Showing papers in "Annals of Human Genetics in 1972"

Extension of covariance selection mathematics

Abstract: This paper gives some extensions of the selection mathematics based on the covariance function published in Price (1970). Application of the mathematics to ‘group selection’ is briefly illustrated. More about applications will be shown in a later paper concerning ‘ Selection in populations with overlapping generations’, which will be submitted to this journal. To facilitate reference in that paper, the equations in this paper are labelled with the letter ‘A. The mathematics given here applies not only to genetical selection but to selection in general. It is intended mainly for use in deriving general relations and constructing theories, and to clarify understanding of selection phenomena, rather than for numerical calculation.

The use of multiple thresholds in determining the mode of transmission of semi-continuous traits.

Abstract: A review of current textbooks of medical genetics (Goodman, 1970; Roberts, 1970) reveals that few, if any, of the common familial illnesses show simple Mendelian ratios. Many of these diseases may be considered semi-continuous traits, so that affected individuals manifest variable severity and normal individuals cannot be graded. Often either severe subforms or mild preclinical forms are defined, and the severity along with the presence or absence of the condition may be inherited in whole or in part. Use of these subforms as parameters in genetic models rather than their exclusion in favour of an all-or-none classification may help in the understanding of the genetic architecture of the trait. Several different modes of transmission have been proposed, including single-locus two-allele models with variable penetrance in one or all genotypes; multifactorial models in which many genes of small effect and environmental sources of variance play a role; and combinations of the two. Attempts to distinguish between the various modes of transmission have not been successful and Morton et al. (1971) has concluded that ‘it is exceedingly difficult, and may be practically impossible, to infer the genetic basis of traits which do not give regular Mendelian ratios.’ To understand the nature of the variation with respect to disease status, it is helpful to postulate an underlying continuous variable, termed the liability by Falconer (1965), which is a linear scale representing the contribution of all genetic and environmental influences that make an individual more or less likely to manifest the disease. A threshold is defined so that individuals whose liability exceeds the threshold manifest the disease. More severely affected individuals are assumed to have a higher liability than less severely affected individuals. If a more severe subform of the disease is clinically distinguishable, a second threshold on the liability scale is defined; individuals with liabilities above this second threshold manifest the more severe subform. The positions of the two thresholds in relation to each other, and in relation to the mean liability of the population, are functions of the population prevalence of the two forms. The narrower form of the illness (less common) is entirely nested within the wider form (more common) and all individuals with the narrower form are counted as suffering the wider form as well. The population may thus be divided into three categories with respect to the trait: ‘unaffected’ (u), ‘wide but not narrow’ (w-n) and ‘narrow’ (n) . Examples of less common and more severe subforms of diseases which fulfil the above criteria are juvenile diabetes, malignant hypertension and catatonic schizophrenia. Mild pre-clinical syndromes when combined with the major forms of the diseases they represent include a greater proportion of the population than the disease alone, and are found in * This work was supported in part by U.S.P.H.S. grants MH-09247 and MH-13002. t Van Ameringen Fellow of the Foundations Fund for Research in Psychiatry. Current address: Department of Psychiatry, Washington University School of Medicine, 4940 Audubon Avenue, St Louis, Missouri 631 100, U.S.A. Address reprint requests to Dr Reich. 1 School of Wool and Pastoral Sciences, The University of New South Wales, Konsington, Australia.

The genetic structure of a tribal population, the Yanomama Indians

Abstract: To the extent that a key issue can ever be identified in biology, understanding the significance of the large amount of genetic variation encountered in all properly studied outbreeding plant and animal species is the key issue in population genetics today. A meaningful discussion of this issue is seriously hampered by lack of data on the breeding structure of natural populations. Human populations offer unusual advantages for the study of population structure. Ancestry and recent patterns of migration of individuals and groups can be determined with a precision not possible for other 'wild' populations, as can individual reproductive performances. History and archaeology supply additional data on population movements in the past also usually not available for other types of organisms. While data on all types of human populations are greatly to be desired, data on the surviving relatively unacculturated, tribal-type populations are especially critical. The parameters of these populations come closest to reflecting the circumstances under which human evolution occurred and under which the vast amount of variability now known to be present in human populations arose. Such populations will not long be available for study. Guided by these and other considerations, in 1961 we initiated a major programme directed

Average heterozygosity per locus in man: an estimate based on the incidence of enzyme polymorphisms

Abstract: SUMMARY 1. Data from electrophoretic surveys of enzymes in European populations are reviewed. 2. Out of the seventy-one structural gene loci determining enzyme structure which have been scrutinized electrophoretically, 20 (28 %) were found to show genetic polymorphism. The average heterozygosity per locus for alleles determining electrophoretic variants is estimated at 0·067. 3. These results are compared with data from some other species. 4. For several different reasons, most of which relate to the techniques used and the enzymes and tissues surveyed, it seems likely that the present data considerably underestimate the true incidence of polymorphism and average heterozygosity per locus.

Alcohol dehydrogenase isozymes in adult human stomach and liver: evidence for activity of the ADH 3 locus.

Abstract: Ann. Hum. Genet., Lond. (1972), 35, 243 Pyinted in Great Britain Alcohol dehydrogenase isozymes in adult human stomach and liver : evidence for activity of the ADH3 locus BY MOYRA SMITH, D. A. HOPKINSON AND HARRY HARRIS M.R.C. Human Biochemical Genetics Unit, Galton Laboratory, University College London I n a previous paper (Smith, Hopkinson & Harris, 1971) we put forward a genetical hypothesis to explain the isozyme patterns of human alcohol dehydrogenase in various tissues and at different times in development. It was suggested that there are three loci each coding for a structurally distinct type of polypeptide chain; that the isozymes are dimers; and that any particular isozyme may be made up of two identical subunits coded by a specific allele at one of the loci, or of two non-identical subunits coded by alleles at two separate loci, or of two non-identical subunits coded by different alleles at the same locus. The loci were called ADH,, ADH, and ADH, and the corresponding polypeptide subunits a, /3 and y . At each of the ADH, and ADH, loci the evidence indicated that two different common alleles occur, coding for structurally distinct forms of the corresponding polypeptide. According to the hypothesis, the isozymes in the cells of a particular tissue at a given time in development depend on the relative activities of the three loci. Thus in liver, a polypeptides determined by ADH, appear to predominate in early foetal life, but in the course of foetal develop- ment /3 polypeptides determined by ADH, appear in increasing amounts, so that while in the early foetus the main isozyme observed is aa, as development proceeds the isozymes a/3 and /3/3 appear in increasing quantities. I n adult liver ADH, activity exceeds ADH, activity. In lung, kidney and the gastro-intestinal tract the total alcohol dehydrogenase activity is very much less than in liver, and the contributions made by the different loci to the total activity show striking differences. I n lung, polypeptides determined by ADH, appear to predominate both in foetal life and in the adult. I n kidney y polypeptides determined by ADH, predominate throughout foetal life but diminish after birth, and in the adult the ADH activity that can be detected appears to be mainly derived from ADH,. I n the gastro-intestinal tract y polypeptides determined by ADH, are found as in the kidney to predominate throughout foetal life. But because of lack of suitable material the situation in adult gastro-intestinal tract was not established in our earlier work. The findings reported in the present paper are concerned with two aspects of the problem. The first concerns the ADH isozymes in the adult gastro-intestinal tract. I n our previous studies we had attempted to examine this question using material from the intestine obtained at autopsy. However, sufficiently clear and consistent isozyme patterns were not obtained. We have now found, however, that adult stomach samples from autopsy give clearly defined isozyme patterns and these correspond to those previously observed in foetal kidney and foetal intestine. Thus it appears that most of the ADH activity in adult stomach is derived from the ADH, locus. The second topic we consider here concerns certain isozymes which had previously been observed in adult liver, but which at that time could not be easily accounted for in terms of the three-locus hypothesis. These isozymes occur in addition to the aa, a/3 and /3/3 isozymes of liver, and it had been noted that they show marked variations from individual to individual in their

Parental exposure to x-irradiation and Down's syndrome.

Abstract: The total dose of medical x irradiation ever received by 465 parents of children with Down's syndrome was compared with the corresponding dose for 465 parents of children with other severe congenital handicaps, matched for time of birth and maternal age. The mothers of those with Down's syndrome had had more total x rays, both in number and dose, before the conception, although overall the difference did not reach a significant level. However, mothers of the cases had received significantly more x rays ten years or more before the conception of the cases. No significant difference was found between the histories of the fathers of the cases and the controls. The practical and theoretical implications of the findings are discussed. (auth)

Parental age effects on the occurrence of new mutations for the Marfan syndrome

Abstract: An elevated paternal age is thought to be a significant factor in the occurrence of new mutations of a number of dominantly inherited disorders. This elevated paternal age has been demonstrated for presumed mutations for the Marfan syndrome (Lynas, 1958), Apert’s acrocephalosyndactyly (Blank, 1960), achondroplastic dwarfism (Penrose, 1957; Murdoch et al. 1970) and fibrodysplasia ossificans progressiva (Tunte, Becker & Von Knorre, 1967). Lynas (1958) in her study of 31 patients with the Marfan syndrome in Northern Ireland found seven sporadic cases. She presented evidence that the mean age of the fathers of these affected children was significantly elevated. This study confirms the elevated paternal age on the basis of 23 additional new mutations for the Marfan syndrome.

Incidence and mutation rates of structural rearrangements of the autosomes in man

Abstract: Several authors have estimated germ-cell mutation rates for interchanges of the Robertsonian type associated with Down’s syndrome (Polani et al. 1963; Kikuchi et al. 1969; Penrose, 1970). In addition, a number of published surveys of constitutional chromosome aberrations in the newborn provide information on the proportion of rearrangements which appear to be due to mutational events (Sergovich et al. 1969; Gerald & Walzer, 1970; Lubs & Ruddle, 1970; Ratcliffe et aZ. 1970). However, these latter data are based on small numbers of rearrangements. In the present report we have attempted to estimate, firstly, the incidence of constitutional structural rearrangements detectable in somatic cells, and secondly, the germ-cell mutation rates for such rearrangements in man. Our estimates are based on the data which we have accumulated in the course of a variety of cytogenetic studies over the past ten years.

The genetic structure of a tribal population, the Yanomama Indians: II. Eleven blood-group systems and the ABH-Le secretor traits*

Abstract: This paper will describe the findings with respect to 13 antigen systems of erythrocytes and saliva in 2516 Yanomama Indians living in villages located in Brazil and Venezuela. Since a principal focus of this investigation is the origin and extent of the genetic microdifferentiation encountered in a relatively undisturbed tribe, the results will be presented by village. The Indians reported on here were drawn from a total of 46 villages, the exact location of which is shown in Ward (1972). However, there were several instances in which the number of persons sampled from a village was obviously too small to reflect gene frequencies adequately. Arbitrarily, the findings in all villages where the number sampled was less than 30 have been pooled into a 'miscellaneous ' sample totalling 100 individuals. The villages contributing to that miscellaneous sample are 03 V, Y, Z, 08 G, H, K, M, P, Z. Results will be presented, then, in terms of 37 separate villages plus one 'miscellaneous ' sample ; the villages contributing to the miscellaneous sample are well distributed throughout the Yanomama range. A preliminary note has been published on the gene (but not phenotype) frequencies of the first 667 individuals (10 villages) typed (Arends et al. 1967). The individuals reported therein have been included in this report for the sake of completeness of the presentation. Minor differences between the village numbers given in the earlier publication and in this paper result from the sampling of additional individuals in the meantime or, in the case of one village (03 J), the elimination from the sample of a group of visitors (see Arends et al. 1967) whose home village was later sampled.

The genetic structure of a tribal population, the Yanomama Indians V. Comparisons of a series of genetic networks*,†

Abstract: SUMMARY The model of Cavalli-Sforza and Edwards was used to investigate the gentic relationships of thirty-seven Yanomama villages. Using gene frequency data from eleven genetic systems (MNS, P, Rh, Duffy, Kidd, Diego, Lewis, haptoglobin, Ge, PGM, and acid phosphatase), three hierarchical levels of analysis were carried out. The first level involved in the construction of a gentic network, based on genetic distance between villages, for each of three historically defined clusters of villages. Upon comparing the results with ethnohistory there was shown to be a good agreement between the historical development of a cluster and its genetic network. At the second level of analysis a genetic network was constructed in similar fashion for nineteen villages of the Western Yanomama subgroup, including the three village clusters previously analysed. At this level the integrity of the village clusters was largely maintaine, exceptions being due to specific socio-political events that resulted in changes of the composition of the village gene pool. The highest level resulted in the construction of a network for all thirty-seven villages which showed three of the five geographically defined tribal subgroups as distinct entities. The result of these analyses indicate that the model of Cavalli-Sforza and Edwards can under certain circimstances be used when the requirements of the midel arenot met, and furthermore that the rate of divergence of human populations may approach a steady state at the level of major tribal subgroupings.

A statistical and genetical study of diabetes. II. Heritability of liability.

Abstract: In the past several different models of inheritance have been fitted to familial data on diabetes, and a plausible fit by the model proposed has usually been obtained (e.g. Harris, 1950; Steinberg, 1959; Post, 1962; Barrai & Cann, 1965; Falconer, 1967; Simpson, 1969). In practice it may be difficult to distinguish between different modes of inheritance, unless a fairly strict Mendelian pattern obtains (Smith, 1971). This is because different models may give similar familial frequencies and similar distributions of segregation patterns among families. In this paper, the main method used in analysis is the heritability of liability model (Crittenden, 1961; Falconer, 1965). Simpson (1964) proposed a multifactorial mode of inheritance for diabetes and the liability model has been used successfully in the analysis and interpretation of familial data (Falconer, 1967; Simpson, 1969). This paper presents further independent estimates of heritability of liability to diabetes and examines several new aspects. These are (1) the effects of common environmental factors on familial frequencies (from data on the spouses of patients and on spouses of relatives), (2) the genetic correlation between ‘early-onset ’ and ‘late-onset ’ diabetes (from data on age of diagnosis in patients and in their affected relatives), (3) estimates of heritability from secondand third-degree relatives, and (4) an appraisal of factors, such as mortality, which may bias the estimates of heritability (this is presented in the Appendix). The variable onset-age and the logarithmic increase in prevalence with age introduce several complications in the genetic analysis, and so the methoda used are described in some detail. Estimation of the population prevalence was described in the first paper of this series (Falconer, Duncan & Smith 1971), where the factors affecting morbidity were examined.

The genetics of peptidase C in man

Abstract: Several distinct peptidases, which may be differentiated by their electrophoretic characteristics, their pattern of substrate specificity and their molecular size, have been demonstrated in human cells (Lewis & Harris, 1967, 1969a; Rapley, Lewis & Harris, 1971). They are referred t o as peptidases A, B, C, D, E, F and S and are thought to be determined by separate gene loci. Genetically determined variants of Pep A, B and D in European, Indian and Negro populations and in Australian aborigines have been described (Lewis & Harris, 1967; Lewis, Corney & Harris, 1968; Lewis & Harris, 1969b; Blake et al. 1970). Genetic variation in Peptidase C (Pep C) has until now only been reported in a group of Babinga pygmies (Santachiara Benerecetti, 1970). She found 5 examples out of 261 random blood samples in which an additional band of Pep C activity appeared, with a lower mobility than the usual Pep C band, and two examples in which the normal band was entirely replaced by the slow band. She also found 11 examples of Pep C absence although Pep A activity remained. On the basis of this and limited family studies she postulated three autosomal alleles, Pep C1, Pep C2 and Pep CO, the product of Pep Co being undetectable electrophoretically. We present here evidence for genetic variation of Pep C in European, Indian and Negro populations, and discuss the relationship of the variants seen with those described by Benerecetti.

A new variant of the placental acid phosphatases: its implications regarding their subunit structures and genetical determination.

Abstract: BIultiple acid phosphatase isozymes active towards the substrate sodium a-naphthyl phosphate have been described in human tissue extracts by several groups of investigators (e.g. Lundin & Allison, 1966a, b ; Beckman & Beckman, 1967; Rozenszajn, Epstein & Shoham, 1968; Beckman et al. (1968); Smith & Whitby, 1968; Beckman, Beckman & Tarnvik (1970); Li, Yam & Lam 1970). Beckman and colleagues reported a rare electrophoretic variant in placenta affecting two of the three main acid phosphatase isozymes of this tissue. This was interpreted as the heterozygous expression of a rare gene determining a polypeptide subunit found in both isozymes. Family studies were done using leucocytes and the inheritance of this variant pattern was confirmed. In the present paper we report a new variant of placental acid phosphatase which also affects two of the main isozymes but only one of these corresponds to those affected in the previously reported variant. The results suggest that a different gene locus is involved, and provide further information as to the subunit structure of the isoenzymes. We also report studies on the molecular size, thermostability, electrophoretic changes on storage and other properties of these acid phosphatases.

Parental X-irradiation and chromosome constitution in their spontaneously aborted foetuses

Abstract: The total dose of x irradiation received before conception by 845 mothers having spontaneous abortions was compared with that received by mothers of livebirths matched for age and time of conception. The mothers of the abortions had had more radiation than their controls. This was true particularly of the mothers of fetuses of abnormal chromosome constitution, that comprise about a quarter of all known constitution. The mothers of these had had significantly more radiation than those of abortions of normal chromosome constitution and significantly more than the controls. It is concluded that maternal irradiation before and during the reproductive period increases the risk of future conceptions of abnormal chromosome constitution, but it should be stressed that most of these are not viable and are lost early in pregnancy. (auth)

Fisher's Malthusian parameter and reproductive value.

Abstract: SUMMARY An explanation is given of Fisher's ‘Malthusian parameter’m (= Lotka's ‘rate of increase’) and ‘reproductive value’v. It is pointed out that there is a flaw in fisher's mathemathics due to his neglect of changes in population charactersitcs under natural selection, with the result that m equals the logarithmic rate of change of the total reproductive value of a population. A modified definition is given that does have this property. however, for practical uses in population genetic it may be better to follow Fisher's original definition despite the flaw in them.

The genetic structure of a tribal population, the Yanomama Indians. IV. Eleven erythrocyte enzymes and summary of protein variants.

Abstract: In this paper, the fourth in a series on the genetic structure of the Yanomama Indians of southern Venezuela and northern Brazil, we report the results of electrophoretic typing for eleven erythrocytic enzymes in up to 2352 individuals per system. Most of the Indians lived in one or the other of 37 villages, each containing more than 30 sampled individuals. The location of the villages and a description of the techniques of blood collection and transport are given in Gershowitz et al. (1972) and Ward (1972). A summary of aome of the enzyme types for some of the individuals in the first ten villages has been previously prepared (Arends et al. 1967). We have also included in the current paper a comparison of these findings and the data of a previous paper (Weitkamp et al. 1972) with the results of similar studies on the Makiritare, northern neighbours of the Yanomama (Arends et aZ. 1970; Weitkamp & Neel, 1970). The findings in both tribes will then be contrasted with some results in Caucasian populations.

'Secondary' isoenzymes derived from the three PGM loci.

Abstract: SUMMARY 1. The isozymes derived from the human phosphoglucomutases - PGM1, PGM2, PGM3 have been examined in three tissues (lymphocytoid cells, placentae and red blood cells) in which the average age of the constituent proteins may be expected to differ. The appearance of one or more more negatively charged isozymes would appear to be correlated with increasing overall protein age. It is suggested that these are ‘secondry’ isozymes formed in vivo from the least negatively chared form which presumed to be the primary post translational product of the particular gene. 2. Changes in the PGM3, isozyme pattern have been observed on storage of the placental extracts. Both the primary and the secondary in vivo isozymes were similarly affected. The storage effects observed are possibly due to reaction with red cell oxidized glutathione contaminating the extract. They may lead to confusion in typing unless controlled. Similar changes were not observed with the PGM1, and PGM2, isozymes. 3. The effects of a number of thiol reagents on the three PGMs have been examined and various changes in isozyme pattern have been produced artificially. Both the primary and the secondary in vivo isozymes derived from each allele were similarly affected by any particular treatment. PGM3, isozymes were more reactive with thiol reagents than PGM1, or PGM2, isozymes. These findings suggest that the primary and secondary isozymes derived from each of the three PGM loci each contain at least one reactive sulphydryl group. However, the in vivo changes by which secondary isozymes are generated do not appear to be due to such thiol effects.

The effect of zygosity on the birth weight of twins

Abstract: SUMMARY Birth weight has been analysed in a series of 528 unselected, newborn twins pairs of known zygosity, in relation to sex, placentation, duration of gestation, maternal age and parity. Monozygotic twins weigh less than dizygotic twins, even when the named variables are allowed for. Possible reasons for this are discussed.

Note on the estimation of parental age effects.

Abstract: As in the paper by Murdoch et al. (1972), we denote the age of the father of an affected case by f, the age of the mother by m, and the birth order by b. Suppose that in the ‘general population’ a randomly chosen birth has probability pmjb of occurring when the mother’s age is m, the father’s age is f, and the birth order is b . (Strictly speaking we should speak of a probability density as regards f and m, since these are continuous variables. The reader who wishes to be strictly accurate in this respect can easily adjust the notation, where necessary replacing sums by integrals in what follows.) Suppose that for a birth under these conditions there is a small probability h m f b that the child is affected. Then the affected children will have the distribution

Distribution of genetic variants of erythrocyte phosphoglycerate kinase (PGK) and phosphohexose isomerase (PHI) among some population groups in south-east Asia and Oceania

Abstract: SUMMARY More than 4000 blood samples from populations in Japan, Micronesia, Singapore, West Irian, New Guinea and Australia have ben typed for phosphoglycerate kinase (PGK) and phosphohexose isomerase (PHI) Normal PGK-1 patterns were observed in all populations except in Micronesia, parts of West Irian and the Western and Eastern Highlands of New Guinea. In Micronesia both PGK-2 and PGK2-1 patterns were observed and the gene frequency of pgk2 was 0.07. In West Irian and the Highlands of New Guinea PGK-4 and PGK 4-1 patterns were observed and the highest pgk4 frequency was 0.051 among males in the Western Highlands. Only nine individuals were detected with PHI variant patterns. One PHI 2-1 was found in a Chinese and two PHI 3-1 persons were observed among Malays in Singapore, four PHI 5-1 in the Western Highlands of New Guinesa and one PHI 5-1 in a Japanese: one PHI 4-1 was found among Aborigines in Northern Australia.

Isochromosome for the short arm of X, a human 46, XXpi syndrome.

Abstract: SUMMARY Cytogeetical and clinical findings in a 17 year-old female with te karyotype 46, XXpi are presented. The patient was 159 cm tall and had never menstruated. The gonads were not palpable and secondary sex characteristics were poorly developed. She had no somatic sgns of Turner's syndrome apart from a renal anomaly. The abnormal X chromosome could be identified as an Xpi by its characteristic fluorescence patterns and Giemsa staining properties after the ASG procedure. Autoradiography showed it to be the latest-labelling chromosome in nearly all cells. Sex chromatin bodies were normal in number and decreased in size (79% of normal). These findings, taken with the incomplete data from two presumptive XXpi cases reported by others, indicate that the karotype 46, XXpi produces a clinical picture distinguishable from Turner's syndrome. The proposita and her father were Xg(a+), and her mother Xg(a−), indicating paternal derivation of the normal X chromosome. Hence the Xpi appears to be of maternal origin. Other interpretations are possible. The findings lend added support to the hupothesis that genes controlling gonodal development are carried in both Xp and Xq, whereas those affecting stature are in Xp but probably not in Xq. It is proposed that at isochromosome formation Xqi is far more likely to be produced than Xpi. This may be because breakage preferentially occcurs at the short-arm end of the centromere region or in the short arm itself, as indicated by the existence of presumptive dicentric Xqi chromosomes.

A search for electrophoretic variants of human adenine phosphoribosyl transferase.

Abstract: Adenine phosphoribosyl transferase (APRT) catalyses the reaction of adenine with 5-pliosphoribosyl-pyrophosphate to give adenosine-5’-monophosphate and pyrophosphate. It is widely distributed in human tissues. There have been several reports of inherited variation of APRT in man. Kelley et nl. (1968) described a family in which four individuals showed a partial deficiency of the enzyme activity in red cells. The trait appeared to be inherited as an autosomal heterozygous character, and it did not appear to be associated with any obvious abnormality in uric acid production. Henderson et al. ( 1968) reported individual differences in therniostability of red cell APRT, which appeared to represent a common polymorphism involving two alleles, one produciiig a relatively more unstable form of the enzyme than the other. Bakay & Nyhan (1971) described the electrophoresis of APRT in acrylamide gels and reported that usually the enzyme migrated as a single symmetrical zone of activity, and in one individual a faster migrating variant was observed. I n the present paper we describe a method for the electrophoresis of APRT in starch gel, and report the results of a search for APRT variants in Caucasian and Negro populations using this technique. We also report briefly some related studies on the usual form of the enzyme and on certain variants.

Observations on the concept of neighbourhood knowledge and the distribution of marriage distances.

Abstract: Migration studies on many different species have shown that mating outside a central homebase decreases in frequency with increasing distance. In addition, they have confirmed that the distribution of mating frequency over distance tends t o be leptokurtic (e.g. Bateman, 1950; Sutter & Tran-Ngoc-Toan, 1957 j. The purpose of this paper is to present information from an historical village population that bears on the problem of migration, and to compare the results with a similar study toward the end of substantiating an explanatory model. A recent study by Boyce, Kuchemann & Harrison (1967) attempts to develop a model for the observation that the frequency of marriage decreases exponentially with distance. Their model is based on the concept of neighbourhood knowledge. Neighbourhood knowledge is defined as the frequency with which surrounding populations are visited by members of a home village. The frequency of visits, in turn, is limited by certain general characteristics of human behaviour and ability to travel. The model, stated verbally and in equations, suggests that ‘neighbourhood knowledge, in conjunction with the size of neighbouring populations, determines the frequency with which mates are chosen from these populations and thus the distribution of marriage distances’ (p. 235). Further, the relationship between mating frequency and distance is, as stated, an exponential one. Boyce et d.’s empirical test of this exponential relationship (1967), made on the parish of Charlton-on-Otmoor, Oxfordshire, England (1861 census), provided the expected distribution. On the basis of twenty-three surrounding communities and their respective contributions of marriages to Charlton, a geometric curve was fitted that indicates agreement with the assumed relationship (using the family of curves y = AXpB, y = 4 . 7 5 X I 9 .