Efficient simulation under a population genetics model of carcinogenesis

A Bayesian Framework for Inferring the Influence of Sequence Context on Point Mutations

The probability of point mutations is expected to be highly influenced by the flanking nucleotides that surround them, known as the sequence context. This phenomenon may be mainly attributed to the enzyme that modifies or mutates the genetic material, because most enzymes tend to have specific sequence contexts that dictate their activity. Here, we develop a statistical model that allows for the detection and evaluation of the effects of different sequence contexts on mutation rates from deep population sequencing data. This task is computationally challenging, as the complexity of the model increases exponentially as the context size increases. We established our novel Bayesian method based on sparse model selection methods, with the leading assumption that the number of actual sequence contexts that directly influence mutation rates is minuscule compared with the number of possible sequence contexts. We show that our method is highly accurate on simulated data using pentanucleotide contexts, even when accounting for noisy data. We next analyze empirical population sequencing data from polioviruses and HIV-1 and detect a significant enrichment in sequence contexts associated with deamination by the cellular deaminases ADAR 1/2 and APOBEC3G, respectively. In the current era, where next-generation sequencing data are highly abundant, our approach can be used on any population sequencing data to reveal context-dependent base alterations and may assist in the discovery of novel mutable sites or editing sites.

Sequence Evolution Under Constraints: Lessons Learned from Sudoku

The complex structures of all proteins in nature are outcomes of a random walk driven by mutation and selection. Reconstructing the fitness landscape staging this process based on first-principle physical rules or experimental measurements is difficult. In this article we turn the popular Sudoku game into an artificial fitness landscape and use it as a model system to study sequence evolution under constraints. The Sudoku rules, which are human-mind friendly, intertwine a rugged landscape for sequences composed of digits, mimicking the functional constraints felt by a tightly folded protein. Simulated evolution reveals interesting properties of the valley-crossing dynamics on this complex landscape. It is found that (i) the mutation accumulation rate during valley-crossing is constant among different evolutionary pathways and depends on the ruggedness of the landscape; (ii) genetic drift and neutral networks play constructive roles during the process of searching for novel functions; and (iii) under strong selection, gene duplication can speed up the evolution by relaxing, but not completely liberating, the redundant copy from selective pressure. Insights gained from this prototype model may help us understand the evolution of real proteins.

The evolution of natural competence: disentangling costs and benefits of sex in bacteria

One of the most challenging questions in evolutionary biology is how sex has evolved in the face of substantial fitness costs. In this study, we focus on the evolution of bacterial sex in the form of natural transformation, where cells take up exogenous DNA and integrate it into the genome. Besides the physiological cost of producing a DNA uptake system, transformation can potentially impose a genetic cost as a result of an overrepresentation of deleterious mutations in the extracellular DNA pool. On the other hand, the uptake of DNA can be beneficial not only because of genetic effects but also because of the immediate nutritional value of the DNA. To disentangle these fitness costs and benefits, we developed a mathematical model and competed three bacterial types during adaptation to a new environment: competent cells capable of DNA import and digestion; competent cells capable of DNA import, digestion, and recombination; and noncompetent cells. Our results indicate a complex interplay between several physiological and ecological factors, including the rate at which DNA is taken up, the rate of DNA decay in the medium, and the nutritional value of DNA. In finite populations, the recombining type is often favored through the Fisher-Muller effect.

Complete numerical solution of the diffusion equation of random genetic drift

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size.

The effect of bacterial recombination on adaptation on fitness landscapes with limited peak accessibility

There is ample empirical evidence revealing that fitness landscapes are often complex: the fitness effect of a newly arisen mutation can depend strongly on the allelic state at other loci. However, little is known about the effects of recombination on adaptation on such fitness landscapes. Here, we investigate how recombination influences the rate of adaptation on a special type of complex fitness landscapes. On these landscapes, the mutational trajectories from the least to the most fit genotype are interrupted by genotypes with low relative fitness. We study the dynamics of adapting populations on landscapes with different compositions and numbers of low fitness genotypes, with and without recombination. Our results of the deterministic model (assuming an infinite population size) show that recombination generally decelerates adaptation on these landscapes. However, in finite populations, this deceleration is outweighed by the accelerating Fisher-Muller effect under certain conditions. We conclude that recombination has complex effects on adaptation that are highly dependent on the particular fitness landscape, population size and recombination rate.

The emergence and persistence of recombination is a long-standing open question in evolutionary biology. Most previous theoretical studies assumed relatively simple fitness landscapes, i.e., simple relationships between allelic states at different loci and fitness. By contrast, empirically determined bacterial and viral fitness landscapes reveal pervasive complex interactions between alleles at different loci. In this study, we explore the effect of recombination on adaptation on fitness landscapes where some trajectories leading to a global fitness peak are interrupted by genotypes of very low fitness. We find that in infinitely large populations, recombination generally reduces the rate of adaptation. However, in finite populations and under certain conditions, recombination can substantially speed up adaptation. Our study provides insights into the effect of recombination on more realistic fitness landscapes. Moreover, it helps gain a better understanding of the dynamics of the spread of adaptive genes in recombining bacterial populations during niche expansion and colonization of new habitats.

Fast stochastic algorithm for simulating evolutionary population dynamics

MOTIVATION

Many important aspects of evolutionary dynamics can only be addressed through simulations. However, accurate simulations of realistically large populations over long periods of time needed for evolution to proceed are computationally expensive. Mutants can be present in very small numbers and yet (if they are more fit than others) be the key part of the evolutionary process. This leads to significant stochasticity that needs to be accounted for. Different evolutionary events occur at very different time scales: mutations are typically much rarer than reproduction and deaths.

RESULTS

We introduce a new exact algorithm for fast fully stochastic simulations of evolutionary dynamics that include birth, death and mutation events. It produces a significant speedup compared to direct stochastic simulations in a typical case when the population size is large and the mutation rates are much smaller than birth and death rates. The algorithm performance is illustrated by several examples that include evolution on a smooth and rugged fitness landscape. We also show how this algorithm can be adapted for approximate simulations of more complex evolutionary problems and illustrate it by simulations of a stochastic competitive growth model.