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N L Kaplan

Publications and source records attributed to N L Kaplan.

At least 37 records · Page 2Linked to original sources
PubMed1995

Are moment bounds on the recombination fraction between a marker and a disease locus too good to be true? Allelic association mapping revisited for simple genetic diseases in the Finnish population.

In the past several years, allelic association has helped map a number of rare genetic diseases in the human genome. A commonly used upper bound on the recombination fraction between the disease gene and an associated marker is known to be biased downward, so there is the possibility that an investigator could be misled. This upper bound is based on a moment equation that can be derived within the context of a Poisson branching process, so its performance can be compared with a recently proposed likelihood bound. We show that the confidence level of the moment upper bound is much lower than expected, while the confidence level of the likelihood bound is in line with expectation. The effects of mutation at either the marker or disease locus on the upper bounds are also investigated. Results indicate that mutation is not an important force for typical mutation rates, unless the recombination fraction between the marker and disease locus is very small or the disease allele is very rare in the general population. Finally, the impact of sample size on the likelihood bound is investigated. The results are illustrated with data on 10 simple genetic diseased in the Finnish population.

Alleles↗
PubMed1992

A statistical test for detecting geographic subdivision.

A statistical test for detecting genetic differentiation of subpopulations is described that uses molecular variation in samples of DNA sequences from two or more localities. The statistical significance of the test is determined with Monte Carlo simulations. The power of the test to detect genetic differentiation in a selectively neutral Wright-Fisher island model depends on both sample size and the rates of migration, mutation, and recombination. It is found that the power of the test is substantial with samples of size 50, when 4Nm less than 10, where N is the subpopulation size and m is the fraction of migrants in each subpopulation each generation. More powerful tests are obtained with genes with recombination than with genes without recombination.

Alcohol Dehydrogenase↗
PubMed1990

Biologically based models for risk assessment.

The modelling problems associated with the estimation of risks from long-term chemical exposures at low dose levels represent a statistical and mathematical challenge with special relevance to environmental research. Determining an adequate model for estimating the relationship between dose and response is critical to reducing potential bias in the risk estimation process. This paper discusses the various assumptions and models used in carcinogenic risk assessment. The emphasis is on our ability to accurately determine the magnitude of the carcinogenic risk, the shape of the dose-response relationship and the overall variability of the risk estimates.

Animals↗
PubMed1989

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.

Genetics, Population↗
PubMed1989

Variability of safe dose estimates when using complicated models of the carcinogenic process. A case study: methylene chloride.

Advances in understanding carcinogenesis have led to the development of mathematical models that have biologically interpretable parameters. These models utilize more of the available scientific data than the empirical models routinely employed for quantifying carcinogenic risk. They also require consideration of sources of uncertainty in risk estimates that were previously ignored, such as animal-to-animal variability of physiological and pharmacological constants. A numerical technique is proposed for studying the consequences of incorporating the intrapopulation variability of biologically interpretable parameters into the risk assessment process. To demonstrate the technique, the variability of safe dose estimates for exposure to methylene chloride is considered. The results suggest that intrapopulation variability of the model parameters can increase the variability of safe dose estimates an appreciable amount.

Animals↗
PubMed1989

The "hitchhiking effect" revisited.

The number of selectively neutral polymorphic sites in a random sample of genes can be affected by ancestral selectively favored substitutions at linked loci. The degree to which this happens depends on when in the history of the sample the selected substitutions happen, the strength of selection and the amount of crossing over between the sampled locus and the loci at which the selected substitutions occur. This phenomenon is commonly called hitchhiking. Using the coalescent process for a random sample of genes from a selectively neutral locus that is linked to a locus at which selection is taking place, a stochastic, finite population model is developed that describes the steady state effect of hitchhiking on the distribution of the number of selectively neutral polymorphic sites in a random sample. A prediction of the model is that, in regions of low crossing over, strongly selected substitutions in the history of the sample can substantially reduce the number of polymorphic sites in a random sample of genes from that expected under a neutral model.

Base Sequence↗
PubMed1988

The coalescent process in models with selection.

Statistical properties of the process describing the genealogical history of a random sample of genes are obtained for a class of population genetics models with selection. For models with selection, in contrast to models without selection, the distribution of this process, the coalescent process, depends on the distribution of the frequencies of alleles in the ancestral generations. If the ancestral frequency process can be approximated by a diffusion, then the mean and the variance of the number of segregating sites due to selectively neutral mutations in random samples can be numerically calculated. The calculations are greatly simplified if the frequencies of the alleles are tightly regulated. If the mutation rates between alleles maintained by balancing selection are low, then the number of selectively neutral segregating sites in a random sample of genes is expected to substantially exceed the number predicted under a neutral model.

Genealogy and Heraldry↗
PubMed1988

The coalescent process in models with selection and recombination.

The statistical properties of the process describing the genealogical history of a random sample of genes at a selectively neutral locus which is linked to a locus at which natural selection operates are investigated. It is found that the equations describing this process are simple modifications of the equations describing the process assuming that the two loci are completely linked. Thus, the statistical properties of the genealogical process for a random sample at a neutral locus linked to a locus with selection follow from the results obtained for the selected locus. Sequence data from the alcohol dehydrogenase (Adh) region of Drosophila melanogaster are examined and compared to predictions based on the theory. It is found that the spatial distribution of nucleotide differences between Fast and Slow alleles of Adh is very similar to the spatial distribution predicted if balancing selection operates to maintain the allozyme variation at the Adh locus. The spatial distribution of nucleotide differences between different Slow alleles of Adh do not match the predictions of this simple model very well.

Alcohol Dehydrogenase↗
PubMed1987

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.

Gene Frequency↗
PubMed1986

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. 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 for a similar model. The effects of gene conversion are also examined. In agreement with Slatkin, we find that gene conversion has a minimal effect on the probability of identity providing that the rate of deletion is sufficiently large.

Animals↗
PubMed1986

On the divergence of alleles in nested subsamples from finite populations.

Within-population variation at the DNA level will rarely be studied by sequencing of loci of randomly chosen individuals. Instead, individuals will usually be chosen for sequencing based on some knowledge of their genotype. Data collected in this way require new sampling theory. Motivated by these observations, we have examined the sampling properties of a finite population model with two mutation processes and with no selection or recombination. One mutation process generates new alleles according to an infinite-alleles model, and the other generates polymorphisms at sites according to an infinite-sites model. A sample of n genes is considered. The stationary distribution of the number of segregating sites in a subsample from one of the allelic classes in the sample conditional on the allelic configuration of the sample is studied. A recursive scheme is developed to compute the moments of this distribution, and it is shown that the distribution is functionally independent of the number of additional alleles in the sample and their respective frequencies in the sample. For the case in which the sample contains only two alleles, the distribution of the number of segregating sites in a subsample containing both alleles conditional on the sample frequencies of the alleles is studied. The results are applied to the analysis of DNA sequences of two alleles found at the Adh locus of Drosophila melanogaster. No significant departure from the neutral model is detected.

Alleles↗
PubMed1985

Statistical properties of the number of recombination events in the history of a sample of DNA sequences.

Some statistical properties of samples of DNA sequences are studied under an infinite-site neutral model with recombination. The two quantities of interest are R, the number of recombination events in the history of a sample of sequences, and RM, the number of recombination events that can be parsimoniously inferred from a sample of sequences. Formulas are derived for the mean and variance of R. In contrast to R, RM can be determined from the sample. Since no formulas are known for the mean and variance of RM, they are estimated with Monte Carlo simulations. It is found that RM is often much less than R, therefore, the number of recombination events may be greatly under-estimated in a parsimonious reconstruction of the history of a sample. The statistic RM can be used to estimate the product of the recombination rate and the population size or, if the recombination rate is known, to estimate the population size. To illustrate this, DNA sequences from the Adh region of Drosophila melanogaster are used to estimate the effective population size of this species.

Alleles↗
PubMed1983

Implication of nonlinear kinetics on risk estimation in carcinogenesis.

Efforts in estimating carcinogenic risk in humans from long-term exposure to chemical carcinogens have centered on the problem of low-dose extrapolation. For chemicals with metabolites that interact with DNA, it may be more meaningful to relate tumor response to the concentration of the DNA adducts in the target organ rather than to the applied dose. Many data suggest that the relation between tumor response and concentration of DNA adducts in the target organ may be linear. This implies that the nonlinearities of the dose-response curve for tumor induction may be due to the kinetic processes involved in the formation of carcinogen metabolite--DNA adducts. Of particular importance is the possibility that the kinetic processes may show a nonlinear "hockey-stick" like behavior which results from saturation of detoxification or DNA repair processes. The mathematical models typically used for low-dose extrapolation are shown potentially to overestimate risk by several orders of magnitude when nonlinear kinetics are present.

Animals↗
PubMed1983

The effect of homozygosity of selective differences between sites of transposable elements.

The behavior of the frequency spectrum of sites of transposable elements for the model proposed by Langley, Brookfield, and Kaplan ((1983) Genetics 104) is studied when some of the sites have weak additive selection against the host. In particular, it is shown that under certain conditions, the expected homozygosity at equilibrium will always be larger when there is variation in selection between sites than when such variation is absent.

Animals↗