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PubMed2001

Sample size requirement for detecting interference under the chi-square model.

The chi-square model (CHS) of recombination has been studied extensively, in recent years, for its ability of capturing the process and estimating the level of crossover interference. Exploration thus far shows that this model yields much better fits to human genetic data than Haldane's no-interference model, and the explicit level of interference can be easily estimated as well. This paper provides calculations of sample sizes required to detect interference under CHS for a variety of settings. Two data types, fully informative meioses and phase-unknown backcross families, are studied. Under each setting, we calculate the number of meioses/families needed to ensure that the expected log-likelihood difference between the chi(2) interference model and Haldane's no-interference model exceeds a prespecified threshold. It is found that joint consideration of multiple (more than three) markers dramatically reduces the number of meioses/families needed when compared to an analysis based on three-point data, a traditional setting for detecting interference using three-point tests. The results indicate that the numbers of meioses needed to detect interference under CHS are well within the reach of most genetic mapping studies.

Chi-Square Distribution↗
PubMed2003

Locally-adaptive and memetic evolutionary pattern search algorithms.

Recent convergence analyses of evolutionary pattern search algorithms (EPSAs) have shown that these methods have a weak stationary point convergence theory for a broad class of unconstrained and linearly constrained problems. This paper describes how the convergence theory for EPSAs can be adapted to allow each individual in a population to have its own mutation step length (similar to the design of evolutionary programing and evolution strategies algorithms). These are called locally-adaptive EPSAs (LA-EPSAs) since each individual's mutation step length is independently adapted in different local neighborhoods. The paper also describes a variety of standard formulations of evolutionary algorithms that can be used for LA-EPSAs. Further, it is shown how this convergence theory can be applied to memetic EPSAs, which use local search to refine points within each iteration.

Algorithms↗
PubMed1999

FDA - a scalable evolutionary algorithm for the optimization of additively decomposed functions.

The Factorized Distribution Algorithm (FDA) is an evolutionary algorithm which combines mutation and recombination by using a distribution. The distribution is estimated from a set of selected points. In general, a discrete distribution defined for n binary variables has 2(n) parameters. Therefore it is too expensive to compute. For additively decomposed discrete functions (ADFs) there exist algorithms which factor the distribution into conditional and marginal distributions. This factorization is used by FDA. The scaling of FDA is investigated theoretically and numerically. The scaling depends on the ADF structure and the specific assignment of function values. Difficult functions on a chain or a tree structure are solved in about O(n radical n) operations. More standard genetic algorithms are not able to optimize these functions. FDA is not restricted to exact factorizations. It also works for approximate factorizations as is shown for a circle and a grid structure. By using results from Bayes networks, FDA is extended to LFDA. LFDA computes an approximate factorization using only the data, not the ADF structure. The scaling of LFDA is compared to the scaling of FDA.

Algorithms↗
PubMed2001

Allele-sharing among affected relatives: non-parametric methods for identifying genes.

Non-parametric linkage analysis examines similarities among affected relatives in alleles of one or more genetic markers (pieces of DNA at known locations on a chromosome). The objective is to evaluate departures from the null hypothesis that the markers are not near a disease gene. Under the null hypothesis, Mendel's laws give the probabilities that a set of relatives exhibits a particular allele-sharing pattern, and the null hypothesis is rejected if the extent of allele sharing among affected relatives exceeds Mendelian expectation. Because the rationale for allele-sharing methods is intuitively plausible and easily grasped, geneticists have used these methods for more than 30 years, well before the advent of the large sets of polymorphic markers that have made linkage analysis so fruitful today. Here we describe methods for assessing whether the extent of marker allele sharing among affected relatives exceeds Mendelian expectation. We first quantify the notion of allele sharing and the probabilities of allele sharing in various sets of relatives. Then we describe allele sharing methods for affected sibs and more general sets of relatives. We also discuss related issues of test size and power. We conclude with a brief discussion of areas in need of further research.

Alleles↗
PubMed2005

Speeding disease gene discovery by sequence based candidate prioritization.

BACKGROUND: Regions of interest identified through genetic linkage studies regularly exceed 30 centimorgans in size and can contain hundreds of genes. Traditionally this number is reduced by matching functional annotation to knowledge of the disease or phenotype in question. However, here we show that disease genes share patterns of sequence-based features that can provide a good basis for automatic prioritization of candidates by machine learning. RESULTS: We examined a variety of sequence-based features and found that for many of them there are significant differences between the sets of genes known to be involved in human hereditary disease and those not known to be involved in disease. We have created an automatic classifier called PROSPECTR based on those features using the alternating decision tree algorithm which ranks genes in the order of likelihood of involvement in disease. On average, PROSPECTR enriches lists for disease genes two-fold 77% of the time, five-fold 37% of the time and twenty-fold 11% of the time. CONCLUSION: PROSPECTR is a simple and effective way to identify genes involved in Mendelian and oligogenic disorders. It performs markedly better than the single existing sequence-based classifier on novel data. PROSPECTR could save investigators looking at large regions of interest time and effort by prioritizing positional candidate genes for mutation detection and case-control association studies.

Algorithms↗
PubMed2005

Validating viral quasispecies with digital organisms: a re-examination of the critical mutation rate.

BACKGROUND: In this report we re-examine some recent experiments with digital organisms to test some predictions of quasispecies theory. These experiments revealed that under high mutation rates populations of less fit organisms previously adapted to such high mutation rates were able to outcompete organisms with higher average fitness but adapted to low mutation rates. RESULTS: We have verified that these results do hold in the original conditions and, by extending the set of initial parameters, we have also detected that the critical mutation rate was independent of population size, a result that we have found to be dependent on a different, contingent factor, the initial fitness vector. Furthermore, in all but one case, the critical mutation rate is higher than the error threshold, a key parameter in quasispecies theory, which prevents its extrapolation to natural viral populations. CONCLUSION: From these results we conclude that digital organisms are useful tools for investigating evolutionary patterns and processes including some predictions from the quasispecies theory.

Adaptation, Biological↗
PubMed1999

Paleo-demography of the Drosophila melanogaster subgroup: application of the maximum likelihood method.

The species divergence times and demographic histories of Drosophila melanogaster and its three sibling species, D. mauritiana, D. simulans, and D. yakuba, were investigated using a maximum likelihood (ML) method. Thirty-nine orthologous loci for these four species were retrieved from DDBJ/EMBL/GenBank database. Both autosomal and X-linked loci were used in this study. A significant degree of rate heterogeneity across loci was observed for each pair of species. Most loci have the GC content greater than 50% at the third codon position. The codon usage bias in Drosophila loci is considered to result in the high GC content and the heterogenous rates across loci. The chi-square, G, and Fisher's exact tests indicated that data sets with 11, 23, and 9 pairs of DNA sequences for the comparison of D. melanogaster with D. mauritiana, D. simulans, and D. yakuba, respectively, retain homogeneous rates across loci. We applied the ML method to these data sets to estimate the DNA sequence divergences before and after speciation of each species pair along with their standard deviations. Using 1.6 x 10(-8) as the rate of nucleotide substitutions per silent site per year, our results indicate that the D. melanogaster lineage split from D. yakuba approximately 5.1 +/- 0.8 million years ago (mya), D. mauritiana 2.7 +/- 0.4 mya, and D. simulans 2.3 +/- 0.3 mya. It implies that D. melanogaster became distinct from D. mauritiana and D. simulans at approximately the same time and from D. yakuba no earlier than 10 mya. The effective ancestral population size of D. melanogaster appears to be stable over evolutionary time. Assuming 10 generations per year for Drosophila, the effective population size in the ancestral lineage immediately prior to the time of species divergence is approximately 3 x 10(6), which is close to that estimated for the extant D. melanogaster population. The D. melanogaster did not encounter any obvious bottleneck during the past 10 million years.

Animals↗
PubMed2004

Maximum-likelihood estimation of rates of recombination within mating-type regions.

Features common to many mating-type regions include recombination suppression over large genomic tracts and cosegregation of genes of various functions, not necessarily related to reproduction. Model systems for homomorphic self-incompatibility (SI) in flowering plants share these characteristics. We introduce a method for the exact computation of the joint probability of numbers of neutral mutations segregating at the determinant of mating type and at a linked marker locus. The underlying Markov model incorporates strong balancing selection into a two-locus coalescent. We apply the method to obtain a maximum-likelihood estimate of the rate of recombination between a marker locus, 48A, and S-RNase, the determinant of SI specificity in pistils of Nicotiana alata. Even though the sampled haplotypes show complete allelic linkage disequilibrium and recombinants have never been detected, a highly significant deficiency of synonymous substitutions at 48A compared to S-RNase suggests a history of recombination. Our maximum-likelihood estimate indicates a rate of recombination of perhaps 3 orders of magnitude greater than the rate of synonymous mutation. This approach may facilitate the construction of genetic maps of regions tightly linked to targets of strong balancing selection.

Animals↗
PubMed2004

Evolution of specialists in an experimental microcosm.

The impact of adaptation on the persistence of a balanced polymorphism was explored using the lactose operon of Escherichia coli as a model system. Competition in chemostats for two substitutable resources, methylgalactoside and lactulose, generates stabilizing frequency-dependent selection when two different naturally isolated lac operons (TD2 and TD10) are used. The fate of this balanced polymorphism was tracked over evolutionary time by monitoring the frequency of fhuA-, a linked neutral genetic marker that confers resistance to the bacteriophage T5. In four out of nine chemostats the lac polymorphism persisted for 400-600 generations when the experiments were terminated. In the other five chemostats the fhuA polymorphism, and consequently the lac operon polymorphism, was lost between 86 and 219 generations. Four of 13 chemostat cultures monomorphic for the lac operon retained the neutral fhuA polymorphism for 450-550 generations until they were terminated; the remainder became monomorphic at fhuA between 63 and 303 generations. Specialists on each galactoside were isolated from chemostats that maintained the fhuA polymorphism, whether polymorphic or monomorphic at the lac operon. Strains isolated from three of four chemostats in which the lac polymorphism was preserved had switched their galactoside preference. Most of the chemostats where the fhuA polymorphism was lost also contained specialists. These results demonstrate that the initial polymorphism at lac was of little consequence to the outcome of long-term adaptive evolution. Instead, the fitnesses of evolved strains were dominated by mutations arising elsewhere in the genome, a fact confirmed by showing that operons isolated from their evolved backgrounds were alone unable to explain the presence of both specialists. Our results suggest that, once stabilized, ecological specialization prevented selective sweeps through the entire population, thereby promoting the maintenance of linked neutral polymorphisms.

Bacterial Outer Membrane Proteins↗
PubMed2005

Self-fertilization and the evolution of recombination.

In this article, we study the effect of self-fertilization on the evolution of a modifier allele that alters the recombination rate between two selected loci. We consider two different life cycles: under gametophytic selfing, a given proportion of fertilizations involves gametes produced by the same haploid individual, while under sporophytic selfing, a proportion of fertilizations involves gametes produced by the same diploid individual. Under both life cycles, we derive approximations for the change in frequency of the recombination modifier when selection is weak relative to recombination, so that the population reaches a state of quasi-linkage equilibrium. We find that gametophytic selfing increases the range of epistasis under which increased recombination is favored; however, this effect is substantial only for high selfing rates. Moreover, gametophytic selfing affects the relative influence of different components of epistasis (additive x additive, additive x dominance, dominance x dominance) on the evolution of the modifier. Sporophytic selfing has much stronger effects: even a small selfing rate greatly increases the parameter range under which recombination is favored, when there is negative dominance x dominance epistasis. This effect is due to the fact that selfing generates a correlation in homozygosity at linked loci, which is reduced by recombination.

Alleles↗
PubMed2006

Effect of varying epistasis on the evolution of recombination.

Whether recombination decelerates or accelerates a population's response to selection depends, at least in part, on how fitness-determining loci interact. Realistically, all genomes likely contain fitness interactions both with positive and with negative epistasis. Therefore, it is crucial to determine the conditions under which the potential beneficial effects of recombination with negative epistasis prevail over the detrimental effects of recombination with positive epistasis. Here, we examine the simultaneous effects of diverse epistatic interactions with different strengths and signs in a simplified model system with independent pairs of interacting loci and selection acting only on the haploid phase. We find that the average form of epistasis does not predict the average amount of linkage disequilibrium generated or the impact on a recombination modifier when compared to results using the entire distribution of epistatic effects and associated single-mutant effects. Moreover, we show that epistatic interactions of a given strength can produce very different effects, having the greatest impact when selection is weak. In summary, we observe that the evolution of recombination at mutation-selection balance might be driven by a small number of interactions with weak selection rather than by the average epistasis of all interactions. We illustrate this effect with an analysis of published data of Saccharomyces cerevisiae. Thus to draw conclusions on the evolution of recombination from experimental data, it is necessary to consider the distribution of epistatic interactions together with the associated selection coefficients.

Biological Evolution↗
PubMed2004

Insights into recombination from patterns of linkage disequilibrium in humans.

An ability to predict levels of linkage disequilibrium (LD) between linked markers would facilitate the design of association studies and help to distinguish between evolutionary models. Unfortunately, levels of LD depend crucially on the rate of recombination, a parameter that is difficult to measure. In humans, rates of genetic exchange between markers megabases apart can be estimated from a comparison of genetic and physical maps; these large-scale estimates can then be interpolated to predict LD at smaller ("local") scales. However, if there is extensive small-scale heterogeneity, as has been recently proposed, local rates of recombination could differ substantially from those averaged over much larger distances. We test this hypothesis by estimating local recombination rates indirectly from patterns of LD in 84 genomic regions surveyed by the SeattleSNPs project in a sample of individuals of European descent and of African-Americans. We find that LD-based estimates are significantly positively correlated with map-based estimates. This implies that large-scale, average rates are informative about local rates of recombination. Conversely, although LD-based estimates are based on a number of simplifying assumptions, it appears that they capture considerable information about the underlying recombination rate or at least about the ordering of regions by recombination rate. Using LD-based estimators, we also find evidence for homologous gene conversion in patterns of polymorphism. However, as we demonstrate by simulation, inferences about gene conversion are unreliable, even with extensive data from homogeneous regions of the genome, and are confounded by genotyping error.

Chromosome Mapping↗
PubMed2005

Statistical tools for linkage analysis and genetic association studies.

Genetic mapping by linkage analysis has been an invaluable tool in the positional strategy to identify the molecular basis of many rare Mendelian disorders. With the attention of the scientific and medical community shifting towards the analysis of more common, complex traits, it has become necessary to develop new approaches that take into account the complexity of the genetic basis of these disorders and their possible interaction with other, nongenetic factors. Linkage disequilibrium studies are now becoming increasingly popular thanks to the advent of genotyping platforms that allow genome-wide searching for association between hundreds of thousands of random polymorphisms and disease phenotypes in large samples of unrelated individuals. Moreover, the definition of the disease phenotype itself is being reconsidered to include quantitative traits that may better define the underlying biologic mechanisms for many pathologic conditions. This article will review classic and new approaches to genetic mapping by linkage and association analysis and discuss the directions this field is likely to take in the near future.

Alleles↗
PubMed2001

AFLP analysis of genetic polymorphism and evolutionary relationships among cultivated and wild Nicotiana species.

Amplified fragment length polymorphism (AFLP) analysis was used to determine the degree of intra- and inter-specific genetic variation in the genus Nicotiana. Forty-six lines of cultivated tobacco (Nicotiana tabacum L.) and seven wild Nicotiana species, including N. sylvestris, N. tomentosiformis, N. otophora, N. glutinosa, N. suaveolens, N. rustica, and N. longiflora, were analyzed, using at least eight different oligonucleotide primer combinations capable of detecting a minimum of 50 polymorphic bands per primer pair. The amount of genetic polymorphism present among cultivated tobacco lines (N. tabacum) was limited, as evidenced by the high degree of similarity in the AFLP profiles of cultivars collected worldwide. Six major clusters were found within cultivated tobacco that were primarily based upon geographic origin and manufacturing quality traits. A greater amount of genetic polymorphism exists among wild species of Nicotiana than among cultivated forms. Pairwise comparisons of the AFLP profiles of wild and cultivated Nicotiana species show that polymorphic bands present in N. tabacum can be found in at least one of three proposed wild progenitor species (i.e., N. sylvestris, N. tomentosiformis, and N. otophora). This observation provides additional support for these species contributing to the origin of N. tabacum.

DNA↗
PubMed2004

Content analysis of the core promoter region of human genes.

We analyzed an extended core promoter regions covering [-70,+60] segment relative to the transcription start site of human promoters contained in the Eukaryotic Promoter Database. The analysis was made by using the Match program ver. 1.9 with an optimized setting and the TRANSFAC Professional database ver. 7.2. This analysis revealed that the most common transcription factor binding site in the examined collection of core promoters appears to be initiator (characterized by GEN_INI), which is expected. The other less obvious sites found were Spz1, E2F-1, ZF5, and C/EBP. The 'cap' site was also in this most common group. Over-representation of these sites relative to the non-promoter background data ranged from 0.3167 to 32.1645. These sites were characterized by being present in more than 60% of promoter sequences. Interestingly, the TATA-box has been found in only 11.63% of all examined promoters. The study is complemented by separate analyses of promoter groups having different GC content. These additional analyses revealed that the most common promoter elements found also include AP-2, CdxA, Pax-2, SRY, STAT1 and STAT5A. It was also observed that a number of promoter elements show strong preference either for the GC-rich or the GC-poor core promoters.

Binding Sites↗
PubMed1990

Linkage strategies for genetically complex traits. III. The effect of marker polymorphism on analysis of affected relative pairs.

The results from the second paper of this series are reexamined for markers that are not completely polymorphic. A maximum lod score (MLS) criterion is defined for affected relative pairs. The expected MLS (EMLS) is calculated as a function of the marker polymorphic information content (PIC) for various values of lambda R (relative risk ratio) and different relative types by using simulations. An m-allele model with equal allele frequencies is employed. The EMLS is calculated for two sampling strategies: scheme 1, which uses pairs only, and scheme 2, which also includes additional informative relatives. For scheme 2, the percent of the maximum achievable EMLS (i.e., for a marker with a PIC of 1.0) is approximately equal to the marker PIC value for all relative types. For scheme 1, the EMLS is greatly diminished unless PIC is high, especially for distant relatives. For example, scheme 1 is not cost-effective for sibs unless PIC greater than .7; for second- and third-degree relatives, PIC must be greater than .85. Therefore, in general, it will be worthwhile to type additional relatives in linkage studies using affected pairs. The comparative value of sibs versus distant relatives depends on lambda R, recombination theta, and PIC. For large lambda R and PIC values, distant relatives are preferred. Alternatively, for smaller lambda R and PIC values, sibs are best.

Female↗