In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale T_c. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (T_c s) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale T_c and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient T_c s. We conclude by discussing the implications of these results for population genetic inferences.

Genetic alterations that drive clonal expansions in ostensibly healthy tissues have implications for cancer risk. However, the total rate at which clonal expansions occur in healthy tissues remains unknown. Synonymous passenger mutations that hitchhike to high variant allele frequency due to a linked driver mutation can be used to estimate the total rate of positive selection across the genome. Because these synonymous hitchhikers are influenced by all mutations under selection, regardless of type or location, they can be used to estimate how many driver mutations are missed by narrow gene-focused sequencing panels. Here we analyse the variant allele frequency spectrum of synonymous passenger mutations to estimate the total rate at which mutations driving clonal expansions occur in healthy tissues. By applying our framework to data from physiologically healthy blood, we find that a large fraction of mutations driving clonal expansions occur outside of canonical cancer driver genes. In contrast, analysis of data from healthy oesophagus reveals little evidence for many driver mutations outside of those in NOTCH1 and TP53. Our framework, which generalizes to other tissues, sheds light on the fraction of drivers mutations that remain undiscovered and has implications for cancer risk prediction.

Evolution in complex high-dimensional phenotype spaces can be very different than the caricature of uphill evolutionary trajectories in a low-dimensional fitness landscape. And slight modifications of the environment can have large consequences for the future evolution. Here, the simplest approximation of evolution, an almost-always clonal population evolving by small effect mutations under deterministic "adaptive" dynamics, is studied. The complexities of organisms and their interactions with their environments are caricatured by population growth rates being smoothly varying random functions in very high dimensional phenotype spaces. In a fixed environment, there are huge numbers of fitness maxima, yet evolutionary trajectories wander around amongst saddles, gradually slowing down but still wandering widely and without committing to any maximum. But with even very small changes of the environment caused by the phenotypic changes, after an initial transient the evolution continues forever without further slowing down. In this Red Queen "phase" the apparent rate of increase of the fitness saturates (at a feedback strength-dependent rate) and the trajectories perpetually wander over large phenotypic distances. Organismic complexities, caricatured by a large number of constraints on the molecular-level phenotype, together with the simplest possible interactions of the organisms with their environment, are shown to be sufficient to cause such Red Queen dynamics. Arguments are made for the ubiquity of such behavior.

One pen feeding study was conducted with 24 wether lambs to compared fecal output (FO) determined by total fecal collection with FO estimated by dosing lambs with chromic oxide controlled-release capsules. Lambs (39 +/- 1.5 kg BW) were fed either alfalfa hay (ALF), Coastal bermudagrass hay (CBG), or a commercially available pelleted (PEL) sheep diet (eight lambs/diet). After dosing, rectal grab samples and total collection of feces were taken daily for 31 d. Constant fecal excretion of Cr was achieved approximately on d 8 (range = d 5 to 13) after dosing. Capsule expiration was accompanied by a sharp peak in Cr excretion approximately on d 27 (range = d 24 to 30). Complete excretion of Cr by d 31 occurred in only seven lambs. Agreement between actual and predicted FO was examined by linear regression from d 8 to 22. Best parameter estimates and highest R2 were observed when sampling a) every other day from d 11 to 19 (five samplings), b) daily from d 8 to 17, c) daily during the entire period, and d) daily from d 13 to 22. Sampling for 5 d chosen at random consistently gave poor results. Sampling every 3rd d gave the poorest results. Controlled-release capsules predicted FO very accurately in lambs fed ALF. Reliable estimates were obtained in 67% of cases investigated with CBG, whereas only 25% of estimates were reliable with PEL. The controlled-release capsules always overestimated FO of wethers fed CBG and PEL, implying that in those lambs the actual release rate of Cr was less than that specified by the manufacturer.