We developed a theoretical framework which explains why the relationship between growth rate (r) and carrying capacity (K) describes a skew parabola, and applied this parabola to the study of of antibiotic resistance. We demonstrate that, to become resistant, microbes need not to increase r at the cost of K (costs of resistance) but, upon abundance of nutrients, the presence of an antibiotic can lead to an increase in r and K creating a `uberbug'.. Reconciling Tradeoff Theories with Antibiotic-Resistant Genotypes that Evolve to Quickly Grow to High Densities

Evolutionary trade-offs arise when mutations that improve one life history trait incur fitness costs in other traits. Trade-offs are thought central to evolution, just as costs are to antibiotic resistance. Since drug resistance by efflux can be associated with a 10%, or more, increase in length of the Escherichia coli chromosome, we sought costs to tetracycline resistance in E. coli. It was, however, difficult to identify costs in evolution experiments because E.coli’s growth rate (r) and maximal population size (K) both increased, as did drug efflux, improvements that remained following drug withdrawal. We sought reasons why resistance mutations would increase r and K, particularly as the latter tradeoff according to rK selection theory. Using prokaryote and eukaryote microbial species, including clinical pathogens, we predicted and subsequently observed that r and K can engage in a tradeoff, but need not do so, because a ‘trade-up’ is present in the parabola constraining r to K. The mechanism supporting the tradeup-tradeoff dichotomy is reduced metabolic efficiency in energy-rich environments. We deployed E. coli ribosomal RNA knockout mutants to show that a specific genetic alteration, a change in rrn operon copy number, can simultaneously optimise r and K within a set of genomes. Moreover, the optimal genome has fewer rrn operons than the ancestral strain. It is, therefore, unsurprising to have observed r-adaptation in the presence of a ribosome-inhibiting antibiotic increase population size. Thus, evolution found resistant bacteria that grew faster to larger population sizes than bacteria that did not encounter the antibiotic; the price E.coli paid for this triple improvement is an elongated lag phase and loss of genes associated with stress protection.