Eco-evolutionary dynamics in finite network-structured populations with migration.

We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We look at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.

Effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines for reducing susceptibility to infection with the Delta variant (B.1.617.2) of SARS-CoV-2.

BACKGROUND: From January to May 2021 the alpha variant (B.1.1.7) of SARS-CoV-2 was the most commonly detected variant in the UK. Following this, the Delta variant (B.1.617.2) then became the predominant variant. The UK COVID-19 vaccination programme started on 8th December 2020. Prior to the Delta variant, most vaccine effectiveness studies focused on the alpha variant. We therefore aimed to estimate the effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines in preventing symptomatic and asymptomatic infection with respect to the Delta variant in a UK setting. METHODS: We used anonymised public health record data linked to infection data (PCR) using the Combined Intelligence for Population Health Action resource. We then constructed an SIR epidemic model to explain SARS-CoV-2 infection data across the Cheshire and Merseyside region of the UK. Vaccines were assumed to be effective after 21 days for 1 dose and 14 days for 2 doses. RESULTS: We determined that the effectiveness of the Oxford-AstraZeneca vaccine in reducing susceptibility to infection is 39% (95% credible interval [34, 43]) and 64% (95% credible interval [61, 67]) for a single dose and a double dose respectively. For the Pfizer-BioNTech vaccine, the effectiveness is 20% (95% credible interval [10, 28]) and 84% (95% credible interval [82, 86]) for a single-dose and a double dose respectively. CONCLUSION: Vaccine effectiveness for reducing susceptibility to SARS-CoV-2 infection shows noticeable improvement after receiving two doses of either vaccine. Findings also suggest that a full course of the Pfizer-BioNTech provides the optimal protection against infection with the Delta variant. This reinforces the need to complete the full course programme to maximise individual protection and reduce transmission.

Impact of climatic, demographic and disease control factors on the transmission dynamics of COVID-19 in large cities worldwide.

Approximately a year into the COVID-19 pandemic caused by the SARS-CoV-2 virus, many countries have seen additional "waves" of infections, especially in the temperate northern hemisphere. Other vulnerable regions, such as South Africa and several parts of South America have also seen cases rise, further impacting local economies and livelihoods. Despite substantial research efforts to date, it remains unresolved as to whether COVID-19 transmission has the same sensitivity to climate observed for other common respiratory viruses such as seasonal influenza. Here, we look for empirical evidence of seasonality using a robust estimation framework. For 359 large cities across the world, we estimated the basic reproduction number (R0) using logistic growth curves fitted to cumulative case data. We then assess evidence for association with climatic variables through ordinary least squares (OLS) regression. We find evidence of seasonality, with lower R0 within cities experiencing greater surface radiation (coefficient = -0.005, p < 0.001), after adjusting for city-level variation in demographic and disease control factors. Additionally, we find association between R0 and temperature during the early phase of the epidemic in China. However, climatic variables had much weaker explanatory power compared to socioeconomic and disease control factors. Rates of transmission and health burden of the continuing pandemic will be ultimately determined by population factors and disease control policies.

Evolutionary graph theory derived from eco-evolutionary dynamics.

A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The evolutionary graph theory model, which considers evolutionary dynamics only, is derived as a special case, highlighting additional assumptions that diverge from real biological processes. This is achieved by introducing a negative ecological feedback loop that suppresses ecological dynamics by forcing births and deaths to be coupled. We also investigate how fitness, a measure of reproductive success used in evolutionary graph theory, is related to the life-history of individuals in terms of their birth and death rates. In simple networks, these ecologically motivated dynamics are used to provide new insight into the spread of adaptive mutations, both with and without clonal interference. For example, the star network, which is known to be an amplifier of selection in evolutionary graph theory, can inhibit the spread of adaptive mutations when individuals can die naturally.

The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population.

We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology.

Dynamics of multiplayer games on complex networks using territorial interactions.

The modeling of evolution in structured populations has been significantly advanced by evolutionary graph theory, which incorporates pairwise relationships between individuals on a network. More recently, a new framework has been developed to allow for multiplayer interactions of variable size in more flexible and potentially changing population structures. While the theory within this framework has been developed and simple structures considered, there has been no systematic consideration of a large range of different population structures, which is the subject of this paper. We consider a large range of underlying graphical structures for the territorial raider model, the most commonly used model in the new structure, and consider a variety of important properties of our structures with the aim of finding factors that determine the fixation probability of mutants. We find that the graphical temperature and the average group size, as previously defined, are strong predictors of fixation probability, while all other properties considered are poor predictors, although the clustering coefficient is a useful secondary predictor when combined with either temperature or group size. The relationship between temperature or average group size and fixation probability is sometimes, however, nonmonotonic, with a directional reverse occurring around the temperature associated with what we term "completely mixed" populations in the case of the hawk-dove game, but not the public goods game.

Generalized Social Dilemmas: The Evolution of Cooperation in Populations with Variable Group Size.

Evolutionary game theory is an important tool to model animal and human behaviour. A key class of games is the social dilemmas, where cooperation benefits the group but defection benefits the individual within any group. Previous works have considered which games qualify as social dilemmas, and different categories of dilemmas, but have generally concentrated on fixed sizes of interacting groups. In this paper, we develop a systematic investigation of social dilemmas on all group sizes. This allows for a richer definition of social dilemmas. For example, while increasing a group size to include another defector is always bad for all existing group members, extra cooperators can be good or bad, depending upon the particular dilemma and group size. We consider a number of commonly used social dilemmas in this context and in particular show the effect of variability in group sizes for the example of a population comprising negative binomially distributed group sizes. The most striking effect is that increasing the variability in group sizes for non-threshold public goods games is favourable for the evolution of cooperation. The situation for threshold public goods games and commons dilemmas is more complex.

Evolutionary dynamics and the evolution of multiplayer cooperation in a subdivided population.

The classical models of evolution have been developed to incorporate structured populations using evolutionary graph theory and, more recently, a new framework has been developed to allow for more flexible population structures which potentially change through time and can accommodate multiplayer games with variable group sizes. In this paper we extend this work in three key ways. Firstly by developing a complete set of evolutionary dynamics so that the range of dynamic processes used in classical evolutionary graph theory can be applied. Secondly, by building upon previous models to allow for a general subpopulation structure, where all subpopulation members have a common movement distribution. Subpopulations can have varying levels of stability, represented by the proportion of interactions occurring between subpopulation members; in our representation of the population all subpopulation members are represented by a single vertex. In conjunction with this we extend the important concept of temperature (the temperature of a vertex is the sum of all the weights coming into that vertex; generally, the higher the temperature, the higher the rate of turnover of individuals at a vertex). Finally, we have used these new developments to consider the evolution of cooperation in a class of populations which possess this subpopulation structure using a multiplayer public goods game. We show that cooperation can evolve providing that subpopulations are sufficiently stable, with the smaller the subpopulations the easier it is for cooperation to evolve. We introduce a new concept of temperature, namely "subgroup temperature", which can be used to explain our results.

A study of the dynamics of multi-player games on small networks using territorial interactions.

Recently, the study of structured populations using models of evolutionary processes on graphs has begun to incorporate a more general type of interaction between individuals, allowing multi-player games to be played among the population. In this paper, we develop a birth-death dynamics for use in such models and consider the evolution of populations for special cases of very small graphs where we can easily identify all of the population states and carry out exact analyses. To do so, we study two multi-player games, a Hawk-Dove game and a public goods game. Our focus is on finding the fixation probability of an individual from one type, cooperator or defector in the case of the public goods game, within a population of the other type. We compare this value for both games on several graphs under different parameter values and assumptions, and identify some interesting general features of our model. In particular there is a very close relationship between the fixation probability and the mean temperature, with high temperatures helping fitter individuals and punishing unfit ones and so enhancing selection, whereas low temperatures give a levelling effect which suppresses selection.