Analytic approach to the evolutionary effects of genetic exchange

We present an approximate analytic study of our previously introduced model of evolution including the effects of genetic exchange. This model is motivated by the process of bacterial transformation. We solve for the velocity, the rate of increase of fitness, as a function of the fixed population size, $N$. We find the velocity increases with $\ln N$, eventually saturated at an $N$ which depends on the strength of the recombination process. The analytical treatment is seen to agree well with direct numerical simulations of our model equations

Maximum principle and mutation thresholds for four-letter sequence evolution

A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness functions, which determine the selection process, come from the permutation-invariant class. Error thresholds can be found for various fitness functions, the phase diagrams are more interesting than for equivalent two-state models. Results for (small) finite sequence lengths are compared with those for infinite sequence length, obtained via a maximum principle that is equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure

Kinetic theory of age-structured stochastic birth-death processes

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution

Recombination dramatically speeds up evolution of finite populations

We study the role of recombination, as practiced by genetically-competent bacteria, in speeding up Darwinian evolution. This is done by adding a new process to a previously-studied Markov model of evolution on a smooth fitness landscape; this new process allows alleles to be exchanged with those in the surrounding medium. Our results, both numerical and analytic, indicate that for a wide range of intermediate population sizes, recombination dramatically speeds up the evolutionary advance

The role of mutation rate variation and genetic diversity in the architecture of human disease

Background We have investigated the role that the mutation rate and the structure of genetic variation at a locus play in determining whether a gene is involved in disease. We predict that the mutation rate and its genetic diversity should be higher in genes associated with disease, unless all genes that could cause disease have already been identified. Results Consistent with our predictions we find that genes associated with Mendelian and complex disease are substantially longer than non-disease genes. However, we find that both Mendelian and complex disease genes are found in regions of the genome with relatively low mutation rates, as inferred from intron divergence between humans and chimpanzees, and they are predicted to have similar rates of non-synonymous mutation as other genes. Finally, we find that disease genes are in regions of significantly elevated genetic diversity, even when variation in the rate of mutation is controlled for. The effect is small nevertheless. Conclusions Our results suggest that gene length contributes to whether a gene is associated with disease. However, the mutation rate and the genetic architecture of the locus appear to play only a minor role in determining whether a gene is associated with disease

Outbreak of tropical rat mite (Ornithonyssus bacoti) dermatitis in a home for disabled persons

Five mentally handicapped individuals living in a home for disabled persons in Southern Germany were seen in our outpatient department with pruritic, red papules predominantly located in groups on the upper extremities, neck, upper trunk and face. Over several weeks 40 inhabitants and 5 caretakers were affected by the same rash. Inspection of their home and the sheds nearby disclosed infestation with rat populations and mites. Finally the diagnosis of tropical rat mite dermatitis was made by the identification of the arthropod Ornithonyssus bacoti or so-called tropical rat mite. The patients were treated with topical corticosteroids and antihistamines. After elimination of the rats and disinfection of the rooms by a professional exterminator no new cases of rat mite dermatitis occurred. The tropical rat mite is an external parasite occurring on rats, mice, gerbils, hamsters and various other small mammals. When the principal animal host is not available, human beings can become the victim of mite infestation. Copyright (c) 2007 S. Karger AG, Base

Strong polarization-induced reduction of addition energies in single-molecule nanojunctions

We address polarization-induced renormalization of molecular levels in solid-state based single-molecule transistors and focus on an organic conjugate molecule where a surprisingly large reduction of the addition energy has been observed. We have developed a scheme that combines a self-consistent solution of a quantum chemical calculation with a realistic description of the screening environment. Our results indeed show a large reduction, and we explain this to be a consequence of both (a) a reduction of the electrostatic molecular charging energy and (b) polarization induced level shifts of the HOMO and LUMO levels. Finally, we calculate the charge stability diagram and explain at a qualitative level general features observed experimentally.Comment: 9 pages, 5 figure

Rapid divergence and expansion of the X chromosome in papaya

X chromosomes have long been thought to conserve the structure and gene content of the ancestral autosome from which the sex chromosomes evolved. We compared the recently evolved papaya sex chromosomes with a homologous autosome of a close relative, the monoecious Vasconcellea monoica, to infer changes since recombination stopped between the papaya sex chromosomes. We sequenced 12 V. monoica bacterial artificial chromosomes, 11 corresponding to the papaya X-specific region, and 1 to a papaya autosomal region. The combined V. monoica X-orthologous sequences are much shorter (1.10 Mb) than the corresponding papaya region (2.56 Mb). Given that the V. monoica genome is 41% larger than that of papaya, this finding suggests considerable expansion of the papaya X; expansion is supported by a higher repetitive sequence content of the X compared with the papaya autosomal sequence. The alignable regions include 27 transcript-encoding sequences, only 6 of which are functional X/V. monoica gene pairs. Sequence divergence from the V. monoica orthologs is almost identical for papaya X and Y alleles; the Carica-Vasconcellea split therefore occurred before the papaya sex chromosomes stopped recombining, making V. monoica a suitable outgroup for inferring changes in papaya sex chromosomes. The papaya X and the hermaphrodite-specific region of the Y(h) chromosome and V. monoica have all gained and lost genes, including a surprising amount of changes in the X

Adaptive walks on time-dependent fitness landscapes

The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of static fitness contributions are investigated for model landscapes derived from Kauffman's $NK$ landscapes. Depending on the amount of static fitness contributions in the landscape, the evolutionary dynamics can be divided into a percolating and a non-percolating phase. In the percolating phase, the walker performs a random walk over the regions of the landscape with high fitness.Comment: 7 pages, 6 eps-figures, RevTeX, submitted to Phys. Rev.

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded introductory and discussion sections, added corollaries, new results on modifier polymorphisms, minor corrections. 49 pages, 64 reference