Measures of Variation at DNA Repeat Loci under a General Stepwise Mutation Model

Polymorphisms at tandem repeat loci are caused by mutations with allele sizes occasionally altered by more than one repeat unit in both forward and backward directions. Such mutational changes may occur with asymmetric probabilities. Therefore, a one-step symmetric stepwise mutation model may not be appropriate for studying the population dynamics at all repeat loci. In this work, we evaluated the expectation and variance of the within-population variance of the allele size distribution in a finite population, and the expected homozygosity at a locus by the coalescence approach under a general stepwise mutation model, where mutational transitions of allele sizes can be arbitrary, including being asymmetric. Under the special cases of symmetric one-step, two-step, and multi-step geometric distributions of mutations, our general results reduce to the corresponding results obtained by earlier investigators. The general results indicate that in a finite population, which has reached a steady state under the (general stepwise) mutation and drift balance, the within-population variance of allele sizes has a simple expectation (i.e., proportional toNν, the product of the mutation rate,ν, and effective population size,N). However, its stochastic variance is a quadratic function of this composite parameter,Nν. Furthermore, this second-order variance does not decay with the number of alleles sampled from a population. Application of this theory to data on allele size distributions in unrelated Caucasians from the CEPH pedigree (obtained from the Genome Data Base) shows that the relationship of the variance and mean of within-population variance of allele sizes at tandem repeat loci, grouped by their chromosomal assignment, has a trend compatible with the theory. However, there is an indication that the second-order variance is generally underestimated. One reason for this departure might be that the CEPH sample may not represent a single homogeneous population that reached equilibrium at all tandem repeat loci.     

MUTANT INVASIONS AND ADAPTIVE DYNAMICS IN VARIABLE ENVIRONMENTS

The evolution of natural organisms is ultimately driven by the invasion and possible fixation of mutant alleles. The invasion process is highly stochastic, however, and the probability of success is generally low, even for advantageous alleles. Additionally, all organisms live in a stochastic environment, which may have a large influence on what alleles are favorable, but also contributes to the uncertainty of the invasion process. We calculate the invasion probability of a beneficial, mutant allele in a monomorphic, large population subject to stochastic environmental fluctuations, taking into account density‐ and frequency‐dependent selection, stochastic population dynamics and temporal autocorrelation of the environment. We treat both discrete and continuous time population dynamics, and allow for overlapping generations in the continuous time case. The results can be generalized to diploid, sexually reproducing organisms embedded in communities of interacting species. We further use these results to derive an extended canonical equation of adaptive dynamics, predicting the rate of evolutionary change of a heritable trait on long evolutionary time scales.     

Evolution of mosaic operons by horizontal gene transfer and gene displacement <Emphasis Type="Italic">in situ</Emphasis>

Background

Shuffling and disruption of operons and horizontal gene transfer are major contributions to the new, dynamic view of prokaryotic evolution. Under the 'selfish operon' hypothesis, operons are viewed as mobile genetic entities that are constantly disseminated via horizontal gene transfer, although their retention could be favored by the advantage of coregulation of functionally linked genes. Here we apply comparative genomics and phylogenetic analysis to examine horizontal transfer of entire operons versus displacement of individual genes within operons by horizontally acquired orthologs and independent assembly of the same or similar operons from genes with different phylogenetic affinities.

Results

Since a substantial number of operons have been identified experimentally in only a few model bacteria, evolutionarily conserved gene strings were analyzed as surrogates of operons. The phylogenetic affinities within these predicted operons were assessed first by sequence similarity analysis and then by phylogenetic analysis, including statistical tests of tree topology. Numerous cases of apparent horizontal transfer of entire operons were detected. However, it was shown that apparent horizontal transfer of individual genes or arrays of genes within operons is not uncommon either and results in xenologous gene displacement in situ, that is, displacement of an ancestral gene by a horizontally transferred ortholog from a taxonomically distant organism without change of the local gene organization. On rarer occasions, operons might have evolved via independent assembly, in part from horizontally acquired genes.

Conclusions

The discovery of in situ gene displacement shows that combination of rampant horizontal gene transfer with selection for preservation of operon structure provides for events in prokaryotic evolution that, a priori, seem improbable. These findings also emphasize that not all aspects of operon evolution are selfish, with operon integrity maintained by purifying selection at the organism level.

     

Simple quasispecies models for the survival-of-the-flattest effect: The role of space

The survival-of-the-flattest effect postulates that under high mutation rates natural selection does not necessarily favor the faster replicators. Under such conditions, genotypes which are robust against deleterious mutational effects may be favored instead, even at the cost of a slower replication. This tantalizing hypothesis has been recently proved using digital organisms, subviral RNA plant pathogens (viroids), and an animal RNA virus. In this work we study a simple theoretical system composed by two competing quasispecies which are located at two widely different fitness landscapes that represent, respectively, a fit and a flat quasispecies. The fit quasispecies is characterized by high replication rate and low mutational robustness, whereas the flat quasispecies is characterized by low replication rate but high mutational robustness. By using a mean field model, in silico simulations with digital replicons and a two-dimensional spatial model given by a stochastic cellular automata (CA), we predict the presence of an absorbing first-order phase transition with critical slowing down between selection for replication speed and selection for mutational robustness, where the surpassing of a critical mutation rate involves the outcompetition of the fit quasispecies by the flat one. Furthermore, it is shown that space, which involves a lower critical mutation rate, broadens the conditions at which the survival-of-the-flattest may occur.     

A rigorous model study of the adaptive dynamics of Mendelian diploids

Adaptive dynamics (AD) so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka–Volterra-like dynamics and single locus genetics (as in Kimura’s in Proc Natl Acad Sci USA 54: 731–736, 1965 infinite allele model). We prove under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous mutations are rare and mutational steps are not too large, the population behaves on the mutational time scale (the ‘long’ time scale of the literature on the genetical foundations of ESS theory) as a jump process moving between homozygous states (the trait substitution sequence of the adaptive dynamics literature). Essential technical ingredients are a rigorous estimate for the probability of invasion in a dynamic diploid population, a rigorous, geometric singular perturbation theory based, invasion implies substitution theorem, and the use of the Skorohod M ₁ topology to arrive at a functional convergence result. In the small mutational steps limit this process in turn gives rise to a differential equation in allele or in phenotype space of a type referred to in the adaptive dynamics literature as ‘canonical equation’.     

Amelioration of Bacterial Genomes: Rates of Change and Exchange

Although bacterial species display wide variation in their overall GC contents, the genes within a particular species' genome are relatively similar in base composition. As a result, sequences that are novel to a bacterial genome—i.e., DNA introduced through recent horizontal transfer—often bear unusual sequence characteristics and can be distinguished from ancestral DNA. At the time of introgression, horizontally transferred genes reflect the base composition of the donor genome; but, over time, these sequences will ameliorate to reflect the DNA composition of the new genome because the introgressed genes are subject to the same mutational processes affecting all genes in the recipient genome. This process of amelioration is evident in a large group of genes involved in host-cell invasion by enteric bacteria and can be modeled to predict the amount of time required after transfer for foreign DNA to resemble native DNA. Furthermore, models of amelioration can be used to estimate the time of introgression of foreign genes in a chromosome. Applying this approach to a 1.43-megabase continuous sequence, we have calculated that the entire Escherichia coli chromosome contains more than 600 kb of horizontally transferred, protein-coding DNA. Estimates of amelioration times indicate that this DNA has accumulated at a rate of 31 kb per million years, which is on the order of the amount of variant DNA introduced by point mutations. This rate predicts that the E. coli and Salmonella enterica lineages have each gained and lost more than 3 megabases of novel DNA since their divergence. Received: 7 July 1996 / Accepted: 27 September 1996     

Computationally exact methods for stochastic periodic dynamics: Spatiotemporal dispersal and temporally forced transmission

The dynamics of many diseases and populations possess distinct recurring phases. For example, many species breed only during a subset of the year and the infection dynamics of many pathogens have transmission rates that vary with season. Here I investigate computational methods for studying transient and long-term behaviour of stochastic models which have periodic phases—several different potential techniques for studying long-term behaviour will be contrasted. I illustrate the results with two studies: The first is of a spatially realistic metapopulation model of malleefowl (Leipoa ocellata), a species which disperses only during a quarter of the year; this model is used to highlight the advantages and disadvantages of the particular methods presented. The second study is of a model for disease dynamics which incorporates seasonality in both the rate of within-population transmission and also in the rate of transmission effected via aerosol importation. This model has applications to studying disease invasion and persistence in captive-breeding populations. We demonstrate, via comparison to appropriately matched models with constant transmission rates and also no aerosol transmission, that seasonality and aerosol importation may alter control choices, with possibly an increase in the threshold population size for local control surveillance, transfer of importance to limiting aerosol transmission, and the use of temporally targetted surveillance. The methodology presented is the gold-standard for dealing with many phased processes in ecology and epidemiology, but its application is limited to systems of small size.     

Horizontal versus vertical transmission of parasites in a stochastic spatial model

A number of pathogens may be transmitted from parent to child at or before birth (vertically) or from one individual to another by contact (horizontally). A natural deterministic and non-spatial model, introduced by Lipsitch et al. [Proc. Roy. Soc. London Ser. B 260 (1995) 3211 shows that an epidemic is possible if the vertical transmission or the horizontal transmission is high enough. In contrast, we introduce a stochastic spatial model that shows that, on a particular graph, if the vertical transmission is not high enough, then the infected individuals disappear even for very high horizontal transmission. This illustrates the fact that introducing space may greatly change the qualitative behavior of a model.     

The fittest versus the flattest: experimental confirmation of the quasispecies effect with subviral pathogens

The "survival of the fittest" is the paradigm of Darwinian evolution in which the best-adapted replicators are favored by natural selection. However, at high mutation rates, the fittest organisms are not necessarily the fastest replicators but rather are those that show the greatest robustness against deleterious mutational effects, even at the cost of a low replication rate. This scenario, dubbed the "survival of the flattest", has so far only been shown to operate in digital organisms. We show that "survival of the flattest" can also occur in biological entities by analyzing the outcome of competition between two viroid species coinfecting the same plant. Under optimal growth conditions, a viroid species characterized by fast population growth and genetic homogeneity outcompeted a viroid species with slow population growth and a high degree of variation. In contrast, the slow-growth species was able to outcompete the fast species when the mutation rate was increased. These experimental results were supported by an in silico model of competing viroid quasispecies.     

Horizontal gene transfer of a plastid gene in the non-photosynthetic flowering plants Orobanche and Phelipanche (Orobanchaceae)

Plastid sequences are among the most widely used in phylogenetic and phylogeographic studies in flowering plants, where they are usually assumed to evolve like non-recombining, uniparentally transmitted, single-copy genes. Among others, this assumption can be violated by intracellular gene transfer (IGT) within cells or by the exchange of genes across mating barriers (horizontal gene transfer, HGT). We report on HGT of a plastid region including rps2, trnL-F, and rbcL in a group of non-photosynthetic flowering plants. Species of the parasitic broomrape genus Phelipanche harbor two copies of rps2, a plastid ribosomal gene, one corresponding to the phylogenetic position of the respective species, the other being horizontally acquired from the related broomrape genus Orobanche. While the vertically transmitted copies probably reside within the plastid genome, the localization of the horizontally acquired copies is not known. With both donor and recipient being parasitic plants, a possible pathway for the exchange of genetic material is via a commonly attacked host.     

Modeling the ecology of parasitic plasmids

Plasmids are autonomous genetic elements that can be exchanged between microorganisms via horizontal gene transfer (HGT). Despite the central role they play in antibiotic resistance and modern biotechnology, our understanding of plasmids’ natural ecology is limited. Recent experiments have shown that plasmids can spread even when they are a burden to the cell, suggesting that natural plasmids may exist as parasites. Here, we use mathematical modeling to explore the ecology of such parasitic plasmids. We first develop models of single plasmids and find that a plasmid’s population dynamics and optimal infection strategy are strongly determined by the plasmid’s HGT mechanism. We then analyze models of co-infecting plasmids and show that parasitic plasmids are prone to a “tragedy of the commons” in which runaway plasmid invasion severely reduces host fitness. We propose that this tragedy of the commons is averted by selection between competing populations and demonstrate this effect in a metapopulation model. We derive predicted distributions of unique plasmid types in genomes—comparison to the distribution of plasmids in a collection of 17,725 genomes supports a model of parasitic plasmids with positive plasmid–plasmid interactions that ameliorate plasmid fitness costs or promote the invasion of new plasmids.Subject terms: Theoretical ecology, Microbial ecology     

Are Anomalous Invasion Speeds Robust to Demographic Stochasticity?

Two important issues for conservation are the range expansion of species as a result of climate change and the invasion of exotic species. Being able to predict the rate at which species spread is key for successful management. In deterministic models, the invasion speed of a polymorphic population can be faster than that of any of the component phenotypes, and these “anomalous” invasion speeds persist even when the mutation rate between phenotypes is vanishingly small. Here we investigate whether the same phenomenon is observed in a model with demographic stochasticity. The model that we use is discrete in time and space and we carry out numerical simulations to determine the invasion speed of a population that has two morphs which differ in their dispersal abilities. We find that anomalous speeds are observed in the stochastic model, but only when the carrying capacity of the population is large or the mutation rate between morphs is high enough. These results suggest that only species with large population sizes, such as many insect species, may be able to invade faster if they are polymorphic than if there is only a single morph present in the population.     

Does environmental stochasticity matter? Analysis of red deer life-histories on Rum

Summary Most life-history theory assumes that short-term variation in an organism's environment does not affect the survivorships and fecundities of the organisms. This assumption is rarely met. Here we investigate the population and evolutionary biology of red deer,Cervus elephas, to see if relaxation of this assumption is likely to make significant differences to the predicted evolutionary biology of this species. To do this we used 21 years of data from a population of deer on Rum, Western Isles, Scotland. Population growth rates in a stochastic environment were estimated using Tuljapurkar's small noise approximation, confirmed by bootstrap simulation. Numerical differentiation was used to see if the selection pressures (i.e. sensitivities of population growth rate to changes in the vital rates) differ between the stochastic and deterministic cases. The data also allow the costs of reproduction to be estimated. These costs, incorporated as trade-offs into the sensitivity analysis, allow investigation of evolutionary benefits of different life-history tactics. Environmentally induced stochastic variation in the red deer vital rates causes a slight reduction ( 1%) in the predicted population growth rate and has little impact on the estimated selection pressures on the deer's life-history. We thus conclude that, even though density-independent stochastic effects on the population are marked, the deer's fitness is not markedly affected by these and they are adapted to the average conditions they experience. However, the selected life-history is sensitive to the trade-offs between current fecundity, survivorship and future fecundity and it is likely that the environmental variance will affect these trade-offs and, thus, affect the life-history favoured by selection. We also show that the current average life-history is non-optimal and suggest this is a result of selection pressures exerted by culling and predation, now much reduced. As the use of stochastic or deterministic methods provide similar estimates in this case, the use of the latter is justified. Thus,r (the annual per capita rate of population growth) is an appropriate measure of fitness in a population with stochastic numerical fluctuations. In a population of constant size lifetime reproductive success is the obvious measure of fitness to use.     

Ecological conditions that favor the evolution of intermediate-virulence in an environmentally transmitted parasite

In this paper we develop and analyze several populaion-dynamic models of an environmentally transmitted symbiotic parasite infecting an isolated population of susceptible hosts. In our most basic model infection acts only to decrease the average lifetime of the infected host, parasites are only transmitted to uninfected hosts, there is no recovery from infection, and the rate of parasite transmission is an increasing function of the level of parasite virulence. It is shown that invasion of the parasite-free equilibrium cannot occur for virulence levels that are either too high or too low. We then incorporate a number of modifications to the model, among them the possibility that host fertility is reduced by infection, and that transmission rate depends additionally on susceptible host density. It is shown that the essential nature of the conditions for invasion are preserved. Thus, natural selection for intermediate virulence is a generic property of a broad class of population models.     

Human skin color diversity is highest in sub-Saharan African populations

Previous studies of genetic and craniometric traits have found higher levels of within-population diversity in sub-Saharan Africa compared to other geographic regions. This study examines regional differences in within-population diversity of human skin color. Published data on skin reflectance were collected for 98 male samples from eight geographic regions: sub-Saharan Africa, North Africa, Europe, West Asia, Southwest Asia, South Asia, Australasia, and the New World. Regional differences in local within-population diversity were examined using two measures of variability: the sample variance and the sample coefficient of variation. For both measures, the average level of within-population diversity is higher in sub-Saharan Africa than in other geographic regions. This difference persists even after adjusting for a correlation between within-population diversity and distance from the equator. Though affected by natural selection, skin color variation shows the same pattern of higher African diversity as found with other traits.     

Virulence evolution in a virus obeys a trade-off

The evolution of virulence was studied in a virus subjected to alternating episodes of vertical and horizontal transmission. Bacteriophage f1 was used as the parasite because it establishes a debilitating but non-fatal infection that can be transmitted vertically (from a host to its progeny) as well as horizontally (infection of new hosts). Horizontal transmission was required of all phage at specific intervals, but was prevented otherwise. Each episode of horizontal transmission was followed by an interval of obligate vertical transmission, followed by an interval of obligate horizontal transmission etc. The duration of vertical transmission was eight times longer per episode in one treatment than in the other, thus varying the relative intensity of selection against virulence while maintaining selection for some level of virus production. Viral lines with the higher enforced rate of infectious transmission evolved higher virulence and higher rates of virus production. These results support the trade-off model for the evolution of virulence.     

Proceedings of the SMBE Tri-National Young Investigators' Workshop 2005. Mutation rate and the cost of complexity

Two recent theoretical studies of adaptation suggest that more complex organisms tend to adapt more slowly. Specifically, in Fisher's "geometric" model of a finite population where multiple traits are under optimizing selection, the average progress ensuing from a single mutation decreases as the number of traits increases--the "cost of complexity." Here, I draw on molecular and histological data to assess the extent to which on a large phylogenetic scale, this predicted decrease in the rate of adaptation per mutation is mitigated by an increase in the number of mutations per generation as complexity increases. As an index of complexity for multicellular organisms, I use the number of visibly distinct types of cell in the body. Mutation rate is the product of mutational target size and population mutation rate per unit target. Despite much scatter, genome size appears to be positively correlated with complexity (as indexed by cell-type number), which along with other considerations suggests that mutational target size tends to increase with complexity. In contrast, effective population mutation rate per unit target appears to be negatively correlated with complexity. The net result is that mutation rate probably does tend to increase with complexity, although probably not fast enough to eliminate the cost of complexity.     

Mutant EF-Tu increases missense error in vitro

Summary We have studied the consequences of mutational alteration in the structure of EF-Tu on the missense errors and proofreading activity of bacterial ribosomes in vitro. Our data show that the EF-Tu Bo mutant form of EF-Tu (van der Meide et al. 1983a) is inactive in polypeptide synthesis on the ribosome, even though it binds aminoacyl-tRNA. A second mutant form, EF-Tu Ar (van der Meide et al. 1983a), is active in polypeptide synthesis but supports a much higher messense incorporation with either leucine isoacceptor 2 or leucine isoacceptor 4 in the in vitro system. Further analysis of the kinetic basis of this enhanced missense frequency revealed that the mutation responsible for the alteration in EF-Tu Ar increases the errors at both the proofreading step and the initial selection. In this respect the effect of this particular mutation is similar to the mode of action of the antibiotic kanamycin (Jelenc and Kurland 1984).     

Detection of recombination among Salmonella enterica strains using the incongruence length difference test

Particular serovars of Salmonella enterica have emerged as significant foodborne pathogens in humans. At the chromosomal level, discrete regions in the Salmonella genome have been identified that are known to play important roles in the maintenance, survival, and virulence of S. enterica within the host. Interestingly, several of these loci appear to have been acquired by horizontal transfer of DNA among and between bacterial species. The profound importance of recombination in pathogen emergence is just now being realized, perhaps explaining the sudden interest in developing novel and facile ways for detecting putative horizontal transfer events in bacteria. The incongruence length difference (ILD) test offers one such means. ILD uses phylogeny to trace sequences that may have been acquired promiscuously by exchange of DNA during chromosome evolution. We show here that the ILD test readily detects recombinations that have taken place in several housekeeping genes in Salmonella as well as genes composing the type 1 pilin complex (14 min) and the inv-spa invasion gene complex (63 min). Moreover, the ILD test indicated that the mutS gene (64 min), whose product helps protect the bacterial genome from invasion by foreign DNA, appears to have undergone intragenic recombination within S. enterica subspecies I. ILD findings were supported using additional tests known to be independent of the ILD approach (e.g., split decomposition analysis and compatibility of sites). Taken together, these data affirm the application of the ILD test as one approach for identifying recombined sequences in the Salmonella chromosome. Furthermore, horizontally acquired sequences within mutS support a model whereby evolutionarily important recombinants of S. enterica are rescued from strains carrying defective mutS alleles via horizontal transfer.     

AN ADAPTIVE WALK BY HUMAN IMMUNODEFICIENCY VIRUS TYPE 1 THROUGH A FLUCTUATING FITNESS LANDSCAPE

The mutational landscape model of adaptive sequence evolution has been used to explain an unexpected strong positive linear relationship between marginal fitness and mean site‐specific amino acid frequency in the functionally important HIV‐1 gp120 V3 protein region. The model predicts a positive linear relationship between the probability that a particular beneficial allele, among several, is the next to spread to fixation during an adaptive walk, its transition probability, and the allele's selection coefficient. Here, stochastic simulation is used to confirm the intuition that the linear relationship between transition probabilities and selection coefficients, predicted by the model, should, under fluctuating selection, produce a linear relationship between allele frequency, averaged across populations, and fitness. In addition, these relationships hold for the effective population size and mutation rate of HIV‐1 and for the moderately strong selection observed for V3. A survey of the strength of mutation for diverse organisms suggests that these relationships may be widely applicable.