Genetic Aspects of Genealogy E. Ya. Tetushkin

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ISSN 10227954, Russian Journal of Genetics, 2011, Vol. 47, No. 11, pp. 1288–1306. © Pleiades Publishing, Inc., 2011.Original Russian Text © E.Ya. Tetushkin, 2011, published in Genetika, 2011, Vol. 47, No.11, pp. 1451–1472.

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INTRODUCTION

Genealogy is among the sciences that have had a sig

nificant impact on genetics, which borrowed from themmethods of pedigree analysis. However, until the late 20thcentury, these disciplines practically did not interact.Their first contact, which resulted in the appearance of genetic, or molecular, genealogy, dates to the turn of the21st century [1–5]. To date, other associations betweengenetics and genealogy are beginning to appear.

Traditional genealogy is a supplementary historicaldiscipline studying pedigrees. However, genetics, from itsown standpoint, also studies pedigrees. Investigating its

specific problems, genetics made a significant, thoughspecialized, contribution to the description and analysisof these subjects of genealogy. What has contributed and

can contribute genetics to the development of genealogy? And vice versa, what are and will be the gains of geneticsfrom contacts with genealogy? What are the perspectivesof interaction of these sciences in the postgenomic era?

LAWS OF GENEALOGY AND HUMAN GENETICS

In the early 20th century, the prominent Russiangenealogist L.M. Savëlov stated in his lecture course:

Genetic Aspects of Genealogy

E. Ya. Tetushkin

Vavilov Institute of General Genetics, Russian Academy of Sciences, Moscow, 119991 Russia;email: [email protected]

Received March 3, 2011

Abstract—The supplementary historical discipline genealogy is also a supplementary genetic discipline. In its formation, genetics borrowed from genealogy some methods of pedigree analysis. In the 21th century, it started receiving contribution from computeraided genealogy and genetic (molecular) genealogy. The former provides noveltools for genetics, while the latter, which employing genetic methods, enriches genetics with new evidence. Genealogists formulated three main laws of genealogy: the law of three generations, the law of doubling the ancestry number, and the law of declining ancestry. The significance and meaning of these laws can be fully understood only in light of genetics. For instance, a controversy between the exponential growth of the number of ancestors of anindividual, i.e., the law of doubling the ancestry number, and the limited number of the humankind is explained by the presence of weak inbreeding because of sibs’ interference; the latter causes the pedigrees’ collapse, i.e., explainsalso the law of diminishing ancestry number. Mathematic modeling of pedigrees’ collapse presented in a number of studies showed that the number of ancestors of each individual attains maximum in a particular generation

termed ancestry saturated generation. All representatives of this and preceding generation that left progeny are common ancestors of all current members of the population. In subdivided populations, these generations are moreancient than in panmictic ones, whereas in small isolates and social strata with limited numbers of partners, they are younger. The genealogical law of three generations, according to which each hundred years contain on averagethree generation intervals, holds for generation lengths for Ychromosomal DNA typically equal to 31–32 years;for autosomal and mtDNA, this time is somewhat shorter. Moving along ascending lines, the number of genetically effective ancestors transmitting their DNA fragments to descendants increases far slower than the number of common ancestors, because the time to the nearest common ancestor is proportional to log2N , and the time to genetically effective ancestor, toN , where N is the population size. In relatively young populations, the number of genetically effective ancestors does not exceed the number of recombination hot spots, which is equal to 25 000–50000.In ancient African populations with weaker linkage disequilibrium, their number may be higher. In genealogy, thedegree of kinship is measured by the number of births separating the individuals under comparison, and in genetics,

by Wright’s coefficients of relationship (R). Genetic frames of a “large family” are limited by the average genomicdifferences among the members of the human population, which constitute approximately 0.1%. Conventionally it can be assumed that it is limited by relatives, associated with the members of the given nuclear family by the 7th

degree of relatedness (R ≈ 0.78%). However, in the course of the HapMap project it was established that 10–30%of pairs of individuals from the same population have at least one common genome region, which they inheritedfrom a recent common ancestor. A nuclear family, if it is not consanguinous, unites two lineages, and indirectly, amultitude of them, constituting a “suprafamily” equivalent to a population. Some problems of genealogy andrelated historical issues can be resolved only with the help of genetics. These problems include identification of “true” and “false” Rurikids and the problem of continuity of the Ychromosomal lineage of the Romanov dynasty.On the other hand, computeraided genealogy and molecular genealogy seem to be promising in resolving geneticproblems connected to recombination and coalescence of genomic regions.

DOI: 10.1134/S1022795411110160

THEORETICAL ARTICLES AND REVIEWS



RUSSIAN JOURNAL OF GENETICS Vol. 47 No. 11 2011

GENETIC ASPECTS OF GENEALOGY 1289

“We do not have genealogy as a science yet; this science is only at its beginning and needs developing,since no definite system has been designed for it so far,and any investigations and studies are impossible without such system” ([6], p. 9). This statement might haveperplexed his audience, because it is generally believedthat practical, or applied genealogy appeared and developed in the 15th–17th centuries, whereas the science of

genealogy, which is also referred to as general, or theoretical genealogy, originated in the 18th century [7, 8].However, in retrospective we can partly agree withSavëlov. “The very subject of genealogy as a scienceseems not to be quite clear,” admitted the modern historian V.B. Kobrin ([9], cited in [10]). Not pretendingto completely resolve the issue, Kobrin proposed thefollowing definition, which was judged as “most complete” by a representative group of Russian archivists[10]: “Genealogy is a historical discipline dealing withstudying and constructing pedigrees, clarifying the originof kins (clans, lineages – E.T.), families, and individualsand determining their relationships together withestablighing main biographic facts and data on the activ

ities, social status, and property of these individuals.” And yet genealogy, prior to its first encounter with

genetics, has travelled a long road from genealogicallegends reflected in ancient epics and religious texts.In the 15th century, in Europe, including Russia, anurgent social need appeared to officially documentand judicially register blood relationships among persons belonging to the higher strata of the society. Thisneed was fueled by the development of the relationships connected to property: the development and useof hereditary laws are impossible without the information on the degrees of relationship. Furthermore, thehigher estates, which had some privileges along with

responsibilities, were interested in retaining their privileged position for their descendants. Genealogicaldocuments preserved the existing social system andhindered movement among the estates. Based on this,in the 15th17th centuries, as mentioned above, practical genealogy was developed. In its framework, three

ways of recording genealogical data were designed:pedigree trees, genealogical tables (transformed trees),and pedigree listings [7, 11].

In genetics, only construction of diverse genealogical tables (sometimes incorrectly named trees) isused. Medical geneticists employ such tables for concise presentation of data from clinical genealogicalfamily records. Eugenic studies of the early 20th century, which are genetic in essence, contain also pedigree lists. According to Yu.A. Filipchenko [12], “theearliest analysis of several genealogies pertaining toartistically, musically, mathematically, literally, or technically gifted families was performed in 1911 by Davenport in his treatise Heredity in Relation to Eugenics” [13]. This and other occational early contacts withgenealogy made an impact on the further developmentof genetics. Interestingly, borrowing the methods of presenting pedigrees from genealogy, geneticists for

some reason interchanged graphic symbols denotingfemales and males. In nobiliary pedigrees, male names

were marked by circles (representing oval cartouches with coatofarms from ancient genealogical trees)positioned at the right from the name, whereas femalenames were marked with squares (see, e.g., [14],p. 136). (Note that the majority of aristocratic pedigrees are those of men; mixed, i.e., including both

sexes, pedigrees are rare). Following this tradition,genealogists of the early 20th century also designatedmen by circles, and women, by squares (see, e.g., [6]).Some modern genealogists also follow this tradition(see pedigree schemes in [7, 8]).

The young science of genetics, in its turn, also hadan impact on genealogy. Historians acknowledge thatthe appearance of genetics opened new perspectivesfor genealogy ([8], p. 10). In the first third of the 20thcentury, genetics influenced genealogy througheugenics. Genetics working in this direction deepenedpedigree analysis in the context of their science [5, 15,16]. Interacting with genetics, genealogy became a

bridge between humanitarian and natural sciences [8].

At that time, “at the dawn of human genetics” [15],the first book by O. Forst Battaglia ([17], cited from[7]) which became a milestone in the development of general genealogy, was issued. His second book waspublished in 1948 ([18], cited from [8]). These booksdeveloped modern views on the tasks, methods, andmajor principles of this supplementary historical discipline. These principles include the three genealogicallaws (see [7, 11]) related, as shown below, to some fundamental genetic notions.

According to the first of these laws, referred to asthe law of three generations, “the activity of three generations falls into the interval of hundred years” ([7],

p. 27). This rule is used for testing signidicance of tables of descending (from ancestors to descendants)kinship. It applies to long pedigrees of six to nine andmore generations. However, this rule is poorly formulated. Apparently, it implies the time or length of generations rather than their activity. This parameter isessential for estimating the time of genetic divergenceof individuals and populations. It varies depending of the population and changes during the population history. Moreover, the length of the “generation interval”depends on the DNA type (Ychromosomal, mitochondrial, autosomal).

The second rule, the law of doubling ancestry number , is related to the tables of ascending (from descendants to ancestors) kinship and reduces to the obviousstatement that “the number of ancestors doubles inevery next generation” ([9], p. 28). This law is supplemented by the third rule, the law of declining ancestry,according to which the actual number of ancestors of the proband is significantly lower than that assumed by the doubling law. The law of decline follows from thediscrepancy between the exponentially increasingnumber of ancestors of the individual, which is 2n inthe nth ancestral generation (where n is the number of



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the ancestral generation), and the limited, retrospectively diminishing number of the humankind and itspopulations (figure). For instance, according to thedoubling law, each of us must have more than a billionancestors in the 30th ancestral generation, i.e., aboutone thousand years ago. In fact, according to paleodemographic data, the size of all humankind apparently did not exceed 300–400 million (see [20], pp. 230–

231). This means that in deep ascending pedigrees, thesame individuals of remote generations are oftenancestors of the proband by several lineages. Theprominent geneticists K. Stern ([21], p. 337) used thestatement of “loss of ancestors” to substantiate the

view on the “brotherhood of all human beings,” whichimplied genetic integrity and connectedness of thehumankind. In essence, Stern derived this from allthree laws of genealogy, which he probably knew.

Recent studies deepened and elaborated the understanding of these genealogical laws. Apparently, their significance and meaning can be understood only inlight of genetics. For instance, doubling of the ancestry number reflects in retrospective replication of geneticmaterial and related biological processes important for understanding individual and family histories. Declineof the ancestry number and its consequences are adequately described in terms of population genetics.Such description contains information not only on thehistory of families but also on the history of wholepopulations. Correct and precise definition of the generation length is also impossible without engagingnotions of genetics.

COMPUTERAIDED AND GENETIC GENEALOGY

As noted above, scientific genealogy is a supplementary historical discipline. In contrast to practicalgenealogy, whose aim is reconstruction of family histories, scientific genealogy employs these histories as amaterial for historical investigations. For this science,studying family histories is a method of research ([7],p. 12–13; [8], p. 5). However, genetics also uses thegenealogical approach. Hence, genealogy can beregarded as a supplementary genetic discipline. A con

vincing illustration of this statement is provided by eugenic studies by classics of Russian genetics. Analysis of pedigrees of renowned scientists and cultural

workers conducted by Kol’tsov, Filipchenko, and others, was focused on establishing the inheritance of particular phenotypic traits (see [5, 15, 16]). Yet, archi

vists include these essentially genetic studies intogenealogical bibliographic lists [22]. In his Lectures on

Anthropogenetics, stored in his personal archive (see[23]), A.S. Serebrovsky proposed to establish a specialized section of the Moscow Eugenic Society,aimed at collecting information on Russian pedigrees.Thus, he well understood the significance of genealogy as a supplementary genetic discipline. In Russia,eugenics initially (i.e., in the 1920s) was included in

genetics as its branch [24–26]. According to Kol’tsov,eugenics “is divided into two parts: pure science(anthropogenetics) and applied science (anthropothechnology)” [27]. Soviet eugenicists focused on theoretical aspects of eugenics, i.e., issues of human genetics, while the other “part” of eugenics was under dispute and an area of a few illconceived projects.

Role of the genealogical approach in the further

development of genetics is selfevident. However, theturn of the 21st century has opened unprecedentedperspectives for the genetics–genealogy alliance. They are connected to the appearance and development of computeraided genealogy [8, 28] and genetic genealogy. The former provides novel tools to genetics, whilethe latter, which employes genetic methods, enrichesgenetics with new evidence.

Computerization of genealogy is a logical stage inthe development of this science, promoted by theadvances in information technologies. Its necessity isdetermined by the scale of tasks of genealogicalresearch. The pedigrees of affluent and prominentpersons, which are the usual subject of this analysis,are traced back sometimes for tens of generations andinclude hundreds of individuals. Moreover, patrilinear and matrilinear lineages, repeatedly intercepting,form large networks, whose investigation, interestingand important in many respects, is laborconsumingand entails substantial difficulties. Informational technologies significantly facilitate ordering and processing of these genealogical materials.

The first genealogical software PAF (Personal Ancestral File) was developed in the 1980s by programers affiliated with FamilySearch Center of theChurch of Jesus Christ of LatterDay Saints (mormoncommunity) from the Salt Lake City. According to

their religious beliefs, the members of this confessioncollect detailed information on their deceased friendsand relatives. The ideas implemented in PAF strongly influenced all further development of computeraidedgenealogy. This primarily concerns the standard of data presentation GEDCOM (Genealogy DataCOMmunications), which was later generally accepted. It permits to export and import files containing genealogical data, among different genealogical programmes working under various operationalsystems.

References at the website http://www.cyndislist.com/software.htm give an idea of the diversity of software used in modern genealogy. Some of thesesoftware programs can supply standard personal genealogical file information (time and place of birth, timeand place of death, parents, husband or wife, time andplace of wedding and divorce, nationality, causes of death, religion, education, titles and awards, references) by genetic data (see references athttp://www.cyndislist.com/dna.htm). These includeprimarily information on hereditary diseases, bothrare monogenic and common multifactorial ones(cancers, cardiovascular diseases, diabetes and oth





ers). To facilitate inputting, electron catalogs of nosological forms of pathologies are provided. Based on thecollected data, users can construct socalled geno

grams, i.e., pedigree schemes reflecting the medicalgenetic family history (http://www.genealogytoday.com/articles/genogram.html and others). Genealogists for some reason believe (http://en.wikipedia.org/wiki/Genogram and others) that genograms

were for the first time presented in the book Genogramsin Family Assessment by McGoldrick and Gerson,published in the mid1980s (the last edition appearedin 2008 [30]).

However, these schemes little differ from pedigreesthat were constructed by clinical geneticists for a longtime. The only difference is that ordinal numbers of individuals are replaced by names and dates of birth and(or) death as in genealogical tables; also, denotations of generations by Roman numbers are omitted. If the dataare sufficient, several genograms can be constructed for each extended family. Not only information on diseasescan be used. Genograms can be based on other heritablecharacters. For this, fields for inputting data on the tem

perament, creativity (e.g., musical gifts), predispositionto alcohol or drug addiction, eye color, blood groups,and other inherited traits. In addition, it is recommended to reflect on genograms diadic (interpersonal)relationships between family members, which can testify to an association of a clinical problem with the family background (see [31], p. 161).

Among Russian specialized software, which arestill few, the package “Russian Genealogy” [7, 8, 28,32] is worth mentioning; this system is also of interestfor geneticists. Its development started in 1992 and wasled by M.I. Smirnov, who founded for this purpose theNAFTAM (renamed later in NaftamINPRO) com

pany. This software is aimed at generalization and systematization of data on pedigrees of families fromRussia from the 10th to the 21st century.

Implementation of modern approaches to processing genealogical information includes designing soft

ware that provides input, storage, and representationof genealogical information and genealogical databases. The “Russian Genealogy” system is based on anumber of pioneering principles, which, in view of itsdesigners (see [8]), will eventually change the standards of computeraided genealogy. Among other things, they provide for “the possibility to maintain

both the official (judiciary) and factual ( genetic; theitalics are mine) version of the pedigree of each person

(if these versions do not coincide)” ([8], p. 181]. A fundamental feature of this system is that it is

aimed at analysis of genealogical information on thepopulation of the whole state. In the past years, thematerial on hundreds of thousands of Russian nobility and thousands of pedigrees uniting them were deposited in the database. The important point is that thesystem can detect interceptions of the lineages basedon the information on females who are at the sametime daughters of the carriers of particular surnames

and mothers of the carriers of other surnames. Theoretically, having the information on sufficiantly highnumber of individuals, this enables to establish relationships between any persons deposited in the data

base, because pedigrees of all people living on the territory of Russia and the neighboring countries repeatedly intercepted in the observable historicalperspective. For instance, using this option, it was

demonstrated that the author Leo Tolstoi was relatedto the Romanov dynasty, because, as it turned out, heand the Romanovs had a common ancestor, the boyar (the highest rank in Moscovian state) NikitaRomanovich Yur’evZakhar’in. Leo Tolstoi was theeight cousin of tsar Alexander II and, correspondingly,eight cousin once removed and twice removed of respectively Alexander III and Nicolai II [8]. In a similar manner, relatedness of three authors, Alexander Pushkin, Leo Tolstoi, and Sergei Michalkov wasshown: their common ancestor was a Moscow nobleman Danilo Moiseevich Glebov, who was a mayor in1648 [7].

The Russian Genealogy software system can bealso used to resolve a reverse problem: finding common descendants of any persons present in the data

base. With its help, common descendants were foundfor two great Russian public figures of the 18th century,tsarina Catherine II and scientist Mikhail Lomonosov.These descendants are the offspring of the duke MecklenburgStrelitz family, currently living in Germany,and prince Sergei Trubetskoi and his sisters, who livein the United States. They “combined in them the

Number of individuals (billions)10

9

8

7

6

5

4

3

2

1

010001100120013001400150016001700180019002000

Time (years)

Expected exponential increase in the number of ancestorsof an individual (hatched line)born in the second half of the 20th century, based on autosomal DNA data, with thegeenration length equal to 30 years and the increase in thenumber of humankind (solid line) according to the empirical formula N = 200/(2025 – T ), where T is the time in years A.D. [19]. This formula, in view of a number of demographers, very precisely reflects the increase in theglobal population during many millenia, but, as can beseen, near the period of demographic transition (around2000) gives greatly overestimated numbers of the worldpopulation.



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genes of a great scientist and an emperess” ([8],pp. 225–226).

Genetic genealogy studies pedigrees of individuals,families, and lineages (clans) by mean of molecular–genetic methods [5]. It has significantly extended thelimits and possibilities of genealogy, combining it withgeneral and population genetics, genomics, forensicgenetics, gene geography, clinical genetics, and com

munity genetics. As comopared to traditionalapproaches, molecular–genetic technologies enableto reconstruct in depth and more completely the family histories. Developing mainly on the commercial

basis, genetic, or molecular. genealogy accumulatedample information on genetic variation in humanpopulations (so far mainly for uniparental Ychromosomal and mitochondrial DNA markers). This appliedscience will obviously be of great help in investigatingproblems of human genetics. It opens additional possibilities for both studying transmission of hereditary factors affecting health and determining phenotypictraits, and investigating historical genetics of thehumankind, which is one enormous family.

PEDIGREES’ COLLAPSE AND SIBLINGS’ INTERFERENCE

An article by the classic of evolutionary geneticsS. Ohno [33], published in the mid1990s, provides akey to genetic interpretation of the laws of genealogy.Ohno was probably the first to formulate and substantiate the idea that the only cause of the “diminished”ancestry number compared to that expected from thedoubling law is the presence of brothers and sisters(siblings, or sibs) among these ancestors. He termedthis rule the law of sibling interference.

Sibling interference is estimated by the socalledaverage sibling size S . This is the number of the parentsof the given generation divided by the number of families from which they originate. For example, if two of greatgrandparents of the proband were cousins, thenfor the grandparent generation, S = 4/3, because hisgrandparents were born not in four, as usual, but inthree families. The number of the nextgenerationancestors by the ascending line is calculated using simple formula N n + 1 = (N n/S n)2, where N n and N n + 1 arethe numbers of ancestors in two consecutive generations. In the above example, N 2 = 4 and S 2 = 4/3 (generations are numbered beginning with the parentalone); thus, the number of greatgrandparents of the

proband N 3 = 6, but not 8, as in most cases).The more distant is the generation of ancestors of

an individual, the more sibs it contains. Hence, theaverage sibling size must increase with time and theactual number of ancestors must be lower than thatexpected with the exponential growth. Ohno simulated this process and obtained the following results(table). Up to generation 9 inclusively, S = 1 (with anaccuracy of three decimal places). Beginning fromgeneration 10, S starts increasing, first slowly, than

faster. The greater S , the lower the actual number of ancestors as compared to the expected one. For example, in generation 20 (600 years ago, if we take the generation length equal to 30 years), the individual musthave more than 1 million ancestors, whereas this num

ber is 616315 according to the simulation. In generation 28 (840 years ago), S attains 2 and the number of ancestors stops growing at about 5.2 million. Theirs

number reaches saturation (Ohno [33] denoted thecorresponding generation as AN SA, ancestry saturated; in the table it is designated GSAT). In generation29 (GSAT + 1) S stabilizes at 2.033, while the number of ancestors remains the same as in the GSAT generation, since N 29 = (N 28/2)2. Beginning with generation30, the number of ancestors of the individual startsdecreasing. This result holds only for freely growing,isolated, and not subdivided population.

To date, the phenomenon of ancestry decline isreferred to as pedigree collapse (http://en.wikipedia.org/wiki/Pedigree_collapse). This appropriate term

was proposed in 1980 by American genealogist R. Gunderson (http://en.wikipedia.org/wiki/Robert_C._Gunderson). Pedigree collapse manifests most strongly insmall population or social groups with a high level of inbreeding. The most illustrative examples are provided

by genealogical tables of some royal dynasties. For instance, practically all texts on the subject list as anexample the pedigree of the Spanish king Alfonso XII(1857–1885) of the Bourbon dynasty. In generation 10of his pedigree there is only 111 ancestors instead of the

expected 1024 (210). The parameter implexe1, measuring the extent of pedigree collapse, calculated as (at –ar )/at, where at is the expected ancestry number and ar

is their real number, is in this case 89%. The pedigree of this king totally collapses in the 17th century, since itascends to a single couple, Loui XIV and Maria Theresia of Austria [7].

Another often cited example of high endogamy also refers to Spanish royalty. It is the pedigree of Charles II (1661–1700), the last king of Spain fromthe House of Habsburgs. In the 8th ancestral generation, he had 82 ancestors out of 256 possible, whichcorresponds to the implexe value of approximately 69%. In their recent study on the effect of inbreedingon the fate of this royal dynasty reigning in 1516through 1700, Alvarez et al. [34] examined its morecomplete pedigree including 16 generations and over 3000 people. Coefficient of inbreeding F of Charles II

was 0.254, i.e., higher than that in the offspring of fullsib marriages or parent–child pairs, for which F =0.25. This result is explained by accumulated distantinbreeding due to regular consanguineous marriagestaking place during nearly 200 years. Even higher F

values were reported for some Egyptian pharaohs, in

1 Russian authors [10] use a French term implexe for pedigree collapse (http://fr.wikipedia.org/wiki/Implexe). Its English variant, implex , is rarely used and considered synonymous to theterm pedigree collapse.





whose dynasties incestous marriages between sibs andhalfsibs were routine. For instance, Aames I from the

XVIII dynasty (1580–1350 B.C.) hadF = 0.375 [35].

In the above examples and other similar cases of extreme endogamy, the pedigrees rapidly ascend to asmall number of ancestors. However, after suchextreme collapse, the number of ancestors of theproband sooner or later starts to gradually increase.Panmictic and close to panmictic populations show acompletely different dynamics of change in the num

ber of ancestors. In that case, as we have seen, thisnumber is increasing for a long time until it reaches acertain value. Ohno [33] made an intuitively plausiblesuggestion that the size of the productive part of a pop

ulation in the ancestry saturated generation is equivalent to the effective size of this population (N e). In thiscase, the increase in the number of proband’s ancestors, accompnied by its relative decrease, would occur

until this number reaches N e. However, Ohno [33]shows on a concrete example that upon stronginbreeding caused by a bottleneck, the ancestral num

ber in the ancestry saturated generation is strikingly different from N e. In any case, all memebers of generation GSAT that produced noninterrupted genealogicallineages are common ancestors of any individual of generation G0 belonging to this population. Evidently,this concerns also the members of more ancient generations than GSAT. In contrast to pedigrees with

Diminishing of the ancestry number of an individual as compared to their expected number

Generation Number of ancestors (expected) Sibling size Number of ancestors (diminished)

31 2147483648 2.033 5009334

30 1073741824 2.033 5091988

29 (GSAT + 1) 536870912 2.033 5176006

28 (GSAT ) 268435 456 2.000 5176 006

27 134217728 1.900 4917205

24 16777216 1.600 3009330

22 4194304 1.400 1589296

20 1048576 1.200 616315

18 262144 1.090 184472

16 65536 1.070 53372

13 8192 1.040 7722

12 4096 1.030 3977

11 2048 1.020 2028

10 1024 1.010 1024

9 512 1.000 512

8 256 1.000 256

7 128 1.000 128

6 64 1.000 64

5 32 1.000 32

4 16 1.000 16

3 8 1.000 8

2 4 1.000 4

1 2 1.000 2

Note: The table was compiled using the data of Ohno presented in [33], after correcting evident misprints.



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strong inbreeding, in which a rapid collapse precedesan increase in the ancestry number, in prosperous (notperishing) panmictic populations the collapse of anindividual pedigree occurs throughout the long history of the population. Clearly, the situation will be different in the case of a perishing population. If its size wasslowly decreasing during the time period examined,then the number of ancestors of an individual in gen

erations preceding GSAT would not diminish going back in time; this number should increase owing to theretrospective increase in the population size.

A catastrophic drop in population size may result ina premature pedigree collapse. In Western Europe,this occurred during the plague epidemic in the 14thcentury (1346–1351) [36], which affected the Russianpopulation to a lesser extent. Another example is adecrease in the population of Russia in the 13th century, during the Mongolian invasion of 1237–1240.Bottleneckcausing events alter the dynamics of growth and reduction in the number of individual’sancestors. Consequently, the population might haveseveral saturated generations. Another reason for adeviation of the ancestry number from the Ohno’spredictions is a long isolation of parts of a subdividedpopulation. In this case, the time of existence of thenearest common ancestors of individuals exceeds thatpreduicted in [33]. Conversely, in small isolates withstrong inbreeding this time is shorter than that in thesimulation model.

I would also like to note the original idea of Ohnothat the decrease in the ancestry number determines

by a Malthusian parameter acting in retrospective[33]. This idea was formulated but nor developed.Fisher [37] termed Malthusian parameter coefficent r in the exponential growth model: N t = N 0e

rt , describ

ing, in particular, population growth. In the case of agrowing population, this parameter reflects the excessof natality over mortality per time unit, which isrelated to natural selection (see [38, 39]). Upon“diminishing growth,” of the individual ancestry number, the Malthusian parameter apparently depends on sibling interference.

COMMON ANCESTORS OF INDIVIDUALS AND DNA COALESCENCE

The issue of most recent common ancestor (MRCA) and most recent common ancestors of two or more individuals is one of the aspects of the pedigreecollapse problem (see [5]). In the 1990s, this issueattracted the attention of several researchers, which

was related to the appearance of several studies on“mitochondrial Eve” ([40, 41], etc.). Using restrictionanalysis and sequencing, the authors of these studiesshowed that all isolated human mtDNA types originated from a single molecule and hence, from a single

woman, who, according to the molecular clock data,lived approximately 100–200 thousand years ago.Mitochondrial Eve, the ancestral mother transmitting

her mitochondrias to all presentday humankind, isthe moost recent common ancestor, from whom allcurrently living people received their mitochondrialgenome (see [42]). However, one should distinguish

between MRCA of particular nucleotide sequences, which is implied in case of mitochondrial Eve, andMRCA of individuals. The time to MRCA of any particular DNA region nearly always is greater than the

time to MRCA of individuals compared.Modeling of coalescence (fusion of genealogical

lineages) of uniparental (mitochondrial and Ychromosomal) markers is performed using haploid models.However, estimation of the time to MRCA of individuals should be based on diploid models. In his study,

which provoked immediate commentaries [44, 45],Chang [43] employed for this purpose a biparental,i.e., diploid Wright–Fisher model, analogous to thestandard, haploid version (see [39)]. This modelassumes constant population size and discrete nonoverlapping generations. Pedigrees are produced as aresult of a random process: for each individual in eachgenerations, two parents are randomly selected from

the preding generation. It was shown that for suchpopulation, if its size N is sufficiently large, the time toMRCA is approximately equal to log2N . Here, MRCA is a single individual who is the common ancestor of allmembers of the given population.

Another result obtained by Chang [43] is that all individuals living 1.77log2N generations ago or earlier and founding any genealogical lineages, are ancestorsof all current population members. More specifically,the representatives of these ancient generations belongto two groups: 80% of them are ancestors of all our contemporaries, forming the given population,

whereas about 20% did not leave offspring and their

lineages stopped.Using another approach to the MRCA problem,

Derrida et al. [46] received similar results. Theseauthors examined the distribution of ancestrors’repeats in genealogical trees in a closed random mating bisexual population of constant size N with nonoverlapping generations. They showed that the distri

bution of ancestrors’ repeats is stationary in generations preceding the generation number log2N . Beyondthis generation, genealogical trees of any two individuals belonging to this population are identical,

because they include the same persons, constituting80% of the corresponding ancestral populations.However, this identity of genealogical trees does not

lead to similarity of the genomes of the individualscompared. Owing to coalescence and recombination,each array of homologous DNA regions has its ownancestral nucleotide sequence [47, 48]. The MRCA of particular DNA regions are distributed among indi

viduals that constitute a relatively small part of theoriginal population [49, 50].

The mathermatical models considered above arenot realistic, which was well understood by their authors. The crudest simplification is the assumption





of complete panmixia. Actual human populationsexhibit a variety of restrictions on random matingcaused by the history of dispersal of the humankindover the Earth, migration, and social stratification.Hence, in modeling processes leading to MRCA, twokey factors should be taken into account: geography that influences the population structure and history that influences the population growth. Simulation

models imitating the effect of these primary factors were developed by Rohde et al. [51, 52].In the first model constructed by these authors,

they considered a population of size N , subdividedinto subpopulations with random mating, which periodically interchanged migrants. This population wasrepresented by graph G , nodes of which correspondedto subpopulations and edges connecting the pairs of nodes, to migration routes. If N ∞, the time (ingenerations) to the MRCA (the most recent commonancestor of all members of this population) is approximately (R + ∆)log2N , wheree R is the radius of G and∆– is a value varying from 0 to 1 depending on the G

structure. The authors termed this individual the (first)universal (i.e., shared by all) ancestor. The time to thenearest generation, all members of which leavingprogeny are ancestors of all current members of thepopulation is approximately equal to (D + 1.77)log2N ,

where D is the graph diameter. This generation wastermed identical ancestry point (IA point). Above, wereferred to it as saturated generation.

The above expressions are similar to those obtainedfor simple models with unlimited panmixia; the coefficients account for population subdivision, which render the datings more ancient. The authors simulated theprocess of transition to common ancestors in populations of different sizes, divided into a different numbers

(one to ten) of subpopulations with adjacent subpopulations exchanging one pair of migrants per generation.The graph with ten nodes superimposed on the worldmap roughly reflected the geographical dispersal of thehumankind. Based on the results of simulation of a population subdivided into ten subpopulations, the authorsmade a conclusion that the universal human ancestor lived 76 generation, i.e., about 2300 years, ago (if thegeneration length is taken to be about 30 years) and theidentical ancestry point was 160 generations (approximately 5000 years) ago.

The second, more complex, model more realistically reflects the demographic history and the population structure dynamics of the humankind. In thismodel, all populated lands were divided into threesubstructural levels: continents, “countries,” and “cities.” “Countries” and “cities” were interpreted notonly as territorial units, but also as correspondingsocial and ethnic groups, within which most marriagecouples are formed. A simplified migration schemegiving probabilities of transfer from one “countries”and “ cities” to others was employed. Each continenthad a definite number of ports, through which intercontinental migrations occurred. Generations were

overlapping; for each individual, longevity, the time of marriage, and the time of childbirth were modeled.The birth rate, depending on the geographical positionof the populations, was matched to the actual data.Under conservative migration conditions, this modeldemonstrates that the MRCA lived in about 1415B.C., while the IA point dates back to the 5353 B.C.More intense migration makes these datings much

more recent: the MRCA, 55 A.D., the IA point, 2158B.C. The fisrst, simpler model, gives intermediateresults: the MRCA, about 300 B.C., the IA point,about 3000 B.C. According to the simulation results,the MRCA (universal ancestor) probably lived in East

Asia.

These results require a commentary. As notedabove, the universal ancestor (MRCA) is the mostrecent individual present in the pedigrees of all currently living people. Evidently, such person existed.Indeed, if in the saturated generation(IA point), 80%of people are ancestors of all our contemporaries, thenin the preceding generations the proportion of suchshared by all ancestors should gradually decrease. Oneof these generations (closest to the present) will haveonly one such individual, and this individual wastermed the universal ancestor. More correctly, heshould be called the first universal ancestor. His contribution to the human gene pool is probably approximately the same as that of many of his contemporaries.However, his position in the genetic tree of thehumankind is unique. The “personification” of theuniversal ancestor and timing of his life are conventional. If a human population was totally isolated anduntil the time of dating did not mix with other populations, the MRCA would be older than the event leading to the isolation. For instance, 9000–12000 years

ago Tasmania was completely separated from Australia by the Bass Strait formed at that time. Hence, beforethe discovery of Tasmania by Europeans in the early 19th century, the universal ancestor of the humankindcould live only be3fore the formation of the BassStrait. To date, all descendants of the indigenous Tasmanians have Europeans or Ausdtralian natives intheir ancestry. Calculations presented in [51] take thisinto account. The datings of the IA point are likewiseconventional. However, in all cases the number of generations until the IA point nearly doubles the number of generations until the MRCA.

The model enables to estimate the proportion of genetic material received by the currently living indi

viduals from populations which inhabit different partsof the world. These proportions are different not only for each ethnoterritorial group, but also for each indi

vidual, in spite of the origin of all people from the sameancestors of the IA generation and their predecessors.The overwhelming majority of the saturated generation made little or no contribution to the contemporary gene pool, which is explained by the limited num

ber of recombining genome regions. Each such DNA fragment is inherited by the modern people from a sin



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gle individual living, as the mitochondrial Eve, inremote past, in many cases even before the appearanceof the species Homo sapiens. The fact is that the timeto universal and identical ancestry in the genealogicalsence is proportional to log2N , and the time to thecommon genetic ancestry is proportional to N , i.e.,population size [44, 51, 52]. Moving along the ascending lineas, the number of genetic ancestors increases

far slower than the number of genealogical ones. Toput it differently, the collapse of genetic diversity is far stronger than that of pedigrees.

Obviously, for a local population the time to theMRCA and saturated generation is far shorter than for the humankind as a whole. This fact is a sound argument in favor of the socalled genealogical myths.

According to the most known of these myths, all nativeElsatians (or even all Western Europeans) descendfrom the Emperor Charles the Great (Charlemagne),

who lived in 742–814 A.D. ([33], http://humphrysfamilytree.com/ca.html, and others). Taking intoaccount that the IA point of the European populationgenerally dates to the first quarter of the 2nd millenium A.D., such genealogical relationships are notonly possible, but very plausible. Similar, and similarly

very plausible myths are common in other regions andcountries, e.g., in Japan [33].

The most conspicuous marks in the ancient andmedieval history were left by highpowered people,such as emperors, kings, princes. They also made anunproportionally large contribution to the humangene pool. Indeed, many of them have left numerousoffspring, both legal and illegal. In this respect, of special interest is the Russian feudal nobility, who had aunique feature distinguishing it from the feudal aristocracy of the Western Europe. The latter typically

belonged to different lineages that had different pedigrees, but Russia for several centuries was ruled by princes who are believed to have one patrilinear ancestor, Rurik [53]. From the 11th to the 16th centuries,they possessed about 110 udels (principalities etc.) andundoubtedly gave rise to a multitude of genealogicaland genetic lineages that survived until the present.

At the end of the last decade, the Family Tree DNA company and Polish geneticist A. Bazhora by therequest of Russian Newsweek studied standard sets of 37 and more Ychromosomal markers of 191 males

who were supposed descendants of the legendary Rurik living in the 9th century. Of these persons, 68%

proved to have haplogroup N1c1 (previously designated N3a); 24%, R1a1; 6%, I; 1.5%, E; and 0.5%, T2.Thus, Rurikids did not have a common patrilinealancestor.Most authors believe that “real” Rurik descendants have haplogroup N1c1, which is mostcommon among Rurikids. According to another and

2 See http://freepages.genealogy.rootsweb.ancestry.com/~mozhayski/teksty/ydna.html, http://www.familytreedna.com/public/rurikid/default.aspx?fixed_columns=on&section=yresults andother websites.

also substantiated view, true Rurikids are characterized by haplogroup R1a1. The former haplogroup isarbitrarily referred to as FinnoUgric; the latter, asSlavic. Both haplogroups are common among Russians. It may well be that medieval Rurikids (and,probably, to a lesser extent Gediminids, the secondlargest group of Russian aristocratic lineages), irrespective of the branches to which they belong, serve as

dominating foci of pedigree collapse in East Europeans and the center of coalescence loci for many DNA sequences from the modern gene pool of this population. This conclusion is supported by the facts testifying to polygamy and concubinate, which were widespread in the Middle Ages and existed even after theadvent of Christianity. As noted in a recent dissertation[54], “in the ancient Russian nobility, church marriage

was introduced relatively quickly, but, owing to their priviledged position, the representatives of higher social strata rather frequently deviated from the Christian norms of marital and familial ethics. Because of this, polygamy and concubinate continued to exist inRussia even after the advent of Christianity. In the

lower social strata, the prevailance of monogamy wasexplained exclusively by economical reasons (theinability of a simple community member to keep several wifes or concubines), rather than by an urge to follow Christian moral norms.”

RECOMBINATION AND GENETICALLYEFFECTIVE ANCESTRY

The average contribution of an ancestor to the offspring genotype is (1/2)n, where n is the number of theancestral generation. However, the actual genetic contribution of different ancestors, beginning from the

second generation, i.e., grandparents, can vary in a very wide range. The probability that some of theancestors did not transmit any nucleotide sequences totheir remote and not so remote descendants increases

with ascending the pedigree. Let us term these ancestors genetically ineffective. The remaining ancestors,

whose DNA was passed to the descendants of the givengeneration, can be termed genetically effective. Theparadox is that each of our ancestors, from most of

whom we did not receive a single nucleotide, is absolutely necessary for our birth. Note that all predecessors in direct male and female lineages are genetically effective, since the former in all cases transmit the

Ychromosome to their sons, and the latter, mtDNA to

their daughters.In the absence of intrachromosomal recombina

tion, at least 18 genetically ineffective ancestors of theproband, who did not transmit him any chromosomes,

would appear as early as in the sixth ancestral generation of 64 individuals. However, in reality, because of limited recombination, the offspring generally receiveseveral chromosome regions from their ancestors.Ohno [33] approximately calculated the number of such regions from the average number of chiasmata





during meiosis, on the assumption that crossingover occurs randomly along the whole chromosome.

According to this estimation, each of us can receivefrom our ancestors in generation 20 no more that 4000chromosome segments. In other words, the number of genetically effective ancestors in the 20th generationconstitutes about 1% of their total number, which,according to the modeling results (see above), is

616315.In the last decade, owing to the advances in

genomics, understanding of recombination processeshas become deeper, more precise and extensive.Ohno’s hypothesis [55] on random localization of crossingover sites, which was later implemented (see[56]) in the model of random breaks, proved to beincorrect. It was shown that the human genome consists of haplotypic blocks with practically no recombination within them ([57] and others). Recombinationsoccur mainly in other, quite small (probably notexceeding 1–2 kb) chromosome regions, which arereferred to as recombination hot spots. Alleles and (or)markers constituting one haplotype are transmittedover generations together. The frequency of theseassociations, testifying to linkage disequilibrium (LD),exceeds theat expected with random combination of these alleles and (or) markers. Quantitative LDparameters reflect recombination in all generationselapsed from the time of appearance of particular mutations [58]. Consequently, the results of population studies of linkage disequilibrium can be used for mapping genetic factors associated with phenotypic

variability (see [59]). With the aim of performing suchassociative mapping, the international project HapMap was set up in 2002. One of its primary goals wasconstructing a haplotype map of the human genome

(hence the name of the project) [60–62].Investigation both in the framework of this projectand conducted independently showed very irregular and far from random distribution of recombinationhot spots [63–67]. Calculations show that on average,recombination hot spots occur in the human genomeevery 50–100 kb. In all, their number is probably 25000–50000. If recombination always occurred inhot spots, this estimate would give the upper limit of the number of genetically effective ancestry. For representatives of many modern ethnoses formed in the lasttwo millenia, the number of genetically effectiveancestry may indeed be restricted to 25000–50000individuals.

However, in the members of more ancient ethnoterritorial communities, the number of genetically effective ancestry can be higher. Recombinationoccurs not only in hot spots, but also, albeit far less frequently, within haplotype blocks. The HapMapproject included analysis of DNA samples from four populations of the African, East Asian, and WestEuropean origin. The boundaries of major haplotype

blocks in the individuals examined were essentially similar, but many amongpopulation differences in

haplotype size and their frequency were found. Of special interest is a strong relative LD deficience observedin Africans. This means that they have much morehaplotype blocks whose average size is far smaller thanthat in persons from other continents. This situation isexplained by the ancient age of African populations,

because the number of recombinations depends on thetime of the population origin. The more generations a

population exists, the more recombinations occur init, which results in a decrease in linkage disequilibrium. The association of alleles in African populationsis much closer to random than that in population of Eurasia and aboriginal populations of North andSouth Americas. In Africans, the number of haplotype

blocks is about 2.5fold higher than in the Asian andEuropean population [68]. Hence, the number of genetically effective ancestry in the average African islikely higher than in the average individual of the Eurasian origin.

The mathematical apparatus used for estimatingthe number of genetically effective ancestors is basedon the coalescence theory. This theory enables toreconstruct the process of coalescence (fusion) of homologous sequences present in the population. Thisis a retrospective stochastic process opposite to divergence, caused largely by genetic drift and mutation.The simplest coalescence model does not take intoaccount such important factors as natural selection,recombination, change in population size, and population subdivision. It is based on the aforementionedhaploid Wright–Fisher model or other neutral modelssimilar to it [48]. However, to estimate the number of genetically effective ancestors of a human individual,one should use more complex coalescence models, by all means taking into account recombination. An

approach to studying evolution of nucleotidesequences in populations taking into account bothcoalescence and recombination was developed by Hudson [47]. In the late 1990s, Wiuf and Hein [49,50],, using this approach, made an attempt to estimatethe number of ancestors to human DNA sequences.These authors examined the distribution of ancestralgenetic material in the chromosomes of individuals,

which was determined only by the product N er , whereN e is the effective population size and r is the expectednumber of recombinations per generation (with regular distribution of recombination points). Particular attention was paid to two key questions: (1) how many ancestors have the modern human chromosome and

(2) how many different sequences from the ancestralpopulation can be detected by sequencing the modernsequences.

Simulation and analytical computations producedthe following results. One human chromosome originate, depending on its size, from 1600–6800 chromosomes, which had all sequences inherited by it. For allpresentday chromosomes, the upper limit of thenumber of such ancestral chromosomes is 86 000, andtheir minimum number, very improbably, is 6800.



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Assuming that the size of the ancestral population of our species 300000 years ago was 1.3 million individuals, the proportion of ancestral chromosomes constituted maximum 3.3% of the total chromosome num

ber. Since the population size was assumed sufficiently large, the probability of positioning the ancestralmaterial on homologous chromosomes is low; themaximum proportion of the “ancestral individuals”

(i.e., the genetically effective ancestors, in our terminology) is 6.4%. Thus, according to these data, thenumber of genetically effective ancestors does notexceed 83200 individuals.

Wiuf and Hein admit that the coalescence model with recombination that they used is based on a num ber of unrealistic assumptions. Complication of thismodel should give other results. For instance, theeffect of bottleneck (which the humankind has indeedpassed, see [42]) decrease N e and thus decrease thenumber of ancestral sequences, whereas subdivision

with migration, increasing N e, have the oppositeeffect. Nevertheless, these authors believe that their assumptions are roughly valid and hence the modelgives an idea on the order of magnitude of the ancestralsequences. However, this model not only leave out thepopulation structure, which was noted by its authors,

but also specific features of recombination processesthat then, more than a decage ago, were not known. Toobtain realistic estimates of the number of genetically effective ancestors, one should take into account thedistribution of recombination hort spots and their evolution, in particular, with gene conversion [69].

GENERATION LENGTH BASEDON AUTOSOMAL, YCHROMOSOMAL,

AND MITOCHONDRIAL DNA

In the previous section, genetic aspects of the lawof doubling ancestry and the law of diminishing ancestry number were considered. Let us discuss here, fromthe viewpoint of genetics, another basic rule of genealogy, the law of three generations. Generation length,

which is also referred to as generation interval or intergenerational time interval, is a key parameter in estimating times of genetic divergence and mutation ratesfrom the pedigree data. Different methods of estimation of this parameter (direct and indirect) areemployed in demographic statistics [70]. In genealogy,genetics, and animal husbandry, generation length isestimated simply as the average age of parents at birthof the progeny [35]. In case of a particular family, generation length is calculated separately for each of theparents as the average age of the father and the mather at birth of their children. The total intergenerationaltime interval is found by averaging these values. For population as a whole, generation length at the giventime period is equal to the average weighted values of total intergenerational intervals for the families comprising it. In some cases, generation intervals are estimated for direct genealogical lineages, for instance,

paternal, and individual pedigrees. In the former case,it is sufficient to know the number of generations and

birthdates of two persons: the first, oldest, ancestor and his latest descendant,who terminates the descending line. The average generation interval is equal to thedifference between their birthdates divided by thenumber of generations.

Genetic studies dealing with divergence of individ

uals and populations by autosomal, Ychromosomal,or mitochondrial DNA, mostly operate with three values of generation length: 20, 25, and 30 years (seereview in [71]). Apparently, only in one of these studies[72], in which the origin of the Iberian population wasinferred from the STR Ychromosomal markers, thegeneration interval was inconventionally taken as35 years. Geneticists in most cases assume generationlength to be 25 and 20 years (see Table 1 in [71]).

In the last decade, three extensive studies on estimation of generation intervals from different DNA types were performed [71, 73, 74]. Tremblay and Vezina [73] examined the population of the francophoneCanadian settlement Saguenay situated to the north

west of Quebec City. The intergenerational time inter vals were estimated using family reconstitution andgenealogical reconstructions. In the former approach,data from large inventory BALZAC Population Register, which had been compiled from parish registers.The authors used data on 3290 women and 3367 mengiving birth in 1850 through 1880 to at least one child

who also registered marriage in the same region. Thelatter approach was based on the information fromBALZACRETRO Genealogical Database on morethan 120000 marriages registered in the time intervalfrom the late 16th century to the present. Generationlengths were calculated for ascending pedigrees of

100 randomly chosen individuals (50 couples), registering marriage in the given region in 1900 through1974. The average length of these pedigrees, comprising 237822 ancestors, was nine generations, but many lines were longer, up to 12–13 generations.

Both approaches yielded similar results with anexception of a remarkable, though small, difference

between female generation intervals, which areexplained by specific features of the demographic history of the population examined. Rounded off, theaverage generation intervals were as follows: 32 yearsfor autosomal loci (all intevals), 35 years for Ychromosomal loci (male intervals), 29 for mitochondrialDNA (female intervals), and 31 for Xchromosomalloci. The latter were calculated as mean weightedfemale intervals with weight of 2/3 and male intervals

with weight of 1/3; the weights reflect contributions of sexes into the formation of the pool of X chromosomes. It is supposed that the demographic parametersof the population examined (high, close to natural,fertility, high mortality, relatively young marriage age)are similar to those in many populations with ancienthistory. These include a number of European populations that probably had the same characteristics during





the last 500 years. However, as in the majority of European populations the marital age was older than in thepopulation studied, the former probably have some

what longer generation intervals.

Helgason et al. [74] studied rates of evolutionary changes occurring during the last 300 years withmtDNA and Ychromosomal haplotypes in Iceland.The pedigrees were constructed on the basis of the

information from the deCODE Genetics genealogicaldatabase, which contains data on 280000 currently living Icelanders. Male and female lineages of 131060individuals born after 1972, were traced to the ancestors born between 1698 and 1742 and between 1848and 1892. These two cohorts of matrilineal and patrilineal ancestors constitute only part of Icelanders bornin the given time intervals. In the course of developingthe main line of research, the authors estimated generation intervals between the modern Icelanders and therepresentatives of the both ancestral cohorts. For thefemale and male lineages extending to 1848–1892, theaverage generation intervals were respectively 28.12and 31.13. In the female and male lineages connectingour contemporaries with their ancestors born in1698–1972, the corresponding intervals were 28.72and 31.93. Thus, the female intervals proved to beabout 10% shorter than the male ones. The generationlength tended to decrease during 300 years.

The above estimates were produced for the pedigrees ascending from the present days to the NewTime, manifesting the beginning of modernity. However, this is a very short period of the human history.Can we apply the results characterizing the populationof the modern Western states, to the communities of huntersgatherers constituting the humankind duringthe most part of its existence? An indepth answer to

this question was provided by Fenner [71], in which acrosscultural comparison of generation intervals wasperformed.

Fenner [71] based his research on the UNO recordof 2000 on the population of 191 countries, constituting 97% of the global population, and statistical recordof the European Counsil for 2002. These data summarize the results of national censuses and special studiesconducted in 1970–1998. Another source was data of ethnographers collected in the 19th–20th centuries inthe investigations of 157 communities of hunters–gatherers from Africa, Asia, Australia, North America,

Arctics, and South America. Generation length wasestimated by indirect methods on the basis of suchparameters as the age at the first and last childbirth,mortality, and mean difference between the male andfemale ages at the first marriage. In the developedcountries, the generation interval was 30.8 in male lineages, 27.3 in female lineages, and 29.1 in mixed(total) lineages. In the developing countries, thisparameter was 31.8 in male lineages, 28.3 in femalelineages, and 30.1 in mixed (total) lineages. In thehunters–gatherers communities, the correspondingparameter was 31.5 in male lineages, 25.6 in female

lineages, and 28.6 in mixed (total) lineages. Theauthor concludes that in studying population divergence by Y chromosomes one should use a generationinterval of 31 or 32 years; by autosomes, 28–30 years;and by mtDNA, 25–28 years.

As we see, the law of three generations is valid only for male lineages. This is explained by the fact thatpractically during the whole history of their science,

genealogists were mostly concerned with male pedigrees. If they had been focused on female pedegrees,they would have formulated ther law of four generations. The above estimates of generation intervals wereobtained for last centuries, but they little differ in thepeople from similar and quite different culture types,including archaic ones. Consequently, these estimatesseem to be fairly universal and applicable to any human pedigrees with any depth. However, in somepopulations (e.g., Australian natives, see [71] for references), characterized by unusual demographic parameters, generation lengths can significantly differ fromthe “standard.” In such cases, special investigation isrequired to verify these estimates. Notwithstanding, inmany genetic works, the generation intervals used areunderestimated, therefore, the datings and mutationrates presented in them need revision.

GENETIC BOUNDARIES OF KINSHIP

According to an online encyclopedia and other sources, ‘some geneticists believe” that any two of our contemporaries are related at least as 50th cousins(http://en.wikipedia.org/wiki/Pedigree_collapse), whichis doubtful, because contradicts datings of identicalancestors point obtained in [51]. The results of “simplified calculation,” presented by the authors of a text

book on human molecular genetics [75], seem moreplausible. According to them, the common ancestor of any two “unrelated” British persons lived, as a rule,not earlier than 22 generations ago. Almost the sameresult was reported by an English genealogist, according to whom such common ancestors of the UnitedKingdom residents lives 23 generations ago(http://www.bpears.org.uk/Misc/AncestorParadox/).The discrepancies concern only absolute dates: thegeneticists state that the interception of the ancestrallineages occurred approximately in 1500, and the genealogist, around 1300. The former apparently strongly underestimated the generation interval, which resultedin an errouneous conclusion [see above]. Several years

ago, one of the Russian genealogical portals presentedthe information according to which the populationconsisting of common ancestors of all residents of Russia also lives 23 generations ago. However, this “finding” was not substantiated. Apparently, the IA point for the inhabitants of Russia, as well as for Russians as such,

because of their complicated enthnic history is situatedmuch farther.

From the viewpoint of both genealogy and genetics, ancestors are dissolved in the descendants, and



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vice versa. Consequently, all members of local population are related. More distant kinship connect mem

bers of different local populations, constituting thehumankind. However, genealogy traditionally deals

with rather close relatives, belonging to one family or kin (lineage). How far should one extend the boundaries of families and lineagess in genetic genealogicalresearch?

Before answering this question, let us clarify thenotions of family and lineage (kin). Social institutesdenoted by these terms are very diverse. Hence, we willgive only the definitions clarifying their use in geneticsand genealogy, where they are of similar meaning. Inhis textbook on clinical genetcis, N.P. Bochkov [76]define them as follows: “Family in the narrow sense isa married couple and their children, sometimes thisterm is applied to a broader circle of relatives, but inthe latter case the term kin (lineage) is preferable.” This implies that lineage is an extended family. However, husband and wife generally originate from different lineages, if the marriage is not consanguineous.Thus, the above definition is obviously contradictory. Ihave not come across satisfactory definitions of family and kin (lineage) in genetic and genealogical literature. The modern sociological and legal definitions of family are vague and cumbersome, while derfinitionsof kin are altogether lacking. The relationships

between the notions of family and kin are clarified inlight of ethnography.

According to the traditional ethnographic definition, kin (lineage) is a group of relatives acknowledging their origin from the common ancestor [77]. In thegenetic sense, a lineage must stem from real rather than mythical ancestry. The members of a patrilinear lineage are related by the male line, and matrilinear, by

the female line (these lineages include mitochondrialclans, see [5]). Bilateral lineages include all descendants of the common ancestor both by male andfemale lines. According to the Code of Laws of the Rus

sian Empire (vol. X, part I, chapter III On the kindred relations, provision 196) “Kin is the union of all family members of male and female sex, stemming from oneand the same forefather, though not all of them may beof his name or sobriquet” (http://civil.consultant.ru/reprint/books/211/20.html#img21). In thissense, kin is not equivalent to the large family, since itdoes not include marriage partners by female lines,

which belong to other kins. The nuclear family, if it isnot consanguineous, combines two family lineages,and indirectly, a multitude of them. Through spouses,the members of different kins are connected via relationships by marriage. In ethnography, the extendedanalog of a family (suprafamily [78]) is a tribe rather than a kin. A tribe includes two or more exogamouslineages related by marriage. In contemporary societies, suprafamilies, by analogy, correspond to a set of family lineages, or, more precisely, the whole population within which the marriages are performed. Considering suprafamily in a wider chronological context,

its lineages correspond to numerous individuals belonging to various haplogroups and haplotypes by uniparental DNA. A population is united intosuprafamily through the saturated generation. Thelarge lineages (supralineages) marked by haplogroupsinclude individuals belonging to different, sometimesgeographically distant populations.

Discussing the issue of genetic boundaries of kin

ship, one cannot dispense with the notion of degree of relationships, which is differently interpreted by geneticists and genealogists. In the Code of Laws of theRussian Empire (ibid., provision 198), the degree of relationship is defined from genealogical positions as“the association of one person with another one by

birth”. Genetic estimates of relationship are based onthe coefficient of relationship (R) introduced by

Wright [79]. The coefficient of relationship is the proportion of genes of common origin shared by two indi

viduals. Using these approaches can result in differentestimates of relatedness. For instance, in terms of genetics, the parent–child pair and a sib pair have thesame first degree of relationship, as in both cases R =0.5. From the genealogical point of view, parents andtheir children also show the first degree of relationship, whereas sibs are related by the secod degree,

because they are separated by two births. The discrepancy between the genetic and the genealogical estimates in this case is explained by the fact that a parentis related to the child directly, and sibs are related collaterally, via their parents. In terms of Wright’s pathcoefficients (see [80, 81]), the child with respect to oneof the parents is a variable with one independentcause, and sibs with respect to one another, variables

with two common causes. Relatives by collateral lines,related by marriage in one of the earlier generations,

are closer by autosomal genes than the direct relativesequivalent to them in genealogical relatedness. Notethat estimation of the degree of relationship by thenumber of births has a profound genetic meaning,since the number of births is proportional to the num

ber of meioses promoting mutation and recombination. Some geneticists of the old school, e.g., Stern[21], evaluated relatedness by the number of births.

F.M. Lancaster, geneticist dealing with genealogy, believes that collecting information on collateral relatives more distant than third cousins is pointless [35].In this case, R = 1/128 ≈ 0.0078, or 0.78%. Somegenealogists reduce investigation of family pedigreesto the reconstruction of four main lines descending

from grandparents. However, the cumulative contri bution of these ancestors in the proband’s genotyperapidly decreases, constituting the same 0.78%(4/512) already in generation 9.

Today it is well known that the average number of nucleotide differences between the genomes of tworandomly chosen individuals ranges from 1 per 1500 to1 per 1000 (see [82]). This number is nothing other than nucleotide diversity π [83]. Typically it is taken to

be 1/1000. This means that genotypes of two unrelated





individuals on average differ by 0.1%. Probably, directrelatives of the seventh degree of relatedness (R =0.78%), collateral relatives of the eigth degree (i.e.,third cousins), and, naturally, more distant relativesgenetically are as distant as unrelated individuals.

However, the situation is not that simple. Accordingto the results, obtained in Phase II of the HapMapproject, 10–30% of couples from the same large popu

lation has at least one shared long genome region thatthey inherited from a recent common ancestor [61]. Inthe Canadian and Iceland populations examined [73,74], the main contribution to the gene pool was made by their founders. However, the values of their individualsconntributions are highly variable; the lion’s share of the genetic material is inherited by the presentday population from a relatively small number of first settlers.

PROBLEMS AND PERSPECTIVES

Geneticists have been and are studying problems of genealogy and related historical issues. Genetic investigation of the genealogy of the Spanish branch of theHabsburg dynasty was mentioned above [34]. Alvarez etal. [34] describe in detail the genetic degradation of thislineage resulting from inbreeding, which caused the War for Spanish Heritage (1701–1714), the largescale andprotracted conflict that had a significant impact on thefates of the European countries. Many examples of theinfluence of hereditary features of prominent personson historical events can be found in the book by

V.P. Efroimson [84], who continued the traditions of the Russian eugenic school (see [5, 15, 16].

The modern stage of development of this researchdirection is connected to genetic genealogy. Molecular genetic identification not only constitutes a part of

complex genealogical investigation, supplementingand correcting the archive data [5], but also is sometimes one and only method that can shed light oninteresting for historians and intriguing “genealogicalmysteries.” One of these, mentioned above, is relatedto the Rurikids dynasty, whose members ruled the

Ancient Russian, and later Moscovian state from the9th to the 16th centuries. This dynasty was interruptedin 1598 by the death of Fedor Ioannovich. In the early 17th century, Vasilii Shuiskii, also a Rurikid, came tothe tsar throne, but very soon was overthrown. Thedetection of haplotypes from different, mainly two

Ychromosomal DNA haplogroups (N1c1 and R1a1,see above) in the presentday Rurikids raised a burningissue on “true” and “false” members of this dynasty (inDecember 2010, it was discussed in several reports at the17 Savëlov Lectures on “Genealogy and Genetics,” seehttp://www.gentis.ru/company/news/savelovconference; these annual lectures are named after the aforementioned classic of Russian genealogy L.M. Savëlov). To resolve this issue, YDNA from theremains of some ancient members of the clan should betyped, which for a number of reasons has not been carried out yet. The resolving of the problem of the genetic

roots of the ruling Rurikid dynasty may bring progress tothe dispute between the adherents of the Normann andantiNormann theories, which has been conducted for nearly three centuries.

Intriguing genetic problems that can be resolvedonly by means of genetics are related to the Romanovdynasty. Investigations ([85] and others) devoted to thegenomic identification of the family members of the

last Russian emperor Nicolai II3 did not shed light on

his patrilineal origin. The problem is as follows. It isknown that the male lineage of this tsar dynasty wasinterrupted in 1730 by the death of Peter II Alekseevich, a grandson of Peter the Great. In 1761, after the decease of tsarina Elisaveta Petrovna, the daughter of Peter the Great, the throne was ascended by Peter III(Carl Peter Ulrich, Duke of Holstein; since 1742, theGrand Duke Peter Fedorovich), another grandson of Peter the Great, a son of his daughter Anna and theDuke of Holstein. He was the founder of the HolsteinGottorp line of the Romanov dynasty, which reigned inRussia up to 1917. After ruling for half a year, Peter III

was demised and a week later killed by the adherents of his wife (and second cousin) Ekaterina Alekseevna,

born Sofia Frederica Augusta, a princess of the AnhaltZerbst House, who mounted the throne in 1762 as Ekaterina II (Catherine the Great). The heir to the throne,Grand Duke Pavel, was born in 1754. However,according to his contemporaries, his father was notPeter Fedorovich, husband of Ekaterina Alekseevna,

but Chamberlain Sergei Vasil’evich Saltykov, adescendant of the ancient boyar family of Morosovs.Some historians find support for this version in Memoirs by Catherine the Great (see [53, 87]). If this istrue, then all subsequent Romanovs inherited the

Ychromosome of Saltykovs, rather than that of theHolsteins. The Materials on the Biography of Emperor Pavel III , published in 1874 in Leipzig, even claimedthat Ekaterina had a stillborn child by Saltykov, who

was changed for a Veps boy (see [87]). In fact, the situation is even more complicated. As argued by Efroimson ([84], p. 359), the biological father of Emperor Nikolai I was not Pavel I, but the “handsomegiant” Bobkov, a manservant of Empress MariaFedorovna (born Sofia Dorothea Luisa Augusta, Princess of Wurtemberg–Stuttgart, the second wife of

3 In 1913, father of the author of the present article, Ya.P. Tetushkin (http://www.rasskazovo.ru/index.php?option=com_con

tent&task=view&id=49&Itemid=25), together with other students of Tambov Ekaterininskii Teachers Institute, participatedin a gymnastic performance given to Nikolai II. The tsar visitedTambov on an inspection tour on the occasion of the 300thanniversary of the Romanov Dynasty. Interestingly, in 1915 Ya.P. Tetushkin graduated from the 2nd Moscow Ensign School,in which studied, almost concurrently, the future renownedgeneticist A.S. Serebrovsky. February 2012 will mark the 120anniversary of this prominent scientist, who in the early 1920scompiled one of the first card catalogs on the kinship of illustrous Russian historians and cultural figures (see [86], p. 43).This card catalog was a prototype of the presentday genealogical databases.



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Pavel I). Pavel Petrovich allegedly knew that fact andrepeatedly commented on it. Efroimson supportedthis version with genetic argumentation: “Indeed, incontext of modern genetics of height, the origin of very tall Nikolai from undersized Pavel I is very implausi

ble.” Thus, whose Y chromosome carried the lastRomanovs, beginning with Nikolai I? Was this chromosome inherited from the “Holstein heir” Peter III,

Saltykov, the unknown veps, or Bobkov? The issue onthe haplogroup attribution of Romanovs’ Ychromosomal DNA is understandingly in the focus of interestof Russian historians; it was raised at the 17th SavëlovLectures.

Many genealogical problems that can be resolvedonly genetically pertain to nobility whose roots go tothe antePeter the Great Russia. When in the 16th–17th centuries, official genealogies came to fashion,noble families typically claimed to descend from a foreigner, because purely Russian origin was at that timeconsidered not prestigious. This resulted in numerouspedigrees descending from foreign kings, dukes, etc.Historians like to debunk these “legends on the foreign origin.” Methods of molecular genealogy are of invaluable importance in such studies.

Let us now consider the potential contribution of genealogy to genetics.

Russian nobility is thought to have two specific features distinguishing it from the Western counterpart[53]. One of them, the domination of a single clan, theRurikid family, ruling for many centuries in the feudalRussia, was already mentioned. The other specificity lies in the extreme ethnic variety of the Russian nobility at the beginning of its existence. In addition to military officers, it included descendents of the nobility of nationalities annexed to Russia, Ordyn feudal lords,

German crusaders, Polish and Lithuanian gentry,Byzantine kings, etc. Largelanded gentry possessedtens of thousands serfs and, like Rurikids, though on asmaller scale, could be centers of pedigree collapseand coalescence foci loci of DNA sequences of theRussian population as a result of a special form of group social selection based on the social prestige [88].Zerjal et al. [88] suggested the exitence of such selection on the basis of the results of their investigation of

Ychromosomal markers in 16 Asian populations.These authors found an unusually frequent haplotypeidentified by 32 and more markers. This haplotypeoccurred in approximately 8% of males from theregion examined and in about 0.5% in males world

wide. The variation pattern of this Ychromosomallineage suggested that it arose in Mongolia about1000 years ago. It was concuded that the carriers of this haplotype are descendants of Genghis Khan (diedin 1227). Men of this clan, Genghizids, for many generations ruled over large territories of Asia and couldmake an enormous contribution to the gene pool of their population. Some genealogists are doubtfulabout these conclusions. However, so far there have

been no publications refuting the results reported by

Zerjal et al. [88]. Therefore, we can assume that largelanded gentry, including Rurikids, also made a disproportionally large contribution to the gene pool of thepopulation, in which they lived. This may partially explain the local genetic identity of the population of Russia. As noted by Kol’tsov [89, 90], the huge cultural and economical gap between the higher andlower strata that had existed in Russia did not prevent

vertical gene migration from the top to the bottom4.The advances in computeraided and molecular genealogy open the avenues for studying this process,

which apparently have greatly influenced the geneticstructurte of the Russian population.

The nobility, particularly titled families, complex investigation of which is of obvious interest, may alsoserve as a model for genetic studies. This is the only estate that has a multitude of deep, intercepting pedigrees of its members. One of the issues here is theseemingly unlikely appearance of constellations of gifted people in different, remote branches of somepedigrees. These include, for instance, the pedigree of

the Tolstoi–Pushkin family well known from the article by Kol’tsov, which is quoted by Efroimson [84] asan example of “dynastic genius.” There are speculations on the role of heredity and social/familial continuity in appearance of such dynasties. Apparently, theleading role in this and other cases is played by maritalselection in the narrow circle of gifted and sometimesnot very distantly related partners. The effect of factorsaltering the probability of transmission of hereditary traits (selection against deleterious mutations, meioticdrive, etc.) cannot be excluded [91]. Investigation of the genomes of numerous offsring of these families canshed light on the reasons of giftedness and other hereditary features of their illustrious ancestors. To

date, it is generally accepted that giftedness, in spite of the presence of a significant environmental and probably stochastic components [92], also has a substantialgenetic component.

As noted above, consideration of general genealogy of the population of distinct areas (Canada, Iceland)from the genetic viewpoint produces interestingresults. In these studies, genealogical and populationanalyses supplement one another. What is the specificity of studying genetic phenomena using genealogicaland population approaches? Which are the advantagesof each of these approaches?

In the recent years, genealogical (familial)

approach is employed in linkage analysis, i.e., methodof gene localization based on detecting cases of jointinheritance of genetic markers and Mendelian phenotypes. However, this approach is unproductive insearching genes responsible for complex traits, e.g.,multifactorial diseases. For this, geneassociative

4 In this connection, Kol’tsov wrote: “Strong were the chains thatconstrained Russian peasantry and high was the wall separatingit socially from the priviledged classes. But biologically, that walldid not exist.” [89].





investigations, which can be performed in the frame work of either familial, or population approach, aremore suitable [93]. In such studies, the search for genes responsible for the given phenotype, is based oncomparing allele frequencies in individuals that haveor lack a particualr traits. The familial version of geneassociative studies requires more funding for genotyping than the population vewrsion. However, the results

produced by the former method are more reliable,since they are not subject to the bias caused by thepopulation structure and migration. On the basis of the data on transmission of familial traits, includingdiseases with hereditary predisposition, in generations, one can establish the genetic factors underlyingthem.

To anal;yze genetic recombination occurring in pedigrees ancestral recombination graphs (ARGs) are used(see [94–96], http://www.stats.ox.ac.uk/ __data/assets/file/0012/3333/counting_args.pdf). ARGs reflectinginterrelationships of numerous homologoussequences subject to recombination are far more

informative than traditioanl binary pedigree schemes.They describe the appearance of mutations, the eventsof recombination and coalescence, which, in transition from the present to the past, ultimately bring eacharray of homologous DNA positions in the population(“suprafamily”) to the single ancestral sequence. Theset of ARG trees related to a particular pedigree givesan idea of main genomic “perturbations” havingoccurred in this pedigree. It may well be that the construction and interpretation of suxch graphs will

become one of the primary dire3ctions in geneticgenealogy.

In this connection, the term phylom comes tomind. Phylom is the set of all phylogenies of all genesin the genome [97–99]. Reducing this evolutionary concept to an individual familial pedigree of a particular species, say Homo sapiens, we obtain, if geneimplies any recombination unit, a set of molecular genealogies descibed with ARGs. This array of DNA genealogies can be termed genealom. Supplementingdata of personal genomics, required for constructinggenealoms, by the data of personal phenomics (see[100, 101], i.e., detailed descriptions of phenotypes(phenoms) of the family members, in distant perspective may shed light on genetic mechanisms underlyingformation and reproduction in generations of stable

familial traits, including creative talents.

ACKNOWLEDGMENTS

I am grateful to the anonymous reviewer for reading the manuscript and giving valuable comments andto Yu. S. Belokon’ (Altukhov Laboratory of Population Genetics, Vavilov Institute of General Genetics)rfor assisting in the preparation of the figure.

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Genetic Aspects of Genealogy E. Ya. Tetushkin

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