A Model for Analysis of Population Structure

Arguments have been presented for the appropriateness of a multinomial Dirichlet distribution for describing single-locus genotypic frequencies in a subdivided population. This distribution is defined as a function of allele frequency, the average (over the entire population) inbreeding coefficient and the correlation between genotypes within a subdivision. Alternative parameterizations and their genetic interpretations are given.-We then show how information from a sample drawn from this subdivided population, in the absence of pedigrees, can be combined with the multinomial Dirichlet model to form a likelihood function. This likelihood function is then used as the basis for estimation and testing hypotheses concerning the genetic parameters of the model. Comparisons of this approach to the alternative procedure of Cockerham (1969) and (1973) are made using human data obtained from Tecumseh, Michigan and Monte Carlo simulations.-Finally, implications of these results to statistical inference and to mutation rates are presented.     

A Three-Dimensional Finite Element Model for Biomechanical Analysis of the Hip

The objective of this study was to construct a three-dimensional (3D) finite element model of the hip. The images of the hip were obtained from Chinese visible human dataset. The hip model includes acetabular bone, cartilage, labrum, and bone. The cartilage of femoral head was constructed using the AutoCAD and Solidworks software. The hip model was imported into ABAQUS analysis system. The contact surface of the hip joint was meshed. To verify the model, the single leg peak force was loaded, and contact area of the cartilage and labrum of the hip and pressure distribution in these structures were observed. The constructed 3D hip model reflected the real hip anatomy. Further, this model reflected biomechanical behavior similar to previous studies. In conclusion, this 3D finite element hip model avoids the disadvantages of other construction methods, such as imprecision of cartilage construction and the absence of labrum. Further, it provides basic data critical for accurately modeling normal and abnormal loads, and the effects of abnormal loads on the hip.     

A Multiplicative Model Imposed More Restrictions on the Quasi-Symmetry Model for the Analysis of Square Contingency Tables

For the analysis of square contingency tables, this note proposes a multiplicative model imposed more restrictions on CAUSSINUS ' (1965) quasi-symmetry (QS) model. The model is not so strict as in the quasi-double symmetry model considered by TOMIZAWA (1985b). The proposed model has the structure of the QS about the main diagonal plus an extended QS about the reverse diagonal of the square contingency table. The model is applied to the data on unaided vision of students in a university in Japan.     

A Chicken Embryo Eye Model for the Analysis of Alphaherpesvirus Neuronal Spread and Virulence

We describe use of developing chicken embryos as a model to study neuronal spread and virulence of pseudorabies virus (PRV). At embryonic day 12, β-galactosidase-expressing PRV strains were injected into the vitreous humor of one eye, and virus replication and spread from the eye to the brain were measured by β-galactosidase activity and the recovery of infectious virus from tissues. The wild-type PRV strain, Becker, replicated in the eye and then spread to the brain, causing extensive pathology characterized by edema, hemorrhage, and necrosis that localized to virally infected tissue. The attenuated vaccine strain, Bartha, replicated in the eye and spread throughout specific regions of the brain, producing little to no overt pathology. Becker mutants lacking membrane proteins gE or gI replicated in the eye and were able to spread to the brain efficiently. The pathology associated with replication of these mutants in the brain was intermediate to that induced by Becker or Bartha. Mixed infection of a gE deletion mutant and a gI deletion mutant restored the pathogenic phenotype to wild-type levels. These data indicate that the replication of virus in embryonic brain tissue is not sufficient to induce the characteristic pathological response and that the gE and gI gene products actively affect pathological responses in the developing chicken brain.     

A Bifurcation Analysis of a Differential Equations Model for Mutualism

We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions. The model is similar in spirit to a commonly cited model [Dean, A.M., Am. Nat. 121(3), 409–417 (1983)], but corrects problems due to singularities in that model. In addition, we investigate our model in more depth by varying the intrinsic growth rate for each of the species and analyzing the resulting bifurcations in system behavior. We are especially interested in transitions between facultative and obligate mutualism. The model reduces to the familiar Lotka–Volterra model locally, but is more realistic for large populations in the case where mutualist interaction is strong. In particular, our model supports population thresholds necessary for survival in certain cases, but does this without allowing unbounded population growth. Experimental implications are discussed for a lichen population.     

Stacking Increments: A New Model and Morphospace for the Analysis of Bivalve Shell Growth

A model employing stacking increments is introduced for the analysis of bivalve shell growth and form. The model is based on the components of shell growth that are potentially independent: the rate of mantle cell proliferation, the rate of precipitation of shell material, and the rate of translation of the pallial line, where the mantle is attached to the shell. This model is defined in terms of the following parameters: (1) the ratio of accretion of shell material at the shell margin to growth of the mantle by cell division, (2) the ratio of shell accretion at the pallial line to mantle growth, and (3) the ratio of the amount of pallial muscle translation, away from the umbo toward the shell margin, to mantle growth. In this model, the shape of a radial section through the shell is simulated by stacking of internal microgrowth increments. The mode of stacking of the increments is determined by the balance among the parameters defining growth. A theoretical morphospace defined on the basis of this model is largely consistent with the range of forms of naturally occurring bivalve shells. Analysis of the distribution of actual shell forms in relation to this morphospace suggests that the absolute rate of shell precipitation and the gradient in precipitation rate away from the shell margin along a radial cross-section are physiologically as well as geometrically constrained.     

A Two-Way Analysis of Covariance Model for Classification of Stability Data

This paper proposes a procedure for testing and classifying data with multiple factors. A two-way analysis of covariance is used to classify the differences among the batches as well as another factor such as package type and/or product strength. In the test procedure, slopes and intercepts of the main effects are tested using a combination of simultaneous and sequential F-tests. Based on the test procedure results, the data are classified into one of four different groups. For each group, shelf life can be calculated accordingly. We examine if the procedure produces satisfactory control of the probability of a Type I error and the power of detecting the difference of degradation rates and intercepts for different nominal levels. The method is evaluated with a Monte Carlo simulation study. The proposed procedure is compared with the current FDA procedure using real data.     

A Discrete Time Model for the Analysis of Medium-Throughput C. elegans Growth Data

Background

As part of a program to predict the toxicity of environmental agents on human health using alternative methods, several in vivo high- and medium-throughput assays are being developed that use C. elegans as a model organism. C. elegans-based toxicological assays utilize the COPAS Biosort flow sorting system that can rapidly measure size, extinction (EXT) and time-of-flight (TOF), of individual nematodes. The use of this technology requires the development of mathematical and statistical tools to properly analyze the large volumes of biological data.

Methodology/Principal Findings

Findings A Markov model was developed that predicts the growth of populations of C. elegans. The model was developed using observations from a 60 h growth study in which five cohorts of 300 nematodes each were aspirated and measured every 12 h. Frequency distributions of log(EXT) measurements that were made when loading C. elegans L1 larvae into 96 well plates (t = 0 h) were used by the model to predict the frequency distributions of the same set of nematodes when measured at 12 h intervals. The model prediction coincided well with the biological observations confirming the validity of the model. The model was also applied to log(TOF) measurements following an adaptation. The adaptation accounted for variability in TOF measurements associated with potential curling or shortening of the nematodes as they passed through the flow cell of the Biosort. By providing accurate estimates of frequencies of EXT or TOF measurements following varying growth periods, the model was able to estimate growth rates. Best model fits showed that C. elegans did not grow at a constant exponential rate. Growth was best described with three different rates. Microscopic observations indicated that the points where the growth rates changed corresponded to specific developmental events: the L1/L2 molt and the start of oogenesis in young adult C. elegans.

Conclusions

Quantitative analysis of COPAS Biosort measurements of C. elegans growth has been hampered by the lack of a mathematical model. In addition, extraneous matter and the inability to assign specific measurements to specific nematodes made it difficult to estimate growth rates. The present model addresses these problems through a population-based Markov model.     

A Model for the Genetics of Handedness

Experimental data and theoretical work on the inheritance of handedness and cerebral dominance are reviewed. A two-gene, four-allele model, one locus pertaining to left or right hemispheric dominance and the other to contralateral or ipsilateral hand control relative to the dominant hemisphere, is constructed. It is in excellent agreement with all quantitative information regarding this problem. Refinements designed to explain relevant qualitative facts are proposed and discussed.     

Moment Analysis for the Probit Model of Directional Selection

An iteration relation is given for the moments of the surviving individuals after probit directional selection if the individuals before selection are normally distributed. The proportion, mean, variance, skewness, and kurtosis are expressed in closed form.     

A Model for the Mechanism of Enzyme Induction

A sequence of reactions is postulated from which are derived equations describing the time course of enzyme induction. The model also yields the observed effect of the inducer concentration on the time constant and final rate of enzyme synthesis. Features of the model are: (a) The inducer acts first to release the protein forming template from its site of synthesis on the gene. (b) The inducer is involved again in the equilibrium dissociation of the free template-inducer complex which is utilized in the synthesis of the enzyme-forming unit. (c) The final enzyme-forming unit is unstable and must be synthesized continuously to maintain enzyme synthesis.     

A Digital Model for the Venous Junctions

The venous network in the lower limbs is composed of a considerable number of confluent junctions. Each of these singularities introduces some blood flow disturbances. Each physiological junction is unique, in terms of its geometry as well as the blood flow rate. In order to account for this great variability, we developed a numerical model based on the use of the N3S code (a software package for solving Navier-Stokes equations). To test the validity of the model, one of the numerical simulations is compared with the data obtained in the corresponding experimental configuration. The velocity measurements were carried out with an ultrasonic pulsed Doppler velocimeter. We also measured pressure differences using differential sensors. The numerical computations were then used to obtain the values of the flow variables at any point, with various geometrical and flow configurations. As far as the velocity field is concerned, a very marked three-dimensional pattern with swirls was observed. The pressure evolution was also strongly disturbed, with a non-linear decrease. All these data indicate that confluence effects cannot be neglected when evaluating pressure decreases. With a tool of this kind, it is possible to accurately predict the disturbances associated with any geometrical configuration or any flow rate.     

A Nonrecursive Estimator for the Cox Model

The Cox regression model is one of the most widely used models to incorporate covariates. The frequently used partial likelihood estimator of the regression parameter has to be computed iteratively. In this paper we propose a noniterative estimator for the regression parameter and show that under certain conditions it dominates another noniterative estimator derived by Kalbfleish and Prentice. The new estimator is demonstrated on lifetime data of rats having been subject to insult with a carcinogen.     

A New Model for the Origin of Bipedality

Scholars have long thought that bipedality evolved gradually in response to the opening of the savanna. Recently, both parts of this concept have come into question. A variety of benefits of bipedality have been posited as responsible, but a trait can not evolve unless a useful mutation appears. Perhaps we need to stop wondering about selective pressures and consider what kind of mutation might be involved in forming a bipedal pelvis. Work on the evolution of development has shown that there are segmental control genes, alterations in which have large effects. These include the hox genes, of which there are four sets in humans, referred to as the HOX A, B, C, and D sequences. Changes in their activation in embryogenesis alter the identity of vertebrae and limb structure. An alteration in the control region of certain of the distal HOX D genes may well be responsible for the sudden appearance of bipedality by moving the boundary between the lumbar and sacral vertebrae, and so moving the position of the pelvis and lower limb origin. Pongids usually have three lumbar vertebrae; early hominids, 6. Pongids also have 48 chromosomes while we have 46. HOX D is located on our 2nd chromosome, the one that is a fusion of two pongid chromosomes. If that fusion altered the onset of perhaps HOX D 10, so that it switched on a couple of segments later, then the sacrum would form further down the vertebral column and might be shorter. In this paper I look at the chromosomal location of HOX D and examine the likelihood that the fusion of two panid chromosomes could have given rise to alterations in its control resulting in the abrupt appearance of bipedality and accompanying changes in the limbs and in the chela in which the HOX sequences are reused.