Richard R. Hudson

On the role of unequal exchange in the containment of transposable element copy number

A population genetics model of the role of asymmetric pairing and unequal exchange in the stabilization of transposable element copy number in natural populations is proposed and analysed. Monte Carlo simulations indicate that the approximations incorporated into the analysis are robust in the relevant parameter ranges. Given several simple assumptions concerning transposition and excision, equal and unequal exchange, and chromosome structure, predictions of the relative numbers of transposable elements in various regions of the Drosophila melanogaster genome are compared to the observed distribution of roo / B104 elements across chromosomal regions with differing rates of exchange, and between X chromosomes and autosomes. There is no indication of an accumulation of elements in the distal regions of chromosomes, which is expected if unequal exchange is reduced concomitantly with normal crossing over in the distal regions. There is, however, an indication of an excess of elements relative to physical length in the proximal regions of the chromosomes, which also have restricted crossing over. This observation is qualitatively consistent with the models predictions. The observed distribution of elements between the mid-sections of the X chromosomes and autosomes is consistent with the predictions of one of two models of unequal exchange.

Gene Trees with Background Selection

Consideration of the coalescent process is shown to be useful for analyzing neutral variation linked to loci at which deleterious variation is maintained by mutation-selection balance. Formulas for expected nucleotide diversity and the expected number of polymorphic sites in a sample are obtained. Simulations based on the coalescent process demonstrate that such background selection will rarely result in rejection of the neutral model using Tajima’s D statistic. Models with recombination are also considered.

The use of sample genealogies for studying a selectively neutral m-loci model with recombination.

A selectively neutral m-loci model with recombination is studied. A general method is developed to calculate the variance of the number of segregating sites in samples of arbitrary size and the m-loci homozygosity. The method is based on properties of the genealogy of the sample rather than diffusion approximations. To demonstrate the scope of the method several calculations are presented.

DNA polymorphism haplotypes of the human apolipoprotein APOA1-APOC3-APOA4 gene cluster

SummaryThe genes coding for apolipoproteins A1, C3, and A4 (APOA1, APOC3, APOA4) are closely linked and tandemly organized within a 15-kilobase (kb) DNA segment on the long arm of human chromosome 11. The nucleotide variability of a 61-kb DNA segment containing these genes and their flanking sequences was studied by restriction analysis of a sample of 18 unrelated Northern Europeans using seven different genomic DNA probes. Eleven restriction site polymorphisms located within this DNA segment were used for haplotype analysis of 129 Mediterranean and 67 American black chromosomes. Estimation of the extent of nonrandom association between these polymorphisms indicated considerable linkage disequilibrium within the APOA1-APOC3-APOA4 gene cluster. Several haplotypes arose by recombination, and the rate of recombination within this gene cluster was estimated to be at least 4 times greater than that expected based on uniform recombination. The polymorphism information content of each of these polymorphisms, taken individually, ranges between 0.053 and 0.375, while that of their haplotypes ranges between 0.858 and 0.862. Therefore, DNA polymorphism haplotypes in the APOA1-APOC3-APOA4 gene cluster constitute a highly informative genetic marker on the long arm of human chromosome 11.

How often are polymorphic restriction sites due to a single mutation

An approximate expression is obtained for the probability that a restriction site, which is polymorphic in a random sample, is a site at which two or more mutations have occurred in the descent to the sample from the most recent common ancestor of the sample. The analysis is based on the assumption that the population from which the sample is obtained is at equilibrium under a selectively neutral Wright-Fisher model. Monte Carlo simulations show that the approximation is quite accurate. For commonly observed levels of genetic variation in humans and in natural populations of Drosophila, it is found that multiple mutations would occur at 5 to 10 percent of polymorphic restriction sites assuming that six-cutter enzymes are used on samples of size 50 to 100. Simulations are also used to investigate the bias and mean square error of four estimators of 4Nu, where N is the population size and u is the neutral mutation rate per nucleotide site. Two of the estimators are biased by approximately 20 percent when levels of variation are similar to those which have been observed in natural populations of Drosophila.

On the divergence of genes in multigene families.

Statistical properties of the amount of divergence of genes in multigene families are studied. The model considered is an infinite-site neutral model with unbiased intrachromosomal conversion, unbiased interchromosomal conversion, and recombination. By considering the time back to the most recent common ancestor of two genes, both the probability of identity and the moments of S, the number of sites that differ between two sampled genes, are obtained. We find that if recombination rates are large or conversion is always interchromosomal, then the expectation of S is 4N mu n where N is the population size, mu is the rate of mutation per generation per gene and n is the number of genes in the gene family, as the conversion rates approach zero, the moments of divergence do not approach the moments of divergence with conversion rates equal to zero, and it is possible for a decrease in the rate of intrachromosomal conversion to result in a higher probability of identity, but a greater mean divergence of the two genes.

On the divergence of members of a transposable element family

Statistical properties of the amount of divergence of members of a transposable element family are studied. The analysis is based on the model proposed by Langley et al. [5], describing the evolution of a family of selectively neutral transposable elements in a finite haploid population of size 2N. By considering the time back to the most recent common ancestor of two copies, both the probability of identity and the moments of the number of sites that differ between two sampled copies are obtained. Our analytic results are consistent with the numerical results of Ohta [8] for a similar model. The effects of gene conversion are also examined. In agreement with Slatkin [9], we find that gene conversion has a minimal effect on the probability of identity providing that the rate of deletion is sufficiently large.

A numerical method for calculating moments of coalescent times in finite populations with selection

A numerical method is developed for solving a nonstandard singular system of second-order differential equations arising from a problem in population genetics concerning the coalescent process for a sample from a population undergoing selection. The nonstandard feature of the system is that there are terms in the equations that approach infinity as one approaches the boundary. The numerical recipe is patterned after the LU decomposition for tridiagonal matrices. Although there is no analytic proof that this method leads to the correct solution, various examples are presented that suggest that the method works. This method allows one to calculate the expected number of segregating sites in a random sample of n genes from a population whose evolution is described by a model which is not selectively neutral.