Robert E. Beardmore

When the Most Potent Combination of Antibiotics Selects for the Greatest Bacterial Load: The Smile-Frown Transition

Finding the most potent combinations of antibiotics in the lab can be a challenge if antibiotic interactions are not robust to evolutionary adaptation.

Bistable expression of virulence genes in Salmonella leads to the formation of an antibiotic-tolerant subpopulation

The bistable expression of virulence genes in Salmonella allows a clonal population to hedge its bets: one subpopulation suffers a growth cost, but is tolerant to antibiotics.

The Singularity-Induced Bifurcation and its Kronecker Normal Form

It is shown that the singularity-induced bifurcation theorem due to Venkatasubramanian, Schattler, and Zaborszky [ Proceedings of the IEEE, 83 (1995), pp. 1530--1558] can be expressed as the perturbation of an infinite eigenvalue of a particular class of parameterized index-1 matrix pencil, denoted

Metabolic trade-offs and the maintenance of the fittest and the flattest

(M,L(\lambda))

Constraints on microbial metabolism drive evolutionary diversification in homogeneous environments

. It is shown that the matrix pencil at the singularity-induced bifurcation point,

Understanding the limits to generalizability of experimental evolutionary models

(M,L(\lambda_{0}))

Using a Sequential Regimen to Eliminate Bacteria at Sublethal Antibiotic Dosages

, has Kronecker index-2. It is also shown that a two-parameter unfolding of a singularity-induced bifurcation point results in a locus of index-0 pencils, denoted

Antibiotic cycling versus mixing: the difficulty of using mathematical models to definitively quantify their relative merits.

(M(\epsilon),L(\lambda(\epsilon)))

ROTATING ANTIBIOTICS SELECTS OPTIMALLY AGAINST ANTIBIOTIC RESISTANCE, IN THEORY

, which has two purely imaginary eigenvalues near infinity.

The Flow of a DAE near a Singular Equilibrium

How is diversity maintained? Environmental heterogeneity is considered to be important, yet diversity in seemingly homogeneous environments is nonetheless observed. This, it is assumed, must either be owing to weak selection, mutational input or a fitness advantage to genotypes when rare. Here we demonstrate the possibility of a new general mechanism of stable diversity maintenance, one that stems from metabolic and physiological trade-offs. The model requires that such trade-offs translate into a fitness landscape in which the most fit has unfit near-mutational neighbours, and a lower fitness peak also exists that is more mutationally robust. The ‘survival of the fittest’ applies at low mutation rates, giving way to ‘survival of the flattest’ at high mutation rates. However, as a consequence of quasispecies-level negative frequency-dependent selection and differences in mutational robustness we observe a transition zone in which both fittest and flattest coexist. Although diversity maintenance is possible for simple organisms in simple environments, the more trade-offs there are, the wider the maintenance zone becomes. The principle may be applied to lineages within a species or species within a community, potentially explaining why competitive exclusion need not be observed in homogeneous environments. This principle predicts the enigmatic richness of metabolic strategies in clonal bacteria and questions the safety of lethal mutagenesis as an antimicrobial treatment.