Real time forecasting of near-future evolution

Competing Heterogeneities in Vaccine Effectiveness Estimation

Understanding the waning of vaccine-induced protection is important for both immunology and public health. Population heterogeneities in underlying (pre-vaccination) susceptibility and vaccine response can cause measured vaccine effectiveness (mVE) to change over time, even in the absence of pathogen evolution and any actual waning of immune responses. We use multi-scale agent-based models parameterized using epidemiological and immunological data, to investigate the effect of these heterogeneities on mVE as measured by the hazard ratio. Based on our previous work, we consider the waning of antibodies according to a power law and link it to protection in two ways: (1) motivated by correlates of risk data and (2) using a within-host model of stochastic viral extinction. The effect of the heterogeneities is given by concise and understandable formulas, one of which is essentially a generalization of Fisher's fundamental theorem of natural selection to include higher derivatives. Heterogeneity in underlying susceptibility accelerates apparent waning, whereas heterogeneity in vaccine response slows down apparent waning. Our models suggest that heterogeneity in underlying susceptibility is likely to dominate. However, heterogeneity in vaccine response offsets <10% to >100% (median of 29%) of this effect in our simulations. Our study suggests heterogeneity is more likely to 'bias' mVE downwards towards the faster waning of immunity but a subtle bias in the opposite direction is also plausible.

Competing Heterogeneities in Vaccine Effectiveness Estimation

Understanding waning of vaccine-induced protection is important for both immunology and public health. Population heterogeneities in underlying (pre-vaccination) susceptibility and vaccine response can cause measured vaccine effectiveness (mVE) to change over time even in the absence of pathogen evolution and any actual waning of immune responses. We use a multi-scale agent-based models parameterized using epidemiological and immunological data, to investigate the effect of these heterogeneities on mVE as measured by the hazard ratio. Based on our previous work, we consider waning of antibodies according to a power law and link it to protection in two ways: 1) motivated by correlates of risk data and 2) using a within-host model of stochastic viral extinction. The effect of the heterogeneities is given by concise and understandable formulas, one of which is essentially a generalization of Fisher's fundamental theorem of natural selection to include higher derivatives. Heterogeneity in underlying susceptibility accelerates apparent waning, whereas heterogeneity in vaccine response slows down apparent waning. Our models suggest that heterogeneity in underlying susceptibility is likely to dominate. However, heterogeneity in vaccine response offsets <10% to >100% (median of 29%) of this effect in our simulations. Our methodology and results may be helpful in understanding competing heterogeneities and waning of immunity and vaccine-induced protection. Our study suggests heterogeneity is more likely to 'bias' mVE downwards towards faster waning of immunity but a subtle bias in the opposite direction is also plausible.

Forecasting emergence of COVID-19 variants of concern

We consider whether one can forecast the emergence of variants of concern in the SARS-CoV-2 outbreak and similar pandemics. We explore methods of population genetics and identify key relevant principles in both deterministic and stochastic models of spread of infectious disease. Finally, we demonstrate that fitness variation, defined as a trait for which an increase in its value is associated with an increase in net Darwinian fitness if the value of other traits are held constant, is a strong indicator of imminent transition in the viral population.

Dynamics and Fate of Beneficial Mutations Under Lineage Contamination by Linked Deleterious Mutations

Beneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane's application of single-type branching process theory showed that genetic drift alone could cause the extinction of newly arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly arising beneficial mutation as a multitype branching process. Our approach accounts for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination We first study the lineage-contamination phenomenon in isolation, deriving dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survival probability is zero when [Formula: see text] where U is deleterious mutation rate and [Formula: see text] is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by [Formula: see text] We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that, under the combined effects of lineage contamination and background selection, ensemble survival probability is never zero but is depressed below classical predictions by a factor bounded from below by [Formula: see text] where [Formula: see text] is mean selective advantage of beneficial mutations, and [Formula: see text] This factor, and other bounds derived from it, are independent of the fitness effects of deleterious mutations. At high enough mutation rates, lineage contamination can depress fixation probabilities to values that approach zero. This fact suggests that high mutation rates can, perhaps paradoxically, (1) alleviate competition among beneficial mutations, or (2) potentially even shut down the adaptive process. We derive critical mutation rates above which these two events become likely.

The Nonstationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation

Various models describe asexual evolution by mutation, selection, and drift. Some focus directly on fitness, typically modeling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (traveling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher's geometric model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift. In all cases, predictions are typically obtained in high or low mutation rate limits and for long-term stationary regimes, thus losing information on transient behaviors and the effect of initial conditions. Here, we connect fitness-based and trait-based models into a single framework, and seek explicit solutions even away from stationarity. The expected fitness distribution is followed over time via its cumulant generating function, using a deterministic approximation that neglects drift. In several cases, explicit trajectories for the full fitness distribution are obtained for arbitrary mutation rates and standing variance. For nonepistatic mutations, especially with beneficial mutations, this approximation fails over the long term but captures the early dynamics, thus complementing stationary stochastic predictions. The approximation also handles several diminishing returns epistasis models (e.g., with an optimal genotype); it can be applied at and away from equilibrium. General results arise at equilibrium, where fitness distributions display a "phase transition" with mutation rate. Beyond this phase transition, in Fisher's geometric model, the full trajectory of fitness and trait distributions takes a simple form; robust to the details of the mutant phenotype distribution. Analytical arguments are explored regarding why and when the deterministic approximation applies.

Forecasting Epidemiological and Evolutionary Dynamics of Infectious Diseases

Mathematical models have been powerful tools in developing mechanistic understanding of infectious diseases. Furthermore, they have allowed detailed forecasting of epidemiological phenomena such as outbreak size, which is of considerable public-health relevance. The short generation time of pathogens and the strong selection they are subjected to (by host immunity, vaccines, chemotherapy, etc.) mean that evolution is also a key driver of infectious disease dynamics. Accurate forecasting of pathogen dynamics therefore calls for the integration of epidemiological and evolutionary processes, yet this integration remains relatively rare. We review previous attempts to model and predict infectious disease dynamics with or without evolution and discuss major challenges facing the development of the emerging science of epidemic forecasting.

Empirical fitness landscapes and the predictability of evolution

The genotype-fitness map (that is, the fitness landscape) is a key determinant of evolution, yet it has mostly been used as a superficial metaphor because we know little about its structure. This is now changing, as real fitness landscapes are being analysed by constructing genotypes with all possible combinations of small sets of mutations observed in phylogenies or in evolution experiments. In turn, these first glimpses of empirical fitness landscapes inspire theoretical analyses of the predictability of evolution. Here, we review these recent empirical and theoretical developments, identify methodological issues and organizing principles, and discuss possibilities to develop more realistic fitness landscape models.

Visualization of evolutionary stability dynamics and competitive fitness of Escherichia coli engineered with randomized multigene circuits

Strain engineering for synthetic biology and metabolic engineering applications often requires the expression of foreign proteins that can reduce cellular fitness. In order to quantify and visualize the evolutionary stability dynamics in engineered populations of Escherichia coli , we constructed randomized CMY (cyan-magenta-yellow) genetic circuits with independently randomized promoters, ribosome binding sites, and transcriptional terminators that express cyan fluorescent protein (CFP), red fluorescent protein (RFP), and yellow fluorescent protein (YFP). Using a CMY color system allows for a spectrum of different colors to be produced under UV light since the relative ratio of fluorescent proteins vary between circuits, and this system can be used for the visualization of evolutionary stability dynamics. Evolutionary stability results from 192 evolved populations (24 CMY circuits with 8 replicates each) indicate that both the number of repeated sequences and overall expression levels contribute to circuit stability. The most evolutionarily robust circuit has no repeated parts, lower expression levels, and is about 3-fold more stable relative to a rationally designed circuit. Visualization results show that evolutionary dynamics are highly stochastic between replicate evolved populations and color changes over evolutionary time are consistent with quantitative data. We also measured the competitive fitness of different mutants in an evolved population and find that fitness is highest in mutants that express a lower number of genes (0 and 1 > 2 > 3). In addition, we find that individual circuits with expression levels below 10% of the maximum have significantly higher evolutionary stability, suggesting there may be a hypothetical "fitness threshold" that can be used for robust circuit design.

Genomic mutation rates that neutralize adaptive evolution and natural selection

When mutation rates are low, natural selection remains effective, and increasing the mutation rate can give rise to an increase in adaptation rate. When mutation rates are high to begin with, however, increasing the mutation rate may have a detrimental effect because of the overwhelming presence of deleterious mutations. Indeed, if mutation rates are high enough: (i) adaptive evolution may be neutralized, resulting in a zero (or negative) adaptation rate despite the continued availability of adaptive and/or compensatory mutations, or (ii) natural selection may be neutralized, because the fitness of lineages bearing adaptive and/or compensatory mutations--whether established or newly arising--is eroded by excessive mutation, causing such lineages to decline in frequency. We apply these two criteria to a standard model of asexual adaptive evolution and derive mathematical expressions--some new, some old in new guise--delineating the mutation rates under which either adaptive evolution or natural selection is neutralized. The expressions are simple and require no a priori knowledge of organism- and/or environment-specific parameters. Our discussion connects these results to each other and to previous theory, showing convergence or equivalence of the different results in most cases.

Cancer in light of experimental evolution

Cancer initiation, progression, and the emergence of therapeutic resistance are evolutionary phenomena of clonal somatic cell populations. Studies in microbial experimental evolution and the theoretical work inspired by such studies are yielding deep insights into the evolutionary dynamics of clonal populations, yet there has been little explicit consideration of the relevance of this rapidly growing field to cancer biology. Here, we examine how the understanding of mutation, selection, and spatial structure in clonal populations that is emerging from experimental evolution may be applicable to cancer. Along the way, we discuss some significant ways in which cancer differs from the model systems used in experimental evolution. Despite these differences, we argue that enhanced prediction and control of cancer may be possible using ideas developed in the context of experimental evolution, and we point out some prospects for future research at the interface between these traditionally separate areas.