Key Words ancestral polymorphism, coalescence theory, maximum likelihood, molecular clock, sequence saturation s Abstract Molecular clocks have profoundly influenced modern views on the 1 In memoriam: Joseph Slowinksi passed away in September 2001 as the result of a snake bite he received while conducting fieldwork in Myanmar. He will be dearly missed by his friends and colleagues.

We used 20 de novo genome assemblies to probe the speciation history and architecture of gene flow in rapidly radiating Heliconius butterflies. Our tests to distinguish incomplete lineage sorting from introgression indicate that gene flow has obscured several ancient phylogenetic relationships in this group over large swathes of the genome. Introgressed loci are underrepresented in low-recombination and gene-rich regions, consistent with the purging of foreign alleles more tightly linked to incompatibility loci. Here, we identify a hitherto unknown inversion that traps a color pattern switch locus. We infer that this inversion was transferred between lineages by introgression and is convergent with a similar rearrangement in another part of the genus. These multiple de novo genome sequences enable improved understanding of the importance of introgression and selective processes in adaptive radiation.

Using a previously undescribed approach, we develop an analytic model that predicts whether an asexual population accumulates advantageous or deleterious mutations over time and the rate at which either process occurs. The model considers a large number of linked identical loci, or nucleotide sites; assumes that the selection coefficient per site is much less than the mutation rate per genome; and includes back and compensating mutations. Using analysis and Monte Carlo simulations, we demonstrate the accuracy of our results over almost the entire range of population sizes. Two limiting cases of our results, when either deleterious or advantageous mutations can be neglected, correspond to the Fisher-Muller effect and Muller's ratchet, respectively. By comparing predictions of our model (no recombination) to those of simple single-locus models (strong recombination), we show that the accumulation of advantageous mutations is slowed by linkage over a broad, finite range of population size. This supports the view of Fisher and Muller, who argued in the 1930s that progressive evolution of organisms is slowed because loci at which beneficial mutations can occur are often linked together on the same chromosome. These results follow from our main finding, that distribution of sequences over the mutation number evolves as a traveling wave whose speed and width depend on population size and other parameters. The model explains a logarithmic dependence of steady-state fitness on the population size reported recently for an RNA virus. T he scope of evolutionary biology ranges from understanding the origin and extinction of species to predicting the accumulation of drug-or antibody-resistant mutations in a population of microbes during an infection of an individual. Viruses like HIV in which persistent infection of individuals lasts for large numbers of viral generations provide a valuable opportunity to test evolutionary theory by comparing model predictions to a wealth of readily obtained data. In addition, evolutionary models can be used to infer important properties of viral populations.The forces that produce and maintain genetic variation in a population are thought to be known. These include the ''systematic pressures'' (1) of mutation, natural selection, and migration. If these were the only forces operating, the fate of the population could be modeled deterministically. However, all evolution occurs in finite-size populations, which is the source of the other major evolutionary factor: random genetic drift. Drift adds a stochastic element to evolution, resulting from the chance sampling of individuals from one generation to the next and from the fact that not all possible genetic variants can be present in a finite population. For given levels of systematic pressure, evolution will be mostly deterministic if the population size is large enough but will be mostly neutral and dominated by drift (2) when the population size is small. Between these two limits there exists a large intermediate region, in which both selec...