Genetics and Genealogy
     It has been known since remote prehistory that children tend to inherit many characteristics from their parents, e.g., physical appearance, temperament, intelligence, etc.  Indeed, it was probably no more than such simple observations that motivated the very first interest in genealogy.  Of course, for most of human history heredity was an entirely mysterious phenomenon and, as such, was commonly attributed to favor of the gods or even more obscure mythological causes.  Furthermore, in antiquity genealogy was typically restricted to families of the most influential members of society, viz., royalty and aristocracy, with lineages of common people generally considered to be of no importance and unworthy of record.  Within this context, pedigrees of "noble bloodlines", were compiled, perhaps, in part to provide social justification for the importance and continued dominance of a ruling dynasty as well as to negotiate and contract marriage alliances between rival family groups.  Alternatively, conquest and enslavement of "inferior" people was an obvious corollary to this kind of thinking, which in more recent times led to such evils as the institutionalization of chattel slavery along racial lines.  Thus, it is to be devoutly hoped that in modern democratic societies such elitist notions have, at the very least, come to be considered as quaintly out-of-date.  More seriously, in light of the misfortunes of the first half of the twentieth century associated with the pseudo-scientific nonsense of eugenics and related political theories, viz., fascism, National Socialism, etc., it has become painfully clear that such ideas actually can be dangerous.  Fortunately, the advent and development of the science of genetics now places genealogy on a completely rational foundation without any trappings of race or nobility.

Genes, Chromosomes, and DNA

     The first really quantitative study of biological heredity was done in obscurity in central Europe during the the middle decades of the nineteenth century by the Augustinian monk, Gregor Johann Mendel.  Through careful breeding and crossing, i.e., hybridization, of ordinary garden pea plants (Pisum sativum), he observed that particular morphological characteristics are transmitted to offspring in a definite and predictable pattern.  Accordingly, Mendel's discovery has subsequently provided a firm foundation for modern genetic science; however, its significance was not recognized for thirty-five years after its original publication in 1865.  Thus, it was not until 1900 that Mendel was "rediscovered" almost simultaneously by Carl Correns in Germany, Hugo de Vries in the Netherlands, and Erich von Tschermak-Seysenegg in Austria.  Two years later in the United States, Walter Stanborough Sutton suggested that minute fibers called chromosomes (first identified in the 1880's as "colored bodies" due to their propensity to become strongly stained by various dyes) located within cell nuclei might actually carry Mendel's hereditary "factors".  In coming to this conclusion, Sutton had noticed through careful microscopic observation that within ordinary nuclei, chromosomes normally occur in pairs.  Moreover, the following year he proposed that each gamete, i.e., each egg (oocyte) and sperm cell (spermatocyte), receives only one chromosome from any particular pair as a consequence of a special form of cell division called meiosis.  In contrast, in the process of ordinary cell division called mitosis, the chromosome pairs are fully replicated in each daughter cell.  Consequently, two apparently separate phenomena were, thus, found to be fundamentally connected, that is to say, Mendel's patterns of "factor inheritance" and the process of segregation of chromosomes in gametes followed by subsequent recombination during formation of a fertilized egg or zygote.  Of course, all cells of any fully developed multicellular organism, be it plant or animal, necessarily descend from an original zygote through successive mitotic cell division..  That chromosomes determined heredity was conclusively proven by Thomas Hunt Morgan in 1910 from results obtained in his famous fruit fly (drosophila) experiments.  As could have been expected, this has led to spectacular practical advances in plant propagation, animal breeding, medicine, etc.
     Even so, the term gene was not used by early researchers and seems to have been first proposed by Wilhelm Johannsen in 1909 as a primitive unit element of heredity or genotype, i.e., the complete genetic consitutution of an individual organism.  (As a scientific term in English, "gene" seems to have first appeared in print in 1911.)  Accordingly, in Johannsen's view, which has come to be generally accepted, genotype determines phenotype, i.e., the totality of inheritable biological traits, but not the reverse.  However, any microscopic physical basis for this relationship long remained beyond observation and, thus, entirely a mystery.  Indeed, Johannsen himself asserted that the gene was an abstract concept "completely free of any hypothesis".  Nevertheless, it became the conviction of other researchers, notably Morgan and his students, Alfred Henry Sturtevant and Herman J. Muller, that genes actually had to exist as material structures and, as such, that they were located in some sort of linear order along the various chromosomes.  Even so, it was the work of another of Morgan's students, Calvin B. Bridges, published in 1914 and afterward that is generally considered to have proven that genes are fundamentally associated with chromosomes.  Such ideas were originally motivated by observations that various traits tended to be inherited together, which suggested that corresponding genes were in some sense "located" in close proximity.  This phenomenon is called gene linkage and contrasts with pure Mendelian inheritance in which all factors assort independently.  Moreover, it was also observed that there is some probability that linked genes will reassociate or cross-over (apparently due to exchange of chromosomal fragments between paired chromosomes) during meiosis.  Concomitantly, Sturtevant realized that the frequency of crossing-over could be interpreted as a measure of separation between specific gene locii and used corresponding observations to construct linkage maps.  Of course, at that time such maps were merely abstractions without any demonstrable physical basis.  However, Muller obtained rather convincing evidence for this physical conception of genotype by further experiments involving fruit flies exposed to x-rays, which caused inheritable changes in phenotype that could best be explained as being caused by radiation damage to the chemical structure of the chromosomes and, hence, to the genes themselves.  In addition, such sudden changes in inheritance or mutations were also rarely known to occur spontaneously in nature.  Presumably, natural mutations were also caused by random changes in the chemical structure of chromosomes.  Obviously, cellular damage due to exposure to ionizing radiation quite reasonably could be expected to greatly increase the frequency of such changes.  Furthermore, it was discovered early in the development of cytology, i.e., the study of cell structure, that chromosomes stained by a particular dye would exhibit characteristic patterns of light and dark bands when observed by high resolution optical microscopy.  These bands could then be used to observe changes in chromosome structure in succeeding generations of organisms, e.g., fruit flies.  Thus, direct microscopic observation of chromosome banding by workers such as Theophilus Painter provided further indication of the materiality of genes-on-chromosomes.  However, collateral research also revealed further complications, viz., such phenomena as translocation (movement of one section of a chromosome out of normal sequence), inversion (reversal of sequence of some particular chromosome segment), and deletion (loss of part of a chromosome).  Clearly, if genes existed in a strict linear arrangement along chromosomes, it would seem that such "errors" should cause large and probably non-viable changes in phenotype.  This did not seem to be true in many cases as shown by the painstaking experiments of Barbara McClintock on Indian corn (zea mays) that demonstrated that such chromosomal changes not only could be viable, but were inheritable.
     This rather unsatisfactory situation prevailed in the 1930's and 1940's, but at the same time motivated what has come to be called molecular biology or molecular genetics of which two fundamental concepts go all the way back to Muller who called them autocatalysis (which corresponds to the modern concept of gene replication) and heterocatalysis (which is to be identified with gene expression).  Clearly, Muller's choice of terms indicates that in the most elementary sense, he believed that the activity of genes must be chemical in nature, but at that time this chemistry was not even remotely understood.  Concurrently, medical research on the virulence of pneumonia bacteria (Diplococcus pneumoniae) carried out by Fred Griffith as early as the 1920's demonstrated that some component contained within heat-killed cells of a disease-causing strain could induce a harmless strain to produce the disease.  These results were confirmed by Dawson in 1930 and then two years later Alloway showed that only a filtered cell extract was necessary to transform harmless pneumococcus into a disease-causing form.  Morever, this virulence was inheritable implying that the necessary gene had been either created or transferred in this process.  A decade later, Avery, Mcleod, and McCarty found that the purified transforming substance could be identified with deoxyribonucleic acid or DNA.  Indeed, for many years nucleic acids had been known as chemical components of cell nuclei distinct from proteins; however, they were thought to be without any identifiable biological function and merely some kind of structural component.  Concomitantly, two types of nucleic acid could be distinguished by associated hydrolysis products.  For one type, typically obtained from thymus gland tissue as well as other sources, hydrolysis produced four organic bases, viz., adenine, guanine, cytosine, thymine; the pentose sugar, deoxyribose; and phosphoric acid.  Of course, this corresponds to DNA.  For the other type extracted from yeast, phosphoric acid, a simple sugar, and four bases were again obtained by hydrolysis.  Moreover, three of the bases remained the same as before in thes case of DNA, but the fourth was found to be uracil rather than thymine.  Likewise, the pentose sugar, ribose, was obtained instead of deoxyribose.  Accordingly, this substance was called ribonucleic acid or simply RNA to distinguish it from DNA.  Even so, it is evident that DNA and RNA are chemically quite similar since thymine differs from uracil by substitution of a single methyl group and ribose and deoxyribose differ only by a single hydroxyl.  Nevertheless, it was not known how these components were arranged to form a complete nucleic acid and, consequently, nothing could be determined regardiing the function of these substances within a living cell.  Thus, Avery, Mcleod, and McCarty rather cautiously suggested that DNA induces a mutation into the genotype of the bacterium; hence, causing the harmless form of pneumococcus to become virulent.  Moreover, subsequent research published in 1952 by A. D. Hershey and Martha Chase on the composition of bacteriophages infecting common intestinal bacteria (Escherichia coli), established the inescapable conclusion that genes themselves must be embodied in the chemical structure of DNA.  By induction, the DNA hypothesis was extended to all biological organisms.  Indeed, this presumption has been spectacularly confirmed in all subsequent research with the exception of a few viruses, viz., retroviruses, in which the genetic material has been found to be RNA rather than DNA but, even so, still a nucleic acid.  Furthermore, during this same period, knowledge of structural chemistry was greatly advanced by Linus Pauling and others who applied the physical concepts of quantum mechanics to molecular systems.  Therefore, the stage was set for a new "annus mirabilis" similar to the year, 1900, during which the importance of Mendel's laws of heredity came to be recognized.
     Consequently, in the following year of 1953, James Watson and Francis Crick proposed a double-stranded, helical, complementary, anti-parallel structure for DNA.  In this picture two polymeric chains composed of deoxyribose molecules linked by phosphates form the "backbone" of a DNA molecule.  These are further linked by hydrogen bonding of pairs of organic base molecules (a purine and a pyrimidine) to form a sort of molecular "ladder", i.e., two "rails" formed by the sugar-phosphate chains linked together by base pair "rungs".  Moreover, from x-ray diffraction observations made by Rosalind Franklin and Maurice Wilkins, Watson and Crick further concluded that rather than a flat planar configuration, DNA molecules must be twisted in a right-handed double helix having a periodicity of 3.4 nm.  It seems probable that this twisting provides additional chemical stability by shielding bonded base pairs from the external environment.  Of course, a substantially stable chemical structure would seem a necessity if DNA is to serve as the elementary substrate for genes.  In addition, it was immediately evident that the double helix structure could elegantly account for the autocatalytic properties of genetic material.  In particular, the four "nucleobases" of DNA are not associated randomly, but in definite combinations, viz., adenine with thymine (with uracil in RNA) and guanine with cytosine.  Consequently, if DNA could be untwisted and divided symmetrically into two complementary halves consisting of one sugar-phosphate chain combined with one member of each of the sequential base pairs, then it would seem reasonable that each half could serve as a template so that two identical copies of the original molecule could be reconstituted from simpler components, e.g., free bases, sugar, and phosphate, which might already be partially combined as nucleosides, i.e., compounds of ribose or deoxyribose with one of the four bases, or nucleotides, i.e., compounds of corresponding nucleosides with phosphate.  Although, it comes as no surprise that the actual details are quite complicated, it is essentially this process that occurs when chromosomes are observed splitting and replicating in mitotic cell division.  Subsequently, using Escherichia coli again, the first example an active enzyme (DNA polymerase I) for biological synthesis of DNA was discovered by Kornberg and his colleagues later in the 1950's.  Likewise, it was also recognized that the structure of DNA can account for heterocatalytic properties as well.  For this it is the particular sequence of nucleotide base pairs arranged along the sugar-phosphate polymeric chain that is significant.  Indeed, the complete sequence must embody the genotype and, thus, contains precisely all the information needed to determine phenotype.  Clearly, this elegantly provides an underlying physical rationale for the original ideas of Morgan and his students as well as for linkage maps constructed by Sturtevant and later researchers.  Concomitantly, it is known that with few exceptions every protein underlying the physiological structure of the human body requires just twenty essential amino acids.  Therefore, it would seem evident that the sequence of bases in DNA must in some way associate uniquely to the sequence of amino acids in the various proteins.  Moreover, from consideration of elementary combinatorial mathematics one may presume that any particular amino acid in a protein sequence must logically correspond to at least one particular group of three nucleotide bases or codon in the DNA sequence.  (To be specific, 42=16, i.e., a number less than 20; hence, pairs of bases are insufficient to define all of the codons, but 43=64, i.e., a number greater than 20, and, thus, a triad of bases is sufficent.)  The existence of such a relationship between codons and amino acids, i.e., the genetic code, was confirmed by Marshall W. Nirenberg and his associates working at the National Institutes of Health in the 1960's.  Furthermore, the code was found to be essentially universal to both prokaryotes, i.e., non-nucleated cells (bacteria, blue-green algae, etc.) and eukaryotes, i.e., nucleated cells (protozoa, multicellular plants and animals, etc.) and, therefore, apparently common to all organisms that have ever lived on earth and, consequently, of very ancient origin.  Within this context, the genetic code is both redundant and unambiguous.  That is to say that in humans as well as all other known lifeforms, each of the essential amino acids corresponds to one or more of the sixty-four codons, but no codon corresponds to more than one amino acid.  Additionally, three of the codons do not correspond to any amino acid and, as such, these have the function of terminating a protein sequence.  These presumptions have been frequently reconfirmed over the last half century and are beyond any reasonable doubt.  Moreover, it is broadly known that DNA directed cellular synthesis of protein occurs in two steps, viz., transcription of DNA within the nucleus into so-called messenger RNA or mRNA, followed by transport of mRNA into the cytoplasm and translation into protein by complementary transfer RNA or tRNA within ribosomes, i.e., cytoplasmic organelles specifically responsible for protein synthesis.  Again, exact details of how genetic codons behave chemically and genes expressed as protein molecules are quite complex, but it is clear that this fundamental process can account for the heredity of all living organisms.  In any case, chromosomes are found to be nothing more or nothing less than large molecules of genetically active DNA combined with genetically inert supporting and stabilizing proteins.

The Human Genome

     The term genome, which has substantially replaced the older term genotype, is precisely defined as a haploid set of chromosomes, i.e., the chromosomes of a gamete, and associated genetic information.  Thus, by this definition the human genome consists of twenty-two non-sex chromosomes or autosomes and one sex chromosome.  Clearly, a zygote and, therefore, all descendant somatic cells are diploid and contain two versions of the genome, one from each parent, i.e., in humans forty-four autosomes and two sex chromosomes.  (In passing, it should be noted that the term "genome" is sometimes used to refer to all members of a diploid set of chromosomes, but this is technically incorrect usage.)  Obviously, it is the mixing of chromosomes in fertilization and conception that accounts for transmission of inheritable traits from both parents to their offspring.  Moreover, it is evident that since each parent nominally contributes only half of the full complement of genetic information that any given individual cannot be identical to either of his or her parents, but in fact will be essentially unique due to the large number of possible ways that maternal and paternal chromosomes can be combined.  This is further complicated by the existence of so-called dominant and recessive traits, terms that derive from the work of Mendel himself, which allow children to exhibit characteristics that were not expressed in either parent, but descend from earlier ancestors.  Within this context, chromosomes can be precisely identified cytologically by their lengths and banding patterns when stained and; hence, for humans the autosomes are conventionally identified by numbers "1" to "22", in order of decreasing length.
       Of course, it has long been known that the sex of humans as well as other mammals is determined by the specific sex chromosomes.  Accordingly, these exist in two forms which, by convention, are known as "X" and "Y".  To be specific, individuals normally always inherit an X-chromosome from their mother, but males inherit a Y-chromosome from their father and females inherit a second X-chromosome, i.e., the diploid combinations, "XY" and "XX", respectively, determine maleness and femaleness.  (For completeness, it should be noted that rare exceptions to this simple picture do occur in which no copy or more than one copy of a sex chromosome is passed; however, these are generally considered as abnormal genetic defects and usually result in sterility and/or associated clinical syndromes.)  Therefore, it is exclusively the paternal genome that determines the sex of offspring.  Morphologically, Y-chromosomes are quite different and much smaller than X-chromosomes, which apparently include additional genetic information absent from Y-chromosomes.  Consequently, it is found that genes for sex-linked and, typically, defective characteristics such as color blindness, hemophilia, etc., are specifically associated with the X-chromosome and, thus, can be passed from mothers to all offspring and from fathers to daughters only.  Accordingly, if such a defective trait is recessive it will be expressed predominantly in male offspring since they have only a single X-chromosome derived from their mother.  In contrast, females having two X-chromosomes derived from both their father and mother are more likely to have not only a copy of the recessive defective gene, but also a copy of a dominant, non-defective gene; hence, the trait will ordinarily not be expressed.  However, such an individual is a "carrier" of the gene and can pass it on to a son in whom it will be expressed.  In contrast, each parent contributes one equivalent copy of each autosome to any offspring; hence, any inheritable characteristic associated with an autosome cannot be sex-linked.  (As in the case of the sex-chromosomes, in rare cases no copy or multiple copies of an autosome will be passed from a parent, again, resulting in genetic defect of which the most notable example is trisomy (three copies) of chromosome twenty-one, causing Down's Syndrome.)  Concomitantly, as with the autosomes, sex chromosomes can be definitively identified by length and banding pattern.  Therefore, if a high resolution optical micrograph is made of the chromosomes at the metaphase of mitotic cell division (when diploid chromosomes are closely paired), then individual images can be extracted and arranged as a karyotype.  These are generally useful diagnostic tools for identification of genetic defects as described above, both in medicine and fundamental biological research.
     In addition, the possibility of mutation further complicates this oversimplified picture of human heredity.  As asserted above, mutations occur due to chemical changes in chromosomes, which may be caused by radiation damage, chemical mutagens, etc.  Moreover, if such a mutation is not lethal, then it may become part of the genome and, consequently, is passed down to subsequent generations.  There are several mechanisms for mutation some even observable in karyotypes among which have been already mentioned, translocation, inversion, and deletion.  Of course, these are related to the fundamental phenomenon of crossing-over, also previously mentioned, in which DNA segments are exchanged between paired chromosomes during meiotic cell division, i.e., gamete formation.  Clearly, if crossing-over did not occur, then all of the traits associated with a given chromosome would be invariably linked and transmitted together to succeeding generations.  Therefore, although crossing-over does not necessarily cause mutation, over time it does randomize genetic information associated with a particular chromosome (as expected by Mendelian genetics).  Accordingly, the combination of mutation with crossing-over accounts for the genetic variation of inheritable traits within the human population or any particular sub-population.  This totality of inheritable traits or alleles is called the gene pool.


     At this point it is now possible to apply elementary principles of genetics to the family relationships of genealogy.  First of all, it would seem obvious that any individual nominally shares half of his or her genotype with each parent.  This is unequivocally true for females, however, males have slightly more maternal DNA since X-chromosomes are longer than Y-chromosomes, which as indicated previously, accounts for specifically sex-linked inheritance patterns.  Therefore, ignoring any particular effects of sex chromosomes, it is trivially evident that the degree of genetic relatedness between parents and children can be taken as fifty per cent or expressed as a decimal kinship ratio, 0.5.  Likewise, it would seem obvious that the corresponding ratio for grandparents and grandchildren should be 0.25.  Accordingly, for great-grandparents and great-grandchildren it must be 0.125.  Clearly, for members of any direct line of descent the reciprocal of kinship ratio is simply the number of direct ancestors for a given individual going back in history some integral number of generations.  Therefore, for n generations "removed", one has in, principle, 2n direct ancestors, i.e., (n-2)th-great-grandparents, and the corresponding kinship ratio would be precisely 1/2n.  Within this context, n can be called generation number, which, by definition must be 0 for any particular individual identified with the "root" position in a pedigree and, thus, is obviously 1 for his or her parents, 2 for grandparents, etc.  Unfortunately, simple calculations of kinship become complicated if ancestral lines merge, i.e., if one descends from a particular ancestor through two or more lines of descent.  One might suppose that this would happen only rarely since social custom generally discourages marriages between close relatives, e.g., first cousins.  Indeed, ancestral lines are almost always separated for generation numbers of two or less, but convergence becomes increasingly more probable for higher values of n.  Even so, it is not difficult to determine appropriate kinship ratios, which are obtained simply as the sum of the ratios obtained by considering each ancestral line as formally independent.  Thus, suppose that one is descended from a particular great-great-grandfather through two separate lines.  In this case, the corresponding kinship ratio is simply two times 1/24 or 0.125.  Of course, this result remains true irrespective of whether the concomitant great-great-grandmother associated with either of the two lines was the same or a different person.  (Obviously, kinship ratios specifically associated with these great-great grandmothers must necessarily reflect whether they were in fact the same or different.)  In addition, it can also happen that generation numbers may differ.  For example an ancestor might be one's great-grandparent through one line of descent and a great-great-grandparent through another.  Indeed, such occurrences are often found in pedigrees due to the prevalence of very large families in previous centuries.  Nevertheless, the correct kinship ratio is, again, merely obtained as a simple sum, viz., 1/23+1/24=3/16 or 0.1875.  For completeness, it should be emphasized that this simple analysis assumes pure Mendelian inheritance in which genes are completely randomized from generation to generation.  In contrast, it is clear that if chromosomes remained rigorously intact during formation of gametes, then a particular individual could inherit genetic contributions, viz., chromosomes, from a maximum of forty-six ancestors of generation number 6 or larger, e.g, great-great-great-great-grandparents.  Consequently, all other ancestors of the same generation would be essentially unrelated to this descendent.  However, as asserted previously, DNA segements may be exchanged during meiosis; hence, the actual situation must lie somewhere between these two extremes (but, probably closer to pure Mendelian inheritance).  In any case, it is important to realize that kinship ratios provide only an estimate of relatedness, rather than any absolute measure.
     Further implications of such elementary calculations become evident upon consideration of one's putative degree of genetic relationship to direct ancestors alive several hundred years ago.  If, for this purpose, it is supposed as a rule-of-thumb that there are about three generations per century, then a thousand years ago an individual presently living would have had roughly one billion direct ancestors (230=1,073,741,824).  Obviously, this is much larger than the entire population of the world was at that time, which implies that in tracing back one's family tree many ancestral lines must necessarily converge and become merged.  Within this context, although one would not expect to be equally related to every individual living on earth a thousand years ago, this simple result does suggest that a person now living probably is directly related to one or more entire ethnic groups defined genetically as sharing a common gene pool.  This can be made more evident if it is further noted that according to the work of Bolton, in the thirteenth century the entire population of England could be realistically estimated to have been somewhere between two and three million persons.  Accordingly, this is commensurate with the number of direct ancestors that an individual of purely English ancestry living at present would have had at that time.  Moreover, in the fourteenth century the epidemic outbreak of bubonic plague, viz., the Black Death, substantially reduced the English population; hence, many lines of descent must have died out.  Therefore, assuming that surviving lines of descent have a reasonable geographic distribution and do not all derive from exactly the same locality, it is reasonable to conclude that a living individual of purely English ethnicity would have substantial probability of being a direct descendant of any person alive in England in the thirteenth century, who has living descendants remaining today.  Consequently, considering the worldwide growth of populations, it seems a rather pointless effort to trace an individual genealogy back beyond such a time or, perhaps, even only as far as five or six centuries.  Indeed, for such a time horizon in all probability one is related to his or her direct ancestors no more closely than to a randomly chosen "unrelated" individual presently living, who is of one's same ethnicity.  Consequently, family history becomes merely identical to ethnic history.
     Again, excluding effects of the sex chromosomes, these same simple principles can also be used to determine degree of relatedness between indirect relatives, i.e., siblings, cousins, etc.  Naturally, siblings each share half of their genotypes with the same parents.  Therefore, one might conclude that they should have a kinship ratio of unity.  However, this would imply that all siblings should have exactly the same genotype, which is obviously untrue, with the exception of identical twins (or more rarely, identical triplets, quadruplets, etc.) who do, indeed, have exactly the same set of genes since they developed from the same zygote, i.e., they are homozygous.  However, ordinary heterozygous siblings develop from different  fertilized eggs and, thus, should share half of half or one quarter of each of their parents' genotypes and, therefore, have a kinship ratio of 0.5.  Accordingly, discounting homozygous siblings as a special case, members of a conventional nuclear family all have the same degree of genetic relatedness.  Even so, it should be noted that in contrast to parents and children for which kinship ratio may be considered as a nominally exact measure because of the fundamental nature of meiosis, for siblings there must be some statistical uncertainty.  What is the source of this variation?  It can be easily understood if one considers maternal and paternal genomes inherited by each of two siblings.  By definition, each parental genome consists of a haploid set of chromosomes, that is to say, half of each parent's genotype, but it cannot be expected to be the same half for each sibling, which, naturally, introduces an additional source of randomness.  Nevertheless, if genes are completely randomized in gametes, then, as asserted previously, the probability is one half that parental genomes for each sibling should share the same gene.  Obviously, this is, again, nothing more than ordinary Mendelian inheritance.  Of course, these considerations can be applied to any degree of indirect relation and one finds than the kinship ratio between and individual and an uncle or aunt is the same as for grandparents, i.e., 0.25.  Concomitantly, the kinship ratio between first cousins is half of this value, i.e., 0.125, and, naturally, is reduced by half in succeeding generations, i.e., first cousin-once-removed, twice-removed, etc.
     Even so, it should come as no surprise that the preceding picture is, in reality, quite a considerable oversimplification, because no accounting has been made of the frequency and distribution of particular genes within the human population.  To understand this in a general sense, one should consider a population of biological organisms, e.g., plants, animals, livestock, human beings, etc., which share a common genetic heritage.  Of course, this defines a gene pool, which for human beings generally corresponds to an ethnic group or a combination of several ethnic groups within which intermarriage (or at least interbreeding) is common.  Clearly, if a particular gene is frequently present within this general population, then it is quite probable that one's parent will have a copy of this particular gene on both chromosomes in his or her diploid set, i.e., such an individual is said to be homozygous in this gene.  In contrast, if an individual has a different copy on each corresponding chromosome, then he or she is heterozygous in the associated gene. Consequently, a homozygous gene will be present in all derived gametes and the probability that it will be passed to any offspring is unity, not one half as simple kinship ratio might suggest.  Therefore, kinship ratio really is indicative of the expected degree to which relatives might share genes in common.  Indeed, naive consideration of kinship ratios generally cannot account for family resemblances that are often evident in close relatives.  Moreover, neither have effects of dominant and recessive genes been considered.  By definition a dominant gene is expressed in the phenotype irrespective of whether it is homozygous or heterozygous in the associated genotype.  Conversely, a recessive gene must be homozygous for the corresponding trait to appear.  Clearly, strong family resemblances are likely to occur if one parent is homozygous in one or more dominant genes controlling particularly evident aspects of appearance, e.g., hair and eye color, facial bone structure, etc.  Within this context, it is worthwhile to note that plant and animal breeders have known for centuries that inbreeding, i.e., mating close genetic relatives, and choosing offspring having preferred traits, i.e., phenotypes, tends to reduce variation within the gene pool.  If this practice is continued for a number of generations the result is a purebreed.  Accordingly, there is a very high probabilty that any purebred individual will be homozygous in precisely the genes that determine the traits of the breed and, furthermore, that any offspring of such parents will "breed true" and also exhibit the desired characteristics.  Unfortunately, inbreeding also can and often does increase the frequency of genes associated with undesirable traits as well and this is the reason why that many purebred varieties of domestic plants and animals often suffer from congenital weaknesses and defects.  Almost certainly, it is also for this reason (generally embodied in folk wisdom and derivative social customs rather than any considered rationale) that marriages between close human relatives are discouraged or even prohibited in most cultures.  Historically, the only exceptions to this general social convention have occurred among various royalties and aristocracies, perhaps, in an attempt to preserve their "exceptional quality".  Of course, such ideas are without merit and even ridiculous.  Indeed, the occurrence of hemophilia and other genetic disorders among royal families is well-documented and the intellectual deficiencies of "bluebloods" remains a frequent source of humor and subject for comedians.

DNA Testing and Analysis

      Conventional or classical genetics is not dependent on any detailed knowledge of DNA.  Indeed, intentional breeding of domestic plants and animals began at the very dawn of civilization and can, quite rightly, be considered as a primitive kind of genetic engineering.  Accordingly, within the last century or so formal breeder associations have been organized to record and maintain accurate pedigrees of purebred varieties of domestic animals, e.g., American Kennel Association (dogs), American Angus Association (cattle), and many more.  This is nothing more than applied genealogy and while it is morally reprehensible to suggest that similar measures should be applied to human beings (that this should be done was the central idea of eugenics), when combined with clinical information, human genealogy can provide useful insight into the nature of inheritable propensities toward various diseases, e.g., cancer, heart disease, etc.  In addition, it also can provide important fine detail in the study of the larger subjects of history and culture.  Of course, throughout history human pedigrees have been constructed from anecdotal accounts and kept in both oral and written form as a possession a particular family or tribe or, perhaps, even an entire national group, e.g., the various Hebrew genealogies appearing in the Old and New Testaments.  Subsequently, a variety of written civil records have been kept by civilized societies, e.g., in Britain since as early as the eleventh century (the Domesday Book).  This practice was later extended in expanding colonial settlements (as in North America) as well as beginning at various times in other countries.  Naturally, genealogical information can be readily obtained from these records.  Moreover, such source documents often are of particular value since they were typically written contemporaneously with events in the lives of one's various ancestors.  Even so, existing civil records of all kinds hardly provide a complete picture and, unfortunately, have often been lost and destroyed due to the vicissitudes of war or natural disasters.  Such was the situation until the 1970's and 1980's when the combination of new molecular genetic techniques and modern computerized data analysis led to the development of direct and rapid analysis of DNA.  Within this context, chromosomal DNA itself can be considered as a kind of chemical "document" that not only contains an individual's biological "blueprint", but by the very nature of heredity also must contain a great deal of genealogical information as well.  Moreover, such information is direct in a way that no actual written document can ever be.
     Naturally, once the fundamental characteristics of the genetic code had been established, scientists began work on techniques for determination of specific nucleotide base sequences.  Accordingly, it would seem obvious that identification and separation of individual chromosomes would be a prerequisite to locating and identifying particular segments of DNA.  Two important modern methods of separating chromosomes have been developed, viz., somatic cell hydridization and flow sorting.  Even so, chromosomal DNA molecules are typically quite large and, thus, difficult to manipulate for analysis.  Therefore, the first discovery of a restriction enzyme in 1970 by Wilcox and Smith provided a practical method of cleaving DNA reliably and repeatably into smaller, more manageable fragments.  This was followed shortly by the development of "recombinant DNA" methods by Berg, Boyer, and Cohen as well as others.  Such techniques allow DNA segments to be modified and propagated readily using bacteriophages and their hosts.  Subsequently, two practical techniques for determining base sequences of DNA were both published in 1977 and have come to be known from the names of their primary inventors as the Sanger-Coulson and Maxam-Gilbert sequencing methods, respectively.  (Concomitantly, Sanger and Coulson had two years previously described the so-called "plus and minus" method for practical DNA sequencing, but their later chain-termination method proved to be more rapid and accurate.)  Even so, the former procedure requires preparation of single-stranded DNA that has been cloned from a primary sample of natural double-stranded DNA using an M13 bacteriophage infecting Escherichia coli.  In contrast, the Maxam-Gilbert or chemical cleavage method does not require this preliminary step.  Nevertheless, the Sanger-Coulson method has been more easily adapted for very large scale sequencing, e.g., the Human Genome Project, and, as such, has become the most widely used technique in practice.  In this procedure, artificial nucleotides containing dideoxyribose (a pentose that differs from ribose by the absence of two hydroxyl groups instead of just one as in deoxyribose) are included at low concentration in a solution also containing higher concentrations of the four ordinary deoxyribonucleotides.  Ignoring precise details, the single-stranded DNA test sample is added to this solution along with DNA polymerase as well as other regulating chemicals.  Consequently, the test DNA serves as a template for replication and DNA fragments of varying length, which are complementary to the original sample, will be produced by action of the enzyme.  Moreover, the length of each fragment is determined by random substitution of one of the dideoxyribonucleotides, which prevents further incorporation of additional normal deoxyribonucleotides, i.e., terminates the chain.  Therefore, the mixture will contain DNA fragments of every possible integral chain length, i.e., one base, two bases, three bases, etc., terminated by one of the four dideoxyribonucleotides corresponding to the normal nucleotide occuring at that particular position in the original sample.  Hence, each fragment unambiguously corresponds to a particular base position in the test DNA strand.  Concomitantly, by using electrophoresis, the fragments can be separated on a "gel" in order of mass, i.e., chain length.  Therefore, if the dideoxyribonucleotides are labeled either radiometrically or by an appropriate fluorescent functional group, then the original nucleotide base sequence can be read off directly from the gel.  As one might expect analysis of a large number of fragements requires substantial data analysis, but, nevertheless the entire human genome has already been sequenced.  Indeed, it is now known that the human genome, which for the purpose of sequencing is redefined to include both sex chromosomes as well as the haploid set of autosomes (i.e., twenty-four instead of twenty-three chromosomes), includes more than three billion nucleotide base pairs (3.1647(109) to be more exact).  Furthermore, the largest chromosome (i.e., chromosome 1) includes over two hundred and fifty million base pairs (more precisely, 2.63(108)) and the smallest (originally thought to be Y, but now known to be chromosome 21) includes fifty million.  Naturally, the number of base pairs associated with any of the remaining twenty-two chromosomes lies between these two figures.  Even so, the number of identifiable genes within the human genome is surprisingly small and is now estimated to be only about thirty thousand.  Accordingly, it is further believed that only about two per cent of the entire nucleotide base sequence of the human genome encodes for synthesis of proteins or other functional products, i.e., can be identified with genes.  The remainder is "silent" and, as such, remains functionally undetermined.  Nevertheless, these non-coding sequences likely affect overall chromosome structure and dynamics and, perhaps, have some regulatory effect on gene expression.  Within this context, by definition an exon is a segment of genomic DNA that is transcribed into mRNA.  Alternatively, a  non-coding segment is called an intron.  Obviously, exons are separated by introns; however, one should not suppose that each exon corresponds to an entire gene.  In general, a gene sequence is composed of one or more exons which are combined by deletion of intervening introns during the transcription process.  The resulting mRNA sequence then directs ribosomal synthesis of protein.  Even so, it can happen that some exon segments do not directly translate into an amino acid sequence.  Nevertheless, they almost certainly have important functions such as enhancing gene expression, stabilizing mRNA, redirecting ribosomes to translate one of the "stop" codons as selenocysteine (which is not one of the essential twenty amino acids), etc.  Clearly, much still remains to be understood regarding the origin and function of the human genome.
     As a practical matter, both Sanger-Coulson and Maxam-Gilbert methods are limited to DNA samples containing only a few hundred nucleotide base pairs.  Therefore, as indicated above, restriction enzymes are generally used to prepare an initial raw sample of DNA by breaking it into a smaller segments.  These can then be separated by electrophoresis or chromatography and, if required, the nucleotide base sequence of each different fragment determined.  Typically, restriction enzymes cut DNA molecules at positions characterized by some particular short nucleotide base sequence and, naturally, different kinds of enzymes act on differing base sequences.  Therefore, if the initial sample is treated with different restriction enzymes, then the original and, of course, much longer sequence can be reassembled by identifying overlapping sequences in the various shorter segments.  (Obviously, such procedures for sequencing the entire human genome embody a huge amount of biological information, which has spawned the entirely new discipline of automated data processing called bioinformatics.)  Fortunately, complete genome sequencing is frequently not necessary for many practical applications.  Indeed, it was found soon after the discovery of restriction enzymes that the distribution of DNA fragments produced is idiosyncratic to its source and has extreme specificity with respect to the arrangement of nucleotide bases in the original sample.  Clearly, this indicates that many small differences in nucleotide sequences typically must exist between individuals and, in addition, most of these do not cause observable changes in biological function or structure.  Moreover, it seems reasonable that such differences must have arisen due to the accumulation of random mutations over time and do not materially affect phenotype because of the degeneracy of the genetic code as well as the low density of genes in the overall human DNA sequence.  This phenomenon is called restriction fragment length polymorphism.  Consequently, since it did not require complete sequencing, fragment analysis quickly became useful in its own right for identifying recurring patterns associated with genetic identity, various inheritable traits, and/or genetic defects.  In addition, sequencing methods were subsequently applied to particular fragments leading to identification of associated DNA markers.  Although, it should not be supposed that such markers correspond precisely to genes themselves, they are strongly linked and, hence, almost certainly located in close proximity in the genomic sequence such that they are inherited together with a high degree of probablilty.  Accordingly, DNA markers have become very useful medical and forensic diagnostic tools.  Furthermore, markers, especially those associated with sex chromosomes, are useful for determining genealogical relationships between individuals.
     For completeness it should be noted that one additional important technological innovation has revolutionized DNA testing and analysis.  This was the invention of the polymerase chain reaction (PCR) by Kary Mullis in 1985.  PCR is a relatively simple technique and allows a vanishingly small sample obtained from almost any biological source containing DNA to be amplified sufficiently for subsequent analysis.  Consequently, DNA testing has become inexpensive and widespread.  Indeed, the idea of a forensic "DNA fingerprint" has now become fixed in popular imagination much as physical fingerprinting did a century ago.

Y-chromosomal DNA

     It is evident that analysis of autosomal DNA can be expected to be extremely effective for establishment of primary genetic identity, i.e., a "fingerprint"; however, because autosomes in offspring are mixed between parents it is not generally useful beyond a few generations for determination of genealogical lines of descent.  Clearly, a similar situation also prevails for X-chromosomal DNA since the X-chromosomes are diploid in females.  An exception to this situation can occur if a sufficiently rare allele is present in an individual's genotype, which also can be easily traced in succeeding generations.  (An notable example of just such an analysis is provided by the occurrence of inherited hemophilia among the descendants of Queen Victoria.)  Even so, not all offspring can be expected to inherit the associated gene.  In contrast, Y-chromosomes are passed unchanged from father to son except in the very rare event of a mutation.  Consequently, Y-chromosomal DNA analysis can be extended deeply into history to identify strictly patrilineal ancestries.  Moreover, this inheritance pattern is congruent with the common social custom of attaching paternal surnames to offspring.  Of course, as discussed elsewhere, one should not uncritically suppose that all individuals having the same surname are related, since surnames frequently arose independently in different geographic locations.  However, coincidence of Y-chromosomes indicates a high probability of a genetic relationship.  Therefore, Y-chromosomal DNA analysis is readily applicable to male individuals bearing the same surname to determine if they have a common ancestor.  Consequently, common family lore, for example asserting the immigration of several brothers to different countries, states, or colonies, can be definitively tested by such genetic methods.  Furthermore, it comes as no surprise that these traditional accounts are often proven false.  As a practical matter, such testing has become increasingly inexpensive and, typically, now to obtain a sufficient sample only requires a mouth swab, rather than a blood sample (as was the case before the advent of PCR methods).  These samples are generally tested for certain standard groups of Y-chromosomal DNA markers, which then can be compared statistically between individuals.  A number of commercial companies currently offer such services.  Obviously, matching of DNA markers between two individuals is a reliable indicator of a common collateral ancestry, which can be confirmed stastically with great precision provided that a sufficient sample group of markers is tested.  Typically, a minimum of at least twelve Y-chromosome markers should be tested to obtain statistically significant results.  Of course, if additional markers are included, e.g., twenty-five or more, precision is greatly enhanced.  (However, this usually increases the cost of the test.)  Futhermore, to facilitate comparison of test results contributed by various individuals (who may be widely separated geographically) various websites have set been set up to collect and exhibit results.  Of course, these are generally organized according to surname, i.e., so-called "one name studies", are usually free of charge, and can be viewed by any interested party.  In any case, Y-chromosomal DNA analysis can provide a definitive indication of a common ancestry (or lack thereof) between presently living individuals.  More rarely, it might be applied to exhumed remains to establish a direct line of descent since bone tissue can effectively preserve DNA for many centuries.  Of course, this is likely to be taken as a last resort when no living paternal line descendants are to be found.  Accordingly, it is to be expected that DNA testing almost certainly will be applied more frequently in the future and clearly is a valuable complement to the ordinary methods of genealogical research involving oral histories, documentary analysis, etc.

Mitochondrial DNA

     All of the preceding assertions are specifically applicable only to chromosomal DNA, which one might have supposed was the only kind of cellular DNA.  However, this is not the case and eukaryotes contain additional DNA that is not located in the nucleus, but rather in mitochondria.  These are cellular organelles, typically rod-shaped, located in the cytoplasm (i.e., outside the cell nucleus) that have the primary biological function of oxidative phosphorylation to produce the ribonucleotide, adenosine triphosphate, or ATP.  Biologically, ATP provides the primary "energy currency" for the vast majority of living organisms, i.e., chemical energy available in food is converted to ATP which then serves as the energy source for nearly all other vital cellular processes.  Within this context, mitochondria share features similar to those of free-living bacteria in that they can reproduce by fission and contain similar genetic material, i.e., a single circular strand of DNA.  Thus, in the 1970's Lynn Margulis (Sagan) revived and expanded upon earlier ideas of Mereschkowsky and others, that mitochondria were, indeed, once external, free living organisms that about a billion years ago became endosymbionts with the ancestor of all eukaryotic cells (including those of the human body).  Consequently, subsequent generations of mitochondria lost the ability to synthesize many necessary proteins; hence, becoming dependent on the internal cytoplasmic environment and no longer able to live externally.  (This endosymbiont hypothesis has also been applied to plastids (organelles in plant cells responsible for photosynthesis (chloroplasts), pigmentation (chromoplasts), biosynthesis and storage (leucoplasts), etc.) which also contain some additional DNA.)  Although, the endosymbiont hypothesis cannot by any means be proven, it does seem to be the most plausible explanation for the existence of DNA in mitochondria (as well as chloroplasts).
     Clearly, mitochondrial DNA can be considered as forming a small and separate mitochondrial genome that, obviously, is not included in the haploid set of chromosomes, i.e., the nuclear genome.  Furthermore, mitochondria are absolutely necessary for the survival of any eukaryotic organism and, hence, they (and, of course, associated mitochondrial DNA) must be transferred to a fertilized zygote when gametes combine.  Within this context, if gametes derived from male and female parents are morphologically similar, then equal contributions of mitochondrial DNA should be expected to be transferred from both parents to their offspring.  Moreover, since the mitochondria are transferred as complete organelles (i.e., there is no mitochondrial process corresponding to meiosis and segregation of chromosomes) mitochondria in offspring cells should consist of distinct maternal and paternal "strains" analogous to bacterial strains as routinely observed by bacteriologists.  This becomes even more confused if one considers that such mixing would have also occurred in all earlier generations.  Accordingly, one might expect the mitochondrial genome to be hopelessly confused and variable.  However, in human beings (as well as most other multicellular animals, especially vertebrates) the gametes are morphologically dissimilar between the sexes, viz., in addition to having motile tails, sperm cells are much smaller and contain much less cytoplasm than do corresponding oocytes (egg cells).  Accordingly, a sperm cell contains at most a very few mitochondria only in a small volume located around the tail.  In contrast, oocytes each contain thousands of mitochondria distributed throughout a relatively large volume of cytoplasm.  Consequently, in a mammalian zygote and its descendant cells, the inherited ratio of maternal to paternal mitochondrial DNA is on the order of approximately 10000:1.  Therefore, as a practical matter, for human beings mitochondrial DNA can be considered to be inherited exclusively from one's mother.  Accordingly, although there are differences in mutation rates as well as other molecular characteristics as might have been expected, it is clear that genetic analysis of mitochondrial DNA provides the maternal equivalent of Y-chromosomal analysis as described above and, hence, can be used to determine strict matrilineal ancestry.  Likewise, mitochondrial DNA analysis is commercially available and relatively inexpensive and, again, samples obtained from living individuals or exhumed remains can be analyzed for DNA markers as is appropriate.

Human Origins

     Of course, perhaps, the most profound genealogical question that can be posed is, "What is the nature of human origins?"  Indeed, this has been a matter of intense controversy since the original assertion of biological evolution by Charles Darwin one hundred and fifty years ago.  Prior to this such questions had been strictly the province of theologians, not scientists and, as such, were considered definitively answered by interpretation of the Holy Scriptures.  Accordingly, competing religious and naturalistic explanations of origins have generated considerable emotional and irrational debate on both sides.  As is a matter of history, Darwin based his conclusions primarily on comparative study of various animal and plant species.  These were further augmented by paleontologists as they studied the fossil record.  Consequently, numerous controversies arose regarding various "missing links", which ultimately could not be resolved satisfactorily by application of paleontology alone.  This situation prevailed until the advent of molecular genetics.  Within this context, Nirenberg himself realized that the universality of the genetic code implies that it almost certainly arose only once in the natural history of planet Earth and, moreover, that this must have occurred a very long time ago, i.e., among the very first living organisms.  Accordingly, it is to be expected that the DNA of various living species should also provide a sort of fossil record since its present form is almost certainly the result of mutations accumulated over time.  This has been substantially confirmed by nucleotide base sequences determined by the methods as described previously and concomitant comparison of accumulated genetic differences between organisms.  To be more specific and ignoring statistical details, it has been asserted with reasonable justification that chimpanzees and human beings share about 98% of their respective genomes in common with each other.  Concomitantly, the degree of genetic similarity between humans and other mammals is not so great, but greater than that found with birds, reptiles, etc.  Likewise, similar relationships are found in the comparison of genomes between other organisms.  As a result, living species can be arranged in an "evolutionary tree" determined by genetic similarity that substantially agrees with results obtained by classical analysis of the fossil record.  Clearly, this remarkable agreement provides strong evidence for biological evolution and although detractors commonly point out supposed inconsistencies, these invariably fall into the logical fallacy of "special pleading" and are of little or no consequence.  Obviously, an important question in any such analysis is what is the expected or base rate of mutation, i.e., how fast does the genetic "clock" run?  Although, this remains a matter of active research, current  indications are that it is of the right order of magnitude to account for plausible evolutionary change.  Moreover, analysis of "functionless" base sequences, which do not correspond to genes and therefore have no relationship to phenotype, also provides strong evidence for biological evolution.  Therefore, in a very real sense, one could regard all living organisms as remotely distant relatives.  Such a conclusion might be troubling to some individuals, but it would seem when considered in a broader context that it, perhaps, should provide some comfort to the human race as belonging to this time and place.  Of course, such ideas are really beyond science and truly are in the realm of religion.
     Within a more immediate context, analysis of Y-chromosome and mitochondrial DNA further suggests that the entire existing human race descends from anatomically modern common ancestors who probably lived in southern Africa within the last one hundred to one hundred and fifty thousand years.  Accordingly, it is believed by many researchers that descendents of this population settled the rest of the world in two distinct waves of migration, viz., out of Africa, to the Indian subcontinent, Southeast Asia, and Australia, perhaps, some sixty thousand years ago and then out of Africa, to the Middle East and Central Asia somewhat later.  This second migration then divided into eastern and western branches that settled East Asia and Western Europe, respectively.  Subsequently, it would seem evident that a few individuals from East Asia must have migrated to the Americas some twelve to twenty thousand years ago (almost certainly through Siberia and Alaska as has long been thought).  Obviously, on any geological time scale these migrations were quite recent events and, in addition, suggest that all living human beings are, in fact, very closely related.  In particular, any genetic basis corresponding to classical racial designations seems to be particularly lacking.  Clearly, these considerations represent a sort of "grand genealogy" that should convince one that distinctions of race and culture are really of much less significance than traditionally thought.  Indeed, it can only be hoped that such a realization will truly point the way toward "Peace on Earth and Goodwill to Men."

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50. Lynn Sagan, "On the Origin of Mitosing Cells", Journal of Theoretical Biology, 14, pgs. 225-74, 1967.

51. Charles Darwin, On the Origin of Species by Means of Natural Selection, John Murray, Albemarle Street, London, UK, 1859: pass.  (Public domain reprints available from various modern publishers, viz., Gramercy, Random House, Penguin, etc.)  (Available electronically at

52. M.-C. King and Allan C. Wilson, "Evolution at Two Levels in Humans and Chimpanzees", Science, 188(4184), pgs. 107-16, 1975.

53. Olivier Verneau, François Catzeflis, and Anthony V. Furano, "Determining and Dating Recent Rodent Speciation Events by Using L1 (LINE-1) Retrotransposons", Proceedings of the National Academy of Sciences USA, 95(19), pgs. 11284-9, 1998.  (Available online at, 2005.)

54. Rebecca L. Cann, Mark Stoneking, and Allan C. Wilson, "Mitochondrial DNA and Human Evolution", Nature, 325, pgs. 31-6, 1987.  (Available electronically at, 1998.)

55. John Simpson (chief ed.), Oxford English Dictionary, Oxford University Press, Oxford, UK, continuously updated.  (Available electronically at

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