Across diverse microbiotas, species abundances vary in time with distinctive statistical behaviors that appear to generalize across hosts, but the origins and implications of these patterns remain unclear. Here, we show that many of these patterns can be quantitatively recapitulated by a simple class of resource-competition models, in which the metabolic capabilities of different species are randomly drawn from a common statistical ensemble. Our coarse-grained model parametrizes the intrinsic consumer-resource properties of a community using a small number of macroscopic parameters, including the total number of resources, typical resource fluctuations over time, and the average overlap in resource-consumption profiles across species. We elucidate how variation in these parameters affects various time series statistics, enabling macroscopic parameter estimation and comparison across wide-ranging microbiotas, including the human gut, saliva, and vagina, as well as mouse gut and rice. The successful recapitulation of time series statistics across microbiotas suggests that resource competition generally acts as a dominant driver of community dynamics. Our work unifies numerous time series patterns under one model, clarifies their origins, and provides a framework to infer macroscopic parameters of resource competition from longitudinal studies of microbial communities.

The statistical associations between mutations, collectively known as linkage disequilibrium (LD), encode important information about the evolutionary forces acting within a population. Yet in contrast to single-site analogues like the site frequency spectrum, our theoretical understanding of linkage disequilibrium remains limited. In particular, little is currently known about how mutations with different ages and fitness costs contribute to expected patterns of LD, even in simple settings where recombination and genetic drift are the major evolutionary forces. Here, we introduce a forward-time framework for predicting linkage disequilibrium between pairs of neutral and deleterious mutations as a function of their present-day frequencies. We show that the dynamics of linkage disequilibrium become much simpler in the limit that mutations are rare, where they admit a simple heuristic picture based on the trajectories of the underlying lineages. We use this approach to derive analytical expressions for a family of frequency-weighted LD statistics as a function of the recombination rate, the frequency scale, and the additive and epistatic fitness costs of the mutations. We find that the frequency scale can have a dramatic impact on the shapes of the resulting LD curves, reflecting the broad range of time scales over which these correlations arise. We also show that the differences between neutral and deleterious LD are not purely driven by differences in their mutation frequencies, and can instead display qualitative features that are reminiscent of epistasis. We conclude by discussing the implications of these results for recent LD measurements in bacteria. This forward-time approach may provide a useful framework for predicting linkage disequilibrium across a range of evolutionary scenarios.

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.