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Estimating inbreeding in large, semi-isolated populations: Effects of varying generation lengths and of migration
Abstract
The purpose of the study reported here was to investigate two important assumptions used in a recently reported new method of estimating inbreeding in large, relatively isolated populations over historic times. The method, based on modeling the genealogical "paradox," produces values of Pearl's coefficients, Z, a measure of inbreeding or genealogical coalescence, as a function of time. In this study, the effects on inbreeding of two important assumptions made in earlier studies, namely those of using a constant generation length and of ignoring migration, have been investigated for the population of Britain. First, by relating the median age of women at childbirth to the development level of various societies, the variation of the generation lengths for different periods in historic Britain were estimated. Values of Z for two types of varying generation lengths were then calculated and compared with the case of constant generation length. Second, the population curve for Britain used in earlier studies was modified to obtain the subpopulation at any time during the past two millennia that was descended from the pre-Roman British Celts. Values of Z for the case with migration were then calculated and compared with the case for no migration. It is shown that these two assumptions may be taken into account if and when required. Both the effect of a varying generation length and the effect of migration on Z were found to be 20-40%, when no known value of inbreeding was used, and 2-5%, when a known value of inbreeding was used.
... An interest in consanguineous marriages and percentage inbreeding values, in addition to casual curiosity (Bramwell, 1939), arises from academic curiosity concerning marital mobility, demographics, population structure, etc. (Brennan, 1981;Coleman, 1980;Day 2010;Day & Smith 2013;Robinson, 1983;Smith, 2001), and medical curiosity concerning whether any genetic detrimental effects have occurred in the resulting offspring (Bell, 1940;Bundey et al., 1990;Darwin, 1875; Mitchell, 1866;Pearson, 1908a,b,c). Inbreeding values have also been used to model inbreeding over the past millennium based on the genealogical paradox (Pattison, 2001(Pattison, , 2003(Pattison, , 2004(Pattison, , 2007, which apparently corrects for the effective breeding population in the modelling method used. These few studies represent the little systematic information obtained to date on past levels of inbreeding in Britain (Day & Smith). ...
... Unfortunately these cousin relationships could not be used separately as 'once removed' data in this study as it was not indicated in which of her five time periods they occurred. A generation length of 28 years was used in this study because it has been shown to be more appropriate than 30 years (Pattison, 2007;Day). However, this was not really an issue, as discussed by Smith) because the allocated ranges of generational years are only rough estimates. ...
... Bramwell;Jacquard 1974;Shoumatoff 1985;and Wachter). There have been a number of different approaches to modelling the pedigree collapse involved in the solution to the 'paradox' (Chang 1999;Derrida et al. 1999Derrida et al. , 2000aPattison 2001Pattison , 2003Pattison , 2004Pattison , 2007Wachter) and each has found that there must have been an increasing trend in inbreeding as one moves back in time. ...
There have been a number of previous estimates of human inbreeding for Britons of British descent in Britain; each generally for different social classes, geographical regions, and/or time periods. In this study an attempt was made to collect all relevant published studies and to combine the results of these disparate studies into an integrated whole for all of Britain. This was achieved by combining weighted means of the percentage of consanguineous marriages (f%) reported in these earlier studies: weighted according to the number of records each author examined, the proportion of social classes or geographical regions covered by the records, and the 'merit' of their individual research methodologies. The percentage occurrences of the various consanguineous marriages, from 1 st to 3 rd cousins, were partitioned into a number of time periods, which allowed the weighted mean percentage inbreeding coefficients (F%) to be obtained as a function of time over the period from 1820 to 1960. The resulting temporal scatter distribution of the weighted F% values closely followed a sigmoidal curve, with a non-linear correlation coefficient of η = 0.974, which fitted well to a generalized logistic function. After about 1900 the value of the weighted F% was essentially constant at about 0.038±0.004, whereas it decreased rapidly from about 0.256±0.011 between 1820 and 1900. The upper-bound value of weighted F%, before 1820, from the fitted logistic function is 0.276. Note that this corresponds to a value of the conventional mean inbreeding coefficient F = 0.00276. As the first known attempt to integrate the earlier disparate values of unweighted F% for Britons of British descent for all of Britain, the results of this analysis are promising and should be useful as reference values in other related studies.
... The common historical inclination of small and isolated populations was to marry those within walking distance (Pattison, 2001). In practical terms, close relatives are likely to live next to somebody, strengthening family ties, to be in the same social class, to share the same religion, culture, tradition, ethnic group, language as well as to be part of the same social circle (Pattison, 2007). This apparent 'genealogy paradox' is also named 'pedigree collapse' (Pattison, 2001). ...
... In fact, a closer look reveals that moderate inbreeding has constantly been the rule, not the exception in human history -some experts assume that up to 80% of all marriages in history have been between second cousins or closer (Pattison, 2007;Conniff, 2003). Some authors, such as Derrida et al. (1999), affirmed, according to their model, that when we look very far in the past, about 80% of the (adult) population appears in the genealogical tree of every individual. ...
... Some authors, such as Derrida et al. (1999), affirmed, according to their model, that when we look very far in the past, about 80% of the (adult) population appears in the genealogical tree of every individual. There are good manuscripts on the subject, relating human biological origins, evolutionary development, inbreeding and genetic diversity, even considering isolated or semi-isolated populations (Pattison, 2001;2007). ...
... Thomas et al.'s (2008) first and principal criticism was on the methodology used for the population reconstruction. I employed the back projection method, which is an established method used by historical demographers for modeling past populations (see Pattison 2007). The population estimates used to construct the historical population curve for Britain were uncertain, but were the best available at the time (Pattison 2003(Pattison , 2004. ...
... Compared to the later medieval period when bastardy was discouraged by the manorial fine of childwyte, it is possible that in Anglo-Saxon times there was a more indulgent attitude (Laslett 1980). Even so, when discouraged in the later medieval period, births outside of marriage were not uncommon, comprising up to 25% of births in some parishes in the pre-plague period, and crossing social boundaries (Pattison 2007). Also, adultery leading to illicit births is hidden within marriages (Laslett 1980). ...
The genetic surveys of the population of Britain conducted by Weale et al. and Capelli et al. produced estimates of the Germani immigration into Britain during the early Anglo-Saxon period, c.430-c.730. These estimates are considerably higher than the estimates of archaeologists. A possible explanation suggests that an apartheid-like social system existed in the early Anglo-Saxon kingdoms resulting in the Germani breeding more quickly than the Britons. Thomas et al. attempted to model this suggestion and showed that it was a possible explanation if all Anglo-Saxon kingdoms had such a system for up to 400 years. I noted that their explanation ignored the probability that Germani have been arriving in Britain for at least the past three millennia, including Belgae and Roman soldiers, and not only during the early Anglo-Saxon period. I produced a population model for Britain taking into account this long term, low level migration that showed that the estimates could be reconciled without the need for introducing an apartheid-like system. In turn, Thomas et al. responded, criticizing my model and arguments, which they considered persuasively written but wanting in terms of methodology, data sources, underlying assumptions, and application. Here, I respond in detail to those criticisms and argue that it is still unnecessary to introduce an apartheid-like system in order to reconcile the different estimates of Germani arrivals. A point of confusion is that geneticists are interested in ancestry, while archaeologists are interested in ethnicity: it is the bones, not the burial rites, which are important in the present context.
... In these cases, it is unlikely that any resulting child would have taken the identity of the father, as stated byThomas et al. (2006). For instance, in the later Medieval period, births outside of marriage were not uncommon and crossed social boundaries (Pattison 2007). ...
It has recently been argued that there was an apartheid-like social structure operating in Early Anglo-Saxon England. This was proposed in order to explain the relatively high degree of similarity between Germanic-speaking areas of northwest Europe and England. Opinions vary as to whether there was a substantial Germanic invasion or only a relatively small number arrived in Britain during this period. Contrary to the assumption of limited intermarriage made in the apartheid simulation, there is evidence that significant mixing of the British and Germanic peoples occurred, and that the early law codes, such as that of King Ine of Wessex, could have deliberately encouraged such mixing. More importantly, the simulation did not take into account any northwest European immigration that arrived both before and after the Early Anglo-Saxon period. In view of the uncertainty of the places of origin of the various Germanic peoples, and their numbers and dates of arrival, the present study adopts an alternative approach to estimate the percentage of indigenous Britons in the current British population. It was found unnecessary to introduce any special social structure among the diverse Anglo-Saxon people in order to account for the estimates of northwest European intrusion into the British population.
It is widely understood that the preservation of cultural heritage sites and objects is underpinned by values projected by the public onto essentially inanimate objects, that these values vary in strength, and that they are mutable qualities. Using hindsight, the contemporary values are projected on past creations that persist into the present. If deemed significant, these past creations will be listed on heritage lists and afforded various levels of protection. As time moves on, new places or objects will be deemed significant and added to the lists. Using a case study, this paper examines the concept of shifting baselines and how they impact on the identification and listing/protection of heritage places. It will demonstrate that generational biases play a significant role in the initial listing and exert a lasting legacy through the static nature of heritage listings.
Professor Wachter’s 1978 seminal paper “Ancestors at the Norman Conquest” estimated the ancestors of an indigenous Briton. As far as I can ascertain, there has been limited further progress on the core question of numbers of ancestors since then. This paper introduces new methods and the accompanying spreadsheet for estimating ancestors. The results are considerably less than Wachter’s 1978 estimates. It also estimates all non-extinct persons in each generation, i.e. the total ancestors of everyone today. It then builds on these estimates to estimate numbers of cousins of any degree.
Czas trwania pokolenia jest istotnym regulatorem tempa przyrostu populacji ludzkich, a co za tym idzie także możliwości działania w nich doboru naturalnego. W tab. 1 zilustrowano zmiany współczynnika przyrostu naturalnego populacji ustabilizowanej r w zależności od czasu trwania pokolenia T przy różnych współczynnikach reprodukcji netto Ro oraz pokazano, jak wpływa zmiana wartości T na ocenę sprawności względnej (relative fitness) obliczanej według równania (4). Posługując się danymi z lat 1950-1977 dla 200 krajów świata [U. S. Bureau of Census] stwierdzono istnienie zależności pomiędzy empirycznym oszacowaniem T a oczekiwanym trwaniem życia noworodka eo, medianą kolejności urodzenia dzieci rodzonych w ciągu roku (MBO) reprezentującą przeciętną dzietność, surowym współczynnikiem urodzeń b oraz punktową miarą zaawansowania rozwoju kulturowego populacji (score), opartą na danych o wymieralności i płodności (rys. 1-4, tab. 2). Zależność ma we wszystkich przypadkach charakter krzywoliniowy, odzwierciedlając ogólną prawidłowość polegającą na tym, że czas trwania pokolenia, niski w populacjach krajów rozwijających się o wysokiej wymieralności i płodności, rośnie wraz z początkowymi stadiami poprawy warunków życia: dalszej poprawie towarzyszy powolny spadek wartości T, a w warunkach krajów wysoko rozwiniętych czas trwania pokolenia ulega stabilizacji po nieznacznym wzroście jego wartości (rys. 4). Autor uważa, że ta stwierdzona na danych przekrojowych prawidłowość da się odnieść do zmian czasu trwania pokolenia w czasie kulturowej i demograficznej ewolucji populacji ludzkich.
A survey of the electrophoretic variation at eleven loci red-blood cell enzymes, hemoglobins and serum proteins-was performed on a sample of 59 Miskitos stemming from the southernmost part of the Mosquito shore of Nicaragua. Seven loci, ALB, α-, β-, γ-globins, LDHA, LDHB, and TPI were monomorphic; AP1, CP, HP and TF were polymorphic representing a proportion of polymorphic loci (P) of 0.364 and an average heterozygosity (Ĥ) of 0.077. Both values are within a range covered by ten Chibchan tribes of Costa Rica and Panama evaluated for the same loci -(P) = 0.364-0.182; (Ĥ) = 0.104-0.052-. The data allowed an estimation of minimum (ml = 0.0), mean (mm = 7.34) and maximum (ms = 21.9) percentages of racial admixture with blacks. For comparison, admixture was also calculated from the data -mainly blood groups- of a previous survey performed in 1960 by A. Matson and his group on a sample of a region near the border between Nicaragua and Honduras; results (ml = 6.05), (mm = 11.0) and (ms = 18.1). The values showed no statistical difference, for the mean estimates, under the assumption that the non-Indian alleles are Poisson-distributed (P=0.42). The documentation of what is supposed to be the beginning of the racial admixture of the Miskito with blacks in 1641 permitted the calculation of the rate of admixture per generation -generation length: 27 years-; its maximum value lies between 1.68 and 1.91 percent. These results indicate that the Miskito gene pool has a preponderance of features characteristic of Amerindian populations.
In his short but authoritative study, Roy Porter examines the impact of disease upon the English and their responses to it before the widespread availability and public provision of medical care. Professor Porter incorporates into the revised second edition new perspectives offered by recent research into provincial medical history, the history of childbirth, and women's studies in the social history of medicine. He begins by sketching a picture of the threats posed by disease to population levels and social continuity from Tudor times to the Industrial Revolution, going on to consider the nature and development of the medical profession, attitudes to doctors and disease, and the growing commitment of the state to public health. Drawing together a wide range of often fragmentary material, and providing a detailed annotated bibliography, this book is an important guide to the history of medicine and to English social history.
English Population History from Family Reconstitution 1580–1837 is the most important single contribution to English historical demography since Wrigley and Schofield's Population History of England. It represents the culmination of work carried out at the Cambridge Group for the History of Population and Social Structure over the past quarter-century. This work demonstrates the value of the technique of family reconstitution as a means of obtaining accurate and detailed information about fertility, morality, and nuptiality in the past. Indeed, more is now known about many aspects of English demography in the parish register period than about the post-1837 period when the Registrar-General collected and published information. Using data from 26 parishes, the authors show clearly that their results are representative not only of the demographic situation of the parishes from which the data were drawn, but also of the country as a whole. Some very surprising features of the behaviour of past populations are brought to light for the first time.
The collaboration between the Forensic Community and the scholars of human population genetics, among whom I place myself, has always been fruitful and of reciprocal benefit in Italy as much as in Europe and in North-America, in the latter with a more dialectical attitude as shown by recent rather hot debates. DNA analysis is today offering new possibilities of collaboration. Case work and search for reference populations complement in the daily activity of the forensic scholars. Substantial DNA databases have already been established for a number of population groups, but the development of new standards and new reference databases is likely in the immediate future following the implementation of PCR-based DNA typing systems, and a strong argument can be made for population geneticists to share protocols and markers with the forensic community in order to type well-defined reference populations and from them to contribute to the analysis of human genetic diversity. My talk, however, does not address to the future, but rather to the past: I have had the chance to analyze, over the past ten years, many genetic data from human populations and I am going to give a short review of our recent analyses. Our main interest lies in their interpretation in terms of prehistory and history of our species: a more comprehensive treatment will appear in a forthcoming book written in collaboration with Cavalli-Sforza and Menozzi [1].
The paper presents a theoretical model of mating distances distribution. In its simplest form the model relates overall exogamy rate, distribution of demes exchanging mates and ecocultural distances separating the demes as variables determining probability of mating between an individual belonging to a given deme with a partner from other deme situated at a given distance. In cases of isotropic migration the general form of the model may be easily reduced to simple formulas describing distances distributions. For the one- and two-dimensional isotropic migration are presented formulas enabling estimates of parameters of distributions to be done on the basis of exogamy rate only. Concordance between expectations derived from the model and empirical distributions has been checked, with positive results, on the data pertaining to 19th-century Poland, Massachussetts, Aland Islands and modern Zu/Wasi (S. Africa). From the model is also derived a method for estimation of local kinship coefficients on the basis of breeding size of demes and overall exogamy rate when migration is of quasi-continuous type.
Previous study of the time to a common ancestor of all present-day individuals has focused on models in which each individual has just one parent in the previous generation. For example, 'mitochondrial Eve' is the most recent common ancestor (MRCA) when ancestry is defined only through maternal lines. In the standard Wright-Fisher model with population size n, the expected number of generations to the MRCA is about 2n, and the standard deviation of this time is also of order n. Here we study a two-parent analog of the Wright-Fisher model that defines ancestry using both parents. In this model, if the population size n is large, the number of generations, T n, back to a MRCA has a distribution that is concentrated around lg n (where lg denotes base-2 logarithm), in the sense that the ratio T n/(lg n) converges in probability to 1 as n → ∞. Also, continuing to trace back further into the past, at about 1.77 lg n generations before the present, all partial ancestry of the current population ends, in the following sense: with high probability for large n, in each generation at least 1.77 lg n generations before the present, all individuals who have any descendants among the present-day individuals are actually ancestors of all present-day individuals.
A 'Past and Present' publication, the volume draws attention to the value of court rolls in demographic analysis during a period for which there is little alternative data. Having outlined the methods and techniques used, the population characteristics of this parish in the West Midlands are reconstructed on the basis of an exceptionally complete series of court rolls for the periods before and after the Black Death, with a chapter devoted sepcifically to the impact of that epidemic. Fresh light is cast on such questions as the age of marriage, incidence of illegitimacy, social mobility, and the supply and market in land. - John Sheail
This book represents the culmination of work carried out at the Cambridge Group for the History of Population and Social Structure over the past quarter-century. It uses Anglican parish registers to illuminate the population history of England between the sixteenth century and the mid-nineteenth century for which period they are the prime source available. This work demonstrates the value of the technique of family reconstitution as a means of obtaining accurate and detailed information about fertility, mortality, and nuptiality in the past. Indeed, more is now known about many aspects of English demography in the parish register period than about the post-1837 period when the Registrar-General collected and published information. Using data from 26 parishes, the authors show clearly that their results are representative not only of the demographic situation of the parishes from which the data were drawn, but also of the country as a whole. While the book largely confirms the earlier findings of the Cambridge Group, many novel and some very surprising features of the behaviour of past populations are brought to light for the first time.
Originally published in 1988, this reference book provides the major economic and social statistical series for the British Isles from the twelfth century up until 1980–81. It is the successor of Abstract of British Historical Statistics and the Second Abstract of British Historical Statistics, which were compiled by the author in collaboration with Phyllis Deane and Hywel Jones respectively. The text presents the user of historical statistics with informed access to a wide range of economic data, without the labour of identifying sources or of transforming many different annual sources into a comparable time series. The statistics selected for presentation are arranged in sixteen chapters. This book will be of value to anyone with an interest in British history and historical statistics.