Group discussion
Titles and Abstracts!
Collections of titles and abstracts for EG+ Winter School
Please find below:
- Names of speakers, titles and abstracts for the Winter School
- Zoom link for attending the talks
Organised Alphabetically
| Speaker | Title | Abstract |
|---|---|---|
| Ali Wajid | More accurate estimation of the basic reproductive ratio from epidemic incidence data using a model conditioned on major outbreaks | The basic reproductive number, R0, is a well-known quantifier of the rate of spread of an epidemic. Here we show that some methods for estimating this quantity from epidemic incidence data can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and the fact that, given the same system, some outbreaks may lead to major epidemics and some may not. Necessarily, an observed epidemic that we wish to control is a major outbreak and this amounts to an implicit conditioning for major outbreaks which leads to the issue just described. In this talk, I will present a conditioned deterministic model as a solution to this problem. |
| Bastian Frank | From nonlinear payoffs in Game theory to modelling cancer including an Allee effect | The Allee model introduced by Vito Volterra is characterised by a nonlinear per capita growth rate in contrast to the model of Verhulst (logistic equation). Revising previous work by Sigmund and Hofbauer, we propose a state-dependent payoff matrix to represent nonlinear per capita growth rates in a Game-theoretic sense of competition. Applying the model by Vito Volterra to cancer coupled with evolutionary dynamics that capture the evolving resistance against a particular treatment, we investigate instabilities explaining different treatment outcomes. |
| Broom Mark | Evolution and games on graphs | In this talk we will consider the evolutionary modelling of finite populations with a population structure represented by a graph. We start with evolution of an unstructured finite population with fixed fitnesses, then consider the same case where fitnesses depend upon game theoretical interactions. We develop these models, both fixed fitness and game theory based, to consider structured populations. We finish by considering the evolution of cooperation in such a case. In each case we consider the fixation probability, the probability of a single mutant to replace the existing resident population, and also consider fixation times |
| Broom Mark | Evolutionary models of animal groups | In this talk we consider the concept of animals groups. We discuss what we mean by a group, and look at multi-level selection where selection can happen at group and individual levels. We move on to consider specific interactions within an animal group using game-theoretical models. How do animals divide resources such as food and mating rights within groups and how do dominant individuals prevent subordinates from challenging them or leaving? We consider several models related to this .We also look into how foraging groups watch out for predators. |
| Erovenko Igor | The art and science of great presentations | We discuss the basic principles of storytelling, slide design, and delivery of presentations. |
| Erovenko Igor | A hands-on approach to ABM in structured populations | We will discuss how to construct and code stochastic simulations of complex processes in structured populations using agent-based modeling. |
| Fic Małgorzata | Collective beliefs and trust in structured populations | Collective beliefs can catalyse cooperation in a population of selfish individuals. This effect is present even when the stories that constitute the belief lack any moralising aspect. The sole fact of altering one’s perception of reality can provoke the development of cooperative behaviour. However, human populations are structured. Social and cultural identities often bias the network of interactions. Hence, we further develop this model by applying the setup assuming a heterogeneous group size and structured population. A belief frequently involves a complex system of stories. It is unlikely to appear in society spontaneously in the same way as actions can change within a generation. Consequently, we assume that actions and beliefs spread at different rates. The person perpetuating a belief might have different degrees of connectedness. We aim to understand the speed at which trust builds in a network when the myth originator has low or high connectedness and depending on network structure. In this work we explore the probability, time and the dynamics of the spread of trust and beliefs on specific network structures such as a random Erd"{o}s and R'{e}nyi network, a scale free Barabási–Albert network and a small world Watts–Strogatz network. Comparing these properties across a variety of network structures allows us to disentangle the effect of the structure, group size diversity and the evolutionary process itself on the evolution of trust and belief. |
| Gokhale Chaitanya | Ecological evolutionary games | Evolutionary game theory has been applied to various fields ranging from life’s origins to language’s evolution. Biologically, the theory might sometimes sound highly simplistic. Simplicity is, however, precisely the power of abstraction that evolutionary games offer us to understand the immense complexity of biology. Keeping games as simple as possible, we have extended themto includemultiple interactions. This simple extension allows us to include some of the overlooked complexities in Nature concerning the number of interacting partners. After presenting some general results of the extension, we will discuss the application of our theory to mutualisms and social dilemmas. Through Tribolium beetles, we will see if it even makes sense to wonder about social dilemmas. Switching to antagonism, including minor ecological dynamics, is already enough to challenge established notions of ecology, such as the Red Queen hypothesis in host-parasite coevolution. Finally, we include ecological dynamics in a classical model of social evolution to test if an existing dilemma-resolution method still holds. We report our findings in this domain and close the discussion with our efforts to understand the feedback between evolutionary games and ecological dynamics. |
| Krakovska Hana | Ultimatum Game with Social Status and Values | For decades, the ultimatum game has been used as the paradigm for studying the emergence of fairness in society. The game involves two players with asymmetric roles and a reward. The proposer’s role is to offer an arbitrary split of the reward between the players. The responder then decides whether they accept or reject the offer. If the offer is accepted, both players receive their share of the reward as proposed. If it is rejected, both players receive nothing. In the basic version of the game, narrow economic self-interest dictates that responders should accept any non-zero split. However, experimental evidence reveals a puzzle whereby responders tend to reject proposals at 10-20% of the reward and the proposers often offer 40-50%. Description of the emergence of this phenomenon is non-trivial and multiple evolutionary game-theoretical models have proposed various mechanisms to explain it. Most frequently, these models assume that the players are equally probable to be in either of the roles. In our work we explore the influence of a hierarchy in the population by introducing a status variable, with higher-status players having a higher likelihood of taking the role of proposer. We will present two evolutionary models on networks. The first model will consider a functional relation between income and status and investigate how the adaptive network and the strategies co-evolve. In the second model, the setting will be in an evolutionary hunter-gatherer context, featuring ageing agents that need to hunt together for a vital nutritional energy resource. The status variable in this model are subjective measures depending on personal values of each player. In the role assignment stage, the players will compare their attributes, evaluate them according to their values, and then mutually agree on the distribution of roles. We will present the results of both models, exploring different initial conditions and network structures. We will focus on the evolved topologies, value and status distributions and ultimatum game strategies. Under certain conditions, we can observe deviations in the strategies in this society from the predictions of narrow maximisation of payoffs in any situation. |
| Krishnan Nandakishor | Genesis of Ecto-symbiotic features based on Commensalistic Syntrophy | Eukaryogenesis and organellogenesis have been recognized as major evolutionary transitions and are subject to in-depth studies. In the endo-symbiotic theory, a eukaryotic cell is assumed to have evolved from an endo-symbiotic association between unicellular hosts and symbionts of different species (non-nucleated bacteria) which were once capable of independent existence. Acknowledging the fact that the initial interactions and conditions of cooperative behavior between free-living single-celled organisms are widely debated, we narrow our scope to a single mutation that could possibly have set off the transition to multi-species intimate associations. We hypothesize that the very first step in the evolution of such cooperative behavior could be a single mutation in a symbiont ancestor genome that results in the formation of an ecto-commensalism with its obligate host ancestor. We investigate the ecological and evolutionary stability of inter-species microbial interactions with vertical transmissions as an association based on uni-directional syntrophy. To the best of our knowledge, this is the first time that a commensalistic model based on the syntrophy hypothesis is considered in the framework of coevolutionary dynamics and invadability by a mutant phenotype into a monomorphic resident system. |
| Marcou Thomas | Cospeciation in a plant-pollinator community | Mutualism can promote diversity by increasing the speciation rate of species involved, for example by increasing ecological opportunities (niche broadening) or through partner shift. Unfortunately, empirical examples and experimentations cannot provide a full picture of the evolutionary processes and the different ecological mechanisms that can drive these speciation events. By using evolutionary game theory (EGT), more precisely Darwinian dynamics (a mix of population dynamics and evolutionary dynamics), we investigate under which conditions speciation can happen in a community initially composed of one monomorphic plant and one monomorphic pollinator species, and where both the plant and the animal have each one a trait that evolves. Plants interact with each other through intraspecific or interspecific competition (Lotka-Volterra competitive equation) and with pollinators through mutualistic interaction (similar to type II functional response). We also consider competition between pollinator individuals, as they need to share resources provided by plants (e.g., nectar). The purpose of the model is to examine speciation in this system, and, in particular, to study how many different plant and pollinator species can co-evolve in a given niche. |
| Mohamadichamgavi Javad | Replicator dynamics with strategy dependent time delays | We construct a microscopic model of the replicator dynamics with strategy dependent time delays. In such a model, new players are born from parents who interacted and received payoffs in the past. We considered small time delay approximation, showed that it has high accuracy and illustrated the effects on Snowdrift and Stag-Hunt games. We show that unlike in all previous models of evolutionary games with time delays, the presence of strategy dependent time delays changes the stationary point of the replicator dynamics. |
| Morison Christo | Using recurrence relations to distinguish healthy and tumorous growth | Simple models of healthy tissue and tumorous growth may depict these as linear and exponential, respectively. Without time series data, however, quantities other than the cell population are required to determine which growth pattern is being followed in a single snapshot of the system: hopeful candidates include variant allele frequency distributions (found from population-level data) and single cell mutational burden distribution (from cell-level data). I will present analysis and accompanying stochastic simulations performed to understand these distributions, along with some open/current problems I am tackling. |
| Pires Diogo | Evolutionary Models of Finite and Structured Populations | Evolutionary game theory has proved to be a powerful tool in understanding the self-organisation of collective behaviour. Even though initial evolutionary models with frequency-dependent fitness assumed infinite populations, the interest in finite population models has grown to establish its own methods and show their particularities. Firstly, the size of a finite population has crucial effects on the stability of strategies and, more generally, on the way fixation processes occur. We perform a systematic analysis of $2\times2$ games in well-mixed populations, focusing on the fixation probabilities of single mutants as functions of population size. A diversity of fixation function shapes emerges under 12 out of the 24 possible games, showing different increasing regions for which we provide explanations. Secondly, finite population models have more flexibility to account for realistic features. We consider a framework initially proposed in 2012, under which interacting groups arise from encounters of individuals moving in a network, thus overcoming the challenges that multiplayer interactions pose in structured populations. We consider particular movement models and study some of their characteristics and interplaying effects with structure. |
| Redondo Javier | A Bayesian approach to parameter estimation. Hamiltonian Monte Carlo | The aim of this work is to use a Bayesian approach to perform parameter estimation of the models. Under this paradigm, the parameters are seen as random variables, so we work with them under probabilistic terms. Specifically, we use Hamiltonian Monte Carlo (HMC), an efficient algorithm that outperforms random-walk methods in exploring complex parameter spaces. This method is applied to calibrate a complex SEIR model with seven compartments, and the results and the evaluation of the method used will be discussed. |
| Satouri Mohammadreza | A game-theoretic approach to contain cancer | Cancer is a complex dynamic system. Several different approaches, including game theory, control theory, and machine learning, have been developed to model and understand cancer and design better treatments. Dynamic game-theoretic approach enables us to analyze complex eco-evolutionary dynamics of cancer and model dynamic interactions between a physician and cancer. Here we model cancer treatment as a Stackelberg evolutionary game between the physician and cancer cells. In this game, physician selects the treatment, including its dosing and timing, to maximize patient’s quality of life. Cancer cells may respond to this treatment by evolving treatment-induced resistance. We consider a model which describes eco-evolutionary dynamics of two cancer cell types: a fully treatment-sensitive type and a type with evolving treatment-induced resistance. We will investigate stability of the equilibria via Lyapunov approach. Since some parameters used in the dynamic models of cancer are varied by changing treatment or are estimated imprecisely in the model identification phase via real data, a sensitivity analysis is needed. We will perform this sensitivity analysis, using robust control techniques, to find upper bounds for the Euclidean norm of the mentioned uncertainties or errors in the parameters of the dynamical model of cancer. If the uncertainties and errors go beyond these upper bounds, the equilibria will enter a region which is dangerous for the patient. We define this region to be the area in which the number of cancer cells exceeds a predefined threshold. We will show how sensitive the treatment protocols are. |
| Sayyar Golsa | Epidemic patterns of emerging variants with dynamical social distancing | Motivated by the emergence of new variants during the COVID-19 pan- demic, we consider an epidemiological model of disease transmission dynamics, where novel strains appear by mutations of the virus. In the considered scenarios, disease prevalence in the population is modulated by social distancing. We study the various patterns that are generated under different assumptions of cross-immunity. If recovery from a given strain provides immunity against all previous strains, but not against more novel strains, then we observe a very regular sequential pattern of strain replacement where newer strains predominate over older strains. However, if protection upon recovery holds only against that particular strain and none of the others, we find much more complicated dynamics with potential recurrence of earlier strains, and co-circulation of various strains. We compare the observed patterns with genomic analysis we have seen during the COVID-19 pandemic. |
| Sharkey Kieran | Modelling structured populations | Focusing on the example of Susceptible-Infectious-Removed (SIR) epidemic dynamics, I will develop Markovian (memoryless) stochastic models in well-mixed and in network-structured populations. I will show how to generate exact stochastic realisations of the underlying models. If time permits, I will then show how to approximate the expected behaviour of the epidemic using pair approximation of the underlying master equations. |
| Stein Alexander | Modelling of genetic intra-tumour heterogeneity and therapy resistance | Intra-tumour genetic heterogeneity is a natural outcome of the cancer evolutionary process. It is a leading contributor to treatment resistance and disease progression. In the past decade, novel personalised therapy schedules have been developed that explicitly consider cancer as a speciation process to improve patient outcomes. These evolutionarily informed therapies are based on mathematical models and, with only a few exceptions, are described by a set of deterministic differential equations. However, these models must make assumptions about the population sizes of resistant clones at the time of diagnosis and ignore stochastic aspects of the dynamics, such as newly arising driver mutations. In my talk, I will introduce a stochastic branching process, including competition between cancer cells and mutation events. I will present the expected heterogeneity of resistant clones at the time of diagnosis and during treatment. |
| Thomsen Frederik | Global features in an eco-evolutionary model of cancer therapy with time-varying treatment | The major obstacle in the design of effective treatment strategies for cancer therapy is the emergence of drug-resistance. Strategies aiming to eliminate the maximum volume of cells through constant-in-time application of treatment are doomed to fail as, inevitably, an initially small subpopulation of at least partially drug-resistant cells becomes dominant. Adaptive therapy is a new paradigm aiming to cure or delay treatment failure by instead dynamically adapting the drug-dosage in response to an observation of the current population state. Recent models of adaptive therapy couple ecological dynamics to an evolving drug-resistance in low-dimensional ODEs. In this talk we consider a simple type of eco-evolutionary model and analyse its global features when the treatment dosage enters as a bounded, time-varying input. We identify limit sets and feasibility of a cure. Our results provide insights into control and uncertainty in a broader class of models and compliment approaches using optimal control. |
| Tjikundi Kausutua | Discovering insight from the close contacts data collected using wearable proximity sensors in developing world settings | Continuous prevalence and re-emergence of infectious diseases such as Tuberculosis (TB), Ebola, Measles, influenza etc. in low-middle income countries necessitate the need to have accurate mining and analysis of face-to-face contact patterns between individuals. Most importantly, contact patterns among individuals are essential in identifying the potential transmission routes of infectious illnesses, particularly respiratory pathogens. Recent technological advancements, particularly wearable sensors have paved the way to measure and quantify real-world person-to-person interactions in space and time in order to best inform epidemic models by estimating the epidemic risk and also provide insights into the design of the intervention and mitigation strategies for social protection. Even though these data are a sample of a sample they provide an accurate number of contacts and duration of the contacts. This is an advantage since the transmission doesn’t only depend on the number of contacts but also on the duration of the contact. Unlike surveys and contact diaries where the number and duration of the contacts are only approximate figures, hence the data collected with wearable sensors yield a better representation of face-to-face contact patterns. Here we present and analyse the data collected from the developing world setting using wearable sensors. We also highlight the limitations and challenges associated with these data. |
| Traulsen Arne | Evolutionary dynamics (with constant fitness) on small networks | Evolutionary dynamics can be strongly affected by spatial structure – even in the absence of game theoretical interactions. A popular way to model such spatial structure are networks, where each node represents an individual and offspring can be placed to other sites via the links. How does such a network affect the probability of a new mutation to take over the entire population? And how does it alter the time this process is expected to take? Of particular interest are structures that increase the probability that advantageous mutations take over. Such amplifiers are surprisingly abundant among all networks. However, they do not necessarily maximize the fitness under long term evolution. Applying these models to real populations typically requires that each node is a subpopulation – leading to a different class of models. References: L. Hindersin and A. Traulsen Most undirected random graphs are amplifiers of selection for Birth-death dynamics, but suppressors of selection for death-Birth dynamics PLoS Computational Biology 11, e1004437 (2015) M. Möller, L. Hindersin and A. Traulsen Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time Communications Biology 2, (2019) S. Yagoobi and A. Traulsen Fixation probabilities in network structured meta-populations Scientific Reports 11, 1-9 (2021) N. Sharma and A. Traulsen Suppressors of fixation can increase average fitness beyond amplifiers of selection Proceedings of the National Academy of Sciences 119, e2205424119 (2022 |