Promiscuous Enzyme Activity as a Driver of Allo and Iso Convergent Evolution, Lessons from the β-Lactamases

The probability of the evolution of a character depends on two factors: the probability of moving from one character state to another character state and the probability of the new character state fixation. The more the evolution of a character is probable, the more the convergent evolution will be witnessed, and consequently, convergent evolution could mean that the convergent character evolution results as a combination of these two factors. We investigated this phenomenon by studying the convergent evolution of biochemical functions. For the investigation we used the case of β-lactamases. β-lactamases hydrolyze β-lactams, which are antimicrobials able to block the DD-peptidases involved in bacterial cell wall synthesis. β-lactamase activity is present in two different superfamilies: the metallo-β-lactamase and the serine β-lactamase. The mechanism used to hydrolyze the β-lactam is different for the two superfamilies. We named this kind of evolution an allo-convergent evolution. We further showed that the β-lactamase activity evolved several times within each superfamily, a convergent evolution type that we named iso-convergent evolution. Both types of convergent evolution can be explained by the two evolutionary mechanisms discussed above. The probability of moving from one state to another is explained by the promiscuous β-lactamase activity present in the ancestral sequences of each superfamily, while the probability of fixation is explained in part by positive selection, as the organisms having β-lactamase activity allows them to resist organisms that secrete β-lactams. Indeed, an organism that has a mutation that increases the β-lactamase activity will be selected, as the organisms having this activity will have an advantage over the others.

Selection on mutators is not frequency-dependent

The evolutionary fate of mutator mutations – genetic variants that raise the genome-wide mutation rate – in asexual populations is often described as being frequency (or number) dependent. Mutators can invade a population by hitchhiking with a sweeping beneficial mutation, but motivated by earlier experiments results, it has been repeatedly suggested that mutators must be sufficiently frequent to produce such a driver mutation before non-mutators do. Here, we use stochastic, agent-based simulations to show that neither the strength nor the sign of selection on mutators depend on their initial frequency, and while the overall probability of hitchhiking increases predictably with frequency, the per-capita probability of fixation remains unchanged.

Allele Based Inference on Evolution and Extinction; A Genetic Drift Approach

In other to present a series of stochastic models from population dynamics capable of describing rudimentary aspects of genetic evolution, we studied two-allele Wright–Fisher and the Moran models for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size “simplest form, selection, and random mutation”. Principal results were presented in qualitative terms, illustrated by Monte Carlo simulations from R and http://www.radford.edu/~rsheehy/Gen_flash/popgen. Moran and the Wright-Fisher Models exhibited the same fixation probabilities, only that the Moran model runs twice as fast as the Wright-Fisher Model. A clue that can help us to understand this result is provided by the variance in reproductive success in the two models. Genetic changes due to drift were neither directional nor predictable in any deterministic way. Nonetheless, genetic drift led to evolutionary change in the absence of mutation (P=0.5), natural selection or gene flow. In general, alleles drift to fixation is significantly faster in smaller populations. Probability of fixation of an allele A was approximately equivalent to the initial frequency of that allele. With the inclusion of selection in our model, probability of fixation of a favoured allele due to natural selection increased with increase in fitness advantage and population size. The time taken to reach fixation is much slower, in case of no selective advantage, than a fixation under mutation with selective advantage.

Selection on mutators is not frequency-dependent

The evolutionary fate of mutator mutations – i.e., genetic variants that raise the genome-wide mutation rate – in asexual populations is often described as being frequency (or number) dependent. This common intuition suggests that mutators can invade a population by hitchhiking with a sweeping beneficial mutation, but only when sufficiently frequent to produce such a mutation before non-mutators do. Here, we use stochastic, agent-based simulations to show that neither the strength nor the sign of selection on mutators depend on their initial frequency, and while the overall probability of hitchhiking increases predictably with frequency, the per-capita probability of fixation remains unchanged.

Haldane’s Probability of Mutant Survival is Not the Probability of Allele Establishment

ABSTRACTHaldane notably showed in 1927 that the probability of fixation for an advantageous allele is approximately 2s, for selective advantage s. This widely known result is variously interpreted as either the fixation probability or the establishment probability, where the latter is considered the likelihood that an allele will survive long enough to have effectively escaped loss by drift. While Haldane was concerned with escape from loss by drift in the same paper, in this short note we point out that: 1) Haldane’s ‘probability of survival’ is analogous to the probability of fixation in a Wright-Fisher model (as also shown by others); and 2) This result is unrelated to Haldane’s consideration of how common an allele must be to ‘probably spread through the species’. We speculate that Haldane’s survival probability may have become misunderstood over time due to a conflation of terminology about surviving drift and ‘ultimately surviving’ (i.e., fixing). Indeed, we find that the probability of establishment remarkably appears to have been overlooked all these years, perhaps as a consequence of this misunderstanding. Using straightforward diffusion and Markov chain methods, we show that under Haldane’s assumptions, where establishment is defined by eventual fixation being more likely that extinction, the establishment probability is actually 4s when the fixation probability is 2s. Generalizing consideration to deleterious, neutral, and adaptive alleles in finite populations, if establishment is defined by the odds ratio between eventual fixation and extinction, k, the general establishment probability is (1 + k)/k times the fixation probability. It is therefore 4s when k = 1, or 3s when k = 2 for beneficial alleles in large populations. As k is made large, establishment becomes indistinguishable from fixation, and ceases to be a useful concept. As a result, we recommend establishment be generally defined as when the odds of ultimate fixation are greater than for extinction (k = 1, following Haldane), or when fixation is twice as likely as extinction (k = 2).

Introduction

Chapter 1, “Introduction: What is molecular population genetics?,” presents the motivations, applications, and historical context for molecular population genetics as a subdiscipline within biology. It describes how changes to DNA are inextricably woven into thinking about evolution and how molecular population genetics can be used to transport our thinking backward and forward through time. Key classic theoretical ideas summarizing allele frequency change, probability of fixation, and the time to fixation are encapsulated in brief vignettes. Both fundamental and applied uses of molecular population genetic perspectives are summarized in this survey of the historical, conceptual, and empirical development of the branch of science that we call population genetics and its integration with DNA sequences.

IMPROVEMENT OF FIDELITY OF MOVING OBJECTS CLASSIFICATION IN GUARD SIGNALING COMPLEXES WITH SEISMIC SENSORS

The effectiveness of guard signaling complexes (GSC), when there is an important validity of the classification of moving objects (MO), is evaluated by the following indexes: probability of GSC task execution; probability of partial fulfillment of the task; probability of user’s “deception”. Accordingly, the performance indicators of the GSC, in turn, depend on the indexes of the functionality of its constituents: probability of fixation of moving object by seismic sensor, probability of correct classification of MO type and probability of receiving radio signal by the system of receiving and displaying information (SRDI). The article describes a discrete-continuous stochastic model of of GSC reaction to moving object crossing control zone, in which three seismic sensors are installed. Majority principle of identifying the type of moving object was used on the receiving part of the complex. A comparative analysis of the effectiveness of guard signaling complexes using one, two and three sensors in control zone are carried out.

Evolution of dispersal can rescue populations from expansion load

Understanding the causes and consequences of range expansions or range shifts has a long history in evolutionary biology. Recent theoretical, experimental, and empirical work has identified two particularly interesting phenomena in the context of species range expansions: (i) gene surfing and the relaxation of natural selection, and (ii) spatial sorting. The former can lead to an accumulation of deleterious mutations at range edges, causing an expansion load and slowing down expansion. The latter can create gradients in dispersal-related traits along the expansion axis and cause an acceleration of expansion. We present a theoretical framework that treats spatial sorting and gene surfing as spatial versions of natural selection and genetic drift, respectively. This model allows us to study analytically how gene surfing and spatial sorting interact, and to derive the probability of fixation of pleiotropic mutations at the expansion front. We use our results to predict the co-evolution of mean fitness and dispersal rates, taking into account the effects of random genetic drift, natural selection and spatial sorting, as well as correlations between fitnessand dispersal-related traits. We identify a “rescue effect” of spatial sorting, where the evolution of higher dispersal rates at the leading edge rescues the population from incurring expansion load.

The Time Scale of Evolution

Fitness is a measure of how quickly alleles change in frequency under natural selection. Time is always implicit in evolutionary models but its units are rarely made explicit. When measuring phenotypes such as absolute growth rate, the units of measurement need to be made explicit. By contrasting measures of fitness and growth rate, we uncovered a curious effect, by which evolutionary time runs at different speeds depending on how restricted population growth is. In other words, when the generation time of a population is externally imposed, relative fitness per generation is no longer an accurate measure of differences between genotypes. We explore this effect and describe how it affects selective sweeps, probability of fixation of beneficial mutations and adaptation dynamics. Moreover, we show that different populations cannot be compared unless they share a common reference and that our inference of epistasis can be biased by this temporal effect. Finally, we suggest less biased ways to measure selection in experimental evolution.

How successful are mutants in multiplayer games with fluctuating environments? Sojourn times, fixation and optimal switching

Using a stochastic model, we investigate the probability of fixation, and the average time taken to achieve fixation, of a mutant in a population of wild-types. We do this in a context where the environment in which the competition takes place is subject to stochastic change. Our model takes into account interactions which can involve multiple participants. That is, the participants take part in multiplayer games. We find that under certain circumstances, there are environmental switching dynamics which minimize the time that it takes for the mutants to fixate. To analyse the dynamics more closely, we develop a method by which to calculate the sojourn times for general birth–death processes in fluctuating environments.