Social mechanisms in the population genetics of Tay-Sachs and other lethal autosomal recessive diseases: a computer simulation model.

A computer simulation model was developed to study the effects of various feudal social customs on the incidence of lethal autosomal recessive genes. Populations of 500 individuals were created in which each person was characterized by sibship, genotype, and sex. The numbered sibships were sorted into numerical order. Each individual then sought a mate from 6 or 12 sibships on either side of his or her own sibship. The resulting couples were sorted in order of the husband's sibship number, after which the couples produced children in accordance with the prevailing birth rate. This ordering of sibships made the probability of a gene remaining in one locality higher than the probability of it drifting to distant localities. A lethal autosomal recessive gene was introduced into populations at a starting carrier rate of 10%. This fell after 20 generations to 2.54 +/- 0.17% (SEM) which was significantly less than the 5.00% carrier rate predicted by a deterministic model in which random mating occurred in an infinite population. The excessive loss of the lethal gene was caused by the high incidence of consanguineous marriages and by the occurrence of random inequalities in the distribution of the gene. The avoidance of sib marriages raised the final carrier frequency (3.28 +/- 0.19%) as did reproductive compensation (4.33 +/- 0.26%). The combination of the incest taboo and reproductive compensation raised the final carrier rate to 5.05 +/- 0.28%. It is concluded that the social factors which may have operated over a period of many centuries in the past have had a significant effect on the population genetics of lethal autosomal recessive genes.

ENDO-LAB: an integrated, portable endocrinology laboratory software system.

ENDO-LAB is an IBM PC-based system which performs calculations and record-keeping for the Vanderbilt University Medical Center Endocrinology Laboratory. It manages maintenance and quality control, and prints reports for regulatory agencies. The system was designed to minimize paperwork without changing laboratory procedures in any way. Key features of ENDO-LAB include a uniform user interface, and error detection mechanisms. The system is designed to detect data which has been incorrectly entered. In addition, where the efficacy of a test can be determined on the basis of limited data, preliminary graphs are screened as soon as possible, so that the user can terminate lengthy calculations whose outcome would be invalid or inconclusive. ENDO-LAB is an integrated system in that the same statistical and calibration programs can be applied to all of the analyses. The system is both extensible and portable; it has been successfully implemented outside Vanderbilt.

A reappraisal of the use of the phi-coefficient in multiple choice examinations.

The phi-coefficient of an item in a multiple choice question (MCQ) examination is often used to determine whether that item is suitable for re-use in future examinations. In order to be of value in this regard, the coefficient must be shown to be an objective and consistent index of the discriminating power of an MCQ item. The behaviour of the phi-coefficient (phi) was investigated in two one-from-five MCQ and two true/false examinations. It is shown that the magnitude of the phi-coefficient for the items in any examination is a function not only of the discriminating power of the items, but also of the magnitude of the countermark for incorrect responses, of the proportion of 'don't know' responses in the examination, and of how the 'don't know' responses are handled in the analysis. It is further shown that the reproducibility of the phi, when calculated for any pair of randomly selected portions of a class of students, is very poor. We conclude that the error of estimation of the phi is of the same order of magnitude as the phi's normal operative range.

Marital mores as a mechanism for the maintenance of ethnic variations of lethal gene frequencies.

A computer simulation model was developed to study the effects of various marital mores on the incidence of lethal autosomal recessive genes in populations that are subdivided into small isolates. The problem was studied in isolates where initial generation size was 30, 40, and 50 individuals. In each of these, the mean fertility rate was varied from 2.3 to 2.7 surviving (to adulthood) children per couple whose marriage had been contracted in accordance with the prevailing convention: marriage between first cousins and siblings prohibited; marriage between siblings prohibited; marriage allowed between any individuals; marriage prohibited between siblings but encouraged between cousins; and marriage encouraged between siblings. In all cases, the mean gene frequency in generation 20 was lower than that predicted by the deterministic model with random mating in an unsubdivided population of infinite size, due to gene loss through random drift (to zero) in many of the isolates. The mores that encouraged consanguineous marriages had the lowest final lethal-gene frequencies. Random mating produced intermediate values, and the restrictive mores, the highest final frequencies. The deterministic model (assuming infinite population size and random mating) predictions of the final gene frequency were exceeded only if there was reproductive compensation. It is concluded that restrictive marital mores significantly reduce the selective pressures on lethal recessive genes in small isolates, but that this is counteracted by the increased rate of gene loss through random drift.

On the perpetuation of relic genes having an inviable homozygote.

Reproductive compensation may be prezygotic or postzygotic. Prezygotic compensation is the replacement of inviable infants by one or more additional births. When the marital fertility rates are greater than necessary to replace the parents, however, many traditional societies ensured that any surviving progeny in excess of two (on average) did not marry, or married only if they replaced an older sib as heir to the family estate. We call this postzygotic compensation. We show that the coefficient of biologically effective compensation approximates unity when normal and genetic-disease-affected sibships were both sufficiently large to ensure that, on average, two or more sibs survived to the end of the reproductive period, irrespective of the level of prezygotic compensation. The impact of these types of compensation on the population genetics of Tay-Sachs disease and cystic fibrosis is discussed.

Tay-Sachs disease and the persistence of lethal autosomal recessive genes in human populations.

Several lethal autosomal recessive genes have stable carrier frequencies of about 1:20-30 in certain communities, while being exceedingly rare in other, biologically equally successful communities sharing the same environment. It is shown that this situation could persist indefinitely, without invoking the concepts of heterozygote advantage or epistasis, if the parents of affected offspring replace such children with additional sibs. We believe that this could be an important biological mechanism which ensures the maintenance of genetic diversity in the face of natural selection.

Tay-Sachs disease and the role of reproductive compensation in the maintenance of ethnic variations in the incidence of autosomal recessive disease.

Several deleterious and lethal autosomal recessive genes appear to exist in equilibrium with their normal alleles at a variety of stable, or near stable frequencies of considerable antiquity. One person in 25 is, for instance, a carrier of the Tay-Sachs gene among Ashkenazi Jews, compared with 1 in 300 among Sephardic and Oriental Jews and non-Jews. The explanations offered for this phenomenon have generally not been entirely satisfactory. It has been shown that parents replace fortuitous infant and childhood deaths with, on average, approximately two surviving sibs each. When mutation rates are low, this practice, which has also been shown to occur among other animals, can maintain considerable variations in the stable incidence of autosomal recessive disease, should such ethnic polymorphism arise through genetic drift, the founder effect or hitch-hiking. High mutation rates would appear to preclude ethnic variations in the stable incidence of genetic disease.

Penalties in multiple-choice and true-false questions.

In multiple-choice and true-false (T-F) questions a student expresses his ignorance by leaving questions unanswered, guessing randomly, answering according to some predetermined formula, or, in T-F tests, by marking all those which are unknown as 'true' or all as 'false'. Each of these no-knowledge strategies should, on average, yield the same score. It is shown that partial knowledge is awarded part-marks in multiple-choice question and T-F tests, since the chance of guessing correctly is greater when students possess some knowledge than when they guess randomly. There is a constant relationship between the score obtained by the informed guesser and the minimum, maximum and random-guessing scores, this relationship being independent of the scoring system. Modifications of the scoring system (i.e. of the magnitude of the penalty for incorrect responses) affect only the reward for unanswered questions: in the absence of a penalty the reward for unanswered questions equals the minimum score--a score which is unattainable by random guessing; with a large penalty the reward for unanswered questions approaches the maximum score obtainable.

Misconceptions and miscarriages in multiple choice questions.

A modification of the standard format of multiple choice question (MCQ) examinations, recently introduced in certain medical schools in this country, is decribed. The scheme allows for the variation of marks allocated to different in the paper, depending upon the relevance, importance and degree of difficulty of each question. However, the manner in which this new system is being implemented in some cases transgresses some fundamental principles of MCQ examinations. The consequence of this is that the average mark for the class is unintentionally low, with the good students separated from the main body of the class by a disproportionate number of marks. In addition, the examination lends itself to abuse by the enterprising student who is familar with the system of mark allocation.