The probability of matching genetic markers in different samples

Hypervariable DNA polymorphisms in humans have been introduced in forensic science for the exclusion of innocent persons, and possibily for the identification of guilty ones, through mismatches and matches of DNA patterns in incriminating samples. Under the assumption of random mating and linkage equilibrium, it is observed that the probability of mismatch, then of exclusion of innocent persons, is very high. The probability of a match on the contrary may be very low, particularly when several hypervariable DNA polymorphisms are used for the DNA pattern. When a match is observed, and the probability of match is calculated, and it is lower than one in five billions, this might be considered incriminating by a judge. It is concluded that an innocent person has all advantages in submitting to the DNA fingerprinting test.     

关于质体随细胞分裂传递的数学模型

本文根据质体是具有遗传功能的细胞器这一事实出发,对质体传递规律首次进行了定量研究,建立了突变质体在细胞分裂中传递的全概率和条件概率公式．并对此公式的应用作了进一步的探讨．本文所提供的方法将为质体遗传开辟一条定量研究的新路．     

πPS Sampling Scheme Through Grouping

A πPS sampling scheme is developed by combining Stevens and Midzuno-Sen Sampling schemes. The restriction on original probabilities is less severe in the proposed scheme than that in Stevens and Midzuno-Sen schemes. The performance of the scheme is satisfactory.     

Assessing probability of paternity and the product rule in DNA systems

The genetic resolution of paternity disputes begins with an intricate detection of inherited traits and finishes with a statistical inference (the probability of paternity,W). Notwithstanding some initial fanfare, statistical inference is a necessary component of DNA-based paternity tests because band patterns may be rare but not yet unique, and even rare events in a vacuum are meaningless. The genetic match must be combined with other evidence for relevancy, thus a Bayesian approach is preferred when computingW. This paper reviews the standard model used to computeW and discusses the model's various properties and assumptions. The standard model is extended to include DNA systems in which alleles are operationally continuous due to measurement error. This extension avoids problems associated with matched/non-matched binned decisions. After outlining the model assumptions for a single DNA system, particular attention is given to the product rule-the procedure of multiplying intermediate probabilities across genetic loci to form a combinedW. An empirical alternative to the product rule is also assessed and correlated with standard procedures.Editor's commentsThe authors present a carefully reasoned account of Bayesian inference in the paternity context. Their presentation of an alternative to the product rule for Paternity Index values offers a means of avoiding objections to the rule.     

On the Analysis and Synthesis of a Four-Field-Table

The real four-field-table measure k is calculable as follows: K₁ for V(a, b, c, d) with k₁ = (arc K₁)/100, K₁₁ for V(a, b, 0, 0) with k₁₁ = (arc K₁₁)/100, K₁₂ for V(c, d, 0, 0) with k₁₂ = (arc K₁₂)/100 and K₁₂₁ for V(0, 0, c, d) with k₁₂₁ = – k₁₂. The equation k₁ = k₁₁ – k₁₂ holds good. It is possible to calculate the probability of error of a four-field-table with small frequencies, indirectly from component values. Two examples are given.     

Uncertain availability of a preferred food affects choice in a captive group of chimpanzees (Pan troglodytes)

Food-choice was investigated in a social group of 16 chimpanzees (Pan troglodytes) maintained in a large outdoor compound. Three feeding stations located along the periphery of the compound were considered analogous to food patches. Color-coded aluminum panels temporarily covered each feeding apparatus, with one color corresponding to nonpreferred food (commercial biscuits) available at two locations and other colors corresponding to the certain or uncertain availability of preferred food (oranges) available at one location. Only nine chimpanzees met the criterion for learning the color/food associations and thus only those animals were included in the analysis. There was a significant decrease in choosing the station associated with oranges when the probability of availability of oranges was reduced from 0.5 to 0.1 but not from 1.0 to 0.5. In addition, there was a significant increase in the frequency with which the subjects made no choice when the probability of availability of oranges was reduced from 1.0 to 0.1. The data indicate that the uncertain availability of preferred food in a choice situation affects choice behavior in a social group of chimpanzees studied under controlled conditions.     

Population processes under the influence of disasters occurring independently of population size

Markov branching processes and in particular birth-and-death processes are considered under the influence of disasters that arrive independently of the present population size. For these processes we derive an integral equation involving a shifted and rescaled argument. The main emphasis, however, is on the (random) probability of extinction. Its distribution density satisfies an equation which can be solved numerically at least up to a multiplicative constant. In an example it is also found by simulation.     

The effect of population structure on the rate of evolution

Ecological factors exert a range of effects on the dynamics of the evolutionary process. A particularly marked effect comes from population structure, which can affect the probability that new mutations reach fixation. Our interest is in population structures, such as those depicted by ‘star graphs’, that amplify the effects of selection by further increasing the fixation probability of advantageous mutants and decreasing the fixation probability of disadvantageous mutants. The fact that star graphs increase the fixation probability of beneficial mutations has lead to the conclusion that evolution proceeds more rapidly in star-structured populations, compared with mixed (unstructured) populations. Here, we show that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and draw attention to the importance of fixation time. By comparing population structures that amplify selection with other population structures, both analytically and numerically, we show that evolution can slow down substantially even in populations where selection is amplified.     

Random Networks of Catalytic Biochemical Reactions

Formulae for the probabilities of cycles and components are obtained for large random networks by combinatorical considerations and computer experiments. Formulae for the occurrence and distribution of cycles and of components of certain number and size are received for random networks.     

Estimating the probability of identity among genotypes in natural populations: cautions and guidelines

Individual identification using DNA fingerprinting methods is emerging as a critical tool in conservation genetics and molecular ecology. Statistical methods that estimate the probability of sampling identical genotypes using theoretical equations generally assume random associations between alleles within and among loci. These calculations are probably inaccurate for many animal and plant populations due to population substructure. We evaluated the accuracy of a probability of identity (P(ID)) estimation by comparing the observed and expected P(ID), using large nuclear DNA microsatellite data sets from three endangered species: the grey wolf (Canis lupus), the brown bear (Ursus arctos), and the Australian northern hairy-nosed wombat (Lasiorinyus krefftii). The theoretical estimates of P(ID) were consistently lower than the observed P(ID), and can differ by as much as three orders of magnitude. To help researchers and managers avoid potential problems associated with this bias, we introduce an equation for P(ID) between sibs. This equation provides an estimator that can be used as a conservative upper bound for the probability of observing identical multilocus genotypes between two individuals sampled from a population. We suggest computing the actual observed P(ID) when possible and give general guidelines for the number of codominant and dominant marker loci required to achieve a reasonably low P(ID) (e.g. 0.01-0.0001).     

Asexuals, polyploids, evolutionary opportunists...: the population genetics of positive but deteriorating mutations

Some genetic phenomena originate as mutations that are initially advantageous but decline in fitness until they become distinctly deleterious. Here I give the condition for a mutation-selection balance to form and describe some of the properties of the resulting equilibrium population. A characterization is also given of the fixation probabilities for such mutations.     

A Sequential Multidecision Procedure

A sequential classification method for the case of many populations is presented. The main feature of the proposed classification method is the population elimination rule. When certain conditions are met, the decision is taken to eliminate specific populations from further consideration, and the classification process is continued with a reduced number of populations. The elimination rule is based on the generalised likelihood ratio.     

Systematic analysis of residual density suggests that a major limitation in well‐refined X‐ray structures of proteins is the omission of ordered solvent

In the residual electron density map of a fully refined X‐ray protein model, there should be no peaks arising from modeling errors or missing atoms. Any residual peaks that do occur should be contributed by random residual intensity differences between the model and the data. If the model is incomplete (i.e., some atoms are missing), there will be more positive peaks than negative ones. On the other hand, if the model includes inappropriately located atoms, there will be an excess of negative peaks. In this study, random residual peaks are quantified using the probability density function P(x), which is defined as the probability for a peak having peak height between x and x + dx. It is found that P(x) is single‐exponential and symmetric for both positive and negative peaks. Thus, P(x) can be used to discriminate residual peaks contributed by random noise in complete models from residual peaks being attributable to modeling errors in incomplete models. For a number of representative structures in the PDB it is found that P(x) has far more large (greater than 5 sigma) positive peaks than large negative peaks. This excess of large positive peaks suggests that the main defect in these refined structures is the omission of ordered water molecules.     

Effectiveness of bovine microsatellites in resolving paternity cases in American bison, Bison bison L.

A set of 33 cattle microsatellite primer pairs was tested with the DNA of American bison from a captive population in Belgium and evaluated for usefulness in parentage testing. Two primer sets did not amplify and three were monomorphic. Among the polymorphic markers, the number of alleles ranged from two to nine. Heterozygosity, polymorphism information content (PIC) and probability of exclusion (PE) values were low by comparison with those obtained with the same markers in cattle. Two methods of estimating PE were used, one which assumed equal allele frequencies between parental sexes and another which took into account differences in allele frequencies between parental sexes. An internationally accepted set of nine microsatellites gives cumulative PE values of 0·98 and 0·97, respectively, for the two methods. The potential of this marker set to identify bison × cattle hybrids is discussed. Because bison and cattle have a common ancestor, these microsatellites are a useful way to establish genetic distances and can lead to the construction of phylogenetic trees.