Fast and strong amplifiers of natural selection

Abstract

Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations. Over the past 15 years, extensive research has produced remarkable structures called strong amplifiers which guarantee that every beneficial mutation fixates with high probability. But strong amplification has come at the cost of considerably delaying the fixation event, which can slow down the overall rate of evolution. However, the precise relationship between fixation probability and time has remained elusive. Here we characterize the slowdown effect of strong amplification. First, we prove that all strong amplifiers must delay the fixation event at least to some extent. Second, we construct strong amplifiers that delay the fixation event only marginally as compared to the well-mixed populations. Our results thus establish a tight relationship between fixation probability and time: Strong amplification always comes at a cost of a slowdown, but more than a marginal slowdown is not needed.

Do amplifiers of selection maximise average fitness?

“…Typically, amplifiers of selection have also a higher fixation time [27][28][29]. Thus, one has to be careful that the assumption of small mutation rate is still fulfilled.…”

“…In Evolutionary graph theory, evolutionary dynamics on graph structures have been studied in great detail. While the field has been mostly driven from the mathematical and computational community [1, 2, 18, 27, 29], partly driven by biological systems [16, 30, 31], now there is increasing interest in applying these ideas to experimental systems in microbiology [32, 33].…”

“…Thus, the validity of this approximation depends not only on the mutation rates, but also the fixation times. Previous research has already indicated that that graphs with higher fixation times call for lower mutation rates for this approximation to hold [26, 28, 29]. The star graph with self-loops is very restrictive to the low mutation approximation compared to the complete graph, while for the star graph and the complete graph the weak mutation approximation starts to fail at similar mutation rates.…”

Emergence of Resistant Escherichia coli Mutants in Microfluidic On-Chip Antibiotic Gradients

“… Zhang et al (2011) observed fast evolution of resistance of Escherichia coli to ciprofloxacin within 10 h in a structured heterogeneous environment in a microfabricated device ( Zhang et al, 2011 ). As suggested by theory, the structure of these microfluidics-based environments may act as selection amplifiers for the evolution of resistance ( Tkadlec et al, 2021 ). Other experiments carried out on soft agar plates suggested that motility (surface-associated swarming behavior and swimming) may have an important role in the adaptation and evolution in structured environments ( Lai et al, 2009 ; Butler et al, 2010 ; Baym et al, 2016 ; Ghaddar et al, 2018 ).…”

Fixation probabilities in network structured meta-populations

“…One of the major goals of evolutionary graph theory 1 is to assess the effect of underlying population structure on the fixation probability (the probability of ultimate fixation of a mutant) [2][3][4][5][6] and the fixation time [7][8][9][10] . An important aim is to find an optimized structure to speed up or slow down the spread of a newly arising mutant [11][12][13] .…”