Aperiodic and correlated disorder in XY-chains: exact results

We study thermodynamic properties, specific heat and susceptibility, of XY quantum chains with coupling constants following arbitrary substitution rules. Generalizing an exact renormalization group transformation, originally formulated for Ising quantum chains, we obtain exact relevance criteria of Harris-Luck type for this class of models. For two-letter substitution rules, a detailed classification is given of sequences leading to irrelevant, marginal or relevant aperiodic modulations. We find that the relevance of the same aperiodic sequence of couplings in general will be different for XY and Ising quantum chains. By our method, continuously varying critical exponents may be calculated exactly for arbitrary (two-letter) substitution rules with marginal aperiodicity. A number of examples are given, including the period-doubling, three-folding and precious mean chains. We also discuss extensions of the renormalization approach to a special class of long-range correlated random chains, generated by random substitutions.Comment: 19 page

The pattern of genetic hitchhiking under recurrent mutation

Genetic hitchhiking describes evolution at a neutral locus that is linked to a selected locus. If a beneficial allele rises to fixation at the selected locus, a characteristic polymorphism pattern (so-called selective sweep) emerges at the neutral locus. The classical model assumes that fixation of the beneficial allele occurs from a single copy of this allele that arises by mutation. However, recent theory (Pennings and Hermisson, 2006a; Pennings and Hermisson, 2006b) has shown that recurrent beneficial mutation at biologically realistic rates can lead to markedly different polymorphism patterns, so called soft selective sweeps. We extend an approach that has recently been developed for the classical hitchhiking model (Schweinsbergand Durrett, 2005; Etheridge, Pfaffelhuber, Wakolbinger, 2006) to study the recurrent mutation scenario. We show that the genealogy at the neutral locus can be approximated (to leading orders in the selection strength) by a marked Yule process with immigration. Using this formalism, we derive an improved analytical approximation for the expected heterozygosity at the neutral locus at the time of fixation of the beneficial allele.Comment: 31 pages, 2 figure

The establishment of hybrids of the Daphnia longispina complex explained by a mathematical model incorporating different overwintering life history strategies

Interspecific hybridization (i.e. mating between species) occurs frequently in animals. Among cyclical parthenogens, hybrids can proliferate and establish through parthenogenetic reproduction, even if their sexual reproduction is impaired. In water fleas of the Daphnia longispina species complex, interspecific hybrids hatch from sexually produced dormant eggs. However, fewer hybrid genotypes contribute to the dormant egg bank and their hatching rate from dormant eggs is reduced, compared to eggs resulting from intraspecific crosses. Therefore, Daphnia hybrids would benefit from adaptations that increase their survival over winter as parthenogenetic lineages, avoiding the need to re-establish populations after winter from sexually produced dormant eggs. Here, we constructed a mathematical model to examine the conditions that could explain the frequently observed establishment of hybrids in the D. longispina species complex. Specifically, we compared the outcome of hybrid and parental taxa competition given a reduced contribution of hybrids to hatchlings from the sexually produced dormant egg bank, but their increased ability to survive winter as parthenogenetic lineages. In addition, different growth rates of parental species and differences in average annual temperatures were evaluated for their influence on hybrid production and establishment. Our model shows that increased overwinter performance as parthenogenetic females can compensate for reduced success in sexual reproduction, across all tested scenarios for varying relative growth rates of parental species. This pattern holds true for lower annual temperatures, but at higher temperatures hybrids were less successful. Consequently, hybrids might become less abundant as temperatures rise due to climate change, resulting in reduced diversity and faster differentiation of the parental species

Aggregation of variables and system decomposition: Applications to fitness landscape analysis

In this paper we present general results on aggregation of variables, specifically as it applies to decomposable (partitionable) dynamical systems. We show that a particular class of transition matrices, namely, those satisfying an equitable partitioning property, are aggregable under appropriate decomposition operators. It is also shown that equitable partitions have a natural application to the description of mutation-selection matrices (fitness landscapes) when their fitness functions have certain symmetries concordant with the neighborhood relationships in the underlying configuration space. We propose that the aggregate variable descriptions of mutation-selection systems offer a potential formal definition of units of selection and evolution

Surface Properties of Aperiodic Ising Quantum Chains

We consider Ising quantum chains with quenched aperiodic disorder of the coupling constants given through general substitution rules. The critical scaling behaviour of several bulk and surface quantities is obtained by exact real space renormalization.Comment: 4 pages, RevTex, reference update

MSMS: a coalescent simulation program including recombination, demographic structure and selection at a single locus

Motivation: We have implemented a coalescent simulation program for a structured population with selection at a single diploid locus. The program includes the functionality of the simulator ms to model population structure and demography, but adds a model for deme- and time-dependent selection using forward simulations. The program can be used, e.g. to study hard and soft selective sweeps in structured populations or the genetic footprint of local adaptation. The implementation is designed to be easily extendable and widely deployable. The interface and output format are compatible with ms. Performance is comparable even with selection included