Original Paper
Hum. Hered. 1992;42:242-252
The Structure of the Polar Eskimo Genealogy A.W.F.
Edwards
Department of Community Medicine, University of Cambridge, UK Key Words Eskimo Genealogy
Abstract The structure of the genealogy of the Polar Eskimos from the Thule District of North Greenland is studied by a variety of computational and graphical means, some of them novel. It is shown that although the level of inbreeding in the population is low, the genealogy is intricately connected, as if conforming to the requirement that spouses are as unrelated as is possible in a small population. Dr. A.W.F. Edwards, Gonville and Caius College, University of Cambridge, Cambridge CB2 ITA (UK)
Introduction One of the most interesting of all human genealogies, that of the Polar Eskimos from the Thule District of North Geenland, ‘the northernmost human native population on Earth’, was published in 1978 by Gilberg et al. [1], having been the subject of investigation since 1928. The following summary (and the above quotation) are abstracted from their introduction to the genealogy. The Polar Eskimos came into contact with white man for the first time in 1818, and since 1909 that contact has been continuous. In 1928 Mogens Holm was appointed the first permanent physician to work among them, and he started to assemble information about their genealogy, continuing the work until he left in 1937. In 1938-1939 Aage Gilberg was the resident physician, and he and his wife Lisbet extended and up-dated the genealogy, and by continued contact with individuals after they left, they ensured that the genealogy was always kept up to date. They visited the area again in 1963, this time accompanied by their son Rolf Gilberg, who paid another visit in 1969. The exceptional devotion of the Gilberg family to the Eskimo population, and the care with which they have assembled information over a period of thirty years, has resulted in a genealogy of great interest, probably the most accurate record of the genetic structure of a population of hunters from anywhere in the world. In addition to the genealogy, genetic and anthropological information is available for some 300 members of the 1963 population, and is also reported in Gilberg et al. [1], where further references are given. The history and demography of the population have been fully described by Gilberg [2]. From 1892 to 1947 the size of the popula-
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tion remained between 200 and 300. It reached 400 in 1959, 500 in 1965, and 600 in 1969. The first estimate of population size was 140 in 1854, but naturally the early estimates may be unreliable. Moreover, they will not include the unrecorded ancestors of late arrivals in the population, though these must have existed elsewhere, which explains why the population of
genetical interest described in this paper will be larger than the demographic estimates for the earlier years. Apart from the attention paid to the Polar Eskimo population by Mogens Holm and the Gilbergs, its importance for population genetics research was also recognised by the World Health Organisation Scientific Group which met in Geneva in 1962 [3], and by its successor which met in 1967 [4]. The Genealogy Gilberg et al. [1] coded all the individuals in the genealogy by an idiosyncratic method whose details need not concern us since in the present study the code name for an individual can be regarded as an arbitrary identifier. A rough outline of the code will, however, serve to explain its otherwise mysterious features. Typical individuals are ABC and ‘A123’. The first letter, here A, indicates a particular child in a sibship, the subsequent characters being the code for the sibship, here BC or 123. Three digits are used for all sibships from the late 1920s on, and two letters for all earlier sibships. Should it be necessary to refer to a sibship rather than an individual we will make this clear by prefixing an asterisk thus: *BC or *123. The first child is coded A and further children B, C, D,... There are refinements to cope with children of unknown order, non-Polar-Eskimo families, and so forth, but, as indicated above, it is unnecessary to dwell on these. In any case, the computer analysis was undertaken using a number for each individual. The genealogy as published has been augmented in three ways for the purpose of the present study. First, births occuring in 1974 and 1975 have been added, together with some new items of information from earlier years [L. Gilberg, pers. commun.]. Secondly, since the brother and sister VYU and UYU occur in the published genealogy (as the husband of UZW and the wife of UYC) yet there is no family coded *YU to which they belong, parents UQZ and URA have been created for them, and are assumed to be individuals not occurring elsewhere in the genealogy. Thirdly, when only one parent of a child is recorded, the other parent has been given a code, it being assumed that he or she does not occur elsewhere in the genealogy. A consequence of this assumption is that the degree of inter-related-ness in the genealogy may be underestimated owing to one and the same individual being given two or more codes. The numbers involved are small, however, and the general picture will not be significantly affected. The reason for adding a ‘missing’ parent in this way is to facilitate the analysis, for then every member of the population either has no parents, and is defined as a founder, or has two. Thus augmented the genealogy has 1,614 members of whom 225 are founders. In time it stretches from a birth in about 1805 (UIR) to one in 1975. In case of any discrepancies it should be noted that the information actually used in the present study was abstracted from the original records in 1977 and has not been taken from the published genealogy. Previous Knowledge of the Structure In his study of the demography of the population, Gilberg [2] did not attempt any genealogical analysis, but Gilberg et al. [1] calcu243 Table 1. Individuals belonging to small groups which are separated from the main genealogy Number in group more detailed investigation of the structure of the genealogy is to examine this further.
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11
UKK, UKM, and their children UKJ, VKJ, WKJ, XKJ, and YKJ; UKJ’s spouse UKP and their children UKL, VKL, and WKL. UQT, UQU, and their children UIE and VIE; UIE’s spouse UKA and their child UZJ. UJC, UJD, and their children UHZ, VHZ, and WHZ. 3 3
UJE, UJF, and their child UIZ. UKC, UMO, and their child UKB. 1 Five individuals: UGP, UIJ, UIW, and UJT. lated an ‘ancestor index’ for each individual which ‘indicates among known ancestors the kind and degree of mixture with non-Polar Eskimos for the children in each nuclear family’. They also calculated inbreeding coefficients for all the inbred individuals, but we may note their omission of two families: *233 and *WK. In the case of *233 our genealogy contains unpublished information, namely that the father of A233 was C090, whilst *WK was omitted by them since its ancestry is wholly from West Greenland (their published list being limited to Polar Eskimo matings). The largest inbreeding coefficient encountered is 1/8 for family *222, arising from the marriage of ZCN to his niece Y080. There are only 5 first-cousin marriages, and in one of those the connection is only via half-siblings. The level of inbreeding seems remarkably low given the small size of the population, and one of the aims of a Contributions of the Founders In order to examine the structure in greater detail the genealogy was stored in a computer. Each individual was listed together with the father and mother. Such a list completely defines a genealogy, but it is convenient if it is ordered so that each individual is preceded (though not necessarily immediately) by the parents, with the founders first. After ordering in this way, the individuals were assigned the nubers 1-1,614 for working purposes, but in reporting the results of our analyses we adhere to the original codes. In the reordered list the first 225 individuals are the founders. On investigating the connectedness of the genealogy we find that it falls into 11 distinct parts, the largest of which contains 1,581 individuals. Further groups contain 11,6,5,3 and 3 members, and there are 5 individuals each unconnected with any other part of the genealogy (in point of fact these 5 all made marriages, but had no children, and it is of course the biological, rather than the legal or social, genealogy that is under study). The members of the small groups are listed in table 1. One of the first computations to be undertaken was an examination of loops in the graph of the genealogy. For example, an uncle-niece marriage gives rise to a loop consisting of 5 parent-offspring links. The marriage of ZCN to Y080 turns out to be the only loop of order 5. There are 6 loops of order 6, one formed by 2 brothers sharing a wife and the other 5 by the first-cousin marriages. If one defines the loop order associated with each individual as the order of the shortest loop of which he or she is a member then the distribution of loop orders can be investigated. The commonest orders turn out to be 8, 9 and 10,
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244 Edwards Eskimo Genealogy
NUMBER OF FOUNDERS CONTRIBUTING FOUNDER! J J 1930 POPULATION SIZE O
lOO
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lllllllllllll Hill! III 111 II 2DO 300 400 SUO 600 TOO nun mi iiiiiiii n 1111 πimi i urn i ni i mil i i m i I i mi limn i i iiiiiiiiiiin i i inn i in SPECTRUM OF CONTRIBUTORS TO 1973 Fig. 1. Genetic contributions of the founders in absolute terms (see text for explanation). indicating a graph with little short-range but substantial medium-range connectedness. Individuals transmit half their autosomal genes to each child, so that the genetic contribution of each founder to each other member of the genealogy may be computed, and thus his or her total contribution to the population alive at any one time found [5]. We may describe this total as being in terms of ‘people-equivalents’, because the numbers do not correspond to actual people but to an amount of genetic material equivalent to that carried by the stated number of people (not usually a whole number). Figure 1 displays these contributions in the form of a ‘Seashore’ chart. The 225 founders are arranged from left to right at the top (year 1819) in reverse order of their contributing to the genealogy. It is assumed, as a working fiction, that every founder was alive in 1819 (otherwise the later founders would have had to have had ancestors invented for them). The genetic contribution of each founder to the population alive in each subsequent year up to 1973 is then calculated and displayed. To understand the display, attention should initially be focussed on the ‘spectrum of contributors to 1973’ at the bottom, which is simply the line of the diagram for 1973 enlarged for greater clarity. Each gap between two spectral lines represents the contribution, in people-equivalents, of each founder (in the order described above) to the 1973 population. The lower scale gives the numbers, the total being, of course, the population size. Under the spectrum a mark is placed for every tenth founder. The results for all the other years are displayed in exactly the same way, but as a row of dots rather than as a spectrum. Consequently, each founder’s contribution over the years is represented by a river of white separated from its neighbour by a line of dots. On the right of the chart is a line recording the number of founders still contributing to the population in each year (upper scale); there 245 1850 1900 1950-jí ~¦ 1 1 1 1 1 1 1 1 1 1 .5 .6 .7 .8 .9 1973 “1 Γ O .1 .2 .3 .4 ■illinium ii ill hi iiiiii n i iiiiiiini ii¦iiiiii ιι i iii iii ill! nun i i ii i mill i i iii i i 11 iii i urn 11 i i minium i i mi ■ :ι SPECTRUH OF CONTRIBUTORS IN 1973 Fig. 2. Relative genetic contributions of the founders (see text for explanation). were 179 in 1973. At the resolution available in figure 1 much of the fine detail is invisible, and in particular the individual founders cannot be resolved into the pattern of vertical lines
which should represent them on the left of the diagram. It is only when the contribution of a founder becomes substantial that his genetic ‘river’ becomes obvious. On the computer screen, however, not only can parts of the diagram be expanded in a window, but founders, or groups of founders, can be allocated different colours. The spectrum shows that the earlier founders (the right-most) contributed more to the 1973 population than the later ones, as one would expect in an expanding population. The two biggest contributors are UWT with 26.375 ‘people-equivalents’ and UEO with 20.1563. In the spectrum UWT lies at about point 160 on the bottom horizontal scale and UEO at about 430. Their associated genetic rivers show that the number of descendants of UWT has grown rapidly in the more recent period. These founders will be mentioned again below. For some purposes it is more informative to examine the relative rather than the absolute contributions of the founders. Figure 2 gives these in the form of an ‘Aurora’ chart in a manner comparable to figure 1; it is simply the same figure with the line for each year stretched so as to fill the space, so that the proportionate contributions can be seen. The final 1973 spectrum is, of course, the same, and the genetic rivers of UWT and UEO are even more marked. The ebb and flow of genetic contributions down the years is clearly depicted. The horizontal ‘fault lines’ in the strata are very striking, and are seen, by comparison with figure 1, to correspond to the periods of serious population decline. Thus in 1901-1902 there was an epidemic, possibly of typhoid,
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246 Edwards Eskimo Genealogy which resulted in 36 deaths [2]. The fault lines are a reflection of the fact that deaths in epidemics tend to be amongst related individuals, so that the proportionate genetic contributions of ancestors are disturbed. These Seashore and Aurora charts were first shown at the 14th International Biometric Conference, Namur, in July 1988 [6]. As a general indication of the importance of each founder, his or her contribution to the population as a whole can be calculated, the genetic contribution to each descendant being counted just once. The contributions of the 10 most important founders calculated in this way are given in table 2. The total number of units to be accounted for is 1,614 (the total population size) less 225 (the founders themselves), giving 1,389. In the fourth column of table 2 the cumulative contribution is given, expressed as a percentage of 1,389. It will be seen that UEO has contributed the most with over 40 units, nearly 3% of the total, and that the 10 main contributors account for over 20% of the total. All 10 are Polar Eskimos except UWT, a West Greenland woman born in 1893 who had 9 children by a Polar Eskimo and 1 by a West Greenlander. She had 71 grandchildren and (up to 1975) 67 great-grandchildren. 50% of the total autosomal gene pool was contributed by 33 founders. Amongst non-founders a similar calculation of contributions to the overall gene pool can be made, though since such contributions may not be mutually exclusive it is meaningless to calculate cumulative contributions. UBU contributed most with 32.5 units, second only to the founder UEO (table 2). Next come UCW and VBK, a marriage-pair, each contributing 28.5 units.
It is also of interest to record the marriages which contributed most. UCW-VBK contributed 2x28.5 = 57 units through sibship *BI, the marriage UCL-UWT 55.75 units through sibship *063, and the marriage UBU-UFR Table 2. Contributions of the 10 most important founders to the overall gene pool
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Code Number Contributio Cumulati descendan peoplecontriequivalents bution, UEO 394 40.1563 2.89 UW 148 31.8750 5.19 UF 411 30.4688 7.38 UFR 281 27.2500 9.34 UEK 331 26.3750 11.24 UEL 331 26.3750 13.14 UFD 416 25.7188 14.99 UFE 416 25.7188 16.84 UIB 349 24.5469 18.61 UJS 349 24.5469 20.38 54.5 units through sibship *CH. Next in order come the marriages UEK-UEL, UFD-UFE, and UIB-UJS (see the last 6 entries of table 2). The founder with the greatest number of descendants was UHW (born 1820) with 452; the 3 others with more than 400 are given in table 2. The greatest number of generations recorded in the genealogy is 8,12 of the founders possessing descendants running through 7 further generations, though it should be noted that inbred descendants might be fewer than 7 generations away by a different route through the genealogy. A significant proportion of Eskimos married more than once (that is, had children by more than 1 partner). Of the 721 members of the genealogy who had children, 563 married only once, but 129 married twice, 21 three times, and 8 four times. These 8 are UFZ, UHW, VAZ, C101, B128, E119, D123, and B115, and they are all women except B128, a reflection partly of our assumption that husbands recorded as ‘unknown’ are distinct. As a consequence of these multiple marriages many people are related to each other by marriage, an important complicating factor in attempt247 A193 A305 A273 A307 A265 A244 A199 A247 A282 A264 A267 Fig. 3.11 marriages amongst 13 individuals, with only the first child of each marriage shown. ing to draw the genealogy. Figure 3 shows a particularly good example, in which 6 men and 7 woman (including 3 brother-sister pairs) are involved in 11 marriages. Drawing the Genealogy A reduced version of the genealogy was drawn in conventional format using the computer program originally developed by M.-F. Landre, M.-T. Valat and P. Jutier at the Centre de Calcul et de Statistique des Facultés de Medicine de Paris, and implemented in Cambridge by P. Stewart. However, not only is the drawing too large to reproduce in a journal ‚ it is also so long, and its lines so difficult to follow, that it is of doubtful value. In order to try to achieve a more informative representation of the genealogy, new techniques have been developed, but even these have had only limited success, reflecting, as it turns out, the complex structure of this particular genealogy. The aim of the new techniques has been to display the principal groupings of closely related individuals, rather than to show individual relationships as in the conventional for-
mat. With 1,614 individuals not only is the latter task essentially impossible but also unnecessary, for it is easy to select all the near relatives of any chosen individual and display their mutual relationships. Moreover, many of the questions which a complete conventional drawing could answer are better answered through direct interrogation of the stored genealogy. What is needed, rather, is an overall view. Since the links in a genealogy are all parent-offspring links the structure may be described most simply as a directed graph. We assume, without loss of generality, that it is a connected graph, and it will also have some special features such as the absence of loops (no person is his or her own ancestor) and a limitation to two incident edges at each node (no person has more than two parents). In an attempt to achieve a satisfactory spread of nodes in a drawing of such a graph, Edwards [7, 8] introduced the idea of geodesic coordinates. If the parentoffspring lines of the graph are each taken to be of unit length and (for this purpose) undirected, then the length of the shortest path between two nodes is known as the geodesic distance between the nodes.
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■ Edwards Eskimo Genealogy With respect to any node, therefore, the other nodes have coordinates, namely their geodesic distances from the chosen node. Any two nodes may thus be used to establish a twodimensional coordinate system consisting of a grid of squares with unit sides. Such a representation has a number of advantageous features, described in Edwards [7, 8], in particular the feature that every individual lies at most one unit in either or both directions from both parents, and is thus a graphical neighbour. The choice of the two reference nodes is obviously critical to the realisation of a satisfactory representation, and these were initially selected on the basis of minimising the maximum occupancy of the grid points. However, in spite of many developments of the basic idea, including its extension to three dimensions, it proved impossible to achieve any representation of the Polar Eskimo genealogy other than as a tangled mass of lines. One such graph was presented as a poster at the 11th International Biometric Conference, Toulouse, in September 1982 [9], but, like the genealogy in conventional format, it is too large to reproduce in a journal. It demonstrated all too clearly, however, the fundamental nature of this particular genealogy: intricate, highly connected, and highly resistant to being split into component parts. More recently, other attempts to draw the genealogy of the related marriage-node graph have only served to confirm its tangled nature [A. Thomas, N. Shee-han, pers. commun.; see also Thomas, 10]. In the light of these difficulties, a final attempt has been made to secure a representation which would at least reveal some of the grosser features of the genealogy, by combining the most promising of the techniques mentioned above with the notion of a ‘waist’ or ‘cleavage’ in a graph, the idea being to find a division of the genealogy into two parts which are as weakly connected as possible. A cleavage in a connected graph is defined as a cutset, such that the transfer of any point between subgraphs increases the number of elements in the cutset, which may be called its order. A program CLEAVE was written, which starts with a random division of the graph into two subgraphs and moves individuals adjacent to the cutset whose transfer to the other subgraph reduces the order of the cutset. Individuals whose transfer makes no difference are randomly allocated. When no further
reduction seems possible the program is continued for some time to give this random allocation a chance to lead to an even better division which might result from the simultaneous random transfer of several individuals. The final division achieved is, by definition, a cleavage. It will be noticed that this final stage is analogous to the technique which has come to be known as ‘simulated annealing’ [10]. CLEAVE is written in PASCAL, and the author will be happy to answer enquiries about its status and availability. Applied to the Polar Eskimo genealogy the best cutset which divided it into two parts comparable in size had order 188, the division being into 775 and 806 individuals. Of all the cleavages found by CLEAVE, this is the one which minimised the ratio (order of the cutset): (size of the smaller group). Many cleavages were also found with orders around 150, but they divided the graph into parts which were considered too disparate in size (the smaller part typically being about one quarter of the whole). By an obvious extension of the idea of geodesic coordinates, the geodesic distance between any node and any set of nodes may be defined as the shortest geodesic distance between that node and each of the nodes of the set. The geodesic coordinate of a node with re-pect to a set of nodes is given by its geodesic distance from that set. When the nodes of a graph are divided into two sets by a cleavage as described above, each node can then be given 249 ⅜ ■⅛ .A. .•V. h·^”·’· .-*■■ V ‘ > ^X ‘ ,-” ⅜. ‘ ■;■’■■-. > í⅛⅛ y ■:-■. i .- “■■■.. > C ⁄ J⅝C X j⅜⅝’ ‘■’■•■■ > ⅝v· ■”■’■■ ^*v ·:’’ J*’” > y i ⅜¾f· ■/×.-. < \ > – ■■■ i ■■■ > o ι⅜χ. . ‚x, ⅜ Λj‚/’·‚Λ. ⅛’⅞⅜ ‘ ■■■ > ■■’ ■ \JÎm⅝/í ⅛í’ ■⅛⅛/T‰I/í V ■ ι
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Fig. 4. Connectedness of the genealogy. Vertical coordinate: generation; horizontal coordinate: geodesic distance (see text). The size of each rectangle is proportional to the number of individuals. a coordinate, being its geodesic distance from the set to which it does not belong, the distances being regarded as positive for the nodes of one of the sets and negative for the others. More colloquially, the coordinate of each individual in a subgraph is the shortest distance to the nearest individual in the other subgraph. The members of each subgraph are thus strung out along a line, and the second of the two lines is reversed and placed end to end with the first. For a two-dimensional representation we need a second coordinate, and on this occasion we use the conventional one of generation number [10], which may be uniquely defined as the rank of each node in the directed graph. The rank of a node is computed by allocating rank 1 to the nodes corresponding to the founders, and then allocating to each child a rank equal to one plus the higher of the parent’s ranks. The founders’ ranks are then themselves modified by allocating to each a rank equal to one less that the lower of the children’s ranks, in order to ensure that founders who enter the genealogy relatively late are more appropriately placed. Further ‘closing up’ can be done of required, although this has not been thought necessary in the present application. This procedure makes allowance for the
fact that inbreeding may introduce ambiguities into the generation number as straightforwardly defined. The result of this procedure is given in figure 4. The area of each rectangle is proportional to the number of individuals at that grid point, and the density of each line is a rough indication of the number of superimposed parent-offspring links it represents. An important property of this representation is that all the ancestors of an individual are contained in the ascending cone and all the descendants within the descending cone, because parent
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250 Edwards Eskimo Genealogy and offspring can be no further apart than in adjacent columns and must belong to different generations. The longest parent-offspring lines are seen to straddle three generations, reflecting a maximum difference of two generations between spouses. Conclusions It is clear from the analysis of the genealogy reported in this paper, and the efforts to draw it described in the preceding section, that the Polar Eskimo genealogy combines, to a possibly unique extent, extreme interconnected-ness and limited inbreeding, apparently conforming to the requirement that within the confines of a very small population, spouses should be chosen to be as unrelated as possible. The efforts to draw the genealogy have amply confirmed the levels of interconnected-ness revealed by other methods, but otherwise have served only to demonstrate that there is little virtue in trying to achieve a printable genealogy when the ready availability of modern computers makes it possible for interactive graphical techniques to portray any part of the genealogy in any desired manner. The Cambridge implementation of the Paris program mentioned above, was eventually developed into the PEDIGREE/DRAW program circulated by the Southwest Foundation for Bio-medical Research, San Antonio, Tex., USA, which has many interactive features, but it is possible that some of the radically different display techniques described in this paper may prove more suitable for studying highly interconnected genealogies such as that of the Polar Eskimos. It is likely, however, that the future lies more in the direction of the numerical and graphical exploration of the stochastic properties of genealogies. The combination of Monte-Carlo simulation of gene flow through a genealogy [11-13] with diagrams of the Seashore and Aurora type (fig. 1, 2) has already proved to be a powerful visual technique, and will be the subject of a subsequent paper. Acknowledgements None of this work could have been accomplished without the generosity, encouragement, and hospitality since 1977 of Lisbet and Aage Gilberg. The provision of computer facilities by Gonville and Caius College, Cambridge, is gratefully acknowledged. A referee kindly provided an improved drawing of figure 3. References Gilberg A, Gilberg L, Gilberg R, Holm M: Polar Eskimo genealogy. Meddelelser om Grønland 1978; 203/4. Gilberg R: The Polar Eskimo population, Thule District, North Greenland. Meddelelser om Grønland 1976;203/3.
Neel JV, Barnicot NA, Kirk RL: Research in population genetics of primitive groups. WHO Tech Rep Ser 1964; No 279. Neel JV, Morton N, Walsh RJ: Research on human population genetics. WHO Tech Rep Ser 1968; No 387. McKusick VA: Genealogic and bibliographic applications of computers in human genetics; in Crow JF, Neel JV (eds): Proc 3rd Int Congr Hum Genet, Plenary Sessions and Symposia. Johns Hopkins, Baltimore, 1967, pp 483^*88. Edwards AWF: Gene-flow simulation in the Polar Eskimo genealogy. 14th Int Biometric Conf, Namur, Belgium, 1988, p 127. Edwards AWF: Parsing a genealogy. Adv Appl Probabil 1979;11:2-3. Edwards AWF: Parsing a genealogy; in Eriksson AW (ed): Population Structure and Genetic Disorders. London, Academic Press, 1980, pp 273-283. Edwards AWF: Drawing genealogies. 11th Int Biometric Conf, Toulouse, France, 1982, p 26. 10 Thomas A: Drawing pedigrees. IMA J Math Appl Med Biol 1988; 5:201-213. Edwards AWF: Simulation studies of genealogies. Heredity 1968;23: 628. Edwards AWF: in Morten NE (ed): Computer Applications in Genetics. Honolulu, University of Hawaii Press, 1969, p 81. Edwards AWF: Computers and genealogies. Biol Soc 1988;5:73-81.
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252 Edwards Eskimo Genealogy
Hum. Hered. 1992;42:242-252
The Structure of the Polar Eskimo Genealogy A.W.F.
Edwards
Department of Community Medicine, University of Cambridge, UK Key Words Eskimo Genealogy
Abstract The structure of the genealogy of the Polar Eskimos from the Thule District of North Greenland is studied by a variety of computational and graphical means, some of them novel. It is shown that although the level of inbreeding in the population is low, the genealogy is intricately connected, as if conforming to the requirement that spouses are as unrelated as is possible in a small population. Dr. A.W.F. Edwards, Gonville and Caius College, University of Cambridge, Cambridge CB2 ITA (UK)
Introduction One of the most interesting of all human genealogies, that of the Polar Eskimos from the Thule District of North Geenland, ‘the northernmost human native population on Earth’, was published in 1978 by Gilberg et al. [1], having been the subject of investigation since 1928. The following summary (and the above quotation) are abstracted from their introduction to the genealogy. The Polar Eskimos came into contact with white man for the first time in 1818, and since 1909 that contact has been continuous. In 1928 Mogens Holm was appointed the first permanent physician to work among them, and he started to assemble information about their genealogy, continuing the work until he left in 1937. In 1938-1939 Aage Gilberg was the resident physician, and he and his wife Lisbet extended and up-dated the genealogy, and by continued contact with individuals after they left, they ensured that the genealogy was always kept up to date. They visited the area again in 1963, this time accompanied by their son Rolf Gilberg, who paid another visit in 1969. The exceptional devotion of the Gilberg family to the Eskimo population, and the care with which they have assembled information over a period of thirty years, has resulted in a genealogy of great interest, probably the most accurate record of the genetic structure of a population of hunters from anywhere in the world. In addition to the genealogy, genetic and anthropological information is available for some 300 members of the 1963 population, and is also reported in Gilberg et al. [1], where further references are given. The history and demography of the population have been fully described by Gilberg [2]. From 1892 to 1947 the size of the popula-
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tion remained between 200 and 300. It reached 400 in 1959, 500 in 1965, and 600 in 1969. The first estimate of population size was 140 in 1854, but naturally the early estimates may be unreliable. Moreover, they will not include the unrecorded ancestors of late arrivals in the population, though these must have existed elsewhere, which explains why the population of
genetical interest described in this paper will be larger than the demographic estimates for the earlier years. Apart from the attention paid to the Polar Eskimo population by Mogens Holm and the Gilbergs, its importance for population genetics research was also recognised by the World Health Organisation Scientific Group which met in Geneva in 1962 [3], and by its successor which met in 1967 [4]. The Genealogy Gilberg et al. [1] coded all the individuals in the genealogy by an idiosyncratic method whose details need not concern us since in the present study the code name for an individual can be regarded as an arbitrary identifier. A rough outline of the code will, however, serve to explain its otherwise mysterious features. Typical individuals are ABC and ‘A123’. The first letter, here A, indicates a particular child in a sibship, the subsequent characters being the code for the sibship, here BC or 123. Three digits are used for all sibships from the late 1920s on, and two letters for all earlier sibships. Should it be necessary to refer to a sibship rather than an individual we will make this clear by prefixing an asterisk thus: *BC or *123. The first child is coded A and further children B, C, D,... There are refinements to cope with children of unknown order, non-Polar-Eskimo families, and so forth, but, as indicated above, it is unnecessary to dwell on these. In any case, the computer analysis was undertaken using a number for each individual. The genealogy as published has been augmented in three ways for the purpose of the present study. First, births occuring in 1974 and 1975 have been added, together with some new items of information from earlier years [L. Gilberg, pers. commun.]. Secondly, since the brother and sister VYU and UYU occur in the published genealogy (as the husband of UZW and the wife of UYC) yet there is no family coded *YU to which they belong, parents UQZ and URA have been created for them, and are assumed to be individuals not occurring elsewhere in the genealogy. Thirdly, when only one parent of a child is recorded, the other parent has been given a code, it being assumed that he or she does not occur elsewhere in the genealogy. A consequence of this assumption is that the degree of inter-related-ness in the genealogy may be underestimated owing to one and the same individual being given two or more codes. The numbers involved are small, however, and the general picture will not be significantly affected. The reason for adding a ‘missing’ parent in this way is to facilitate the analysis, for then every member of the population either has no parents, and is defined as a founder, or has two. Thus augmented the genealogy has 1,614 members of whom 225 are founders. In time it stretches from a birth in about 1805 (UIR) to one in 1975. In case of any discrepancies it should be noted that the information actually used in the present study was abstracted from the original records in 1977 and has not been taken from the published genealogy. Previous Knowledge of the Structure In his study of the demography of the population, Gilberg [2] did not attempt any genealogical analysis, but Gilberg et al. [1] calcu243 Table 1. Individuals belonging to small groups which are separated from the main genealogy Number in group more detailed investigation of the structure of the genealogy is to examine this further.
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11
UKK, UKM, and their children UKJ, VKJ, WKJ, XKJ, and YKJ; UKJ’s spouse UKP and their children UKL, VKL, and WKL. UQT, UQU, and their children UIE and VIE; UIE’s spouse UKA and their child UZJ. UJC, UJD, and their children UHZ, VHZ, and WHZ. 3 3
UJE, UJF, and their child UIZ. UKC, UMO, and their child UKB. 1 Five individuals: UGP, UIJ, UIW, and UJT. lated an ‘ancestor index’ for each individual which ‘indicates among known ancestors the kind and degree of mixture with non-Polar Eskimos for the children in each nuclear family’. They also calculated inbreeding coefficients for all the inbred individuals, but we may note their omission of two families: *233 and *WK. In the case of *233 our genealogy contains unpublished information, namely that the father of A233 was C090, whilst *WK was omitted by them since its ancestry is wholly from West Greenland (their published list being limited to Polar Eskimo matings). The largest inbreeding coefficient encountered is 1/8 for family *222, arising from the marriage of ZCN to his niece Y080. There are only 5 first-cousin marriages, and in one of those the connection is only via half-siblings. The level of inbreeding seems remarkably low given the small size of the population, and one of the aims of a Contributions of the Founders In order to examine the structure in greater detail the genealogy was stored in a computer. Each individual was listed together with the father and mother. Such a list completely defines a genealogy, but it is convenient if it is ordered so that each individual is preceded (though not necessarily immediately) by the parents, with the founders first. After ordering in this way, the individuals were assigned the nubers 1-1,614 for working purposes, but in reporting the results of our analyses we adhere to the original codes. In the reordered list the first 225 individuals are the founders. On investigating the connectedness of the genealogy we find that it falls into 11 distinct parts, the largest of which contains 1,581 individuals. Further groups contain 11,6,5,3 and 3 members, and there are 5 individuals each unconnected with any other part of the genealogy (in point of fact these 5 all made marriages, but had no children, and it is of course the biological, rather than the legal or social, genealogy that is under study). The members of the small groups are listed in table 1. One of the first computations to be undertaken was an examination of loops in the graph of the genealogy. For example, an uncle-niece marriage gives rise to a loop consisting of 5 parent-offspring links. The marriage of ZCN to Y080 turns out to be the only loop of order 5. There are 6 loops of order 6, one formed by 2 brothers sharing a wife and the other 5 by the first-cousin marriages. If one defines the loop order associated with each individual as the order of the shortest loop of which he or she is a member then the distribution of loop orders can be investigated. The commonest orders turn out to be 8, 9 and 10,
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244 Edwards Eskimo Genealogy
NUMBER OF FOUNDERS CONTRIBUTING FOUNDER! J J 1930 POPULATION SIZE O
lOO
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lllllllllllll Hill! III 111 II 2DO 300 400 SUO 600 TOO nun mi iiiiiiii n 1111 πimi i urn i ni i mil i i m i I i mi limn i i iiiiiiiiiiin i i inn i in SPECTRUM OF CONTRIBUTORS TO 1973 Fig. 1. Genetic contributions of the founders in absolute terms (see text for explanation). indicating a graph with little short-range but substantial medium-range connectedness. Individuals transmit half their autosomal genes to each child, so that the genetic contribution of each founder to each other member of the genealogy may be computed, and thus his or her total contribution to the population alive at any one time found [5]. We may describe this total as being in terms of ‘people-equivalents’, because the numbers do not correspond to actual people but to an amount of genetic material equivalent to that carried by the stated number of people (not usually a whole number). Figure 1 displays these contributions in the form of a ‘Seashore’ chart. The 225 founders are arranged from left to right at the top (year 1819) in reverse order of their contributing to the genealogy. It is assumed, as a working fiction, that every founder was alive in 1819 (otherwise the later founders would have had to have had ancestors invented for them). The genetic contribution of each founder to the population alive in each subsequent year up to 1973 is then calculated and displayed. To understand the display, attention should initially be focussed on the ‘spectrum of contributors to 1973’ at the bottom, which is simply the line of the diagram for 1973 enlarged for greater clarity. Each gap between two spectral lines represents the contribution, in people-equivalents, of each founder (in the order described above) to the 1973 population. The lower scale gives the numbers, the total being, of course, the population size. Under the spectrum a mark is placed for every tenth founder. The results for all the other years are displayed in exactly the same way, but as a row of dots rather than as a spectrum. Consequently, each founder’s contribution over the years is represented by a river of white separated from its neighbour by a line of dots. On the right of the chart is a line recording the number of founders still contributing to the population in each year (upper scale); there 245 1850 1900 1950-jí ~¦ 1 1 1 1 1 1 1 1 1 1 .5 .6 .7 .8 .9 1973 “1 Γ O .1 .2 .3 .4 ■illinium ii ill hi iiiiii n i iiiiiiini ii¦iiiiii ιι i iii iii ill! nun i i ii i mill i i iii i i 11 iii i urn 11 i i minium i i mi ■ :ι SPECTRUH OF CONTRIBUTORS IN 1973 Fig. 2. Relative genetic contributions of the founders (see text for explanation). were 179 in 1973. At the resolution available in figure 1 much of the fine detail is invisible, and in particular the individual founders cannot be resolved into the pattern of vertical lines
which should represent them on the left of the diagram. It is only when the contribution of a founder becomes substantial that his genetic ‘river’ becomes obvious. On the computer screen, however, not only can parts of the diagram be expanded in a window, but founders, or groups of founders, can be allocated different colours. The spectrum shows that the earlier founders (the right-most) contributed more to the 1973 population than the later ones, as one would expect in an expanding population. The two biggest contributors are UWT with 26.375 ‘people-equivalents’ and UEO with 20.1563. In the spectrum UWT lies at about point 160 on the bottom horizontal scale and UEO at about 430. Their associated genetic rivers show that the number of descendants of UWT has grown rapidly in the more recent period. These founders will be mentioned again below. For some purposes it is more informative to examine the relative rather than the absolute contributions of the founders. Figure 2 gives these in the form of an ‘Aurora’ chart in a manner comparable to figure 1; it is simply the same figure with the line for each year stretched so as to fill the space, so that the proportionate contributions can be seen. The final 1973 spectrum is, of course, the same, and the genetic rivers of UWT and UEO are even more marked. The ebb and flow of genetic contributions down the years is clearly depicted. The horizontal ‘fault lines’ in the strata are very striking, and are seen, by comparison with figure 1, to correspond to the periods of serious population decline. Thus in 1901-1902 there was an epidemic, possibly of typhoid,
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246 Edwards Eskimo Genealogy which resulted in 36 deaths [2]. The fault lines are a reflection of the fact that deaths in epidemics tend to be amongst related individuals, so that the proportionate genetic contributions of ancestors are disturbed. These Seashore and Aurora charts were first shown at the 14th International Biometric Conference, Namur, in July 1988 [6]. As a general indication of the importance of each founder, his or her contribution to the population as a whole can be calculated, the genetic contribution to each descendant being counted just once. The contributions of the 10 most important founders calculated in this way are given in table 2. The total number of units to be accounted for is 1,614 (the total population size) less 225 (the founders themselves), giving 1,389. In the fourth column of table 2 the cumulative contribution is given, expressed as a percentage of 1,389. It will be seen that UEO has contributed the most with over 40 units, nearly 3% of the total, and that the 10 main contributors account for over 20% of the total. All 10 are Polar Eskimos except UWT, a West Greenland woman born in 1893 who had 9 children by a Polar Eskimo and 1 by a West Greenlander. She had 71 grandchildren and (up to 1975) 67 great-grandchildren. 50% of the total autosomal gene pool was contributed by 33 founders. Amongst non-founders a similar calculation of contributions to the overall gene pool can be made, though since such contributions may not be mutually exclusive it is meaningless to calculate cumulative contributions. UBU contributed most with 32.5 units, second only to the founder UEO (table 2). Next come UCW and VBK, a marriage-pair, each contributing 28.5 units.
It is also of interest to record the marriages which contributed most. UCW-VBK contributed 2x28.5 = 57 units through sibship *BI, the marriage UCL-UWT 55.75 units through sibship *063, and the marriage UBU-UFR Table 2. Contributions of the 10 most important founders to the overall gene pool
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Code Number Contributio Cumulati descendan peoplecontriequivalents bution, UEO 394 40.1563 2.89 UW 148 31.8750 5.19 UF 411 30.4688 7.38 UFR 281 27.2500 9.34 UEK 331 26.3750 11.24 UEL 331 26.3750 13.14 UFD 416 25.7188 14.99 UFE 416 25.7188 16.84 UIB 349 24.5469 18.61 UJS 349 24.5469 20.38 54.5 units through sibship *CH. Next in order come the marriages UEK-UEL, UFD-UFE, and UIB-UJS (see the last 6 entries of table 2). The founder with the greatest number of descendants was UHW (born 1820) with 452; the 3 others with more than 400 are given in table 2. The greatest number of generations recorded in the genealogy is 8,12 of the founders possessing descendants running through 7 further generations, though it should be noted that inbred descendants might be fewer than 7 generations away by a different route through the genealogy. A significant proportion of Eskimos married more than once (that is, had children by more than 1 partner). Of the 721 members of the genealogy who had children, 563 married only once, but 129 married twice, 21 three times, and 8 four times. These 8 are UFZ, UHW, VAZ, C101, B128, E119, D123, and B115, and they are all women except B128, a reflection partly of our assumption that husbands recorded as ‘unknown’ are distinct. As a consequence of these multiple marriages many people are related to each other by marriage, an important complicating factor in attempt247 A193 A305 A273 A307 A265 A244 A199 A247 A282 A264 A267 Fig. 3.11 marriages amongst 13 individuals, with only the first child of each marriage shown. ing to draw the genealogy. Figure 3 shows a particularly good example, in which 6 men and 7 woman (including 3 brother-sister pairs) are involved in 11 marriages. Drawing the Genealogy A reduced version of the genealogy was drawn in conventional format using the computer program originally developed by M.-F. Landre, M.-T. Valat and P. Jutier at the Centre de Calcul et de Statistique des Facultés de Medicine de Paris, and implemented in Cambridge by P. Stewart. However, not only is the drawing too large to reproduce in a journal ‚ it is also so long, and its lines so difficult to follow, that it is of doubtful value. In order to try to achieve a more informative representation of the genealogy, new techniques have been developed, but even these have had only limited success, reflecting, as it turns out, the complex structure of this particular genealogy. The aim of the new techniques has been to display the principal groupings of closely related individuals, rather than to show individual relationships as in the conventional for-
mat. With 1,614 individuals not only is the latter task essentially impossible but also unnecessary, for it is easy to select all the near relatives of any chosen individual and display their mutual relationships. Moreover, many of the questions which a complete conventional drawing could answer are better answered through direct interrogation of the stored genealogy. What is needed, rather, is an overall view. Since the links in a genealogy are all parent-offspring links the structure may be described most simply as a directed graph. We assume, without loss of generality, that it is a connected graph, and it will also have some special features such as the absence of loops (no person is his or her own ancestor) and a limitation to two incident edges at each node (no person has more than two parents). In an attempt to achieve a satisfactory spread of nodes in a drawing of such a graph, Edwards [7, 8] introduced the idea of geodesic coordinates. If the parentoffspring lines of the graph are each taken to be of unit length and (for this purpose) undirected, then the length of the shortest path between two nodes is known as the geodesic distance between the nodes.
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■ Edwards Eskimo Genealogy With respect to any node, therefore, the other nodes have coordinates, namely their geodesic distances from the chosen node. Any two nodes may thus be used to establish a twodimensional coordinate system consisting of a grid of squares with unit sides. Such a representation has a number of advantageous features, described in Edwards [7, 8], in particular the feature that every individual lies at most one unit in either or both directions from both parents, and is thus a graphical neighbour. The choice of the two reference nodes is obviously critical to the realisation of a satisfactory representation, and these were initially selected on the basis of minimising the maximum occupancy of the grid points. However, in spite of many developments of the basic idea, including its extension to three dimensions, it proved impossible to achieve any representation of the Polar Eskimo genealogy other than as a tangled mass of lines. One such graph was presented as a poster at the 11th International Biometric Conference, Toulouse, in September 1982 [9], but, like the genealogy in conventional format, it is too large to reproduce in a journal. It demonstrated all too clearly, however, the fundamental nature of this particular genealogy: intricate, highly connected, and highly resistant to being split into component parts. More recently, other attempts to draw the genealogy of the related marriage-node graph have only served to confirm its tangled nature [A. Thomas, N. Shee-han, pers. commun.; see also Thomas, 10]. In the light of these difficulties, a final attempt has been made to secure a representation which would at least reveal some of the grosser features of the genealogy, by combining the most promising of the techniques mentioned above with the notion of a ‘waist’ or ‘cleavage’ in a graph, the idea being to find a division of the genealogy into two parts which are as weakly connected as possible. A cleavage in a connected graph is defined as a cutset, such that the transfer of any point between subgraphs increases the number of elements in the cutset, which may be called its order. A program CLEAVE was written, which starts with a random division of the graph into two subgraphs and moves individuals adjacent to the cutset whose transfer to the other subgraph reduces the order of the cutset. Individuals whose transfer makes no difference are randomly allocated. When no further
reduction seems possible the program is continued for some time to give this random allocation a chance to lead to an even better division which might result from the simultaneous random transfer of several individuals. The final division achieved is, by definition, a cleavage. It will be noticed that this final stage is analogous to the technique which has come to be known as ‘simulated annealing’ [10]. CLEAVE is written in PASCAL, and the author will be happy to answer enquiries about its status and availability. Applied to the Polar Eskimo genealogy the best cutset which divided it into two parts comparable in size had order 188, the division being into 775 and 806 individuals. Of all the cleavages found by CLEAVE, this is the one which minimised the ratio (order of the cutset): (size of the smaller group). Many cleavages were also found with orders around 150, but they divided the graph into parts which were considered too disparate in size (the smaller part typically being about one quarter of the whole). By an obvious extension of the idea of geodesic coordinates, the geodesic distance between any node and any set of nodes may be defined as the shortest geodesic distance between that node and each of the nodes of the set. The geodesic coordinate of a node with re-pect to a set of nodes is given by its geodesic distance from that set. When the nodes of a graph are divided into two sets by a cleavage as described above, each node can then be given 249 ⅜ ■⅛ .A. .•V. h·^”·’· .-*■■ V ‘ > ^X ‘ ,-” ⅜. ‘ ■;■’■■-. > í⅛⅛ y ■:-■. i .- “■■■.. > C ⁄ J⅝C X j⅜⅝’ ‘■’■•■■ > ⅝v· ■”■’■■ ^*v ·:’’ J*’” > y i ⅜¾f· ■/×.-. < \ > – ■■■ i ■■■ > o ι⅜χ. . ‚x, ⅜ Λj‚/’·‚Λ. ⅛’⅞⅜ ‘ ■■■ > ■■’ ■ \JÎm⅝/í ⅛í’ ■⅛⅛/T‰I/í V ■ ι
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Fig. 4. Connectedness of the genealogy. Vertical coordinate: generation; horizontal coordinate: geodesic distance (see text). The size of each rectangle is proportional to the number of individuals. a coordinate, being its geodesic distance from the set to which it does not belong, the distances being regarded as positive for the nodes of one of the sets and negative for the others. More colloquially, the coordinate of each individual in a subgraph is the shortest distance to the nearest individual in the other subgraph. The members of each subgraph are thus strung out along a line, and the second of the two lines is reversed and placed end to end with the first. For a two-dimensional representation we need a second coordinate, and on this occasion we use the conventional one of generation number [10], which may be uniquely defined as the rank of each node in the directed graph. The rank of a node is computed by allocating rank 1 to the nodes corresponding to the founders, and then allocating to each child a rank equal to one plus the higher of the parent’s ranks. The founders’ ranks are then themselves modified by allocating to each a rank equal to one less that the lower of the children’s ranks, in order to ensure that founders who enter the genealogy relatively late are more appropriately placed. Further ‘closing up’ can be done of required, although this has not been thought necessary in the present application. This procedure makes allowance for the
fact that inbreeding may introduce ambiguities into the generation number as straightforwardly defined. The result of this procedure is given in figure 4. The area of each rectangle is proportional to the number of individuals at that grid point, and the density of each line is a rough indication of the number of superimposed parent-offspring links it represents. An important property of this representation is that all the ancestors of an individual are contained in the ascending cone and all the descendants within the descending cone, because parent
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250 Edwards Eskimo Genealogy and offspring can be no further apart than in adjacent columns and must belong to different generations. The longest parent-offspring lines are seen to straddle three generations, reflecting a maximum difference of two generations between spouses. Conclusions It is clear from the analysis of the genealogy reported in this paper, and the efforts to draw it described in the preceding section, that the Polar Eskimo genealogy combines, to a possibly unique extent, extreme interconnected-ness and limited inbreeding, apparently conforming to the requirement that within the confines of a very small population, spouses should be chosen to be as unrelated as possible. The efforts to draw the genealogy have amply confirmed the levels of interconnected-ness revealed by other methods, but otherwise have served only to demonstrate that there is little virtue in trying to achieve a printable genealogy when the ready availability of modern computers makes it possible for interactive graphical techniques to portray any part of the genealogy in any desired manner. The Cambridge implementation of the Paris program mentioned above, was eventually developed into the PEDIGREE/DRAW program circulated by the Southwest Foundation for Bio-medical Research, San Antonio, Tex., USA, which has many interactive features, but it is possible that some of the radically different display techniques described in this paper may prove more suitable for studying highly interconnected genealogies such as that of the Polar Eskimos. It is likely, however, that the future lies more in the direction of the numerical and graphical exploration of the stochastic properties of genealogies. The combination of Monte-Carlo simulation of gene flow through a genealogy [11-13] with diagrams of the Seashore and Aurora type (fig. 1, 2) has already proved to be a powerful visual technique, and will be the subject of a subsequent paper. Acknowledgements None of this work could have been accomplished without the generosity, encouragement, and hospitality since 1977 of Lisbet and Aage Gilberg. The provision of computer facilities by Gonville and Caius College, Cambridge, is gratefully acknowledged. A referee kindly provided an improved drawing of figure 3. References Gilberg A, Gilberg L, Gilberg R, Holm M: Polar Eskimo genealogy. Meddelelser om Grønland 1978; 203/4. Gilberg R: The Polar Eskimo population, Thule District, North Greenland. Meddelelser om Grønland 1976;203/3.
Neel JV, Barnicot NA, Kirk RL: Research in population genetics of primitive groups. WHO Tech Rep Ser 1964; No 279. Neel JV, Morton N, Walsh RJ: Research on human population genetics. WHO Tech Rep Ser 1968; No 387. McKusick VA: Genealogic and bibliographic applications of computers in human genetics; in Crow JF, Neel JV (eds): Proc 3rd Int Congr Hum Genet, Plenary Sessions and Symposia. Johns Hopkins, Baltimore, 1967, pp 483^*88. Edwards AWF: Gene-flow simulation in the Polar Eskimo genealogy. 14th Int Biometric Conf, Namur, Belgium, 1988, p 127. Edwards AWF: Parsing a genealogy. Adv Appl Probabil 1979;11:2-3. Edwards AWF: Parsing a genealogy; in Eriksson AW (ed): Population Structure and Genetic Disorders. London, Academic Press, 1980, pp 273-283. Edwards AWF: Drawing genealogies. 11th Int Biometric Conf, Toulouse, France, 1982, p 26. 10 Thomas A: Drawing pedigrees. IMA J Math Appl Med Biol 1988; 5:201-213. Edwards AWF: Simulation studies of genealogies. Heredity 1968;23: 628. Edwards AWF: in Morten NE (ed): Computer Applications in Genetics. Honolulu, University of Hawaii Press, 1969, p 81. Edwards AWF: Computers and genealogies. Biol Soc 1988;5:73-81.
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252 Edwards Eskimo Genealogy
