@article {manhart2018trade,
	title = {Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection},
	journal = {Proc. R. Soc. B},
	volume = {285},
	year = {2018},
	pages = {20172459},
	publisher = {The Royal Society},
	abstract = {Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple life-history traits to selection is a critical question for evolutionary biology as we seek to predict the evolutionary fates of mutations. Here we use a model of microbial growth to show that there are two distinct components of selection corresponding to the growth and lag phases, while the yield modulates their relative importance. The model predicts rich population dynamics when there are trade-offs between phases: multiple strains can coexist or exhibit bistability due to frequency-dependent selection, and strains can engage in rock{\textendash}paper{\textendash}scissors interactions due to non-transitive selection. We characterize the environmental conditions and patterns of traits necessary to realize these phenomena, which we show to be readily accessible to experiments. Our results provide a theoretical framework for analysing high-throughput measurements of microbial growth traits, especially interpreting the pleiotropy and correlations between traits across mutants. This work also highlights the need for more comprehensive measurements of selection in simple microbial systems, where the concept of an ordinary fitness landscape breaks down.},
	url = {http://rspb.royalsocietypublishing.org/content/285/1872/20172459},
	author = {Manhart, Michael and Adkar, Bharat V and Shakhnovich, EugeneI.}
}
