimer's disease treatment?

To date, Alzheimer's disease (AD) clinical trials have been largely unsuccessful. Failures have been attributed to a number of factors including ineffective drugs, inadequate targets, and poor trial design, of which the choice of endpoint is crucial. Using data from the Alzheimer's Disease Neuroimaging Initiative, we have calculated the minimum detectable effect size (MDES) in change from baseline of a range of measures over time, and in different diagnostic groups along the AD development trajectory. The Functional Activities Questionnaire score had the smallest MDES for a single endpoint where an effect of 27% could be detected within 3 years in participants with Late Mild Cognitive Impairment (LMCI) at baseline, closely followed by the Clinical Dementia Rating Sum of Boxes (CDRSB) score at 28% after 2 years in the same group. Composite measures were even more successful than single endpoints with an MDES of 21% in 3 years. Using alternative cognitive, imaging, functional, or composite endpoints, and recruiting patients that have LMCI could improve the success rate of AD clinical trials