AN ANALYSIS OF VARIABILITY IN NUMBER OF DIGITS IN AN INBRED STRAIN OF GUINEA PIGS

Threshold model for misclassified binary responses with applications to animal breeding

A Bayesian procedure for misclassified binary data was developed. An animal breeding simulation indicated that, when error of classification was ignored, the variance between clusters was inferred incorrectly. Data were reanalyzed assuming that the probability of misclassification was either known or unknown. In the first case, input parameter values were recovered in the analysis. When the probability was unknown, there was a slight bias; the true probability of misclassification and the true number of miscoded observations appeared within high credibility regions. An analysis of fertility in dairy cows is presented.

Bayesian analysis of liability of clinical mastitis in Norwegian cattle with a threshold model: effects of data sampling method and model specification

First-lactation records of Norwegian Cattle were used to infer heritability of liability to clinical mastitis with a threshold sire model. Mastitis was defined as a binary response (presence or absence) in a defined period of first lactation (opportunity period). Length of opportunity period (from 30 d before calving up to 120 or 300 d of lactation) had less effect on heritability estimates than data sampling methods (include or exclude records of cows culled before the end of the opportunity period) whereas sire ranking was more affected by the former. Including all cows, whether culled before the end of the opportunity period or not, gave a sharper and more symmetric posterior distribution of heritability of liability to clinical mastitis. When we analyzed data for all cows, model specification had a small effect on heritability estimates, while sire ranking was affected markedly. Posterior means of heritability range from 0.058 to 0.074. A model regressing on the length of the opportunity period for culled cows without mastitis, was shown favorable for the two opportunity periods using Bayes factors and the deviance information criterion for model comparison. This model, in which liability of mastitis depends on time to culling, may allow utilizing information from all first lactations in genetic evaluation, irrespectively of duration and culling outcome.

The genetics of complex autoimmune diseases: non-MHC susceptibility genes

Susceptibility to complex autoimmune diseases (AIDs) is a multigenic phenotype affected by a variety of genetic and environmental or stochastic factors. After over a decade of linkage analyses, the identification of non-major histocompatibility complex (non-MHC) susceptibility alleles has proved to be difficult, predominantly because of extensive genetic heterogeneity and possible epistatic interactions among the multiple genes required for disease development. Despite these difficulties, progress has been made in elucidating the genetic mechanisms that influence the inheritance of susceptibility, and the pace of gene discovery is accelerating. An intriguing new finding has been the colocalization of several AID susceptibility genes in both rodent models and human linkage studies. This may indicate that several susceptibility alleles affect multiple AIDs, or alternatively that genomic organization has resulted in the clustering of many immune system genes. The completion of the human genome sequence, coupled with the imminent completion of the mouse genome, should yield key information that will dramatically enhance the rate of gene discovery in complex conditions such as AID susceptibility.

Heritability estimations for diseases, coat color, body weight, and height in a birth cohort of Boxers

OBJECTIVE

To obtain heritability estimates for diseases and characteristics in Boxers.

ANIMALS

Birth cohort of 2,929 purebred Boxers from 414 litters.

PROCEDURE

Heritability estimates were determined for cheiloschisis-palatoschisis, cryptorchidism, epilepsy, stifle disorders, cardiac disorders, coat color, birth weight, and adult weight, and height. Binary traits were analyzed by use of a mixed-effects probit model. Some traits also were analyzed by use of a model that postulated monogenic inheritance. Full pedigree analyses were performed. Variation in incidences of disease among clusters of related dogs was evaluated.

RESULTS

Heritability estimates were virtually zero for cardiac disorders, medium (0.17 to 0.36) for most other traits, and high (> 0.55) for coat color, birth weight, and adult height. Litter effects and risk factors affected cheiloschisis-palatoschisis, heart murmur, coat color, broadly defined epilepsy, and adult weight. Litter effects may be attributable to common environmental effects for littermates but also may be attributable to dominance variation caused by a recessive gene. Heritability estimates increased when stricter definitions for epilepsy and stifle disorders were used. The monogenic model did not reveal higher heritability estimates for 6 traits analyzed. Incidences for white coat differed significantly for 10 familial clusters, confirming high heritability and effects of familial lineage.

CONCLUSIONS AND CLINICAL RELEVANCE

Results indicate that genetic improvement of most traits should be feasible, except for cardiac disorders. However, because most traits are influenced by environmental effects as well as genetic effects, genetic counseling based on polygenic inheritance and use of familial information rather than strict exclusion of parents is preferred.

Statistical modeling of interlocus interactions in a complex disease: rejection of the multiplicative model of epistasis in type 1 diabetes

In general, common diseases do not follow a Mendelian inheritance pattern. To identify disease mechanisms and etiology, their genetic dissection may be assisted by evaluation of linkage in mouse models of human disease. Statistical modeling of multiple-locus linkage data from the nonobese diabetic (NOD) mouse model of type 1 diabetes has previously provided evidence for epistasis between alleles of several Idd (insulin-dependent diabetes) loci. The construction of NOD congenic strains containing selected segments of the diabetes-resistant strain genome allows analysis of the joint effects of alleles of different loci in isolation, without the complication of other segregating Idd loci. In this article, we analyze data from congenic strains carrying two chromosome intervals (a double congenic strain) for two pairs of loci: Idd3 and Idd10 and Idd3 and Idd5. The joint action of both pairs is consistent with models of additivity on either the log odds of the penetrance, or the liability scale, rather than with the previously proposed multiplicative model of epistasis. For Idd3 and Idd5 we would also not reject a model of additivity on the penetrance scale, which might indicate a disease model mediated by more than one pathway leading to beta-cell destruction and development of diabetes. However, there has been confusion between different definitions of interaction or epistasis as used in the biological, statistical, epidemiological, and quantitative and human genetics fields. The degree to which statistical analyses can elucidate underlying biologic mechanisms may be limited and may require prior knowledge of the underlying etiology.

Lessons from the NZM2410 model and related strains

SLE susceptibility requires the interplay of an unknown number of genes and equally unidentified triggering events. The past few years have seen significant advances in our understanding of SLE susceptibility through the genetic analysis of murine models. The NZM2410 strain, which is derived from the NZB/WF1 model has played a significant role in these advances. The main advantages presented by this strain over other models are the genetic homozygozity at all loci and an highly penetrant early onset lupus nephritis in both males and females, indicating that the strongest BWF1 susceptibility loci were retained in NZM2410. After identification of NZM2410 susceptibility loci via linkage analyses, congenic strains have been derived in order to convert a polygenic system into a series of monogenic traits. These congenic strains have been analyzed in an integrated process which has provided simultaneously 1) novel functional characterization of the Sle susceptibility loci, 2) high resolution genetic maps that will lead to the identification of the corresponding susceptibility genes by either candidate locus or positional cloning, and 3) insights into the mechanisms by which these loci interact to produce systemic autoimmunity with fatal end-organ damage.

A random model approach to mapping quantitative trait loci for complex binary traits in outbred populations

Mapping quantitative trait loci (QTL) for complex binary traits is more challenging than for normally distributed traits due to the nonlinear relationship between the observed phenotype and unobservable genetic effects, especially when the mapping population contains multiple outbred families. Because the number of alleles of a QTL depends on the number of founders in an outbred population, it is more appropriate to treat the effect of each allele as a random variable so that a single variance rather than individual allelic effects is estimated and tested. Such a method is called the random model approach. In this study, we develop the random model approach of QTL mapping for binary traits in outbred populations. An EM-algorithm with a Fisher-scoring algorithm embedded in each E-step is adopted here to estimate the genetic variances. A simple Monte Carlo integration technique is used here to calculate the likelihood-ratio test statistic. For the first time we show that QTL of complex binary traits in an outbred population can be scanned along a chromosome for their positions, estimated for their explained variances, and tested for their statistical significance. Application of the method is illustrated using a set of simulated data.

Joint multipoint linkage analysis of multivariate qualitative and quantitative traits. I. Likelihood formulation and simulation results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.

Modelos linear e não linear em análises genéticas para sobrevivência de crias de ovinos da raça Santa Inês

Registros de sobrevivência do nascimento ao desmame de 3846 crias de ovinos da raça Santa Inês foram analisados por modelos de reprodutor linear e não linear (modelo de limiar), para estimar componentes de variância e herdabilidade. Os modelos usados para sobrevivência, analisada como característica da cria, incluíram os efeitos fixos de sexo, da combinação tipo de nascimento-criação da cria e da idade da ovelha ao parto, efeito da covariável peso da cria ao nascer e efeitos aleatórios de reprodutor, da classe rebanho-ano-estação e do resíduo. Componentes de variância para o modelo linear foram estimados pelo método da máxima verossimilhança restrita (REML) e para o modelo não linear por uma aproximação da máxima verossimilhança marginal (MML), pelo programa CMMAT2. O coeficiente de herdabilidade (h²) estimado pelo modelo de limiar foi de 0,29, e pelo modelo linear, 0,14. A correlação de ordem de Spearman entre as capacidades de transmissão dos reprodutores, com base nos dois modelos foi de 0,96. As estimativas de h² obtidas indicam a possibilidade de se obter, por seleção, ganho genético para sobrevivência.

Mapping quantitative trait loci for complex binary traits in outbred populations

Complex binary traits have a dichotomous phenotypic expression but do not show a simple Mendelian segregation ratio. These traits are considered to be jointly controlled by the actions of several genes and a random environmental effect. The binary phenotype and the underlying factor are assumed to be linked through a threshold model. The underlying factor, referred to as the liability, is treated as a regular but unobservable quantitative character. Mapping quantitative trait loci (QTL) can be performed directly on the liability. Methods of QTL mapping for the liability of a complex binary trait have been well developed in line-crossing experiments. However, such a method is not available in outbred populations which usually consist of many independent pedigrees (families). In this study, we develop a method to analyse jointly multiple families of an outbred population. The method is developed based on a fixed-model approach, i.e. the QTL effects, rather than the variance, are estimated and tested. After the test, the estimated effects are then converted into a single estimate of the QTL variance by taking into consideration errors in the estimated effects. The QTL effects and variance-covariance matrix of the estimates are obtained by a fast Fisher-scoring method. Monte Carlo simulations show that the method is not only powerful but also generates very accurate estimates of QTL variances.

Estimation of genetic and phenotypic parameters for clinical mastitis, somatic cell production deviance, and protein yield in dairy cattle using Gibbs sampling

When including clinical mastitis in the breeding goal, it is useful to know what measure of the trait is most appropriate and its relationship to the primary production traits and indicator traits in the relevant population. In this paper, genetic and phenotypic parameters for clinical mastitis, somatic cell production deviance, and protein yield were estimated for the dairy breed Danish Red. In preliminary analyses, the heritability for clinical mastitis was found to be highest in early lactation, and its genetic correlation to clinical mastitis at other stages of lactation were high. Therefore, clinical mastitis defined in early lactation was the measure of clinical mastitis used in subsequent analyses. Two bivariate analyses were performed. Each analysis fitted clinical mastitis and either somatic cell production deviance or protein yield as a continuous trait. The bivariate model was composed of a Gaussian model for the continuous trait and a threshold model for mastitis. The analyses were performed in a Bayesian setting, using the Gibbs sampler. Point estimates (mean of marginal posterior densities) of heritability for mastitis on the underlying scale were estimated to be 0.10 and 0.12 in the two analyses. The genetic correlation between mastitis and protein yield was 0.43 and between mastitis and somatic cell production deviance was 0.80. These results make clear the importance of including clinical mastitis in the breeding goal and the usefulness of somatic cell production deviance as the indicator trait for clinical mastitis. The best measure of clinical mastitis was to consider only cases in early lactation.

Mapping quantitative trait loci for ordered categorical traits in four-way crosses

Many quantitative traits of economical importance are ordinal in nature. Although methods of mapping quantitative trait loci (QTLs) for continuous quantitative characters are well developed, such methods for ordinal characters are generally lacking. In this paper, we develop a method based on the framework of a generalized linear model using four-way cross populations. The method estimates and tests the average effects of a gene substitution in the parents. All markers in the same linkage group are simultaneously used to infer the allelic transmission of a putative QTL. General results of the method are demonstrated by a few simulation experiments. We discuss extensions of the method to QTL mapping in full-sib families.

QTL analysis in plants; where are we now?

We have briefly reviewed the methods currently available for QTL analysis in segregating populations and summarized some of the conclusions arising from such analyses in plant populations. We show that the analytical methods locate QTL with poor precision (10-30 cM), unless the heritability of an individual QTL is high. Also the estimates of the QTL effects, particularly the dominance effects tend to be inflated because only large estimates are significant. Estimates of numbers of QTL per trait are generally low (< 8) for individual trials. This may suggest that there are few QTL but probably reflects the power of the methods. There is no large correlation between the numbers of QTL found and the amount of the variation explained. Of those cases where dominance is measurable, dominance ratios are often > 1, but seldom significantly greater. These latter cases need further analysis. Many QTL map close to candidate genes, and there is growing evidence from synteny studies of corresponding chromosome regions carrying similar QTL in different species. However, unreliability of QTL location may suggest false candidates.

Genetic threshold hypothesis of neocortical spike-and-wave discharges in the rat: an animal model of petit mal epilepsy

Neocortical high-voltage spike-and-wave discharges (HVS) in the rat are an animal model of petit mal epilepsy. Genetic analysis of total duration of HVS (s/12 hr) in reciprocal F1 and F2 hybrids of F344 and BN rats indicated that the phenotypic variability of HVS cannot be explained by a simple, monogenic Mendelian model. Biometrical analysis suggested the presence of additive, dominance, and sex-linked-epistatic effects, buffering maternal influence, and heterosis. High correlation was observed between average duration (s/episode) and frequency of occurrence of spike-and-wave episodes (n/12 hr) in parental and segregating generations, indicating that common genes affect both duration and frequency of the spike-and-wave pattern. We propose that both genetic and developmental-environmental factors control an underlying quantitative variable, which, above a certain threshold level, precipitates HVS discharges. These findings, together with the recent availability of rat DNA markers for total genome mapping, pave the way to the identification of genes that control the susceptibility of the brain to spike-and-wave discharges.

Dollo's law and the death and resurrection of genes

Dollo's law, the concept that evolution is not substantively reversible, implies that the degradation of genetic information is sufficiently fast that genes or developmental pathways released from selective pressure will rapidly become nonfunctional. Using empirical data to assess the rate of loss of coding information in genes for proteins with varying degrees of tolerance to mutational change, we show that, in fact, there is a significant probability over evolutionary time scales of 0.5-6 million years for successful reactivation of silenced genes or "lost" developmental programs. Conversely, the reactivation of long (> 10 million years)-unexpressed genes and dormant developmental pathways is not possible unless function is maintained by other selective constraints; the classic example of the resurrection of "hen's teeth" is most likely an experimental artifact, and the experimental reactivation of the Archaeopteryx limb developmental program has been shown to be a misinterpretation. For groups undergoing adaptive radiations, lost features may "flicker" on and off, resulting in a distribution of character states that does not reflect the phylogeny of the group.

Comparison of prediction methodology for binary traits through Monte-Carlo simulation

SUMMARY

The purpose of this study was to evaluate simple alternatives to threshold models within the framework of a mixed-model procedure. Four models-linear model, threshold model, normit-transformation and pseudo-linear model-were compared by Monte-Carlo computer simulation. The normit-transformation model was based on simple normit transformation within a subclass while taking into account binomial error. The simulation experiments were carried out with combinations of five subclass sizes (5, 15, 25, 35, 45), five heritabilities (0.05, 0.15, 0.25, 0.35, 0.45) and 100 replications for each experiment. The loss of accuracy in the prediction models based on binary response was greater than that in the linear model based on continuous records. The accuracy of the threshold model was superior to that of the normit-transformation model and the pseudo-linear model in all the experiments. But the difference in accuracy between the threshold model and the pseudo-linear model was small when the heritability was low and the subclass size was small, while the difference in accuracy between the threshold and the normit transformation was small when the subclass size was large. ZUSAMMENFASSUNG: Vergleich von Michmodell-Voraussagen mittels Monte-Carlo Simulation Die Absicht dieser Untersuchung war die Bewertung einfacher Alternativen für Schwellenwert-Modelle im Rahmen von Mischmodell Methoden. Folgende vier Modelle wurden untersucht: Lineares, Schwellenwert, Normittransformation und pseudo-lineares Modell wurden mittels Monte-Carlo Computersimulation verglichen. Das Normittransformationsmodell beruhte auf einfachen Normittransformation innerhalb einer Unterklasse unter Berücksichtigung des binomialen Fehlers. Die Simulationsexperimente wurden mit fünf Unterklassen-Größen (5, 15, 25, 35, 45), fünf Heritabilitäten (0,05, 0,15, 0,25, 0,35, 0,45) und 100 Wiederholungen für jeden Versuch durchgeführt. Der Genauigkeitsverlust in den Modellen für binäre Ergebnisse war größer als in linearen Modellen mit kontinuierlichen Daten. Die Genauigkeit des Schwellenwert-Modells war der Normittransformation und dem pseudo-linearen Modell in alien Untersuchungen überlegen. Bei geringem h(2) und kleinen Unterklassen war die Genauigkeitsdifferenz zwischen Schwellenwert- und pseudolinearem Modell klein, ebenso wie die zwischen ersterem und Normittransformation bei großen Unterklassen.

Effect of divergent selection for immune responsiveness and of major histocompatibility complex on resistance to Marek's disease in chickens

Lines of chickens selected for nine generations for high (H) or low (L) antibody response to SRBC, a randombred control (C) line, and an F1 cross between H and L lines were challenged for resistance to Marek's disease (MD). Hens only were challenged at day-old by contact with virulent MD Strain K. Birds were serologically typed for MHC erythrocyte antigens. Chicks from the L and H lines died earlier and later, respectively, than the C chicks, whereas time of death did not differ between F1 birds and the L chicks. Mortality in the L line (70.1%) was higher than in the C line (42.8%), but mortality in the H line (40.9%) was not lower than in the C line or the F1 cross (47.5%). Effects of MHC genotypes and haplotypes on mortality from MD were estimated within lines with a logistic regression model. Effect of MHC was moderate in the H line (P < .10) and highly significant in the C line (P < .005). Effects of MHC genotypes were similar in the H and C line but differed in the L and F1. Heritability of mortality from MD estimated with a threshold model including relationships between individuals was .40 when all lines were grouped together, whereas heritability estimated for each line separately was .45, .51, and .78 in the H, C, and L lines, respectively. Correlations between estimated breeding values for antibody response to SRBC and mortality from MD varied between lines and sexes. Correlations also were affected by whether or not the MHC effect was taken into account.

Angular homeostasis. IX. Polygonal orbits with a moving target: implications for anomalous numbers of digits in congenital heart disease

This paper explores properties of discrete processes in which a pursuer seeks a target that is moving at constant velocity r that is a fixed proportion of the speed of the pursuer. The pursuer is subjected to proportional angular homeostasis, so chosen that the number of steps per circuit is small. The orbits relative to the target may assume any of four forms: polygons that reverse their sense an infinite number of times; or polygons that after a finite number of reversals ultimately come to have an integer numbers of sides; or have a rational numbers of sides; or have an irrational number of sides that densely fill an annulus. None of the polygons is regular. In the parameter space, the boundary line between the first of these sets and the other three has a somewhat bizarre pattern and may possibly be fractal, but no proof is forthcoming. Unlike the pattern with a stationary target, there may be a set or catchment of diverse values of the speed ratio, r, and the correction coefficient, b that all result in figures of some specified number, n, of sides (although with vertices in differing locations). Catchments have been found for only those polygons that have the winding number of 1. The implications are discussed that this property has for the genetic coding of biological traits that are countable. Some attention is also paid to the relevance of polygons with few sides to ontogenic growth when the correction coefficient is cyclically arc- or time-dependent.

Palatine and mandibular tori. A morphologic study in the current Norwegian population

Five thousand Norwegians, 2783 females and 2217 males, ranging in age from 16 to 89 years, have been screened for the presence of torus palatinus and/or torus mandibularis and analyzed with regard to size and shape of tori, sex, and age. The tori have been classified according to size as small, medium, and large. No measurements have been made, consistent with the view that these characteristics are non-metrical and should be assessed by means of a standard procedure. The prevalence figures of both tori were fairly low, in accordance with former reports. In torus palatinus there was female predominance, with a sex ratio of 5:3. In torus mandibularis the males were in majority, and the sex proportion was 4:3. In both sexes prevalence of the two tori was highest in the 35- to 65-year age group. Further analysis indicated in both tori a real correlation between prevalence and size and some correlation also between size and shape of torus palatinus but not of torus mandibularis. The figures of concurrence of the two tori were low, denoting a non-significant correlation. Still, the analysis showed that each torus occurred more than twice as frequently in an individual bearing the other torus. Torus morphoanalysis, explaining diverging patterns of clinical conduct in the two tori, and the relative weight of hereditary versus environmental factors as morphogenetic determinants of the condition, including a quasi-continuous genetic or threshold model, have contributed to shed new light on the torus phenomenon. The occurrence and propagation of torus mandibularis complies reasonably well with this model, and the present analysis indicates that even torus palatinus should appropriately be considered a threshold character.

Angular homeostasis. VIII. Pursuit of a slowly moving target in a plane: relevance to lateralization in cardiovascular ontogeny

We explore the pursuit in a plane of a target moving at constant slow speed in a straight line. Two models of the pursuit are given. In the continuous case, the pursuer is moving at constant speed and is subject to proportionate angular homeostasis with correction constant b. In the discrete version movement occurs at a constant speed in a sequence of straight line segments of constant length (called the step size, s) the end of the segments being called the vertices. The pattern considered is not the absolute position of the pursuer, but its distance and orientation relative to the target. Both the transients and the asymptotic orbit are addressed. A key quantity is r, the speed of the target expressed as a fraction of that of the pursuer. If the speed of the pursuer is defined as unity, r is also the ratio of the speeds. There exists a critical speed fraction, R(b,s), a function of b and s, that defines what the term slow designates. R(b,s), which has to be found numerically, has the following property. For r less than R(b,s), the asymptotic path is a simple closed curve. In the discrete case the vertices converge to a simple closed curve. The larger r, the more the path (or in the discrete analogue its set of vertices) departs from a circle, and the more eccentric the target is with respect to it. Interest centers on two issues. First we address the transient patterns of the path, notably whether or not the sense of any particular path (clockwise or counterclockwise) is the same throughout, or changes at some stage.(ABSTRACT TRUNCATED AT 250 WORDS)

The genetic epidemiology of schizophrenia and the design of linkage studies

There are three aspects of schizophrenia that are challenges to the design of linkage studies. First, analysis of twin and family data have consistently failed to identify a single major gene effect. Second, ascertainment of multiplex families does not guarantee the sampling of families in whom a major gene is segregating even if such a gene exists. Third, environmental influences appear to play an essential role in the etiology of at least some schizophrenia. The implications of these features for linkage strategies in schizophrenia are discussed.

Twin studies and the genetics of Parkinson's disease--a reappraisal

Parkinson's disease (PD) has long been regarded as having a hereditary component. However, three recent twin studies have been interpreted as excluding any significant genetic component in the etiology of PD. In this article, we reexamine these twin studies and argue that such a conclusion is premature. We review statistical tests of twin concordance rates, including calculation of G, the coefficient of genetic determination. When variation in a trait is due entirely to genetic factors G = 1, and when variation in a trait is due entirely to nongenetic factors G = 0. We conclude that: (a) low monozygotic concordance rates can be compatible with substantial genetic contribution to etiology; (b) the PD twin study data give substantial optimal values of G (up to 0.78) but the very broad 95% confidence limits for G make it impossible for the twin study data to prove or disprove a substantial genetic component to the etiology of PD; and (c) changing clinical concepts of PD have undermined the assumptions underlying the methodology of the PD twin studies. We review three genetic models that are biologically plausible for PD and are compatible with the low twin concordance rates. Finally, we suggest that further family studies, including linkage studies, are needed to resolve this question.

Torus mandibularis: an estimation of the degree of genetic determination

Torus mandibularis has frustrated several attempts to make family patterns of variation fit modifications of Mendelian models. It is suggested that the quasi-continuous model of inheritance provides a rational explanation for the diverging opinions. The model implies an underlying continuous and normally distributed variable, 'liability', with a threshold value beyond which individuals will be affected. Both genetic and environmental factors determine liability, making the system multifactorial. The incidence of variable degrees of torus was examined in two groups of patients with different stresses on the jaws: one group with bruxism and one comparison group. The transformation of incidences to group means and variances of liability was demonstrated. Muscular forces during bruxism were shown to influence liability. The relative importance of environmental and genetic components of variance could, however, not be estimated directly from the entire groups, since both were mixed with regard to the genetic predisposition. To achieve materials with uniform genotypes, all individuals without torus were omitted. The estimate of the genotypic variance (VG) was obtained by subtracting the variance of the bruxism sub-group--the environmental component associated with bruxism (VEB)--from the total phenotypic variance of the comparison sub-group (VP). The estimate of the genetic determination of torus (VG/VP) turned out to be about 30%, whereas approximately 70% of the causes seemed to be attributable to environmental influence in terms of occlusal stress. Gene effects on the morphologic level are usually pleiotropic, and it is suggested that the correlation of torus mandibularis with other clinical variables might make an interesting subject for further investigation.

Contingency table estimation of genetic parameters and disease risks

Many genetic variables, categorical in nature, allow for analysis by use of contingency table techniques and thereby lead to maximum likelihood estimators. This paper describes these techniques for the classical direct effect model under Mendelian segregation to illustrate how one obtains maximum likelihood estimators for penetrance probabilities and recurrence risks when the data appear in the form of a semi-symmetric intraclass contingency table. The method presented for the 2(3) table is based exclusively on the generalized cross-product ratio and the Pearson chi-squared statistic, and thereby avoids complex statistical methodology and unwieldy computations.

Genetic evaluation of traits distributed as Poisson-binomial with reference to reproductive characters

A procedure of genetic evaluation of reproductive traits such as litter size and survival in a polytocous species under the assumption of polygenic inheritance is described. Conditional distributions of these traits are assumed to be Poisson and Bernoulli, respectively. Using the concept of generalized linear models, logarithmic (litter size) and probit (survival) functions are described as linear combinations of "nuisance" environmental effects and of transmitting abilities of sires or individual breeding values. The liability of survival is expressed conditionally to the logarithm of litter size. Inferences on location parameters are based on the mode of their joint posterior density assuming a prior multivariate normal distribution. A method of estimation of the dispersion parameters is also presented. The use of a "truncated" Poisson distribution is suggested to account for missing records on litter size.

Sire evaluation for multiple binary responses when information is missing on some traits

A procedure of sire evaluation for multiple binary responses when information is missing for some traits is described. The genetic model assumes a conceptual underlying multivariate normal distribution rendered discrete by abrupt thresholds. Statistical inferences are made from a posterior distribution consisting of several conditionally independent likelihood functions and a multivariate normal prior distribution. Each likelihood function corresponds to a particular class of information available. Point estimators and predictors of fixed and random effects are the values that maximize the posterior distribution conditionally on heritabilities and genetic correlations. The procedure involves nonlinear maximization. An example involving joint selection for calving ease and skeletal development illustrates the principles. Application of the methodology as a potential means of removing bias due to selection for categorical traits is discussed.

The first Meckel oration: on the causes of morphological differences in a population of guinea pigs

The first morphological abnormality considered here was of a very superficial sort: deviations from the smooth coat of wild cavies and most guinea pigs. The deviations of "rough-furred" individuals range from a single irregularity or a single pair of rosettes to the "full rough" pattern. Roughness may be restricted to the hind toes, forehead, or hair around the eyes or belly, or (very rarely) to a small area on one side of the back. There is no indication of gene control in the last, and no analysis of the only strain (in Professor Castle's laboratory) that I have seen, of roughness restricted to the belly. A dominant gene, R, in combination with a semidominant modifier, M, account for the fancier roughs (R-MM toes only, R-mm full rough). A gene, st, that is completely dominant in the absence of R, semidominant in its presence, was descended from 3 animals from outside the colony. It accounts for a large forehead rosette, usually with a small white spot in front of its center. A statistically semidominant gene, Re, with extremely irregular, often asymmetric penetrance tends to cause rosettes about the eyes. This arose by mutation late in the history of the Whitman colony. It is strengthened by presence of R MM. Considerable variation occurs in the numbers of dorsal rosettes of R Mm and R mm. These have not been analyzed satisfactorily because the genetic differences are confounded by nongenetic ones. It is not practicable to summarize briefly all of the complex interaction effects of these factors, but it may be noted that the most surprising one had to do with genes St and R. The forehead rosette due to rr St closely resembles that of R mm (except for the absence of the pleiotropic white spot). The combination, R mm St St, shows none of the expected enhancement but instead shows nearly complete cancellation of the rosette. Moreover, the anterior dorsal rosettes of R mm st st are much reduced and seemingly shoved backward and laterally to give a large smooth shield back of the ears. St St also reduces the usual dorsal pair of rosettes of R Mm. With St st, all of these antagonistic effects are weaker and less regular. Another morphological deviation to be considered was the fairly common restoration of an atavistic little toe.(ABSTRACT TRUNCATED AT 400 WORDS)

Autosomal dominant inheritance of hereditary canine spinal muscular atrophy

Hereditary canine spinal muscular atrophy ( HCSMA ) is a motor neuron disease in Brittany spaniels. Three phenotypes are recognized (accelerated, intermediate, and chronic) and are distinguished on the basis of rate of progression and age at onset. Breeding studies within a kindred of more than 125 dogs (Brittany spaniel and beagle-Brittany outcrosses ) have established an autosomal dominant inheritance for HCSMA . Pups homozygous for the trait have accelerated disease whereas heterozygous dogs have intermediate or chronic disease. The reason for the two phenotypes in heterozygotes is under study. HCSMA provides a unique opportunity to study the genetic and pathophysiological mechanisms of a motor neuron disease, and findings may have broad relevance to investigations of autosomal dominant degenerative disorders of the central nervous system.

Appendicular skeletal morphology in minute salamanders, genus Thorius (amphibia: Plethodontidae): Growth regulation, adult size determination, and natural variation

Patterns of growth and variation of the appendicular skeleton were examined in Thorius, a speciose genus of minute terrestrial plethodontid salamanders from southern Mexico. Observations were based primarily on ontogenetic series of each of five species that collectively span the range of adult body size in the genus; samples of adults of each of seven additional species provided supplemental estimates of the full range of variation of limb skeletal morphology. Limbs are generally reduced, i.e., pedomorphic, in both overall size and development, and they are characterized by a pattern of extreme variation in the composition of the limb skeleton, especially mesopodial elements, both within and between species. Fifteen different combinations of fused carpal or tarsal elements are variably present in the genus, producing at least 18 different overall carpal or tarsal arrangements, many of which occur in no other plethodontid genus. As many as four carpal or tarsal arrangements were observed in single population samples of each of several; five tarsal arrangements were observed in one population of T. minutissimus. Left-right asymmetry of mesopodial arrangement in a given specimen is also common. In contrast, several unique, nonpedomorphic features of the limb skeleton, including ossification of the typically cartilaginous adult mesopodial elements and ontogenetic increase in the degree of ossification of long bones, are characteristic of all species and distinguish Thorius from most related genera. They form part of a mechanism of determinate skeletal growth that restricts skeletal growth after sexual maturity. Interspecific differences in the timing of the processes of appendicular skeletal maturation relative to body size are well correlated with interspecific differences in mean adult size and size at sexual maturity, suggesting that shifts in the timing of skeletal maturation provide a mechanism of achieving adult size differentiation among species. Processes of skeletal maturation that confer determinate skeletal growth in Thorius are analogous to those typical of most amniotes - both groups exhibit ontogenetic reduction and eventual disappearance of the complex of stratified layers of proliferating and maturing cartilage in long bone epiphyses - but, unlike most amniotes, Thorius lacks secondary ossification centers. Thus, the presence of secondary ossification centers cannot be used as a criterion for establishing determinate skeletal growth in all vertebrates.

Genetic analysis of audiogenic seizure susceptibility in C57BL/6J X DBA/2J recombinant inbred strains of mice

The inheritance of susceptibility to audiogenic seizures (ASs) was studied in the C57BL/6J (B6) and DBA/2J (D2) progenitor strains, their reciprocal F(1) hybrids, backcross generations and in 21 B6 x D2 recombinant inbred (RI) strains of mice at 21 days of age. All of the D2 mice tested experienced ASs, whereas none of the B6 mice responded to the sound. Although 23% of the F(1) mice experienced wild running, they were generally as resistant to ASs as their B6 parents. Mice of the F(1)x B6 backcross generation were also resistant to ASs. In the F(1)x D2 backcross generation, however, a significant preponderance (72%) of AS-susceptible mice was found. No significant association was observed between any of the four coat-color phenotypes that were segregating in this generation and susceptibility to ASs. A continuous distribution of mean seizure severity scores and several new audiogenic response phenotypes, distinctly different from the phenotypes of either progenitor strain, were found among the 21 RI strains. These and the results from the F(1)x D2 backcross generation suggest that the difference in AS susceptibility between 21-day-old B6 and D2 mice cannot be under the control of a single locus. In addition, no association was found between AS susceptibility and the chromosome 4 markers Lyb-2, Mup-1 and b among the 21 RI strains. An association was observed, however, between AS susceptibility and the Ah locus. Several of the RI strains that were AS resistant at 21 days of age became AS susceptible as adults. One RI strain was susceptible to ASs at both young and adult ages. The B6, D2 and F(1) mice were completely resistant to ASs at adult ages. Genetic differences were found among the RI strains for the incidence, onset, duration, and type of severity of ASs. A remarkable amount of phenotypic variability in the audiogenic response, which can be attributed only to the influence of environmental factors, occurred within several of the RI strains. A multiple-factor mode of inheritance involving a physiological threshold can account for our observations.

Sensitivity patterns for the induction of homeotic shifts in a favorable strain of mice

In an effort to develop a prescreening system that is sensitive, is compatible with in-vivo administration of presumptive teratogens, and utilizes morphological endpoints, we are studying the induction of homeotic shifts in the axial skeleton. Our earlier work had demonstrated the existence of critical periods for certain such shifts, even though the (C57BL x NB)F1 hybrid used was not entirely suitable for this purpose. Using 100 R X-rays on successive days during the period of major organogenesis, we have now analyzed the sensitivity pattern of the BALB/c, since this strain normally straddles thresholds for the position of axial borders. Mortality, birthweight, and skeletal anomalies were analyzed, in addition to the homeotic shifts. --Day 9 1/4 postconception was clearly the most sensitive stage for the production of posterior shifts at the thoraco-lumbar border and the lumbo-sacral border, and for increases in the number of sternebrae and costo-sternal junctions. Anterior shift could be induced three days later, on day 12 1/4, but this was confined to only one of the four characters, the thoraco-lumbar border. There are a number of indications that, at given stages during the study period, BALB/c embryos correspond developmentally to chronologically somewhat earlier stages of two strains studied previously. The present results do not support the hypothesis that factors influencing the quantitative skeletal characters act by way of body size. --Since homeotic shifts can be produced by a number of mechanisms and are obvious indications that developmental interference has occurred, and since such shifts are easy to score and convenient to analyze quantitatively, our identification of a highly suitable strain and of stages of maximum sensitivity in this strain should aid in making the system useful in the prescreening for chemical teratogens.

Gamma-ray-induced dominant mutations that cause skeletal abnormalities in mice. II. Description of proved mutations

In a mutation-rate experiment described earlier, 31 dominant skeletal mutations were confirmed by breeding tests. Skeletal abnormalities were detected in the skeletons of some of the sons of irradiated males, and for 31 of these sons the study of skeletons in subsequent generations showed that they transmitted abnormalities. The detailed descriptions of these mutations, together with descriptions of 6 presumed mutations found in a later paper, provide the basis for determining which mutations cause effects that would, if they occurred in humans, cause a serious handicap. Such a determination is necessary before these data can be used to estimate genetic hazard to humans. Furthermore, these descriptions of syndromes caused by individual dominant mutations should be useful to clinicians interested in skeletal defects. The statistical analysis of the frequency of each abnormality in the mutant line versus an approximation of the frequency of the malformation in the absence of new mutations is essential to be sure that a mutation is indeed the cause of each abnormality. These analyses, together with analyses of the correlation of abnormalities caused by individual mutations, clearly demonstrate that dominant mutations exhibit low penetrance for many of their effects. A few of the mutations also cause the death of some heterozygotes. No externally visible effects have been detected in heterozygotes for most of these mutations. Externally visible effects found in some of the heterozygotes for a few of the mutations include hydrocephalus, circling behavior, increased nervous activity, gray coat color, webbing of digits, and small size. Two coat-color mutations were found that caused no detected skeletal abnormalities. The data suggest that a few of the mutations may be reciprocal translocations. In most of the mutant lines tested cytologically, however, there was no indication of chromosomal aberrations.

The multifactorial/threshold concept -- uses and misuses

The common congenital malformations have familial distributions that cannot be accounted for by simple Mendelian models, but can be explained in terms of a continuous variable, "liability," with a threshold value beyond which individuals will be affected. Both genetic and environmental factors determine liability, making the system multifactorial. Cleft palate is a useful experimental model, illustrating a number of factors that contribute to palate closure, the nature of a developmental threshold, and how genes and teratogens can alter the components of liability to increase the probability of cleft palate. The nature of the genetic component to liability in human malformations in not clear, and various possibilities, ranging from polygenic in the strict sense to a major gene with reduced penetrance are compatible with the data -- but the important feature is the threshold. Much of the confusion over the concept results from inconsistent use of terminology. The term "multifactorial" should be used for "determined by a combination of genetic and environmental factors," without reference to the nature of the genetic factor(s). "Polygenic" should be reserved for "a large number of genes, each with a small effect, acting additively." When several genes, with more major effects are involved, "multilocal" can be used. When it is not clear which of these is applicable the term "plurilocal" is suggested, in the sense of "genetic variation more complex than a simple Mendelian difference." Since teratological data often represent threshold characters the concept also has important implications for the interpretation of data on dose-response curves, synergisms, and strain differences in response to teratogens.