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PubMed1976

Testing for selective neutrality of electrophoretically detectable protein polymorphisms.

The statistical assessment of gene-frequency data on protein polymorphisms in natural populations remains a contentious issue. Here we formulate a test of whether polymorphisms detected by electrophoresis are in accordance with the stepwise, or charge-state, model of mutation in finite populations in the absence of selection. First, estimates of the model parameters are derived by minimizing chi-square deviations of the observed frequencies of genotypes with alleles (0,1,2...) units apart from their theoretical expected values. Then the remaining deviation is tested under the null hypothesis of neutrality. The procedure was found to be conservative for false rejections in simulation data. We applied the test to Ayala and Tracey 's data on 27 allozymic loci in six populations of Drosophila willistoni . About one-quarter of polymorphic loci showed significant departure from the neutral theory predictions in virtually all populations. A further quarter showed significant departure in some populations. The remaining data showed an acceptable fit to the charge state model. A predominating mode of selection was selection against alleles associated with extreme electrophoretic mobilities. The advantageous properties and the difficulties of the procedure are discussed.

Animals↗
PubMed2003

Estimating polygenic effects using markers of the entire genome.

Molecular markers have been used to map quantitative trait loci. However, they are rarely used to evaluate effects of chromosome segments of the entire genome. The original interval-mapping approach and various modified versions of it may have limited use in evaluating the genetic effects of the entire genome because they require evaluation of multiple models and model selection. Here we present a Bayesian regression method to simultaneously estimate genetic effects associated with markers of the entire genome. With the Bayesian method, we were able to handle situations in which the number of effects is even larger than the number of observations. The key to the success is that we allow each marker effect to have its own variance parameter, which in turn has its own prior distribution so that the variance can be estimated from the data. Under this hierarchical model, we were able to handle a large number of markers and most of the markers may have negligible effects. As a result, it is possible to evaluate the distribution of the marker effects. Using data from the North American Barley Genome Mapping Project in double-haploid barley, we found that the distribution of gene effects follows closely an L-shaped Gamma distribution, which is in contrast to the bell-shaped Gamma distribution when the gene effects were estimated from interval mapping. In addition, we show that the Bayesian method serves as an alternative or even better QTL mapping method because it produces clearer signals for QTL. Similar results were found from simulated data sets of F(2) and backcross (BC) families.

Bayes Theorem↗
PubMed2004

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.

Chromosome Mapping↗
PubMed1999

Genetic dissection of a complex trait.

A number of genetic and statistical tools were applied to various partitions of the simulated data to identify susceptibility loci, relevant environmental factors, and their interaction(s). The distribution of genotypes at D1G24 among affected children in the first population was found to differ significantly from Hardy-Weinberg expectation. Two transmission/disequilibrium tests identified the preferential transmission of allele 1 as the source of the disequilibrium. Simple contingency table analysis revealed a positive association between exposure to environmental factor E1 and disease phenotype. Multipoint linkage analyses on various subsets of the data identified three "signal" regions (in addition to the aforementioned D1G24) localized at D1G9-10, D3G45, and D5G38. The even numbered chromosomes appeared to be devoid of susceptibility loci. Further analyses of subsamples of affected sib pairs, selected according to their disease phenotype and their exposure to E1, clarified some linkage relationships, particularly for D3G45, thereby suggesting the presence of a specific gene x environment interaction. Logistic analysis designed to clarify the relationship between disease phenotype and two risk factors (E1 exposure and the presence of allele 1 at D1G24) in the first population, revealed a significantly negative interaction which, upon learning the details of the generating model, we now attribute to the presence of heterogeneity.

Environment↗
PubMedDate not supplied

Comparisons of likelihood and machine learning methods of individual classification.

Classification methods used in machine learning (e.g., artificial neural networks, decision trees, and k-nearest neighbor clustering) are rarely used with population genetic data. We compare different nonparametric machine learning techniques with parametric likelihood estimations commonly employed in population genetics for purposes of assigning individuals to their population of origin ("assignment tests"). Classifier accuracy was compared across simulated data sets representing different levels of population differentiation (low and high F(ST)), number of loci surveyed (5 and 10), and allelic diversity (average of three or eight alleles per locus). Empirical data for the lake trout (Salvelinus namaycush) exhibiting levels of population differentiation comparable to those used in simulations were examined to further evaluate and compare classification methods. Classification error rates associated with artificial neural networks and likelihood estimators were lower for simulated data sets compared to k-nearest neighbor and decision tree classifiers over the entire range of parameters considered. Artificial neural networks only marginally outperformed the likelihood method for simulated data (0-2.8% lower error rates). The relative performance of each machine learning classifier improved relative likelihood estimators for empirical data sets, suggesting an ability to "learn" and utilize properties of empirical genotypic arrays intrinsic to each population. Likelihood-based estimation methods provide a more accessible option for reliable assignment of individuals to the population of origin due to the intricacies in development and evaluation of artificial neural networks.

Animals↗
PubMed2004

Predicting the annual effective size of livestock populations.

Effective population size (Ne) is an important parameter determining the genetic structure of small populations. In natural populations, the number of adults (N) is usually known and Ne can be estimated on the basis of an assumed ratio Ne/N, usually found to be close to 0.5. In farm animal populations, apart from using pedigrees or genetic marker information, Ne can be estimated from the number N of breeding animals, and a value of 1 is commonly assumed for the ratio Ne/N. The purpose of this paper is to show the relation between effective population size and breeding herd size in livestock species. With overlapping generations, Ne can be predicted knowing the number of individuals entering the population per generation and the variance of family size, the latter being directly related to the survival pattern (or replacement policy) in the breeding herd. Assuming an ideal survivorship leading to a geometric age distribution, it can be shown that the number of breeding animals tends to overestimate effective size, particularly in early-maturing species. The ratio of annual effective size to the number of breeding animals is shown to be equal to [1 + (a- 1)(1 - s)]2/(1 - s2), where a is the age at first offspring and s is the survival rate (including culling) of the parents between successive births. This expression shows to what extent inbreeding may be determined by demography or culling policy independently of the actual herd size. In many situations a fast replacement or an early culling will increase annual effective size. Consequences for the management of small populations are discussed.

Animals↗
PubMed2003

Adding further power to the Haseman and Elston method for detecting linkage in larger sibships: weighting sums and differences.

Haseman and Elston (H-E) proposed a robust test to detect linkage between a quantitative trait and a genetic marker. In their method the squared sib-pair trait difference is regressed on the estimated proportion of alleles at a locus shared identical by descent by sib pairs. This method has recently been improved by changing the dependent variable from the squared difference to the mean-corrected product of the sib-pair trait values, a significantly positive regression indicating linkage. Because situations arise in which the original test is more powerful, a further improvement of the H-E method occurs when the dependent variable is changed to a weighted average of the squared sib-pair trait difference and the squared sib-pair mean-corrected trait sum. Here we propose an optimal method of performing this weighting for larger sibships, allowing for the correlation between pairs within a sibship. The optimal weights are inversely proportional to the residual variances obtained from the two different regressions based on the squared sib-pair trait differences and the squared sib-pair mean-corrected trait sums, respectively, allowing for correlations among sib pairs. The proposed method is compared with the existing extension of the H-E approach for larger sibships. Control of the type I error probabilities for sibships of any size can be improved by using a generalized estimating equation approach and the robust sandwich estimate of the variance, or a Monte-Carlo permutation test.

Computer Simulation↗
PubMed1998

Mitochondrial DNA diversity and historical biogeography of a wet forest-restricted frog (Litoria pearsoniana) from mid-east Australia.

MtDNA sequencing was used to investigate the genetic population structure of Litoria pearsoniana, a wet forest-restricted hylid frog, endemic to southeast Queensland and northeast New South Wales, Australia. L. pearsoniana is regarded as endangered under Queensland legislation. Significant genetic divergence among populations of frogs from different rainforest isolates was identified, but the lack of reciprocal monophyly among adjacent isolates suggests this is the result of a relatively recent disruption to gene flow. A paired catchment study within a single rainforest isolate, the Conondale Range, revealed no substantial genetic structuring, indicating the occurrence of terrestrial dispersal among nearby streams either in the recent past or currently. Two major reciprocally monophyletic clades of mtDNA alleles were identified. These corresponded to two geographical regions separated by the Brisbane River valley; one consisting of the Conondale and D'Aguilar Ranges, and the other of the southern isolates in the Main, Border and Gibraltar Ranges. Sequence divergence between the two regions was more consistent with a late Miocene or Pliocene rather than late Pleistocene separation, and is similar to that found among phylogeographic divisions of rainforest reptiles and amphibians in north Queensland rainforests. The molecular evidence for long-term separation of these two regions is corroborated by the pattern of species turnover in the distributions of species of rainforest-restricted amphibians and reptiles. Bioclimatic modelling suggests that appropriate conditions for L. pearsoniana would have been restricted to isolated refugees in each phylogeographic division under cooler and drier climates, such as predicted for the last glacial maximum. Currently isolated montane areas may have been connected transiently during the past 2000 years. Identification of long-term zoogeographic divisions among southeast Queensland rainforest herpetofauna has important implications for conservation and management. Conservation management of L. pearsoniana should be applied at the scale of major rainforest isolates and the conservation status of the species should be assessed independently north and south of the historical division.

Animals↗
PubMed2002

Perspective: purging the genetic load: a review of the experimental evidence.

Inbreeding depression, the reduction in fitness that accompanies inbreeding, is one of the most important topics of research in evolutionary and conservation genetics. In the recent literature, much attention has been paid to the possibility of purging the genetic load. If inbreeding depression is due to deleterious alleles, whose effect on fitness are negative when in a homozygous state, then successive generations of inbreeding may result in a rebound in fitness due to the selective decrease in frequency of deleterious alleles. Here we examine the experimental evidence for purging of the genetic load by collating empirical tests of rebounds in fitness-related traits with inbreeding in animals and plants. We gathered data from 28 studies including five mammal, three insect, one mollusc, and 13 plant species. We tested for purging by examining three measures of fitness-component variation with serial generations of inbreeding: (1) changes in inbreeding depression, (2) changes in fitness components of inbred lines relative to the original outbred line, and (3) purged population (outcrossed inbred lines) trait means as a function of ancestral outbred trait means. Frequent and substantial purging was found using all three measures, but was particularly pronounced when tracking changes in inbreeding depression. Despite this, we found little correspondence between the three measures of purging within individual studies, indicating that the manner in which a researcher chooses to estimate purging will affect interpretation of the results obtained. The discrepancy suggests an alternative hypothesis: rebounds in fitness with inbreeding may have resulted from adaptation to laboratory conditions and not to purging when using outcrossed inbred lines. However, the pronounced reduction in inbreeding depression for a number of studies provides evidence for purging, as the measure is likely less affected by selection for laboratory conditions. Unlike other taxon-specific reviews on this topic, our results provide support for the purging hypothesis, but firm predictions about the situations in which purging is likely or the magnitude of fitness rebound possible when populations are inbred remain difficult. Further research is required to resolve the discrepancy between the results obtained using different experimental approaches.

Animals↗
PubMed1999

Role of the alpha2B-adrenergic receptor in the development of salt-induced hypertension.

Salt sensitivity is a common trait in patients with essential hypertension and seems to have both an inherited and an acquired component (eg, is influenced by aging and renal insufficiency). Experimental evidence suggests that salt loading induces hypertension via a neurogenic mechanism mediated by the alpha2-adrenergic receptors (alpha2-AR). To explore the alpha2-AR subtype involved in this mechanism, we studied 2 groups of mice genetically engineered to be deficient in one of the 3 alpha2-AR subtype genes (either alpha2B-AR +/- or alpha2C-AR -/- knockout mice) compared with their wild-type counterparts. The mice (n=10 to 14 in each group) were submitted to subtotal nephrectomy and given 1% saline as drinking water for up to 35 days. Blood pressure (BP) was monitored by tail-cuff readings and confirmed at the end point by direct intra-arterial BP recording. The alpha2B-AR-deficient mice had an attenuated BP response in this protocol (baseline 101.8+/-2.7 versus end point 109.9+/-2.8 mm Hg), whereas the BP of their wild-type counterparts went from a baseline 101.9+/-2.3 to an end point 141.4+/-7.1 mm Hg. The other 2 groups had BP increases of 44. 6+/-5.17 and 46.7+/-7.01 mm Hg, with no difference between the mice deficient in the alpha2C-AR gene subtype versus their wild-type counterparts. Body weight, renal remnant weight, and residual renal function were no different among groups. These data suggest that a full complement of alpha2B-AR genes is necessary to raise BP in response to dietary salt loading, whereas complete absence of the alpha2C-AR subtype does not preclude salt-induced BP elevation. It is unclear whether the mechanism(s) involved in this process are of central origin (inability to increase sympathetic outflow), vascular origin (inability to vasoconstrict), or renal origin (inability to retain excess salt and fluid).

Aging↗
PubMed2004

Value of p16INK4a and RASSF1A promoter hypermethylation in prognosis of patients with resectable non-small cell lung cancer.

The p16INK4a and RASSF1A are tumor suppressor genes frequently inactivated by de novo promoter hypermethylation in non-small cell lung cancer. We studied 119 patients with non-small cell lung cancer (70 stage I/II and 49 stage IIIA) who had undergone surgery with curative intent. The p16INK4a and RASSF1A promoter methylation statuses were determined by methylation-specific PCR. Statistical analyses, all two-sided, were performed to determine the prognostic effect of hypermethylation on various clinical parameters. Hypermethylation of the p16INK4a and RASSF1A promoters was found in 58 (49%) and 46 (39%) tumors, respectively, and 30 tumors (25%) exhibited hypermethylation of both gene promoters. In patients with stage I/II tumors, only p16INK4a promoter hypermethylation was associated with a poor 5-year overall survival rate (P=0.002). In patients with stage IIIA disease, however, RASSF1A promoter hypermethylation was a stronger predictor of a poor 5-year overall survival rate (P < 0.0001) than p16INK4a promoter hypermethylation. Among the 49 patients with stage IIIA tumors, 16 (89%) of the 18 patients whose tumors showed RASSF1A promoter hypermethylation died within 3 years after surgery, as compared with only 12 (39%) of the 31 patients whose tumors had no RASSF1A promoter hypermethylation (P < 0.0001). Multivariate analysis indicated that RASSF1A promoter hypermethylation was the stronger independent predictor for survival in patients with locally advanced non-small cell lung cancer. Our results indicate that p16INK4a promoter hypermethylation predicts a poor 5-year survival rates for patients with resectable non-small cell lung cancer, particularly for those with early stage tumors, whereas RASSF1A promoter hypermethylation is a profound prognostic predictor for patients with locally advanced non-small cell lung cancer, suggesting an important role of RASSF1A in non-small cell lung cancer progression.

Adult↗
PubMed2004

Approaches to familial aggregation: hypothesis testing and estimation when families are selected through parent probands under a variant of single ascertainment.

Epidemiologic approaches to testing and estimating familial aggregation of a disease consist of comparing rates of disease in relatives of individuals with the disease (known as case probands) with rates of disease in relatives of individuals without the disease (known as control probands). Gold et al. (J Am Stat Ass 1967;62: 409-420) derived an explicit mathematical model and sampling methods, under which this approach is equivalent to testing the null hypotheses that the disease risk in families is homogenous. A basic assumption of this model is that every family member has the same risk of disease and that disease status is independent among family members, although the disease risk may vary between families. When the disease is suspected of having a genetic component, rather than being purely environmental, this model has been shown to be appropriate for detecting disease aggregation in siblings, when relatives are siblings of probands. This model however is unrealistic for use in nuclear families when the affected status of offspring is not independent of the affected status of parents, and these families are selected through an affected or an unaffected parent, so that a parent is the proband and relatives are offspring of probands. We extend the Gold et al. model to allow for the disease risk in offspring to vary with the affected status of the parent. We assume that families are selected through affected and unaffected parents, under a variation of single ascertainment. Under this study design, we show that the usual test of association between affected status of probands and relatives, performed by comparing sample proportions of affected relatives of affected and unaffected probands, respectively, is no longer equivalent to a test of homogeneity of disease risk in offspring. Instead, it is equivalent to testing that the disease risk in offspring is independent of the number of affected parents. This test reduces to a test of homogeneity if and only if one assumes that the variation in disease risk in offspring, between families, is solely due to the variation in the number of affected parents. As a result, we show that under this study design, the standard chi2 test must be modified in order to obtain a valid test of familial aggregation. In addition the sample proportions of affected relatives of case and control probands, respectively, are shown to provide unbiased estimates of the expected risk of disease in an offspring given an affected/unaffected parent. We apply these results to methods of sample selection and discuss the practical implications of these findings.

Data Interpretation, Statistical↗
PubMed2004

Case-sibling gene-association studies for diseases with variable age at onset.

Studies which compare cases to disease-free siblings are useful for assessing association between a genetic locus and a phenotypic trait, as they eliminate the possibility of confounding by population stratification. Many analytic methods for such family-based studies are based on a binary disease model. However, complex diseases have variable age at onset. Consequently, binary-outcome methods can be inefficient or biased. We review methods for analysing censored age-at-onset data from family studies, including stratified Cox regression and genotype-decomposition regression, an unstratified procedure which regresses age-at-onset on between- and within-family genotype components. We also introduce a retrospective likelihood for censored age-at-onset data, which requires an external estimate of the baseline hazard. Stratified Cox regression does not use controls who have not attained the age of their case sibling(s), potentially leading to a loss of efficiency. Both genotype-decomposition regression and the retrospective likelihood use these younger controls. We assess the performance of these methods via simulation studies. Stratified Cox regression and the retrospective likelihood have appropriate type I error rates in almost all situations studied; genotype-decomposition regression is often anti-conservative. Away from the null, confidence intervals for the relative risk derived from stratified Cox regression are anti-conservative when the disease is rare and case-rich families are sampled. The retrospective likelihood is more efficient than stratified Cox regression and its confidence intervals have correct coverage when the disease is rare or the estimate of the baseline hazard is reasonably accurate. These results suggest that when estimating genotype relative risks is the principal analytic goal, stratified Cox regression is appropriate as long as the disease is common; when the disease is rare, the retrospective likelihood may be more appropriate.

Age of Onset↗
PubMed2003

Haplotyping as perfect phylogeny: a direct approach.

A full haplotype map of the human genome will prove extremely valuable as it will be used in large-scale screens of populations to associate specific haplotypes with specific complex genetic-influenced diseases. A haplotype map project has been announced by NIH. The biological key to that project is the surprising fact that some human genomic DNA can be partitioned into long blocks where genetic recombination has been rare, leading to strikingly fewer distinct haplotypes in the population than previously expected (Helmuth, 2001; Daly et al., 2001; Stephens et al., 2001; Friss et al., 2001). In this paper we explore the algorithmic implications of the no-recombination in long blocks observation, for the problem of inferring haplotypes in populations. This assumption, together with the standard population-genetic assumption of infinite sites, motivates a model of haplotype evolution where the haplotypes in a population are assumed to evolve along a coalescent, which as a rooted tree is a perfect phylogeny. We consider the following algorithmic problem, called the perfect phylogeny haplotyping problem (PPH), which was introduced by Gusfield (2002) - given n genotypes of length m each, does there exist a set of at most 2n haplotypes such that each genotype is generated by a pair of haplotypes from this set, and such that this set can be derived on a perfect phylogeny? The approach taken by Gusfield (2002) to solve this problem reduces it to established, deep results and algorithms from matroid and graph theory. Although that reduction is quite simple and the resulting algorithm nearly optimal in speed, taken as a whole that approach is quite involved, and in particular, challenging to program. Moreover, anyone wishing to fully establish, by reading existing literature, the correctness of the entire algorithm would need to read several deep and difficult papers in graph and matroid theory. However, as stated by Gusfield (2002), many simplifications are possible and the list of "future work" in Gusfield (2002) began with the task of developing a simpler, more direct, yet still efficient algorithm. This paper accomplishes that goal, for both the rooted and unrooted PPH problems. It establishes a simple, easy-to-program, O(nm(2))-time algorithm that determines whether there is a PPH solution for input genotypes and produces a linear-space data structure to represent all of the solutions. The approach allows complete, self-contained proofs. In addition to algorithmic simplicity, the approach here makes the representation of all solutions more intuitive than in Gusfield (2002), and solves another goal from that paper, namely, to prove a nontrivial upper bound on the number of PPH solutions, showing that that number is vastly smaller than the number of haplotype solutions (each solution being a set of n pairs of haplotypes that can generate the genotypes) when the perfect phylogeny requirement is not imposed.

Algorithms↗
PubMed2003

Effect of Box-Cox transformation on power of Haseman-Elston and maximum-likelihood variance components tests to detect quantitative trait Loci.

Non-normality of the phenotypic distribution can affect power to detect quantitative trait loci in sib pair studies. Previously, we observed that Winsorizing the sib pair phenotypes increased the power of quantitative trait locus (QTL) detection for both Haseman-Elston (HE) least-squares tests [Hum Hered 2002;53:59-67] and maximum likelihood-based variance components (MLVC) analysis [Behav Genet (in press)]. Winsorizing the phenotypes led to a slight increase in type 1 error in H-E tests and a slight decrease in type I error for MLVC analysis. Herein, we considered transforming the sib pair phenotypes using the Box-Cox family of transformations. Data were simulated for normal and non-normal (skewed and kurtic) distributions. Phenotypic values were replaced by Box-Cox transformed values. Twenty thousand replications were performed for three H-E tests of linkage and the likelihood ratio test (LRT), the Wald test and other robust versions based on the MLVC method. We calculated the relative nominal inflation rate as the ratio of observed empirical type 1 error divided by the set alpha level (5, 1 and 0.1% alpha levels). MLVC tests applied to non-normal data had inflated type I errors (rate ratio greater than 1.0), which were controlled best by Box-Cox transformation and to a lesser degree by Winsorizing. For example, for non-transformed, skewed phenotypes (derived from a chi2 distribution with 2 degrees of freedom), the rates of empirical type 1 error with respect to set alpha level=0.01 were 0.80, 4.35 and 7.33 for the original H-E test, LRT and Wald test, respectively. For the same alpha level=0.01, these rates were 1.12, 3.095 and 4.088 after Winsorizing and 0.723, 1.195 and 1.905 after Box-Cox transformation. Winsorizing reduced inflated error rates for the leptokurtic distribution (derived from a Laplace distribution with mean 0 and variance 8). Further, power (adjusted for empirical type 1 error) at the 0.01 alpha level ranged from 4.7 to 17.3% across all tests using the non-transformed, skewed phenotypes, from 7.5 to 20.1% after Winsorizing and from 12.6 to 33.2% after Box-Cox transformation. Likewise, power (adjusted for empirical type 1 error) using leptokurtic phenotypes at the 0.01 alpha level ranged from 4.4 to 12.5% across all tests with no transformation, from 7 to 19.2% after Winsorizing and from 4.5 to 13.8% after Box-Cox transformation. Thus the Box-Cox transformation apparently provided the best type 1 error control and maximal power among the procedures we considered for analyzing a non-normal, skewed distribution (chi2) while Winzorizing worked best for the non-normal, kurtic distribution (Laplace). We repeated the same simulations using a larger sample size (200 sib pairs) and found similar results.

Chromosome Mapping↗
PubMed1993

The relationship between the number of loci and the statistical support for the topology of UPGMA trees obtained from genetic distance data.

An analysis of the relationship between the number of loci utilized in an electrophoretic study of genetic relationships and the statistical support for the topology of UPGMA trees is reported for two published data sets. These are Highton and Larson (Syst. Zool.28:579-599, 1979), an analysis of the relationships of 28 species of plethodonine salamanders, and Hedges (Syst. Zool., 35:1-21, 1986), a similar study of 30 taxa of Holarctic hylid frogs. As the number of loci increases, the statistical support for the topology at each node in UPGMA trees was determined by both the bootstrap and jackknife methods. The results show that the bootstrap and jackknife probabilities supporting the topology at some nodes of UPGMA trees increase as the number of loci utilized in a study is increased, as expected for nodes that have groupings that reflect phylogenetic relationships. The pattern of increase varies and is especially rapid in the case of groups with no close relatives. At nodes that likely do not represent correct phylogenetic relationships, the bootstrap probabilities do not increase and often decline with the addition of more loci.

Algorithms↗
PubMed1991

Replication index in cultured human lymphocytes: methods for statistical analysis and possible role in genetic toxicology.

The replication index (RI) is an index of cytokinetics in cultured cells. This paper presents statistical methods for the analysis of RI data. It also proposes formulas for the calculation of RI and its standard error. The proposed statistical analysis may be applied only in cases when replicate cultures are used. If duplicate or repeated cultures are used, the interculture variation may provide a more suitable error term for RI. Determining the RI in human blood cultures may be useful in genotoxicity testing, because inhibition of DNA synthesis will result in a decrease of the RI. Monte Carlo methods are used to show that the sensitivity of the proposed method is roughly equivalent to that of a chi 2 test. Power studies indicate that for the study sample, no less than 200 cells should be analyzed when assessing the RI.

Cell Division↗
PubMed2003

Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network.

We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. Selecting the optimal graph, which gives the best representation of the system among genes, is still a problem to be solved. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes.

Bayes Theorem↗