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PubMed1995

The Fundamental Theorem of Natural Selection in Ewens' sense (case of fertility selection).

We show that the Fundamental Theorem of Natural Selection in Ewens' sense is valid in the case of fertility selection: the additive genetic variance in fertility divided by the mean fertility is exactly equal to the partial change in the mean fertility from the current generation to the next. This partial change is the increase in the mean additive value caused by frequency changes from on generation to the next. This partial change is the increase in the mean additive value caused by frequency changes from one generation to the next but keeping unchanged the additive values. The only hypothesis on mating is that it does not affect the allelic frequencies in the sense that these are the same before and after mating in the parental generation, which occurs for a wide range of mating patterns going from random mating to several regular systems of inbreeding and cases of assortative mating. The fertility of couples is determined by the genes at an arbitrary number of loci, and the additive (average) allelic allelic effects are defined by a linear system of equations, which is used to extend Ewens' optimality principle to the case of fertility selection.

Animals↗
PubMed1998

Statistical analysis of half-tetrads.

Half-tetrads, where two meiotic products from a single meiosis are recovered together, arise in different forms in a variety of organisms. Closely related to ordered tetrads, half-tetrads yield information on chromatid interference, chiasma interference, and centromere positions. In this article, for different half-tetrad types and different marker configurations, we derive the relations between multilocus half-tetrad probabilities and multilocus ordered tetrad probabilities. These relations are used to obtain equality and inequality constraints among multilocus half-tetrad probabilities that are imposed by the assumption of no chromatid interference. We illustrate how to apply these results to study chiasma interference and to map centromeres using multilocus half-tetrad data.

Animals↗
PubMed1999

Improving the efficiency of artificial selection: more selection pressure with less inbreeding.

The use of population genetic variability in present-day selection schemes can be improved to reduce inbreeding rate and inbreeding depression without impairing genetic progress. We performed an experiment with Drosophila melanogaster to test mate selection, an optimizing method that uses linear programming to maximize the selection differential applied while at the same time respecting a restriction on the increase in inbreeding expected in the next generation. Previous studies about mate selection used computer simulation on simple additive genetic models, and no experiment with a real character in a real population had been carried out. After six selection generations, the optimized lines showed an increase in cumulated phenotypic selection differential of 10.76%, and at the same time, a reduction of 19.91 and 60.47% in inbreeding coefficient mean and variance, respectively. The increased selection pressure would bring greater selection response, and in fact, the observed change in the selected trait was on average 31.03% greater in the optimized lines. These improvements in the selection scheme were not made at the expense of the long-term expectations of genetic variability in the population, as these expectations were very similar for both mate selection and conventionally selected lines in our experiment.

Animals↗
PubMed1999

The ancestry of a sample of sequences subject to recombination.

In this article we discuss the ancestry of sequences sampled from the coalescent with recombination with constant population size 2N. We have studied a number of variables based on simulations of sample histories, and some analytical results are derived. Consider the leftmost nucleotide in the sequences. We show that the number of nucleotides sharing a most recent common ancestor (MRCA) with the leftmost nucleotide is approximately log(1 + 4N Lr)/4Nr when two sequences are compared, where L denotes sequence length in nucleotides, and r the recombination rate between any two neighboring nucleotides per generation. For larger samples, the number of nucleotides sharing MRCA with the leftmost nucleotide decreases and becomes almost independent of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA consists in mean of 3/8Nr nucleotides, when two sequences are compared, and that this decreases toward 1/4Nr nucleotides when the whole population is sampled. A measure of the correlation between the genealogies of two nucleotides on two sequences is introduced. We show analytically that even when the nucleotides are separated by a large genetic distance, but share MRCA, the genealogies will show only little correlation. This is surprising, because the time until the two nucleotides shared MRCA is reciprocal to the genetic distance. Using simulations, the mean time until all positions in the sample have found a MRCA increases logarithmically with increasing sequence length and is considerably lower than a theoretically predicted upper bound. On the basis of simulations, it turns out that important properties of the coalescent with recombinations of the whole population are reflected in the properties of a sample of low size.

Genome, Human↗
PubMed1999

The age of nonsynonymous and synonymous mutations in animal mtDNA and implications for the mildly deleterious theory.

McDonald/Kreitman tests performed on animal mtDNA consistently reveal significant deviations from strict neutrality in the direction of an excess number of polymorphic nonsynonymous sites, which is consistent with purifying selection acting on nonsynonymous sites. We show that under models of recurrent neutral and deleterious mutations, the mean age of segregating neutral mutations is greater than the mean age of segregating selected mutations, even in the absence of recombination. We develop a test of the hypothesis that the mean age of segregating synonymous mutations equals the mean age of segregating nonsynonymous mutations in a sample of DNA sequences. The power of this age-of-mutation test and the power of the McDonald/Kreitman test are explored by computer simulations. We apply the new test to 25 previously published mitochondrial data sets and find weak evidence for selection against nonsynonymous mutations.

Alleles↗
PubMed2000

Detecting ancient admixture in humans using sequence polymorphism data.

A debate of long-standing interest in human evolution centers around whether archaic human populations (such as the Neanderthals) have contributed to the modern gene pool. A model of ancient population structure with recent mixing is introduced, and it is determined how much information (i.e., sequence data from how many unlinked nuclear loci) would be necessary to distinguish between different demographic scenarios. It is found that approximately 50-100 loci are necessary if plausible parameter estimates are used. There are not enough data available at the present to support either the "single origin" or the "multiregional" model of modern human evolution. However, this information should be available in a few years.

Humans↗
PubMed2000

When did the human population size start increasing?

We analyze the frequency spectra of all available human nuclear sequence data sets by using a model of constant population size followed by exponential growth. Parameters of growth (more extreme than or) comparable to what has been suggested from mtDNA data can be rejected for 6 out of the 10 largest data sets. When the data are separated into African and non-African samples, a constant size no-growth model can be rejected for 4 out of 8 non-African samples. Long-term growth (i.e., starting 50-100 kya) can be rejected for 2 out of 8 African samples and 5 out of 8 non-African ones. Under more complex demographic models, including a bottleneck or population subdivision, more of the data are compatible with long-term growth. One problem with the data used here is that a subset of loci may reflect the action of natural selection as well as of demography. It remains possible that the correct demographic model is one of constant population size followed by long-term growth but that at several loci the demographic signature has been obscured by balancing or diversifying selection. However, it is not clear that the data at these loci are consistent with a simple model of balancing selection; more complicated selective alternatives cannot be tested unless they are made explicit. An alternative explanation is that population size growth is more recent (e.g., upper Paleolithic) and that some of the loci have experienced recent directional selection. Given the available data, the latter hypothesis seems more likely.

Africa↗
PubMed2000

Quantitative trait loci for floral morphology in Arabidopsis thaliana.

A central question in biology is how genes control the expression of quantitative variation. We used statistical methods to estimate genetic variation in eight Arabidopsis thaliana floral characters (fresh flower mass, petal length, petal width, sepal length, sepal width, long stamen length, short stamen length, and pistil length) in a cosmopolitan sample of 15 ecotypes. In addition, we used genome-wide quantitative trait locus (QTL) mapping to evaluate the genetic basis of variation in these same traits in the Landsberg erecta x Columbia recombinant inbred line population. There was significant genetic variation for all traits in both the sample of naturally occurring ecotypes and in the Ler x Col recombinant inbred line population. In addition, broad-sense genetic correlations among the traits were positive and high. A composite interval mapping (CIM) analysis detected 18 significant QTL affecting at least one floral character. Eleven QTL were associated with several floral traits, supporting either pleiotropy or tight linkage as major determinants of flower morphological integration. We propose several candidate genes that may underlie these QTL on the basis of positional information and functional arguments. Genome-wide QTL mapping is a promising tool for the discovery of candidate genes controlling morphological development, the detection of novel phenotypic effects for known genes, and in generating a more complete understanding of the genetic basis of floral development.

Arabidopsis↗
PubMed2000

Maximum likelihood estimation of recombination rates from population data.

We describe a method for co-estimating r = C/mu (where C is the per-site recombination rate and mu is the per-site neutral mutation rate) and Theta = 4N(e)mu (where N(e) is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting according to their posterior probability with regard to the data and working values of the parameters. Different relative rates of recombination at different locations can be accommodated if they are known from external evidence, but the algorithm cannot itself estimate rate differences. The estimates of Theta are accurate and apparently unbiased for a wide range of parameter values. However, when both Theta and r are relatively low, very long sequences are needed to estimate r accurately, and the estimates tend to be biased upward. We apply this method to data from the human lipoprotein lipase locus.

Genetics, Population↗
PubMed2000

Models for chromatid interference with applications to recombination data.

Genetic interference means that the occurrence of one crossover affects the occurrence and/or location of other crossovers in its neighborhood. Of the three components of genetic interference, two are well modeled: the distribution of the number and the locations of chiasmata. For the third component, chromatid interference, there exists only one model. Its application to real data has not yet been published. A further, new model for chromatid interference is presented here. In contrast to the existing model, it is assumed that chromatid interference acts only in the neighborhood of a chiasma. The appropriateness of this model is demonstrated by its application to three sets of recombination data. Both models for chromatid interference increased fit significantly compared to assuming no chromatid interference, at least for parts of the chromosomes. Interference does not necessarily act homogeneously. After extending both models to allow for heterogeneity of chromatid interference, a further improvement in fit was achieved.

Animals↗
PubMed2001

The length of the intact donor chromosome segment around a target gene in marker-assisted backcrossing.

Recurrent backcrossing is an established procedure to transfer target genes from a donor into the genetic background of a recipient genotype. By assessing the parental origin of alleles at markers flanking the target locus one can select individuals with a short intact donor chromosome segment around the target gene and thus reduce the linkage drag. We investigated the probability distribution of the length of the intact donor chromosome segment around the target gene in recurrent backcrossing with selection for heterozygosity at the target locus and homozygosity for the recurrent parent allele at flanking markers for a diploid species. Assuming no interference in crossover formation, we derived the cumulative density function, probability density function, expected value, and variance of the length of the intact chromosome segment for the following cases: (1) backcross generations prior to detection of a recombinant individual between the target gene and the flanking marker; (2) the backcross generation in which for the first time a recombinant individual is detected, which is selected for further backcrossing; and (3) subsequent backcross generations after selection of a recombinant. Examples are given of how these results can be applied to investigate the efficiency of marker-assisted backcrossing for reducing the length of the intact donor chromosome segment around the target gene under various situations relevant in breeding and genetic research.

Alleles↗
PubMed2001

Dense genetic linkage maps of three Populus species (Populus deltoides, P. nigra and P. trichocarpa) based on AFLP and microsatellite markers.

Populus deltoides, P. nigra, and P. trichocarpa are the most important species for poplar breeding programs worldwide. In addition, Populus has become a model for fundamental research on trees. Linkage maps were constructed for these three species by analyzing progeny of two controlled crosses sharing the same female parent, Populus deltoides cv. S9-2 x P. nigra cv. Ghoy and P. deltoides cv. S9-2 x P. trichocarpa cv. V24. The two-way pseudotestcross mapping strategy was used to construct the maps. Amplified fragment length polymorphism (AFLP) markers that segregated 1:1 were used to form the four parental maps. Microsatellites and sequence-tagged sites were used to align homoeologous groups between the maps and to merge linkage groups within the individual maps. Linkage analysis and alignment of the homoeologous groups resulted in 566 markers distributed over 19 groups for P. deltoides covering 86% of the genome, 339 markers distributed over 19 groups for P. trichocarpa covering 73%, and 369 markers distributed over 28 groups for P. nigra covering 61%. Several tests for randomness showed that the AFLP markers were randomly distributed over the genome.

Chromosome Mapping↗
PubMed2002

Interactions between natural selection, recombination and gene density in the genes of Drosophila.

In Drosophila, as in many organisms, natural selection leads to high levels of codon bias in genes that are highly expressed. Thus codon bias is an indicator of the intensity of one kind of selection that is experienced by genes and can be used to assess the impact of other genomic factors on natural selection. Among 13,000 genes in the Drosophila genome, codon bias has a slight positive, and strongly significant, association with recombination--as expected if recombination allows natural selection to act more efficiently when multiple linked sites segregate functional variation. The same reasoning leads to the expectation that the efficiency of selection, and thus average codon bias, should decline with gene density. However, this prediction is not confirmed. Levels of codon bias and gene expression are highest for those genes in an intermediate range of gene density, a pattern that may be the result of a tradeoff between the advantages for gene expression of close gene spacing and disadvantages arising from regulatory conflicts among tightly packed genes. These factors appear to overlay the more subtle effect of linkage among selected sites that gives rise to the association between recombination rate and codon bias.

Animals↗
PubMed2003

Effects of population structure and admixture on exact tests for association between Loci.

The probability of multilocus genotype counts conditional on allelic counts and on allelic independence provides a test statistic for independence within and between loci. As the number of loci increases and each sampled genotype becomes unique, the conditional probability becomes a function of total heterozygosity. In that case, it does not address between-locus dependence directly but only indirectly through detection of the Wahlund effect. Moreover, the test will reject the hypothesis of allelic independence only for small values of heterozygosity. Low heterozygosity is expected for population subdivision but not for population admixture. The test may therefore be inappropriate for admixed populations. If individuals with parents in two different populations are always considered to belong to one of the populations, then heterozygosity is increased in that population and the exact test should not be used for sparse data sets from that population. If such a case is suspected, then alternative testing strategies are suggested.

Data Interpretation, Statistical↗