  Evolution has fascinated quantitative and physical scientists for decades:
how can the random process of mutation, recombination, and duplication of
genetic information generate the diversity of life? What determines the rate of
evolution? Are there quantitative laws that govern and constrain evolution? Is
evolution repeatable or predictable? Historically, the study of evolution
involved classifying and comparing species, typically based on morphology. In
addition to phenotypes on the organismal and molecular scales, we now use
whole-genome sequencing to uncover not only the differences between species but
also to characterize genetic diversity within-species in unprecedented detail.
This diversity can be compared to predictions of quantitative models of
evolutionary dynamics. Here, we review key theoretical models of population
genetics and evolution along with examples of data from lab evolution
experiments, longitudinal sampling of viral populations, microbial communities
and the studies of immune repertoires. In all these systems, evolution is
shaped by often variable biological and physical environments. While these
variable environments can be modeled implicitly in cases such as host-pathogen
co-evolution, the dynamic environment, and emerging ecology often cannot be
ignored. Integrating dynamics on different scales, both in terms of observation
and theoretical models, remains a major challenge towards a better
understanding of evolution.
