Funded Grants

The evolutionary dynamics and population genetics of selection in asexual populations

Evolution is striking for its seemingly incredible improbability. How could so many unlikely mutations create something as intricate as an eye or a wing? Biologists can only answer that nature had billions of years, so such things are possible. This answer is wholly unsatisfactory. Can anyone explain why the eye evolved over billions of years, rather than millions? Or trillions?

These questions are hopelessly broad. Yet even in very simple and well-defined circumstances, surprisingly little is known about what is possible in evolution, over what timescales and in which conditions. In the early 1900s, R. A. Fisher, Sewall Wright, J.B.S. Haldane, and many others studied the basic forces driving evolution. They analyzed simple models of general processes, such as genetic drift and natural selection. This work forms the basis for decades of subsequent work in population genetics, but it is limited primarily to situations where natural selection is absent, or where selection acts on only one or two things at a time.

Yet in a wide range of primarily asexual populations such as viruses and microbes, selection faces a crucial problem: there is too much going on at once. Many mutations are often present simultaneously in these populations, some of them beneficial and others deleterious. If natural selection could act on them all independently, it could keep all of the good while eliminating the bad, and the population would quickly adapt. But it cannot. A mutation cannot increase or decrease in frequency without all the other mutations in that particular chromosome doing the same; these mutations are physically linked. Mutations are constantly occurring in a variety of linked combinations, and selection can only act on these combinations as a whole. This reduces the efficiency of natural selection and can place enormous constraints on how these populations can evolve.

Sex allows biology to avoid this problem by mixing up chromosomes and causing recombination within them. This breaks the linkage between mutations and allows each to be selected on its own merits. But even in obligately sexual organisms, recombination occurs at most at a few points within each chromosome per generation, so sex only slowly mixes up genomes. In asexual organisms such as viruses and microbes, including many pathogens, linkage is even more extensive. In these populations selection acts on multiple linked variants at once, and evolutionary dynamics are radically different from the usual intuition.

I propose to develop theoretical frameworks to study selection acting on these asexual populations. My first aim is to study evolutionary dynamics, to better understand what evolution can do in an asexual population. The basic question is simple: given a particular fitness landscape - that is, a set of possible evolutionary pathways, each characterized by a set of mutations with given mutation rates and selection strengths - what is the probability that a population will take a particular trajectory and what is the rate at which it will do so? We need a quantitative understanding of this question if we hope to learn from what we see in the evolution of natural and experimental populations. For example, what does it mean if a set of experimental yeast populations maintained in identical conditions evolve in very similar (or very different) ways? What precisely does that tell us about the space of possible evolutionary pathways that were available to these populations? How should the result depend on population size or other details of the experiments?

Despite much work on this subject, understanding of these questions remains limited. The central difficulty is that the evolution of the population as a whole is an emergent property, arising out of the interactions between mutations at many different loci. Each mutation follows the relatively simple rules of selection and genetic drift, but many mutations act together nonlinearly to determine the patterns of evolution at a population level. Since rare mutational events can have a dramatic impact when they are amplified by selection, stochastic fluctuations are often crucial. Methods common in theoretical population genetics have struggled to understand how the dynamics of the system at large emerges from the basic laws governing individual mutations. To address this problem, I have developed methods combining explicit stochastic analysis of rare types with the statistical behavior of large numbers of non-independent random processes. These techniques allow us to understand how nonlinear population-level dynamics affect the stochastic dynamics of individual mutants, and then self-consistently determine how these individual results add up to produce the correct population-level dynamics. I now propose to build on this framework to analyze evolutionary dynamics in the presence of linkage. These methods may also be of broad applicability to related problems in complex systems involving dynamics across multiple scales.

This theoretical work will help us understand how populations evolve given a particular fitness landscape. It remains to ask what such fitness landscapes typically look like. To address this question, I propose to complement my theoretical work with experimental evolution in budding yeast. I have constructed a set of yeast strains which allows us to directly observe particular classes of beneficial mutations as they occur and spread through populations. This allows us to correlate changes in phenotypic characteristics, such as increases in fitness, with the observed dynamics of particular mutants. I will use this in combination with high-throughput methods of strain maintenance, which I have recently developed to allow the simultaneous evolution of thousands of experimental lines. This view of evolutionary dynamics in a massively parallel setting will allow me to explore the relative probabilities of a large set of possible evolutionary trajectories, using the information contained in the variation between identically evolved lines. From this we will be able to infer the structure of underlying fitness landscapes.

Despite its advantages, experimental evolution may not always be representative of evolution in the wild. Thus I also plan to study how selection acts in natural populations, based on the signatures it leaves in sequence data. An extensive body of work has been devoted to this subject, resulting in numerous inference techniques. By and large, these techniques are based on knowing what patterns of genetic variation would look like if everything were neutral. Population geneticists then find ways to look for deviations from these neutral expectations in a direction which suggests particular selective forces. But with a few limited exceptions, there are no models of what sequence variation should look like in the presence of selection on linked selected sites. Thus when population geneticists look for selection, they do not know precisely what they are looking for. This makes it hard to find the most powerful ways to distinguish selection from other evolutionary forces. I plan to develop explicit models describing how selection shapes the statistics of genetic variation in asexual populations, which will make it possible to systematically develop more powerful methods for interpreting sequence data.

The main difficulty in developing these models is that because mutations are linked, selection at one site can affect the genetic variation at another. I plan to use my earlier analysis of the evolutionary dynamics of linked beneficial and deleterious mutations as a basis for solving this problem. These models describe how variation in fitness within a population is created and maintained. I propose to study how this variation in fitness is determined by the collective dynamics of many lineages of individual mutants. Each lineage is founded by a single mutation, fluctuates in frequency due to selection and genetic drift, and may spawn further lineages with additional mutations. We can calculate the statistics of the frequencies of these lineages, and then trace the mutational ancestry of each lineage. This ancestry tells us whether two mutations occur in the same individual, and hence whether selection at one of those sites affected genetic variation at the other. This makes it possible to calculate the full distribution of genetic diversity within the population. We will test these results by sequencing our experimental yeast lines, relating this data to the known selective events within those populations. I hope that our understanding of the expected patterns of genetic diversity within selected asexual populations will form the basis for more powerful and efficient methods of learning about evolutionary histories from sequence data.

Together, these theoretical and experimental approaches will provide a deeper understanding of how natural selection shapes the evolution of asexual populations despite the constraints imposed by linkage. Our theoretical work treats this evolution as a multi-scale system, linking the dynamics of individual mutants with the population-level behavior that they collectively determine. This approach develops general tools which may be widely useful for the analysis of complex systems involving both nonlinearities and stochastic fluctuations on multiple scales. In the process, it lays a basis for understanding and interpreting evolution in both natural and experimental populations.