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PubMed2006

Bayesian analysis for the meiosis I non-disjunction fraction in numerical chromosomal anomalies.

The main causes of numerical chromosomal anomalies, including trisomies, arise from an error in the chromosomal segregation during the meiotic process, named a non-disjunction. One of the most used techniques to analyze chromosomal anomalies nowadays is the polymerase chain reaction (PCR), which counts the number of peaks or alleles in a polymorphic microsatellite locus. It was shown in previous works that the number of peaks has a multinomial distribution whose probabilities depend on the non-disjunction fraction F. In this work, we propose a Bayesian approach for estimating the meiosis I non-disjunction fraction F. in the absence of the parental information. Since samples of trisomic patients are, in general, small, the Bayesian approach can be a good alternative for solving this problem. We consider the sampling/importance resampling technique and the Simpson rule to extract information from the posterior distribution of F. Bayes and maximum likelihood estimators are compared through a Monte Carlo simulation, focusing on the influence of different sample sizes and prior specifications in the estimates. We apply the proposed method to estimate F. for patients with trisomy of chromosome 21 providing a sensitivity analysis for the method. The results obtained show that Bayes estimators are better in almost all situations.

Algorithms↗
PubMed1990

Murine lambda gene rearrangements: the stochastic model prevails over the ordered model.

The ontogeny of the immunoglobulin (Ig) gene rearrangement in mammalian B cells seems to be ordered. Heavy chain gene segments rearrange first, followed by light chain gene segments, kappa before lambda. The genomic organization of murine lambda locus does not preclude the simultaneous expression of two subtypes from the same chromosome. In order to distinguish between an ordered and a stochastic model of rearrangement, a panel of 67 B cell hybridomas secreting either lambda 1, lambda 2, lambda 3 or lambda x (recently described) were analysed for V lambda J lambda rearrangements. The results show that in 97% of cases, a single rearrangement occurred, favouring the stochastic model over the ordered one. Strikingly, the possibility of having a productive rearrangement if the first try results in an aberrant one is rare. We propose therefore, that the lambda Ig is not necessarily required to ensure allelic and subtypic exclusion mechanisms. Moreover, in 97% of the cases, at least one kappa allele is rearranged. Furthermore, the RS recombination has been detected in 77% of the cases. This suggests that, although the stimulation of kappa precedes that of lambda locus, the RS recombination acts as a transacting albeit dispensable lambda activator.

Animals↗
PubMed2004

Tree and spline based association analysis of gene-gene interaction models for ischemic stroke.

In the biology of complex disorders, such as atherothrombosis, interactions among genetic factors may play an important role, and theoretical considerations suggest that gene-gene interactions are quite common in such diseases. We used a nested case-control sample from the Physicians' Health Study, a randomized trial assessing the effects of aspirin and beta-carotene on cardiovascular disease and cancer among 22071 US male physicians, to examine these relationships for ischemic stroke. Data were available on 92 polymorphisms from 56 candidate genes related to inflammation, thrombosis and lipid metabolism, assessed in 319 incident cases of ischemic stroke and 2090 disease-free controls. We used classification and regression trees (CART) and multivariate adaptive regression spline (MARS) models to explore the presence of genetic interactions in these data. These models offer advantages over typical logistic regression methods in that they may uncover interactions among genes that do not exhibit strong marginal effects. Final models were selected using either the Bayes Information Criterion or cross-validation. Model fit was assessed using 10-fold cross-validation of the entire selection process. Both the CART and two-way MARS-logit models identified an interaction between two polymorphisms linked to inflammation, the P-selectin (val640leu) and interleukin-4 (C(582) T) genes. Internal validation of these models, however, suggested that effects of these polymorphisms are additive. Although further external validation of these models is necessary, these methods may be valuable in exploring and identifying potential gene-gene as well as gene-environment interactions in association studies.

Adult↗
PubMed2005

Meta-analysis of genetic studies using Mendelian randomization--a multivariate approach.

In traditional epidemiological studies the association between phenotype (risk factor) and disease is often biased by confounding and reverse causation. As a person's genotype is assigned by a seemingly random process, genes are potentially useful instrumental variables for adjusting for such bias. This type of adjustment combines information on the genotype-disease association and the genotype-phenotype association to estimate the phenotype-disease association and has become known as Mendelian randomization. The information on genotype-disease and genotype-phenotype may well come from a meta-analysis. In such a synthesis, a multivariate approach needs to be used whenever some studies provide evidence on both the genotype-phenotype and genotype-disease associations. This paper presents two multivariate meta-analytical models, which differ in their treatment of the heterogeneities (between-study variances). Heterogeneities on the genotype-phenotype and genotype-disease associations may be highly correlated, but a multivariate model that parameterizes the heterogeneity directly is difficult to fit because that correlation is poorly estimated. We advocate an alternative model that treats the heterogeneities on genotype-phenotype and phenotype-disease as being independent. This model fits readily and implicitly defines the correlation between the heterogeneities on genotype-phenotype and genotype-disease. We show how either maximum likelihood or a Bayesian approach with vague prior distributions can be used to fit the alternative model.

Coronary Disease↗
PubMed2001

Improved inference of mutation rates: I. An integral representation for the Luria-Delbrück distribution.

The estimation of mutation rates is ordinarily performed using results based on the Luria-Delbrück distribution. There are certain difficulties associated with the use of this distribution in practice, some of which we address in this paper (others in the companion paper, Oprea and Kepler, Theor. Popul. Biol., 2001). The distribution is difficult to compute exactly, especially for large values of the random variable. To overcome this problem, we derive an integral representation of the Luria-Delbrück distribution that can be computed easily for large culture sizes. In addition, we introduce the usual assumption of very small probability of having a large proportion of mutants only after the generating function has been computed. Thus, we obtain information on the moments for the more general case. We examine the asymptotic behavior of this system. We find a scaling or "standardization" technique that reduces the family of distributions parameterized by three parameters (mutation rate, initial cell number, and final cell number) to a single distribution with no parameters, valid so long as the product of the mutation rate and the final culture is sufficiently large. We provide a pair of techniques for computing confidence intervals for the mutation rate. In the second paper of this series, we use the distribution derived here to find approximate distributions for the case where the cell cycle time is not well-described as an exponential random variable as is implicitly assumed by Luria-Delbrück distribution.

Cell Cycle↗
PubMed2001

Selection and segregation distortion in a sex-differentiated population.

We extend the classical model for selection at an autosomal locus in a sex-differentiated population to include segregation distortion. The equations remain the same, but the fitness parameters are interpreted differently and refer to alleles instead of genotypes. We derive conditions for internal and external stability of the equilibria, i.e., stability with respect to perturbations of alleles that are already present at equilibrium and stability with respect to invasion attempts by newly arising alleles. We show that, in a sex-differentiated population, external stability of an equilibrium can be judged on the basis of Shaw--Mohler criteria. Throughout, we compare the situation in populations with and without sex differentiation. Interestingly, internal stability is more difficult to achieve in a population without sex differentiation than in a population in which selection and segregation distortion are restricted to one sex. In a companion paper we show how the general results of the present paper can lead to new insights into specific systems such as the t complex of the house mouse.

Alleles↗
PubMed2002

Spatial mosaic and interfacial dynamics in a Müllerian mimicry system.

Uncovering why spatial mosaics of mimetic morphs are maintained in a Müllerian mimicry system has been a challenging issue in evolutionary biology. In this article, we analyze the reaction diffusion system that describes two-species Müllerian mimicry in one- and two-dimensional habitats. Due to positive frequency-dependent selection, a local population first approaches the state where one of the comimicking patterns predominates, which is followed by slow movement of boundaries where different patterns meet. We then analyze the interfacial dynamics of the boundaries to find whether a stable cline is maintained and to obtain the wave speed if the cline is unstable. The results are: (1) In a spatially uniform habitat the morph with greater base fitness spreads both in one and two species system. (2) The strength of cross-species interaction determines whether the mimetic morph clines of model and mimic species coalesce into the same geographical region or pass through each other. The joint wave speed of clines decreases by increasing the number of comimicking species in the mimicry ring. (3) In spatial heterogeneous habitats, stable clines can be maintained due to the balance between the base fitness gradient and the biased gene flow by negative curvature of boundary. This allows the persistence of a spatial mosaic even if one of the morphs is in every place advantageous over the other. A balanced cline is also maintained if there is a gradient in the population density. (4) A new advantageous morph occurring at a local region is doomed to go to extinction in a finite time if the "radius" of initial distribution is below a threshold. Possible applications to the heliconiine butterfly mimicry ring, heterozygous disadvantage systems of chromosomal rearrangement and hybrid zone, the third phase of Wright's Shifting Balance theory, and cytoplasmic incompatibility are discussed.

Animals↗
PubMed2002

Analysis of genetic diversity and population structure within Florida coconut (Cocos nucifera L.) germplasm using microsatellite DNA, with special emphasis on the Fiji Dwarf cultivar.

Using 15 simple sequence repeat (SSR) microsatellite DNA loci, we analyzed genetic variation within Cocos nucifera germplasm collections at two locations in south Florida, representing eight cultivars. The loci were also used in a parentage analysis of progeny of the 'Fiji Dwarf' variety at both locations. A total of 67 alleles were detected, with eight the highest number at any one locus. These loci identified 83 of the 110 individual palms. Gene diversity of the 15 loci ranged from 0.778 to 0.223, with a mean of 0.574. 'Fiji Dwarf', 'Malayan Dwarf', 'Green Niño' and 'Red Spicata' cultivars resolve as distinct clusters in a neighbor joining tree using modified Rogers distance, while the tall varieties form two aggregates. The highest gene diversity was found in the tall cultivars (H = 0.583 cumulatively), and the lowest in the 'Malayan Dwarf' (H = 0.202). After the tall coconuts, the 'Fiji Dwarf' was most genetically diverse (H = 0.436), and had the largest number of unique alleles. Genetic identity is highest among the 'Malayan Dwarf' phenotypes, and between the tall varieties. The 'Red Malayan Dwarf' is genetically distinct from the 'Green' and 'Yellow Malayan Dwarf' phenotypes, which cannot be distinguished with the SSR loci used. Off-type 'Malayan Dwarf' phenotypes (putative hybrids with talls) can be identified genotypically. Parentage analyses of 30 'Fiji Dwarf' progeny propagated from five adults surrounded by other cultivars estimate that only 20% of the progeny were out-crossed to the other varieties, while 40-46% were possible selfs. This suggests that a seed-production orchard of the variety maintained at reasonable distance from other varieties, will likely yield only 'Fiji Dwarf' genotypes. Our data are discussed in the context of hypotheses of coconut dissemination around the world.

Alleles↗
PubMed2006

Genetic diversity and variety composition of cassava on small-scale farms in Uganda: an interdisciplinary study using genetic markers and farmer interviews.

Cassava is a tropical crop and grown for its tuberous starchy roots. In Africa it is mainly cultivated by small-scale farmers who observe, select and name their cassava varieties based on morphology, food, social and economic interest. Here we have used an interdisciplinary approach involving farmer interviews, genetic markers and morphological descriptors to study the composition of cassava varieties on small-scale farms in 11 villages located in three districts in Uganda, the genetic structure within and between these varieties and their morphology. The composition of local, newly introduced and improved varieties differed widely between villages and districts. The Ugandan farmers in our study seemed to adopt improved varieties to a greater extent when there was a nearby market, prevalence of disease epidemics and good extension service. We found considerable genetic variation both within and between cassava varieties though the variation was larger between varieties. However, most local and improved varieties showed predominating genotypes at many loci. Accessions of commonly grown varieties meeting farmers' preferences could therefore be selected and implemented in future breeding programmes involving development, dissemination and adoption. The like-named varieties in different villages were genetically similar, demonstrating farmers' ability to differentiate and maintain the same variety over large areas. However, some varieties with different names in different villages showed both genetic and morphological similarity, suggesting that farmers may rename plants when they are introduced into their fields. The large differences found in variety and genetic composition between villages and districts in Uganda may be a result of the diverse needs and growing conditions characteristic for traditional farming system. This suggests that efforts to conserve and increase the genetic diversity in farmers' fields will require policies tailored to each area.

Africa↗
PubMed1989

Comparison of linkage maps of mouse chromosome 12 derived from laboratory strain intraspecific and Mus spretus interspecific backcrosses.

Progeny from an interspecific backcross between laboratory mice and Mus spretus were typed for inheritance of eight genetic markers on chromosome 12. Marker order determined by segregation analyses of 115 meiotic events was in good agreement with that determined previously using intraspecific laboratory strain backcrosses. Two additional markers, D12Nyu5 and Lamb-1, previously not ordered, were located in the middle of the interval between D12Nyu12 and D12Nyu1. Marker spacing was reduced in the interspecific cross relative to that observed in intraspecific crosses. Furthermore, the interspecific cross was characterized by marked deviation from 1:1 segregation in the recombinant chromosomes and very strong positive interference. These data suggest that comparisons of different mouse crosses may facilitate the understanding of underlying mechanisms that govern recombination events in complex genomes.

Alleles↗
PubMed2005

On the use of the Price equation.

This paper distinguishes two categories of questions that the Price equation can help us answer. The two different types of questions require two different disciplines that are related, but nonetheless move in opposite directions. These disciplines are probability theory on the one hand and statistical inference on the other. In the literature on the Price equation this distinction is not made. As a result of this, questions that require a probability model are regularly approached with statistical tools. In this paper, we examine the possibilities of the Price equation for answering questions of either type. By spending extra attention on mathematical formalities, we avoid the two disciplines to get mixed up. After that, we look at some examples, both from kin selection and from group selection, that show how the inappropriate use of statistical terminology can put us on the wrong track. Statements that are 'derived' with the help of the Price equation are, therefore, in many cases not the answers they seem to be. Going through the derivations in reverse can, however, be helpful as a guide how to build proper (probabilistic) models that do give answers.

Animals↗
PubMed2006

Uninvadability in N-species frequency models for resident-mutant systems with discrete or continuous time.

The uninvadability concept, that was originally introduced through static comparisons of individual fitness in resident-mutant systems for a single species, is developed for multi-species models with frequency-dependent fitness by extending its equivalent single-species dynamic characterization. This multi-species definition is then reinterpreted in terms of individual fitness functions based on intra and interspecific interactions. The resultant concept is discussed in relation to that of an N-species ESS (evolutionarily stable strategy) and to dynamic stability of monomorphic and polymorphic evolutionary systems.

Biological Evolution↗
PubMed2003

Finding signals for plant promoters.

The strongest signal of plant promoter is searched with the model of single motif with two types. It turns out that the dominant type is the TATA-box. The other type may be called TATA-less signal, and may be used in gene finders for promoter recognition. While the TATA signals are very close for the monocot and the dicot, their TATA-less signals are significantly different. A general and flexible multi-motif model is also proposed for promoter analysis based on dynamic programming. By extending the Gibbs sampler to the dynamic programming and introducing temperature, an efficient algorithm is developed for searching signals in plant promoters.

Algorithms↗
PubMed2001

Rapid mutational declines of viability in Drosophila.

High rates of mildly deleterious mutation could cause the extinction of small populations, reduce neutral genetic variation and provide an evolutionary advantage for sex. In the first attempts to estimate the rate of mildly deleterious mutation, Mukai and Ohnishi allowed spontaneous mutations to accumulate on D. melanogaster second chromosomes shielded from recombination and selection. Viability of the shielded chromosomes appeared to decline rapidly, implying a deleterious mutation rate on the order of one per zygote per generation. These results have been challenged, however; at issue is whether Mukai and Ohnishi may have confounded viability declines caused by mutation with declines resulting from environmental changes or other extraneous factors. Here, using a method not sensitive to non-mutational viability changes, I reanalyse the previous mutation-accumulation (MA) experiments, and report the results of a new one. I show that in each of four experiments, including Mukai's two experiments, viability declines due to mildly deleterious mutations were rapid. The results give no support for the view that Mukai overestimated the declines. Although there is substantial variation in estimates of genomic mutation rates from the experiments, this variation is probably due to some combination of sampling error, strain differences and differences in assay conditions, rather than to failure to distinguish mutational and non-mutational viability changes.

Animals↗
PubMed2005

Chromosomal phylogeny of Robertsonian races of the house mouse on the island of Madeira: testing between alternative mutational processes.

The ancestral karyotype of the house mouse (Mus musculus) consists of 40 acrocentric chromosomes, but numerous races exist within the domesticus subspecies characterized by different metacentric chromosomes formed by the joining at the centromere of two acrocentrics. An exemplary case is present on the island of Madeira where six highly divergent chromosomal races have accumulated different combinations of 20 metacentrics in 500-1000 years. Chromosomal cladistic phylogenies were performed to test the relative performance of Robertsonian (Rb) fusions, Rb fissions and whole-arm reciprocal translocations (WARTs) in resolving relationships between the chromosomal races. The different trees yielded roughly similar topologies, but varied in the number of steps and branch support. The analyses using Rb fusions/fissions as characters resulted in poorly supported trees requiring six to eight homoplasious events. Allowance for WARTs considerably increased nodal support and yielded the most parsimonious trees since homoplasy was reduced to a single event. The WART-based trees required five to nine WARTs and 12 to 16 Rb fusions. These analyses provide support for the role of WARTs in generating the extensive chromosomal diversification observed in house mice. The repeated occurrence of Rb fusions and WARTs highlights the contribution of centromere-related rearrangements to accelerated rates of chromosomal change in the house mouse.

Animals↗
PubMed2005

In silico analysis of disease-association mapping strategies using the coalescent process and incorporating ascertainment and selection.

We present a new method for simulating samples of marker haplotypes, genotypes, or diplotypes in case-control studies in which the markers are linked to a disease locus in any specified region of the genome. The method allows realistic features to be incorporated into the simulations, including selection acting on disease alleles, sample ascertainment of disease chromosomes and polymorphic markers, a genetic dominance model of disease expression that allows incomplete penetrance and phenocopies, and an accurate genetic map of recombination rates and hotspots for recombination in the human genome (or, alternatively, an improved method for simulating the distribution of hotspots). The new method uses an approach that combines simulation of the coalescent process for the sampled chromosomes with a diffusion process used to model the evolution of the disease-mutation frequency over time. Examples illustrate how the method may be used to study the expected power of a marker-disease association study.

Alleles↗
PubMed2001

Stable integration of transgenes delivered by a retrotransposon-adenovirus hybrid vector.

Helper-dependent adenoviruses show great promise as gene delivery vectors. However, because they do not integrate into the host chromosome, transgene expression cannot be maintained indefinitely. To overcome these limitations, we have inserted an L1 retrotransposon/transgene element into a helper-dependent adenovirus to create a novel chimeric gene delivery vector. Efficient adenovirus-mediated delivery of the L1 element into cultured human cells results in subsequent retrotransposition and stable integration of the transgene. L1 retrotransposition frequency was found to correlate with increasing multiplicity of infection by the chimeric vector, and further retrotransposition from newly integrated elements was not observed on prolonged culture. Therefore, this vector, which utilizes components of low immunogenic potential, represents a novel two-stage gene delivery system capable of achieving high titers via the initial helper-dependent adenovirus stage and permanent transgene integration via the retrotransposition stage.

Adenoviridae↗