Transposable elements and fitness of bacteria

A stochastic model was designed to describe the evolution of bacterial cultures during 10,000 generations. It is based on a decreasing law for the generation of beneficial mutations as they become fixed in the genomes. Seven beneficial mutations on average were necessary to improve the relative fitness from 1.0 to 1.43 and the model was consistent with the population biology and the genetic data of 12 experimental lines. In one bacterial line, comparison between the model and the data suggests that pivotal mutations mediated by insertion sequences account for a large part of bacterial adaptation. In a more detailed analysis of one simulation, it was shown that only 0.01% of the mutations generated by a population over 10,000 generations can go to fixation as a consequence of their improved fitness. However in the model, the probability of being better fit than its parent should be set initially at ca. 10% to promote an evolution similar to the observed data.     

Critical Mutation Rate Has an Exponential Dependence on Population Size in Haploid and Diploid Populations

Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has significant potential in aiding population management to prevent local (and global) extinction events.     

Genetic algorithms and parallel processing in maximum-likelihood phylogeny inference

We investigated the usefulness of a parallel genetic algorithm for phylogenetic inference under the maximum-likelihood (ML) optimality criterion. Parallelization was accomplished by assigning each "individual" in the genetic algorithm "population" to a separate processor so that the number of processors used was equal to the size of the evolving population (plus one additional processor for the control of operations). The genetic algorithm incorporated branch-length and topological mutation, recombination, selection on the ML score, and (in some cases) migration and recombination among subpopulations. We tested this parallel genetic algorithm with large (228 taxa) data sets of both empirically observed DNA sequence data (for angiosperms) as well as simulated DNA sequence data. For both observed and simulated data, search-time improvement was nearly linear with respect to the number of processors, so the parallelization strategy appears to be highly effective at improving computation time for large phylogenetic problems using the genetic algorithm. We also explored various ways of optimizing and tuning the parameters of the genetic algorithm. Under the conditions of our analyses, we did not find the best-known solution using the genetic algorithm approach before terminating each run. We discuss some possible limitations of the current implementation of this genetic algorithm as well as of avenues for its future improvement.     

EXTRA‐PAIR PATERNITY AND THE VARIANCE IN MALE FITNESS IN SONG SPARROWS (MELOSPIZA MELODIA)

The variance in fitness across population members can influence major evolutionary processes. In socially monogamous but genetically polygynandrous species, extra‐pair paternity (EPP) is widely hypothesized to increase the variance in male fitness compared to that arising given the socially monogamous mating system. This hypothesis has not been definitively tested because comprehensive data describing males’ apparent (social) and realized (genetic) fitness have been lacking. We used 16 years of comprehensive social and genetic paternity data for an entire free‐living song sparrow (Melospiza melodia) population to quantify and compare variances in male apparent and realized fitness, and to quantify the contribution of the variances in within‐pair reproductive success (WPRS) and extra‐pair reproductive success (EPRS) and their covariance to the variance in realized fitness. Overall, EPP increased the variance in male fitness by only 0–27% across different fitness and variance measures. This relatively small effect reflected the presence of socially unpaired males with zero apparent and low realized fitness, small covariance between WPRS and EPRS, and large variance in WPRS that was relatively unaffected by EPP. Therefore, although EPP altered individual males’ contributions to future generations, its impact on population‐level parameters such as the opportunity for selection and effective population size was limited.     

A genetic algorithm-based protocol for docking ensembles of small ligands using experimental restraints

Summary A genetic algorithm (GA) based method for docking ensembles of small, flexible ligands to receptor proteins using NMR-derived constraints is described. In this method, three translations and rotations of the ligand and the dihedral angles of the ligand are represented by binary strings and evolve under the genetic operators of cross-over, mutation, migration and selection. The fitness function for the selection process includes distance and dihedral restraints and a repulsive van der Waals term. The GA was applied to a three-atom model system as well as to the streptavidin-biotin complex using simulated intermolecular distance restraints. In both systems, the GA was able to obtain low-energy conformations when only a single binding site was simulated. Calculations were also performed using distance restraints from two distinct binding sites. In these simulations, the GA was able to obtain low-energy conformations corresponding to ligand molecules in each of the two sites. The inclusion of additional ligands in the ensemble did not result in an energetic benefit, confirming that only two ligand conformations were necessary to fulfill the distance restraints. This method allows for a direct investigation of the minimum number of ligand orientations necessary to fulfill experimental distance restraints, and simultaneously yields detailed structural information about each site.     

Optimization of a stochastically simulated gene network model via simulated annealing

By rearranging naturally occurring genetic components, gene networks can be created that display novel functions. When designing these networks, the kinetic parameters describing DNA/protein binding are of great importance, as these parameters strongly influence the behavior of the resulting gene network. This article presents an optimization method based on simulated annealing to locate combinations of kinetic parameters that produce a desired behavior in a genetic network. Since gene expression is an inherently stochastic process, the simulation component of simulated annealing optimization is conducted using an accurate multiscale simulation algorithm to calculate an ensemble of network trajectories at each iteration of the simulated annealing algorithm. Using the three-gene repressilator of Elowitz and Leibler as an example, we show that gene network optimizations can be conducted using a mechanistically realistic model integrated stochastically. The repressilator is optimized to give oscillations of an arbitrary specified period. These optimized designs may then provide a starting-point for the selection of genetic components needed to realize an in vivo system.     

Prediction of common secondary structures of RNAs: a genetic algorithm approach

In this study we apply a genetic algorithm to a set of RNA sequences to find common RNA secondary structures. Our method is a three-step procedure. At the first stage of the procedure for each sequence, a genetic algorithm is used to optimize the structures in a population to a certain degree of stability. In this step, the free energy of a structure is the fitness criterion for the algorithm. Next, for each structure, we define a measure of structural conservation with respect to those in other sequences. We use this measure in a genetic algorithm to improve the structural similarity among sequences for the structures in the population of a sequence. Finally, we select those structures satisfying certain conditions of structural stability and similarity as predicted common structures for a set of RNA sequences. We have obtained satisfactory results from a set of tRNA, 5S rRNA, rev response elements (RRE) of HIV-1 and RRE of HIV-2/SIV, respectively.     

A genetic algorithm based molecular modeling technique for RNA stem-loop structures.

A new modeling technique for arriving at the three dimensional (3-D) structure of an RNA stem-loop has been developed based on a conformational search by a genetic algorithm and the following refinement by energy minimization. The genetic algorithm simultaneously optimizes a population of conformations in the predefined conformational space and generates 3-D models of RNA. The fitness function to be optimized by the algorithm has been defined to reflect the satisfaction of known conformational constraints. In addition to a term for distance constraints, the fitness function contains a term to constrain each local conformation near to a prepared template conformation. The technique has been applied to the two loops of tRNA, the anticodon loop and the T-loop, and has found good models with small root mean square deviations from the crystal structure. Slightly different models have also been found for the anticodon loop. The analysis of a collection of alternative models obtained has revealed statistical features of local variations at each base position.     

Viabilities of Third Chromosomes of DROSOPHILA PSEUDOOBSCURA Differing in Relative Competitive Fitness

Arrowhead (AR) third chromosome arrangements of Drosophila pseudoobscura, whose competitive fitnesses had been determined in population cages, were tested for their genetic loads in homozygous, heterozygous (homokaryotypic), and heterokaryotypic (AR/CH) combinations. The results showed that their competitive population cage performances were correlated to their viabilities as homozygotes but were not correlated to their viabilities as heterozygotes or as heterokaryotypes. However, the results do not fit in too simply with the mutational model of population structure, since the improvement of homozygous viability with increased competitive fitness was not accompanied by a significant degree of dominance as measured by the regression of viabilities of heterozygotes on homozygotes. Only the AR chromosomes derived from the population with poorest competitive fitness showed marked partial dominance (h=.35). The viabilities of heterokaryotypes were markedly uniform for all chromosomes tested and produced significantly greater numbers of flies per culture than the homokaryotypes. In general, the results show that the ranking of relative competitive fitnesses of these chromosomes is not a simple extrapolation of their viabilities, although marked changes in the populations tested have occurred. It is proposed that the differences in competitive fitness, homozygous viability, and degree of dominance observed among these chromosomes, arise from differences in genetic variability which enable different linkage relationships to be established for genes affecting these attributes.     

Fitness landscapes for coupled map lattices

Our goal is to match some dynamical aspects of biological systems with that of networks of coupled logistic maps. With these networks we generate sequences of iterates, convert them to symbol sequences by coarse-graining, and count the number of times combinations of symbols occur. Comparison of this with the number of times these combinations occur in experimental data—a sequence of interbeat intervals for example—is a measure of the fitness of each network to describe the target data. The most fit networks provide a cartoon that suggests a decomposition of the experimental data into a component that may be produced by a simple dynamical subsystem, and a residual component, the result of detailed, particular characteristics of the system that generated the target data. In the space of all network parameters, each point corresponds to a particular network. We construct a fitness landscape when we assign a fitness to each point. Because the parameters are distributed continuously over their ranges, and because fitnesses are estimated numerically, any plot of the landscape involves a finite sample of parameter values. We’ll investigate how the local landscape geometry changes when the array of sample parameters is refined, and use the landscape geometry to explore complex relations between local fitness maxima.     

REJECTOR: software for population history inference from genetic data via a rejection algorithm

We introduce REJECTOR, software for parameter estimation and comparison of alternate models of population history from genetic data via a rejection algorithm. Through coalescent simulation, REJECTOR generates numerous gene genealogies, and hence simulated data, under a model of population history specified by the user. Summary statistics derived from such simulated data are compared with observed statistics, leading to acceptance or rejection of a given set of parameter values. We performed tests of the software using known parameter values in order to assess the inferential power provided by each summary statistic. The tests demonstrate the precision and accuracy of estimation made possible using this approach. AVAILABILITY: http://www.rejector.org     

Genetic Loads in Heterogeneous Environments

A model of population structure in heterogeneous environments is described with attention focused on genetic variation at a single locus. The existence of equilibria at which there is no genetic load is examined.--The absolute fitness of any genotype is regarded as a function of location in the niche space and the population density at that location. It is assumed that each organism chooses to live in that habitat in which it is most fit ("optimal habitat selection").--Equilibria at which there is no segregation load ("loadless equilibria") may exist. Necessary and sufficient conditions for the existence of such equilibria are very weak. If there is a sufficient amount of dominance or area in which the alleles are selectively neutral, then there exist equilibria without segregational loads. In the N2p phase plane defined by population size, N, and gene frequency, p, these equilibria generally consist of a line segment which is parallel to the p axis. These equilibria are frequently stable.     

Interplay of Darwinian and frequency-dependent selection in the host-associated microbial populations

In order to analyze the microevolutionary processes in host-associated microorganisms, we simulated the dynamics of rhizobia populations composed of a parental strain and its mutants possessing the altered fitness within "plant-soil" system. The population dynamics was presented as a series of cycles (each one involves "soil-->rhizosphere-->nodules-->soil" succession) described using recurrent equations. For representing the selection and mutation pressures, we used a universal approach based on calculating the shifts in the genetic ratios of competing bacterial genotypes within the particular habitats and across several habitats. Analysis of the model demonstrated that a balanced polymorphism may be established in rhizobia population: mutants with an improved fitness do not supplant completely the parental strain while mutants with a decreased fitness may be maintained stably. This polymorphism is caused by a rescue of low-fitted genotypes via negative frequency-dependent selection (FDS) that is implemented during inoculation of nodules and balances the Darwinian selection that occurs during multiplication or extinction of bacteria at different habitats. The most diverse populations are formed if the rhizobia are equally successful in soil and nodules, while a marked preference for any of these habitats results in the decrease of diversity. Our simulation suggests that FDS can maintain the mutualistic rhizobia-legume interactions under the stress conditions deleterious for surviving the bacterial strains capable for intensive N2 fixation. Genetic consequences of releasing the modified rhizobia strains may be addressed using the presented model.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Evolution of mechanoregulation of bone growth will lead to non-optimal bone phenotypes

Mechanical forces acting on the bones during growth affect their final shape and strength. Mechanoregulation of bone growth may be recognized in embryogenesis, and also in the adaptation of the adult skeleton to changes in mechanical loading. Mechanoregulatory responses for tissues have arisen during evolution, but does evolution give rise to responses that produce optimal skeletal phenotypes? In this paper, we investigate the emergence of an optimal mechanoregulation response in a population. By combining equations describing long bone growth with a genetic algorithm to describe evolutionary change, we created a computational model to simulate the evolution of mechanoregulation in bone growth. A population of individuals is created where each individual is assigned a diploid gene set which controls the growth and remodelling of the bone. At maturity, each bone is assessed and its 'fitness' calculated; fitness is quantified as bone strength relative to bone mass. The simulation continues for many generations, and includes mutations and a varying environment. The genes present in the population are tracked and the evolution of parameters governing mechanoregulation is calculated. The results indicate that a population may converge to one bone growth algorithm but, more usually, a range of mechanoregulation algorithms for different individuals will persist after many generations. Even if the population converges to one mechanoregulation law, convergence to the 'optimum' bone was never found. Although many researchers propose that natural selection has pushed skeletal structure towards an optimum, our computational model suggests that this is unlikely to be the case.     

Finding associations in dense genetic maps: a genetic algorithm approach

Large-scale association studies hold promise for discovering the genetic basis of common human disease. These studies will consist of a large number of individuals, as well as large number of genetic markers, such as single nucleotide polymorphisms (SNPs). The potential size of the data and the resulting model space require the development of efficient methodology to unravel associations between phenotypes and SNPs in dense genetic maps. Our approach uses a genetic algorithm (GA) to construct logic trees consisting of Boolean expressions involving strings or blocks of SNPs. These blocks or nodes of the logic trees consist of SNPs in high linkage disequilibrium (LD), that is, SNPs that are highly correlated with each other due to evolutionary processes. At each generation of our GA, a population of logic tree models is modified using selection, cross-over and mutation moves. Logic trees are selected for the next generation using a fitness function based on the marginal likelihood in a Bayesian regression frame-work. Mutation and cross-over moves use LD measures to pro pose changes to the trees, and facilitate the movement through the model space. We demonstrate our method and the flexibility of logic tree structure with variable nodal lengths on simulated data from a coalescent model, as well as data from a candidate gene study of quantitative genetic variation.     

Forward-time simulations of human populations with complex diseases

Due to the increasing power of personal computers, as well as the availability of flexible forward-time simulation programs like simuPOP, it is now possible to simulate the evolution of complex human diseases using a forward-time approach. This approach is potentially more powerful than the coalescent approach since it allows simulations of more than one disease susceptibility locus using almost arbitrary genetic and demographic models. However, the application of such simulations has been deterred by the lack of a suitable simulation framework. For example, it is not clear when and how to introduce disease mutants—especially those under purifying selection—to an evolving population, and how to control the disease allele frequencies at the last generation. In this paper, we introduce a forward-time simulation framework that allows us to generate large multi-generation populations with complex diseases caused by unlinked disease susceptibility loci, according to specified demographic and evolutionary properties. Unrelated individuals, small or large pedigrees can be drawn from the resulting population and provide samples for a wide range of study designs and ascertainment methods. We demonstrate our simulation framework using three examples that map genes associated with affection status, a quantitative trait, and the age of onset of a hypothetical cancer, respectively. Nonadditive fitness models, population structure, and gene–gene interactions are simulated. Case-control, sibpair, and large pedigree samples are drawn from the simulated populations and are examined by a variety of gene-mapping methods.     

Variation, natural selection, and information content--a simulation

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms that propel biological evolution. Variation implies changes in the gene pool of a population, enlarging the genetic variability from which natural selection can choose. But in the absence of natural selection, variation causes dissipation and randomization. Natural selection, in contrast, constrains this variability by decreasing the survival and fertility of the less-adapted organisms. The objective of this study is to propose a highly simplified simulation of variation and natural selection, and to relate the observed evolutionary changes in a population to its information content. The model involves an imaginary population of individuals. A quantifiable character allows the individuals to be categorized into bins. The distribution of bins (a histogram) was assumed to be Gaussian. The content of each bin was calculated after one to twelve cycles, each cycle spanning N generations (N being undefined). In a first study, selection was simulated in the absence of variation. This was modeled by assuming a differential fertility factor F that increased linearly from the lower bins (F<1.00) to the higher bins (F>1.00). The fertility factor was applied as a multiplication factor during each cycle. Several ranges of fertility were investigated. The resulting histograms became skewed to the right. In a second study, variation was simulated in the absence of selection. This was modeled by assuming that during each cycle each bin lost a fixed percentage of its content (variation factor Y) to its two adjacent bins. The resulting histograms became broader and flatter, while retaining their bilateral symmetry. Different values of Y were monitored. In a third study, various values of F and Y were combined. Our model allows the straightforward application of Shannon's equation and the calculation of a Shannon-entropy (SE) values for each histogram. Natural selection was, thus, shown to result in a progressive decrease in SE as a function of F. In other words, natural selection, when acting alone, progressively increased the information content of the population. In contrast, variation resulted in a progressive increase in SE as a function of Y. In other words, variation acting alone progressively decreased the information content of a population. When both factors, F and Y, were applied simultaneously, their relative weight determined the progressive change in SE.     

LONG-TERM EXPERIMENTAL EVOLUTION IN ESCHERICHIA COLI. VII. MECHANISMS MAINTAINING GENETIC VARIABILITY WITHIN POPULATIONS

Six replicate populations of the bacterium Escherichia coli were propagated for more than 10,000 generations in a defined environment. We sought to quantify the variation among clones within these populations with respect to their relative fitness, and to evaluate the roles of three distinct population genetic processes in maintaining this variation. On average, a pair of clones from the same population differed from one another in their relative fitness by approximately 4%. This within-population variation was small compared with the average fitness gain relative to the common ancestor, but it was statistically significant. According to one hypothesis, the variation in fitness is transient and reflects the ongoing substitution of beneficial alleles. We used Fisher's fundamental theorem to compare the observed rate of each population's change in mean fitness with the extent of variation for fitness within that population, but we failed to discern any correspondence between these quantities. A second hypothesis supposes that the variation in fitness is maintained by recurrent deleterious mutations that give rise to a mutation-selection balance. To test this hypothesis, we made use of the fact that two of the six replicate populations had evolved mutator phenotypes, which gave them a genomic mutation rate approximately 100-fold higher than that of the other populations. There was a marginally significant correlation between a population's mutation rate and the extent of its within-population variance for fitness, but this correlation was driven by only one population (whereas two of the populations had elevated mutation rates). Under a third hypothesis, this variation is maintained by frequency-dependent selection, whereby genotypes have an advantage when they are rare relative to when they are common. In all six populations, clones were more fit, on average, when they were rare than when they were common, although the magnitude of the advantage when rare was usually small (~1% in five populations and ~5% in the other). These three hypotheses are not mutually exclusive, but frequency-dependent selection appears to be the primary force maintaining the fitness variation within these experimental populations.     

Very low levels of direct additive genetic variance in fitness and fitness components in a red squirrel population

A trait must genetically correlate with fitness in order to evolve in response to natural selection, but theory suggests that strong directional selection should erode additive genetic variance in fitness and limit future evolutionary potential. Balancing selection has been proposed as a mechanism that could maintain genetic variance if fitness components trade off with one another and has been invoked to account for empirical observations of higher levels of additive genetic variance in fitness components than would be expected from mutation–selection balance. Here, we used a long‐term study of an individually marked population of North American red squirrels (Tamiasciurus hudsonicus) to look for evidence of (1) additive genetic variance in lifetime reproductive success and (2) fitness trade‐offs between fitness components, such as male and female fitness or fitness in high‐ and low‐resource environments. “Animal model” analyses of a multigenerational pedigree revealed modest maternal effects on fitness, but very low levels of additive genetic variance in lifetime reproductive success overall as well as fitness measures within each sex and environment. It therefore appears that there are very low levels of direct genetic variance in fitness and fitness components in red squirrels to facilitate contemporary adaptation in this population.