The Population Genetics of Pleiotropy, and the Evolution of Collateral Resistance and Sensitivity in Bacteria
TL;DR: This work derives simple statistics of the JDFE that predict the expected slope, variance and co-variance of non-home fitness trajectories of Escherichia coli knock-out collection in the presence of antibiotics and provides simple theoretically grounded guidelines for designing robust sequential drug protocols.
Abstract: Pleiotropic fitness tradeoffs and their opposite, buttressing pleiotropy, underlie many important phenomena in ecology and evolution. Yet, predicting whether a population adapting to one (“home”) environment will concomitantly gain or lose fitness in another (“non-home”) environment remains challenging, especially when adaptive mutations have diverse pleiotropic effects. Here, we address this problem using the concept of the joint distribution of fitness effects (JDFE), a local measurable property of the fitness landscape. We derive simple statistics of the JDFE that predict the expected slope, variance and co-variance of non-home fitness trajectories. We estimate these statistics from published data from the Escherichia coli knock-out collection in the presence of antibiotics. We find that, for some drug pairs, the average trend towards collateral sensitivity may be masked by large uncertainty, even in the absence of epistasis. We provide simple theoretically grounded guidelines for designing robust sequential drug protocols.
Citations
More filters
Posted Content•
TL;DR: The results imply that mutator phenotypes are less effective in larger asexual populations, and have consequences for the advantages (or disadvantages) of sex via the Fisher–Muller effect.
Abstract: When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population concurrently. In an asexual population, these different mutant lineages interfere and not all can fix simultaneously. In addition, further beneficial mutations can accumulate in mutant lineages while these are still a minority of the population. In this paper, we analyze the dynamics of such multiple mutations and the interplay between multiple mutations and interference between clones. These result in substantial variation in fitness accumulating within a single asexual population. The amount of variation is determined by a balance between selection, which destroys variation, and beneficial mutations, which create more. The behavior depends in a subtle way on the population parameters: the population size, the beneficial mutation rate, and the distribution of the fitness increments of the potential beneficial mutations. The mutation-selection balance leads to a continually evolving population with a steady-state fitness variation. This variation increases logarithmically with both population size and mutation rate and sets the rate at which the population accumulates beneficial mutations, which thus also grows only logarithmically with population size and mutation rate. These results imply that mutator phenotypes are less effective in larger asexual populations. They also have consequences for the advantages (or disadvantages) of sex via the Fisher-Muller effect; these are discussed briefly.
64 citations
TL;DR: It is shown that evolved resistance to the component drugs – and in turn, the adaptation of growth rate – is governed by a Price equation whose covariance terms encode geometric features of both the two-drug-response surface in ancestral cells and the correlations between resistance levels to those drugs.
Abstract: Bacterial adaptation to antibiotic combinations depends on the joint inhibitory effects of the two drugs (drug interaction [DI]) and how resistance to one drug impacts resistance to the other (collateral effects [CE]). Here we model these evolutionary dynamics on two-dimensional phenotype spaces that leverage scaling relations between the drug-response surfaces of drug-sensitive (ancestral) and drug-resistant (mutant) populations. We show that evolved resistance to the component drugs - and in turn, the adaptation of growth rate - is governed by a Price equation whose covariance terms encode geometric features of both the two-drug-response surface (DI) in ancestral cells and the correlations between resistance levels to those drugs (CE). Within this framework, mean evolutionary trajectories reduce to a type of weighted gradient dynamics, with the drug interaction dictating the shape of the underlying landscape and the collateral effects constraining the motion on those landscapes. We also demonstrate how constraints on available mutational pathways can be incorporated into the framework, adding a third key driver of evolution. Our results clarify the complex relationship between drug interactions and collateral effects in multidrug environments and illustrate how specific dosage combinations can shift the weighting of these two effects, leading to different and temporally explicit selective outcomes.
14 citations
Cites background from "The Population Genetics of Pleiotro..."
..., 2017); and statistical correlations between resistance profiles for different drugs (Imamovic and Sommer, 2013; Kim et al., 2014; Pál et al., 2015; Barbosa et al., 2017; Rodriguez de Evgrafov et al., 2015; Nichol et al., 2019; Podnecky et al., 2018; Imamovic et al., 2018; Barbosa et al., 2019; Rosenkilde et al., 2019; Apjok et al., 2019; Maltas and Wood, 2019; Maltas et al., 2020; Hernando-Amado et al., 2020; Roemhild et al., 2020; Ardell and Kryazhimskiy, 2020)....
[...]
...…Rodriguez de Evgrafov et al., 2015; Nichol et al., 2019; Podnecky et al., 2018; Imamovic et al., 2018; Barbosa et al., 2019; Rosenkilde et al., 2019; Apjok et al., 2019; Maltas and Wood, 2019; Maltas et al., 2020; Hernando-Amado et al., 2020; Roemhild et al., 2020; Ardell and Kryazhimskiy, 2020)....
[...]
TL;DR: This article found that replicas evolved in the same condition share common patterns of pleiotropic effects across other environments, which emerge within the first several hundred generations of evolution, and also found dynamic and environment-specific variability within these trends.
Abstract: Evolutionary adaptation to a constant environment is driven by the accumulation of mutations which can have a range of unrealized pleiotropic effects in other environments. These pleiotropic consequences of adaptation can influence the emergence of specialists or generalists, and are critical for evolution in temporally or spatially fluctuating environments. While many experiments have examined the pleiotropic effects of adaptation at a snapshot in time, very few have observed the dynamics by which these effects emerge and evolve. Here, we propagated hundreds of diploid and haploid laboratory budding yeast populations in each of three environments, and then assayed their fitness in multiple environments over 1000 generations of evolution. We find that replicate populations evolved in the same condition share common patterns of pleiotropic effects across other environments, which emerge within the first several hundred generations of evolution. However, we also find dynamic and environment-specific variability within these trends: variability in pleiotropic effects tends to increase over time, with the extent of variability depending on the evolution environment. These results suggest shifting and overlapping contributions of chance and contingency to the pleiotropic effects of adaptation, which could influence evolutionary trajectories in complex environments that fluctuate across space and time.
10 citations
TL;DR: It is argued that the mutation effect reaction norm (Mu‐RN), a new instrument through which one can analyze the phenotypic consequences of mutations and interactions across environmental contexts, may help resolve the dynamism and unpredictability of evolution.
Abstract: Since the modern synthesis, the fitness effects of mutations and epistasis have been central yet provocative concepts in evolutionary and population genetics. Studies of how the interactions between parcels of genetic information can change as a function of environmental context have added a layer of complexity to these discussions. Here, I introduce the “mutation effect reaction norm” (Mu‐RN), a new instrument through which one can analyze the phenotypic consequences of mutations and interactions across environmental contexts. It embodies the fusion of measurements of genetic interactions with the reaction norm, a classic depiction of the performance of genotypes across environments. I demonstrate the utility of the Mu‐RN through a case study: the signature of a “compensatory ratchet” mutation that undermines reverse evolution of antimicrobial resistance. In closing, I argue that the mutation effect reaction norm may help us resolve the dynamism and unpredictability of evolution, with implications for theoretical biology, biotechnology, and public health.
9 citations
TL;DR: This paper found that replicas evolved in the same condition share common patterns of pleiotropic effects across other environments, which emerge within the first several hundred generations of evolution, and also found dynamic and environment-specific variability within these trends.
Abstract: Evolutionary adaptation to a constant environment is driven by the accumulation of mutations which can have a range of unrealized pleiotropic effects in other environments. These pleiotropic consequences of adaptation can influence the emergence of specialists or generalists, and are critical for evolution in temporally or spatially fluctuating environments. While many experiments have examined the pleiotropic effects of adaptation at a snapshot in time, very few have observed the dynamics by which these effects emerge and evolve. Here, we propagated hundreds of diploid and haploid laboratory budding yeast populations in each of three environments, and then assayed their fitness in multiple environments over 1000 generations of evolution. We find that replicate populations evolved in the same condition share common patterns of pleiotropic effects across other environments, which emerge within the first several hundred generations of evolution. However, we also find dynamic and environment-specific variability within these trends: variability in pleiotropic effects tends to increase over time, with the extent of variability depending on the evolution environment. These results suggest shifting and overlapping contributions of chance and contingency to the pleiotropic effects of adaptation, which could influence evolutionary trajectories in complex environments that fluctuate across space and time.
8 citations
References
More filters
01 Jan 1992
Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
6,887 citations
TL;DR: In this paper, an exact method is presented for numerically calculating, within the framework of the stochastic formulation of chemical kinetics, the time evolution of any spatially homogeneous mixture of molecular species which interreact through a specified set of coupled chemical reaction channels.
5,875 citations
"The Population Genetics of Pleiotro..." refers methods in this paper
...The SSWM simulations were carried out using the Gillespie algorithm (Gillespie, 1976), 612 as follows....
[...]
...610 Strong selection weak mutation 611 The SSWM simulations were carried out using the Gillespie algorithm (Gillespie, 1976), 612 as follows....
[...]
TL;DR: Measures of directional and stabilizing selection on each of a set of phenotypically correlated characters are derived, retrospective, based on observed changes in the multivariate distribution of characters within a generation, not on the evolutionary response to selection.
Abstract: Natural selection acts on phenotypes, regardless of their genetic basis, and produces immediate phenotypic effects within a generation that can be measured without recourse to principles of heredity or evolution. In contrast, evolutionary response to selection, the genetic change that occurs from one generation to the next, does depend on genetic variation. Animal and plant breeders routinely distinguish phenotypic selection from evolutionary response to selection (Mayo, 1980; Falconer, 1981). Upon making this critical distinction, emphasized by Haldane (1954), precise methods can be formulated for the measurement of phenotypic natural selection. Correlations between characters seriously complicate the measurement of phenotypic selection, because selection on a particular trait produces not only a direct effect on the distribution of that trait in a population, but also produces indirect effects on the distribution of correlated characters. The problem of character correlations has been largely ignored in current methods for measuring natural selection on quantitative traits. Selection has usually been treated as if it acted only on single characters (e.g., Haldane, 1954; Van Valen, 1965a; O'Donald, 1968, 1970; reviewed by Johnson, 1976 Ch. 7). This is obviously a tremendous oversimplification, since natural selection acts on many characters simultaneously and phenotypic correlations between traits are ubiquitous. In an important but neglected paper, Pearson (1903) showed that multivariate statistics could be used to disentangle the direct and indirect effects of selection to determine which traits in a correlated ensemble are the focus of direct selection. Here we extend and generalize Pearson's major results. The purpose of this paper is to derive measures of directional and stabilizing (or disruptive) selection on each of a set of phenotypically correlated characters. The analysis is retrospective, based on observed changes in the multivariate distribution of characters within a generation, not on the evolutionary response to selection. Nevertheless, the measures we propose have a close connection with equations for evolutionary change. Many other commonly used measures of the intensity of selection (such as selective mortality, change in mean fitness, variance in fitness, or estimates of particular forms of fitness functions) have little predictive value in relation to evolutionary change in quantitative traits. To demonstrate the utility of our approach, we analyze selection on four morphological characters in a population of pentatomid bugs during a brief period of high mortality. We also summarize a multivariate selection analysis on nine morphological characters of house sparrows caught in a severe winter storm, using the classic data of Bumpus (1899). Direct observations and measurements of natural selection serve to clarify one of the major factors of evolution. Critiques of the "adaptationist program" (Lewontin, 1978; Gould and Lewontin, 1979) stress that adaptation and selection are often invoked without strong supporting evidence. We suggest quantitative measurements of selection as the best alternative to the fabrication of adaptive scenarios. Our optimism that measurement can replace rhetorical claims for adaptation and selection is founded in the growing success of field workers in their efforts to measure major components of fitness in natural populations (e.g., Thornhill, 1976; Howard, 1979; Downhower and Brown, 1980; Boag and Grant, 1981; Clutton-Brock et
4,990 citations
"The Population Genetics of Pleiotro..." refers background in this paper
...64 Classical theoretical work on pleiotropy has been done in the field of quantitative ge- 65 netics (Lande and Arnold, 1983; Rose, 1982; Barton, 1990; Slatkin and Frank, 1990; Jones 66 et al., 2003; Johnson and Barton, 2005)....
[...]
...64 Classical theoretical work on pleiotropy has been done in the field of quantitative ge- 65 netics (Lande and Arnold, 1983; Rose, 1982; Barton, 1990; Slatkin and Frank, 1990; Jones 66 et al., 2003; Johnson and Barton, 2005)....
[...]
TL;DR: An introduction to population genetics theory, An introduction to Population Genetics Theory, Population Genetics theory, Population genetics theory as discussed by the authors, Population genetics, population genetics, and population genetics theories, Population Genetic Theory
Abstract: An introduction to population genetics theory , An introduction to population genetics theory , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
4,817 citations
3,009 citations
Additional excerpts
...(7) When beneficial mutations with large effects are sufficiently rare, equation (6) can be 512 approximated by the Fokker-Planck equation (Van Kampen, 1992) 513 ∂p ∂t = −r1 ∂p ∂x − r2 ∂p ∂y + D11 2 ∂2p ∂x2 +D12 ∂2p ∂x∂y + D22 2 ∂2p ∂y2 , (8) where r1 and r2 are given by equations (3), (4) and…...
[...]
...(5) The probability distribution p(x, y, t) satisfies the integro-differential forward Kol- 509 mogorov equation (Van Kampen, 1992) 510 ∂p ∂t (x, y, t) = ∫ ∞ −∞ dη ∫ ∞ −∞ dξ ( p(ξ, η, t)Q(x, y|ξ, η)− p(x, y, t)Q(ξ, η|x, y) ) (6) with the initial condition 511 p(x, y, 0) = δ(x− x0) δ(y − y0)....
[...]