Evaluating the impact of population bottlenecks in experimental evolution

Experimental evolution involves severe, periodic reductions in population size when fresh media are inoculated during serial transfer. These bottlenecks affect the dynamics of evolution, reducing the probability that a beneficial mutation will reach fixation. We quantify the impact of these bottlenecks on the evolutionary dynamics, for populations that grow exponentially between transfers and for populations in which growth is curbed by a resource-limited environment. We find that in both cases, mutations that survive bottlenecks are equally likely to occur, per unit time, at all times during the growth phase. We estimate the total fraction of beneficial mutations that are lost due to bottlenecks during experimental evolution protocols and derive the "optimal" dilution ratio, the ratio that maximizes the number of surviving beneficial mutations. Although more severe dilution ratios are often used in the literature, we find that a ratio of 0.1-0.2 minimizes the chances that rare beneficial mutations are lost. Finally, we provide a number of useful approximate results and illustrate our approach with applications to experimental evolution protocols in the literature.     

Statistical Significance of Mutation Frequencies,and the Power of Statistical Testing,Using the Poisson Distribution

The Poisson distribution may be employed to test whether mutation frequencies differ from control frequencies. This paper describes how this testing procedure may be used for either one-tailed or two-tailed hypotheses. It is also shown how the power of the statistical test can be calculated, the power being the probability of correctly concluding the null hypothesis to be false.     

The effect of population bottlenecks on mutation rate evolution in asexual populations

In the absence of recombination, a mutator allele can spread through a population by hitchhiking with beneficial mutations that appear in its genetic background. Theoretical studies over the past decade have shown that the survival and fixation probability of beneficial mutations can be severely reduced by population size bottlenecks. Here, we use computational modelling and evolution experiments with the yeast S. cerevisiae to examine whether population bottlenecks can affect mutator dynamics in adapting asexual populations. In simulation, we show that population bottlenecks can inhibit mutator hitchhiking with beneficial mutations and are most effective at lower beneficial mutation supply rates. We then subjected experimental populations of yeast propagated at the same effective population size to three different bottleneck regimes and observed that the speed of mutator hitchhiking was significantly slower at smaller bottlenecks, consistent with our theoretical expectations. Our results, thus, suggest that bottlenecks can be an important factor in mutation rate evolution and can in certain circumstances act to stabilize or, at least, delay the progressive elevation of mutation rates in asexual populations. Additionally, our findings provide the first experimental support for the theoretically postulated effect of population bottlenecks on beneficial mutations and demonstrate the usefulness of studying mutator frequency dynamics for understanding the underlying dynamics of fitness‐affecting mutations.     

In silico modelling of directed evolution: Implications for experimental design and stepwise evolution

We model the process of directed evolution (DE) in silico using genetic algorithms. Making use of the NK fitness landscape model, we analyse the effects of mutation rate, crossover and selection pressure on the performance of DE. A range of values of K, the epistatic interaction of the landscape, are considered, and high- and low-throughput modes of evolution are compared. Our findings suggest that for runs of or around ten generations’ duration—as is typical in DE—there is little difference between the way in which DE needs to be configured in the high- and low-throughput regimes, nor across different degrees of landscape epistasis. In all cases, a high selection pressure (but not an extreme one) combined with a moderately high mutation rate works best, while crossover provides some benefit but only on the less rugged landscapes. These genetic algorithms were also compared with a “model-based approach” from the literature, which uses sequential fixing of the problem parameters based on fitting a linear model. Overall, we find that purely evolutionary techniques fare better than do model-based approaches across all but the smoothest landscapes.     

Mutating away from your enemies: The evolution of mutation rate in a host–parasite system

The rate at which mutations occur in nature is itself under natural selection. While a general reduction of mutation rates is advantageous for species inhabiting constant environments, higher mutation rates can be advantageous for those inhabiting fluctuating environments that impose on-going directional selection. Analogously, species involved in antagonistic co-evolutionary arms races, such as hosts and parasites, can also benefit from higher mutation rates. We use modifier theory, combined with simulations, to investigate the evolution of mutation rate in such a host–parasite system. We derive an expression for the evolutionary stable mutation rate between two alleles, each of whose fitness depends on the current genetic composition of the other species. Recombination has been shown to weaken the strength of selection acting on mutation modifiers, and accordingly, we find that the evolutionarily attracting mutation rate is lower when recombination between the selected and the modifier locus is high. Cyclical dynamics are potentially commonplace for loci governing antagonistic species interactions. We characterize the parameter space where such cyclical dynamics occur and show that the evolution of large mutation rates tends to inhibit cycling and thus eliminates further selection on modifiers of the mutation rate. We then find using computer simulations that stochastic fluctuations in finite populations can increase the size of the region where cycles occur, creating selection for higher mutation rates. We finally use simulations to investigate the model behaviour when there are more than two alleles, finding that the region where cycling occurs becomes smaller and the evolutionarily attracting mutation rate lower when there are more alleles.     

Microsatellite variation, population structure, and bottlenecks in the threatened copperbelly water snake

Habitat loss and isolation is pervasive in the Midwest U.S. Wetlands are experiencing particularly dramatic declines, yet there is a paucity of information on the genetic impacts of these losses to obligate wetland vertebrates. We quantified the genetic variation of extant populations of a shallow wetland specialist and evaluated potential reductions in population size (i.e. bottlenecks) using seven polymorphic microsatellite DNA markers. We analyzed 228 copperbelly water snakes (Nerodia erythrogaster neglecta), representing populations from three states. Moderate genetic differentiation exists among all three regions (F _ST = 0.12, P < 0.001), with evidence for low levels of differentiation within the federally protected Ohio region (F _ST = 0.025, P = 0.007), and moderate to strong differentiation within the Indiana region (F _ST = 0.23, P < 0.001). Furthermore, Bayesian clustering (i.e. STRUCTURE) supports the separation of the Indiana sites, both from each other and from all other sampling sites. However, it does not support the separation of the Ohio sites from the Kentucky sites. Differentiation among sampling sites did not appear to be related to geographic distance, but rather depended on the quality of terrestrial corridors used for dispersal. Mode shifts in allele frequencies and excess heterozygosity tests were negative, while M-ratio tests were nearly all positive, indicating the likelihood of historical rather than contemporary population bottlenecks. However, potential subspecific intergradation in the Kentucky region may have artificially lowered the M-ratio, and we suggest caution when using the M-ratio approach if intergradation is suspected. Our results have conservation implications for wetland management and management of the copperbelly populations, and emphasizes the importance of protecting wetland complexes.     

A simulation study comparing the impact of experimental error on the performance of experimental designs and artificial neural networks used for process screening

Many variables and their interactions can affect a biotechnological process. Testing a large number of variables and all their possible interactions is a cumbersome task and its cost can be prohibitive. Several screening strategies, with a relatively low number of experiments, can be used to find which variables have the largest impact on the process and estimate the magnitude of their effect. One approach for process screening is the use of experimental designs, among which fractional factorial and Plackett–Burman designs are frequent choices. Other screening strategies involve the use of artificial neural networks (ANNs). The advantage of ANNs is that they have fewer assumptions than experimental designs, but they render black-box models (i.e., little information can be extracted about the process mechanics). In this paper, we simulate a biotechnological process (fed-batch growth of bakers yeast) to analyze and compare the effect of random experimental errors of different magnitudes and statistical distributions on experimental designs and ANNs. Except for the situation in which the error has a normal distribution and the standard deviation is constant, it was not possible to determine a clear-cut rule for favoring one screening strategy over the other. Instead, we found that the data can be better analyzed using both strategies simultaneously.     

Male-biased mutation, sex linkage, and the rate of adaptive evolution

An interaction between sex-linked inheritance and sex-biased mutation rates may affect the rate of adaptive evolution. Males have much higher mutation rates than females in several vertebrate and plant taxa. When evolutionary rates are limited by the supply of favorable new mutations, then genes will evolve faster when located on sex chromosomes that spend more time in males. For mutations with additive effects, Y-linked genes evolve fastest, followed by Z-linked genes, autosomal genes, X-linked genes, and finally W-linked and cytoplasmic genes. This ordering can change when mutations show dominance. The predicted differences in substitution rates may be detectable at the molecular level. Male-biased mutation could cause adaptive changes to accumulate more readily on certain kinds of chromosomes and favor animals with Z-W sex determination to have rapidly evolving male sexual displays.     

Exclusion rules, bottlenecks and the evolution of stochastic phenotype switching

Stochastic phenotype switching--often considered a bet hedging or risk-reducing strategy--can enhance the probability of survival in fluctuating environments. A recent experiment provided direct evidence for an adaptive origin by showing the de novo evolution of switching in bacterial populations propagated under a selective regime that captured essential features of the host immune response. The regime involved strong frequency-dependent selection realized via dual imposition of an exclusion rule and population bottleneck. Applied at the point of transfer between environments, the phenotype common in the current environment was assigned a fitness of zero and was thus excluded from participating in the next round (the exclusion rule). In addition, also at the point of transfer, and so as to found the next bout of selection, a single phenotypically distinct type was selected at random from among the survivors (the bottleneck). Motivated by this experiment, we develop a mathematical model to explore the broader significance of key features of the selective regime. Through a combination of analytical and numerical results, we show that exclusion rules and population bottlenecks act in tandem as potent selective agents for stochastic phenotype switching, such that even when initially rare, and when switching engenders a cost in Malthusian fitness, organisms with the capacity to switch can invade non-switching populations and replace non-switching types. Simulations demonstrate the robustness of our findings to alterations in switching rate, fidelity of exclusion, bottleneck size, duration of environmental state and growth rate. We also demonstrate the relevance of our model to a range of biological scenarios such as bacterial persistence and the evolution of sex.     

Estimating the intensity of male-driven evolution in rodents by using X-linked and Y-linked Ube 1 genes and pseudogenes

Using sequence data from the last introns of ZFX and ZFY genes, we previously estimated the male-to-female ratio () of mutation rate to be close to 6 in higher primates and 1.8 in rodents. As the mutation rate may vary among different regions of the mammalian genome, it is interesting to see whether sequence data from other regions will give similar estimates. In this study, we have determined the partial genomic sequences of the ubiquitin-activating enzyme El genes (Ube 1x and Ube 1y for the X-linked and Y-linked homologues, respectively) of mice and rats and two mouse Ube 1y pseudogenes. From the intron sequences of the Ube 1 genes, we calculated the divergence of the Y-linked genes (Y = 0.161) and that of the X-linked genes (X = 0.107) between mouse and rat, and found the Y/X ratio to be 1.50. This ratio led to an estimate of = 2.0 with a 95% confidence interval of (1.0, 3.9). Similar estimates of were obtained if mouse Ube 1y pseudogenes were used instead of the mouse Ube 1y functional gene. These estimates are consistent with our previous estimate for rodents and suggest that the sex ratio of mutation rate in rodents is approximately only one-third of that in higher primates. Our estimate of the divergence time between Ube 1x and Ube 1y supports the view that the two genes separated before the eutherian radiation.Correspondence to: W.-H. Li     

Effect of changes in population size on the correlation between mutation rate and heterozygosity

Summary The effect of changes in population size on the correlation between mutation rate and heterozygosity was studied by using two models: sudden change in population size and gradual change. It was shown that the results for the two models are close to each other, unless the rate of change for the latter is exceedingly slow. Thus, in many cases, the former model, which is much simpler than the latter, can be used to treat the present problem. Numerical computations showed that the correlation in a population that is expanding or has expanded in the recent past is stronger while the correlation in a population that is decreasing or has experienced a population reduction or bottleneck in the recent past is weaker than that for an equilibrium population with the same mean heterozygosity. However, regardless of whether the population is at equilibrium or not, the proportion of variation in heterozygosity that is attributable to variation in molecular weight over loci is rather small if the mean heterozygosity of the population is low, say of the order 0.05 or smaller.     

Reconstructing community relationships: the impact of sampling error, ordination approach, and gradient length

Effectively summarizing complex community relationships is an important feature in studies such as biodiversity, global change, and invasion ecology. The reliability of such community summaries depends on the degree of sampling variability that is present in the data, the structure of the data, and the choice of ordination method, but the relative importance of these factors is not understood. We compared the validity of results from different ordination methods by applying five levels of sampling error to a simulated coenoplane model at two gradient lengths using two types of data (abundance and presence–absence). The multivariate methods we compared were correspondence analysis (CA), detrended correspondence analysis (DCA), non-metric multidimensional scaling (NMDS), principal component analysis (PCA) and principal coordinates analysis (PCoA). Our results showed CA and PCA using presence–absence data were the most successful methods regardless of sampling error and gradient length, closely followed by the other methods using presence–absence data. With abundance data, PCA and CA were the most successful approaches with the short and long gradients, respectively. Approaches based on PCoA and NMDS using abundance data did not perform well regardless of the choice of distance measure used in the analysis. Both of these methods, along with the PCA using abundance data, were strongly affected by the longer gradient, leading to more distorted results.     

Modeling the dependence between the number of trials and the success probability in binary trials

A model for binary trials based on a bivariate generalization of the Poisson process for both the number of successes and number of trials with the transition rates dependent on the accumulating numbers of successes and trials is used to reanalyze some recently published data of Zhu, Eickhoff, and Kaiser (2003, Biometrics59, 955-961). This modeling admits alternative distributions for the numbers of trials and the numbers of successes conditional on the number of trials which generalize the Poisson and binomial distributions, without some of the restrictions apparent in the beta-binomial-Poisson mixed modeling of Zhu et al. (2003). Some quite marked differences between the results of this analysis and those described in Zhu et al. (2003) are apparent.     

Directional mutation pressure,mutator mutations,and dynamics of molecular evolution

Using a general form of the directional mutation theory, this paper analyzes the effect of mutations in mutator genes on the G + C content of DNA, the frequency of substitution mutations, and evolutionary changes (cumulative mutations) under various degrees of selective constraints. Directional mutation theory predicts that when the mutational bias between A/T and G/C nucleotide pairs is equilibrated with the base composition of a neutral set of DNA nucleotides, the mutation frequency per gene will be much lower than the frequency immediately after the mutator mutation takes place. This prediction explains the wide variation of the DNA G + C content among unicellular organisms and possibly also the wide intragenomic heterogeneity of third codon positions for the genes of multicellular eukaryotes. The present analyses lead to several predictions that are not consistent with a number of the frequently held assumptions in the field of molecular evolution, including belief in a constant rate of evolution, symmetric branching of phylogenetic trees, the generality of higher mutation frequency for neutral sets of nucleotides, the notion that mutator mutations are generally deleterious because of their high mutation rates, and teleological explanations of DNA base composition. Presented at the NATO Advanced Research Workshop onGenome Organization and Evolution, Spetsai, Greece, 16–22 September 1992     

Ethnology in the metropole: Robert Knox, Robert Gordon Latham and local sites of observational training

Anthropologists have traditionally separated the history of their discipline into two main diverging methodological paradigms: nineteenth-century armchair theorizing, and twentieth-century field-based research. But this tradition obscures both the complexity of the observational practices of early nineteenth-century researchers and the high degree of continuity between these practices and the techniques that came later. While historians have long since abandoned the notion that nineteenth-century ethnologists and anthropologists were merely ‘armchair’ theorists, this paper shows that there is still much to learn once one asks more insistently what the observational practices of early researchers were actually like. By way of bringing out this complexity and continuity, this essay re-examines the work of two well-known British ethnologists, Robert Knox, and Robert Gordon Latham; looking in particular at their methods of observing, analysing and representing different racial groups. In the work of each figure, early training in natural history, anatomy and physiology can be seen to have influenced their observational practices when it came to identifying and classifying human varieties. Moreover, in both cases, Knox and Latham developed locally-based observational training sites.     

The drift approximation solves the Poisson, Nernst-Planck, and continuum equations in the limit of large external voltages

Nearly linear current-voltage curves are frequently found in biological ion channels. Using the drift limit of the substantially non-linear Poisson-Nernst-Planck equations, we explain such behavior of diffusion-controlled charge transport systems. Starting from Gauss' law, drift, and continuity equations we derive a simple analytical current-voltage relation, which accounts for this deviation from linearity. As shown previously, the drift limit of the Nernst-Planck equation applies if the total electric current is dominated by the electric field, and integral contributions from concentration gradients are small. The simple analytical form of the drift current-voltage relations makes it an ideal tool to analyze experiment current-voltage curves. We also solved the complete Poisson-Nernst-Planck equations numerically, and determined current-voltage curves over a wide range of voltages, concentrations, and Debye lengths. The simulation fully supports the analytical estimate that the current-voltage curves of simple charge transport systems are dominated by the drift mechanism. Even those relations containing the most extensive approximations remained qualitatively within the correct order of magnitude. Received: 24 September 1998 / Revised version: 22 January 1999 / Accepted: 22 January 1999     

The effects of sex and mutation rate on adaptation in test tubes and to mouse hosts by Saccharomyces cerevisiae

Some hypotheses for the evolution of sex focus on adaptation to changing or heterogeneous environments, but these hypotheses have rarely been tested. We tested for advantages of sex and of increased mutation rates in yeast strains in two contrasting environments: a standard and relatively homogeneous laboratory environment of minimal medium in test tubes, and the variable environment of a mouse brain experienced by pathogenic strains. Evolving populations were founded as equal mixtures of sexual and obligately asexual genotypes. In the sexuals, cycles of sporulation, meiosis, and mating were induced approximately every 50 mitotic generations, with the asexuals undergoing sporulation but not ploidy cycles or recombination. In both environments, replicate negative control populations established with the same pair of strains were propagated with neither mating nor meiosis. In test tubes with no sex induced, sexuals were fixed in all five replicates within 250 mitotic generations, whereas in mice with no sex induced, asexuals were fixed in all four replicates by 170 generations. Inducing sex altered these outcomes in opposite directions in test tubes and mice, decreasing the fixation frequencies of sexuals in test tubes but increasing them in mice. These contrasts with asexual controls suggest an advantage for sex in mice but not in test tubes, although there was no difference between test tubes and mice in the numbers of populations fixed-for sexuals. In analogous experiments testing for an advantage of increased mutation rates, wild-type genotypes became fixed at the expense of mutators in every replicate of both test tube and mouse populations, indicating a disadvantage for mutators in both environments. Increased rates of point mutation do not appear to accelerate adaptation.     

Comparison of group testing algorithms for case identification in the presence of test error

We derive and compare the operating characteristics of hierarchical and square array-based testing algorithms for case identification in the presence of testing error. The operating characteristics investigated include efficiency (i.e., expected number of tests per specimen) and error rates (i.e., sensitivity, specificity, positive and negative predictive values, per-family error rate, and per-comparison error rate). The methodology is illustrated by comparing different pooling algorithms for the detection of individuals recently infected with HIV in North Carolina and Malawi.     

Modeling and experimental validation of carbon dioxide evolution in alkalophilic cultures

The chemical reactions involving carbon dioxide in mineral culture media are considered. A mathematic model is set up, based on published data, which is valid at pH values below 9, and in which the nonideality of the solution is taken into account. The crucial parameter is the constant expressing the equilibrium between carbon dioxide and bicarbonate, K(1).The reactions were studied in three different aqueous solutions: water, mineral salt medium, and a suspension with nongrowing bacterial cells. For each situation, three methods were compared for the determination of the bicarbonate concentration in the solution: equilibrium state total carbon analysis, dynamic monitoring of the rate of acid or alkali addition, and dynamic measurement of the carbon dioxide gas phase mole fraction.In a batch-stirred tank reactor, the equilibrium constant K(1) agreed with the published value, and the three bicarbonate analysis methods give the same results. If the nonideality is not taken into account, the result significantly differed from the published value and is likely to be incorrect.A real alkalophilic process, using Acinetobacter calcoaceticus in a continuous stirred tank reactor at steady state, also gave results that are in accord with the literature. However, the results do not allow validation of the equation expressing the nonideality.The steady state in the batch system and in continuous culture can be well described with the mathematical model. However, in the transient state there are some unexplained differences between simulation and measurement.