Non-zero Recombination Research Articles

An adaptive multilevel Monte Carlo algorithm for the stochastic drift–diffusion–Poisson system

We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift–diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the spatial dimensions, while the a-priori error is estimated to guarantee linear convergence of the H1 error. In the adaptive mesh refinement, efficient estimation of the error indicator gives rise to better error control. For the stochastic dimensions, we use the multilevel Monte Carlo method to solve this system of stochastic partial differential equations. Finally, the advantage of the technique developed here compared to uniform mesh refinement is discussed using a realistic numerical example.

The evolutionary advantage of fitness-dependent recombination in diploids: A deterministic mutation-selection balance model.

Recombination's omnipresence in nature is one of the most intriguing problems in evolutionary biology. The question of why recombination exhibits certain general features is no less interesting than that of why it exists at all. One such feature is recombination's fitness dependence (FD). The so far developed population genetics models have focused on the evolution of FD recombination mainly in haploids, although the empirical evidence for this phenomenon comes mostly from diploids. Using numerical analysis of modifier models for infinite panmictic populations, we show here that FD recombination can be evolutionarily advantageous in diploids subjected to purifying selection. We ascribe this advantage to the differential rate of disruption of lower‐ versus higher‐fitness genotypes, which can be manifested in selected systems with at least three loci. We also show that if the modifier is linked to such selected system, it can additionally benefit from modifying this linkage in a fitness‐dependent manner. The revealed evolutionary advantage of FD recombination appeared robust to crossover interference within the selected system, either positive or negative. Remarkably, FD recombination was often favored in situations where any constant nonzero recombination was evolutionarily disfavored, implying a relaxation of the rather strict constraints on major parameters (e.g., selection intensity and epistasis) required for the evolutionary advantage of nonzero recombination formulated by classical models.

What drives the evolution of condition-dependent recombination in diploids? Some insights from simulation modelling.

While the evolutionary advantages of non-zero recombination rates have prompted diverse theoretical explanations, the evolution of essential recombination features remains underexplored. We focused on one such feature, the condition dependence of recombination, viewed as the variation in within-generation sensitivity of recombination to external (environment) and/or internal (genotype) conditions. Limited empirical evidence for its existence comes mainly from diploids, whereas theoretical models show that it only easily evolves in haploids. The evolution of condition-dependent recombination can be explained by its advantage for the selected system (indirect effect), or by benefits to modifier alleles, ensuring this strategy regardless of effects on the selected system (direct effect). We considered infinite panmictic populations of diploids exposed to a cyclical two-state environment. Each organism had three selected loci. Examining allele dynamics at a fourth, selectively neutral recombination modifier locus, we frequently observed that a modifier allele conferring condition-dependent recombination between the selected loci displaced the allele conferring the optimal constant recombination rate. Our simulations also confirm the results of theoretical studies showing that condition-dependent recombination cannot evolve in diploids on the basis of direct fitness-dependent effects alone. Therefore, the evolution of condition-dependent recombination in diploids can be driven by indirect effects alone, i.e. by modifier effects on the selected system.This article is part of the themed issue 'Evolutionary causes and consequences of recombination rate variation in sexual organisms'.

Automixis in Artemia: solving a century-old controversy.

Parthenogenesis (reproduction through unfertilized eggs) encompasses a variety of reproduction modes with (automixis) or without (apomixis) meiosis. Different modes of automixis have very different genetic and evolutionary consequences but can be particularly difficult to tease apart. In this study, we propose a new method to discriminate different types of automixis from population-level genetic data. We apply this method to diploid Artemia parthenogenetica, a crustacean whose reproductive mode remains controversial despite a century of intensive cytogenetic observations. We focus on A.parthenogenetica from two western Mediterranean populations. We show that they are diploid and that markers remain heterozygous in cultures maintained up to ~36 generations in the laboratory. Moreover, parallel patterns of population-wide heterozygosity levels between the two natural populations strongly support the conclusion that diploid A.parthenogenetica reproduce by automictic parthenogenesis with central fusion and low, but nonzero recombination. This settles a century-old controversy on Artemia, and, more generally, suggests that many automictic organisms harbour steep within-chromosome gradients of heterozygosity due to a transition from clonal transmission in centromere-proximal regions to a form of inbreeding similar to self-fertilization in centromere-distal regions. Such systems therefore offer a new avenue for contrasting the genomic consequences of asexuality and inbreeding.

The effect of linkage on establishment and survival of locally beneficial mutations.

We study invasion and survival of weakly beneficial mutations arising in linkage to an established migration–selection polymorphism. Our focus is on a continent–island model of migration, with selection at two biallelic loci for adaptation to the island environment. Combining branching and diffusion processes, we provide the theoretical basis for understanding the evolution of islands of divergence, the genetic architecture of locally adaptive traits, and the importance of so-called “divergence hitchhiking” relative to other mechanisms, such as “genomic hitchhiking”, chromosomal inversions, or translocations. We derive approximations to the invasion probability and the extinction time of a de novo mutation. Interestingly, the invasion probability is maximized at a nonzero recombination rate if the focal mutation is sufficiently beneficial. If a proportion of migrants carries a beneficial background allele, the mutation is less likely to become established. Linked selection may increase the survival time by several orders of magnitude. By altering the timescale of stochastic loss, it can therefore affect the dynamics at the focal site to an extent that is of evolutionary importance, especially in small populations. We derive an effective migration rate experienced by the weakly beneficial mutation, which accounts for the reduction in gene flow imposed by linked selection. Using the concept of the effective migration rate, we also quantify the long-term effects on neutral variation embedded in a genome with arbitrarily many sites under selection. Patterns of neutral diversity change qualitatively and quantitatively as the position of the neutral locus is moved along the chromosome. This will be useful for population-genomic inference. Our results strengthen the emerging view that physically linked selection is biologically relevant if linkage is tight or if selection at the background locus is strong.

Evolution of recombination rates in a multi-locus, haploid-selection, symmetric-viability model

A fast algorithm for computing multi-locus recombination is extended to include a recombination-modifier locus. This algorithm and a linear stability analysis is used to investigate the evolution of recombination rates in a multi-locus, haploid-selection, symmetric-viability model for which stable equilibria have recently been determined. When the starting equilibrium is symmetric with two selected loci, we show analytically that modifier alleles that reduce recombination always invade. When the starting equilibrium is monomorphic, and there is a fixed nonzero recombination rate between the modifier locus and the selected loci, we determine analytical conditions for which a modifier allele can invade. In particular, we show that a gap exists between the recombination rates of modifiers that can invade and the recombination rate that specifies the lower stability boundary of the monomorphic equilibrium. A numerical investigation shows that a similar gap exists in a weakened form when the starting equilibrium is fully polymorphic but asymmetric.

Estimating and testing linkage disequilibrium from sib data

We consider estimation and testing of linkage equilibrium from genotypic data on a random sample of sibs, such as monozygotic and dizygotic twins. We compute the maximum likelihood estimator with an EM-algorithm and a likelihood ratio statistic that takes the family structure into account. As we are interested in applying this to twin data we also allow observations on single children, so that monozygotic twins can be included. We allow non-zero recombination fraction between the loci of interest, so that linkage disequilibrium between both linked and unlinked loci can be tested. The EM-algorithm for computing the maximum likelihood estimator of the haplotype frequencies and the likelihood ratio test-statistic, are described in detail. It is shown that the usual estimators of haplotype frequencies based on ignoring that the sibs are related are inefficient, and the likelihood ratio test for testing that the loci are in linkage disequilibrium.

Peculiarities of magnetic field and spin effects in a three-spin system with regard to the long-distance character of exchange interaction

The biradical recombination probability and its field dependence in the presence of a paramagnetic particle was calculated in balance approximation taking into account the extended character of the exchange interaction in the biradical. Previously, to describe the effect of the third spin on the spin evolution in the biradical, we considered the constant spin exchange interaction both inside the biradical and between the added spin and one of the paramagnetic biradical centers. In the present work we considered the long-distance character of the exchange interaction of the biradical with the third spin. It is shown that the field dependence retains the main characteristic peculiarities of the three-spin system in the approximation of the constancy of the exchange interaction, i.e., the existence of several extrema, their shift along the field depending on the values of the exchange integrals, and the existence of a field-independent, nonzero recombination probability, known as spin catalysis.

The dynamics of the rec-system in variable environments: Haploid selection in a cyclical two-state environment

The dynamics of a 3-locus infinite population with non-overlapping generations and panmixia was studied. Loci are di-allelic: two loci affect fitness under cyclical symmetric haploid selection while the third one is a modifier of recombination ( rec-modifier). Selection favors alternatively haplotypes AB and ab or Ab and aB. It has been proven that under alternating selection (when period of selection consists of two generations) a dominant suppressor of recombination is displaced and the allele for non-zero recombination becomes fixed within the population. For populations with inversion heterozygosity within the selective system (i.e. with zero recombination in heterozygote for rec-modifier and non-zero for homozygotes) fixation of one of the alleles (depending on the initial point) at the rec-modifier locus is predicted. For other values of recombination parameters, the behavior of the system was studied numerically. A full bifurcation picture of parameters was obtained. Many of the results related to the case of a two-generation period hold also in the case of longer period lengths.

Power calculations for the transmission/disequilibrium and affected sib pair tests using elementary probability methods.

The transmission/disequilibrium test (TDT) and the affected sib pair test (ASP) both test for the association of a marker allele with some conditions. Here, we present methods for calculating the probability of detecting the association (power) for a study examining a fixed number of families for suitability for the study and for calculating the number of such families to be examined. Both calculations use a genetic model for the association. The model considered posits a bi-allelic marker locus that is linked to a bi-allelic disease locus with a possibly nonzero recombination fraction between the loci. The penetrance of the disease is an increasing function of the number of disease alleles. The TDT tests whether the transmission by a heterozygous parent of a particular allele at a marker locus to an affected offspring occurs with probability greater than 0.5. The ASP tests whether transmission of the same allele to two affected sibs occurs with probability greater than 0.5. In either case, evidence that the probability is greater than 0.5 is evidence for association between the marker and the disease. Study inclusion criteria (IC) can greatly affect the necessary sample size of a TDT or ASP study. IC considered by us include a randomly selected parent at least one parent or both parents required to be heterozygous. It also allows a specified minimum number of affected offspring to be required (TDT only). We use elementary probability calculations rather than complex mathematical manipulations or asymptotic methods (large sample size approximations) to compute power and requisite sample size for a proposed study. The advantages of these methods are simplicity and generality.

A Markov Chain Model of Coalescence with Recombination

Trees that describe the ancestry of DNA sequences sampled from a population may differ between loci because of genetic recombination. We seek to understand the relationship between such trees for loci that are linked with non-zero recombination rate. We consider a coalescent process model with recombination, as described by Hudson (1983; 1990). For two loci and a sample size of two sequences, a detailed analysis of this process yields the joint distribution of the two trees (one at each locus). A number of interesting results follow from this analysis, including the distribution of the number of recombination events in the history of the sample. For the general case ofmloci and samples of sizen, we describe an algorithm for simulating the tree building process. Because analytic results are difficult to obtain in this case, we use simulation to study properties of trees at multiple linked loci such as total tree time and number of recombination events.

Solvation Ultrafast Dynamics of Reactions. 12. Probing along the Reaction Coordinate and Dynamics in Supercritical Argon

In this paper, our focus is on the influence of the solvent density on the caging, recombination dynamics, and the nature of the reaction coordinate of iodine in supercritical argon at pressures of 0−2500 bar. Femtosecond probing with widely tunable pulses allows us to directly resolve the geminate recombination of iodine atoms and the subsequent relaxation processes. A nonzero recombination yield is found at argon pressures as low as 200 bar, and this yield increases strongly with increasing solvent density. The mechanism involves recombination onto the A/A‘ states. At high pressures, a large fraction of the iodine atoms undergo an ultrafast “in-cage” recombination which is measured on the subpicosecond time scale at 2500 bar of argon. In addition, a fraction of the iodine atoms break through the solvent cage and begin a diffusive motion through the rare-gas solvent. Experimental evidence is presented and indicates that this diffusive motion leads to reencounters and subsequent recombination of the geminate iodine pair. This diffusive recombination occurs on a significantly longer time scale than the rapid “in-cage” recombination. The newly-formed iodine molecules undergo vibrational relaxation within the A/A‘ state, and the dynamics of this process and its dependence on the solvent density are revealed. A key concept here is the solvent density-induced control of the rigidity of the first solvent shell surrounding the dissociating iodine atoms. As shown before [Liu et al. Nature 1993, 364, 427], such studies of solvation present a unique opportunity of examining the microscopic influence of the solvent structure on reaction dynamics in clusters and solutions.

Increased recombination frequencies resulting from directional selection for geotaxis in Drosophila.

Several classes of models have been suggested to explain how natural selection can favour non-zero recombination. Directional and fluctuating selection, abiotic and biotic, and selection against harmful mutations seem to be the most plausible factors, but little has been done to test the problem experimentally. Here we show that long-term selection for positive or negative geotaxis in Drosophila melanogaster results in a dramatic increase in recombination rates in different genomic regions. The total increment in recombination for the genome portion considered is 78 cM for geo+ and 66 cM for geo-. Selection for negative geotaxis did not result in recombination changes in chromosome 2 whereas selection in the opposite direction caused nearly a four-fold increase in the b-cn segment and a significant, albeit not as high, increase in the adjacent regions, al-b and cn-vg. In chromosomes X and 3, a significant increase in recombination was found in both selected lines. In total, the increment in exchange frequency in chromosome X (y-cv-ct-v-car) was from 72.6 per cent (the control level) to 124.7 and 110.3 per cent geo- and geo+, respectively, whereas for the studied portion of chromosome 3 (ru-h-cu-sr-e) we obtained, correspondingly, 60.8, 76.4 and 73.8 per cent. Thus, in general, selection for geotaxis resulted in increased recombination frequencies regardless of the direction of selection.(ABSTRACT TRUNCATED AT 250 WORDS)

Photovoltaic processes in metal-semicrystalline silicon Schottky barriers and implications for grating solar cells

Experimental investigations of the photovoltaic properties of metal-silicon Schottky barriers are reported, in which edge collection of the photocurrent is dominant as in the majority-carrier grating solar cells proposed by Green. Both elemental metals and alloy Schottky electrodes, and both crystalline and semicrystalline cast silicon have been studied. The superposition principle for dark currents and photocurrents is shown unambiguously to be violated, and the effects of grain-boundary recombination and shunt resistance are identified. Limitations to the operation of these devices above the semiempirical limit of continuous Schottky barrier solar cells is seriously compromised by enhanced space-charge recombination current. This results from the large photocurrent densities for low contact area/active area ratios. The treatment of the space-charge recombination mechanism under optical illumination follows the normal Sah-Noyce-Shockley approach, but we introduce here a built-in “recombination potential” to encompass the non-zero recombination for short-circuit conditions.

Approximating the transient response of double-heterojunction devices

Two techniques of approximating the transient response of a double-heterojunction light-emitting diode or diode laser in which there is a nonzero recombination velocity at the heterojunctions are compared to the results of a recently published exact series solution for the transient behavior of such structures. It is shown that both approximations can lead to large quantitative errors—one overestimating and the other underestimating the speed of response—when the active region is wide and the interface recombination is large, but that both approximations are useful and yield similar results when the active region is narrow and interface recombination is small. For devices with narrow active regions and small recombination velocities, it is shown that the transient response can be represented as a single exponential with a characteristic lifetime given by τ[1+(Sv1+Sv2)/D]−1, where Svi and D are the normalized interface recombination velocities and active region width, respectively.