Every gene present in an individual is inherited as a copy of a gene carried by one of the parents, which was itself inherited from a grandparent, and so on backwards through many generations. Tracing these lines of descent produces a genealogical tree of a gene.
When such lines of descent are followed back far enough, they eventually converge upon a single ancestral copy of the gene. This convergence of lineages into a common ancestor is known as coalescence, and it forms one of the central theoretical tools of population genetics for studying the history of populations and the fixation of mutations.
1. Uniparentally Inherited Markers
Genealogical trees are simplest to construct for genes that are inherited through only one parental sex, since such genes are transmitted without recombination. In humans, two markers fulfil this condition:
- Mitochondrial DNA (mtDNA) – inherited through the maternal line; both sons and daughters receive their mtDNA from their mother.
- Y-chromosome DNA – inherited through the paternal line; only sons receive the Y chromosome from their father.
Since neither type of DNA undergoes recombination, in the absence of new mutations each copy of these sequences is an exact replica of the parental copy. This property makes them ideal for constructing simple genealogical trees.
2. The Coalescence Process
A genealogical tree of a gene can be represented with each generation forming a row, and each gene copy in a generation being linked by a line to the specific parental copy from which it was inherited. If all individuals in the current generation are traced backwards, their lines of descent will eventually converge on a single shared ancestral gene copy. This process of convergence, called coalescence, is inevitable and will always occur given sufficient time, though the exact number of generations required depends on population size and other demographic factors.
2.1 Why Coalescence Is Inevitable
Coalescence occurs because not every individual in a generation contributes surviving copies of a uniparentally inherited gene to future generations:
- A woman who has no daughters does not pass on her mitochondrial DNA; this represents a “dead end” in the mtDNA family tree.
- A man who has no sons does not pass on his Y chromosome; this is a dead end in the Y-chromosome family tree.
- Conversely, some individuals pass on their gene copy to more than one descendant (for example, a mother with two or more daughters). Viewed forward in time, these are branch points; viewed backward in time, they are coalescence points.
Because some lineages continually die out while others branch and persist, the total number of distinct lineages steadily decreases going backwards in time, until only one remains.
3. Mitochondrial Eve and Human Population History
3.1 The Concept of Mitochondrial Eve
Analysis of human mitochondrial DNA shows that every existing mtDNA sequence variant can be traced back to a single woman who lived in Africa approximately 200,000 years ago. This individual is popularly referred to as mitochondrial Eve. It is important to understand what this finding does and does not imply:
- It does not mean that only one woman existed in Africa at that time; there was certainly a full breeding population.
- Eve was simply the one woman among that population whose mtDNA lineage happened to survive uninterrupted to the present day, through an unbroken line of daughters.
- There was likely nothing biologically special distinguishing her from other women of her time; her survival in the genealogical record is a matter of chance lineage persistence, not selection or unique fitness.
3.2 The “Out of Africa” Hypothesis
Human populations are known to have existed in many parts of the world well before the estimated date of mitochondrial Eve. The mtDNA evidence supports the “out of Africa” hypothesis, which proposes that modern humans descend from an African population that later spread across the world and replaced other, previously existing human groups.
3.3 Evidence from the D-loop and Whole Mitochondrial Genomes
Early studies of human mtDNA relied mainly on a highly variable, non-coding region called the D-loop. More recent research has used complete mitochondrial genome sequences from many individuals to reconstruct human population history. Key findings include:
- The average number of sequence differences between pairs of complete mitochondrial genomes sampled worldwide was found to be substantially lower than would be expected if diversity were evenly distributed, once the sample was divided by geography.
- The average pairwise difference among African individuals was considerably higher than the average pairwise difference among non-African individuals, indicating that divergent mitochondrial lineages have existed within Africa for a much longer time than outside it.
- Although the D-loop shows a higher density of variable sites than the rest of the mitochondrial genome, the remaining genome (which largely codes for proteins, rRNAs, and tRNAs) evolves more predictably and is considered more reliable for estimating substitution rates and divergence times.
3.4 Interpreting Phylogenetic Trees from mtDNA Data
When constructing phylogenetic trees from population mtDNA data, only polymorphic sites — sites where more than one base occurs at appreciable frequency in the population — provide useful phylogenetic information. Sites that are identical across all individuals, or that differ in only a single individual, do not indicate shared ancestry and are excluded. Important features of such data include:
- Blockiness of shared variants: Because mtDNA is inherited without recombination, individuals sharing one derived variant at a site frequently share other derived variants at different sites as well, since all these substitutions occurred along the same unbroken line of descent. This correlated pattern would be disrupted if recombination occurred.
- Recurrent mutation (homoplasy): At some sites, the same substitution appears to have arisen independently more than once in unrelated lineages. Such sites give phylogenetic signals that conflict with the true evolutionary tree, but as long as a sufficient number of informative sites are available overall, the correct relationships among lineages can still be reliably inferred.
Phylogenetic reconstruction of worldwide mtDNA data shows early-branching lineages that are exclusively African, followed by a closely related African group, and then further groups containing individuals from many other parts of the world (Europe, China, Australia) but no Africans. This branching pattern is consistent with a small population having left Africa and spread throughout the rest of the world, carrying its mitochondrial DNA along with it. Statistical confidence in the major branch points of such trees is typically assessed using bootstrapping, a resampling technique used to test the reliability of tree topology.
3.5 Estimated Dates
- The estimated age of the most recent common ancestor of all human mtDNA sequences (mitochondrial Eve) is approximately 170,000 ± 50,000 years ago.
- The estimated date of the most recent common ancestor of non-African sequences, corresponding to the migration out of Africa, is approximately 52,000 ± 27,000 years ago.
4. Y-Chromosome Adam
A parallel line of evidence comes from the human Y chromosome, which is inherited exclusively through the paternal line. Large-scale studies of polymorphisms in the non-recombining region of the Y chromosome, based on samples of over a thousand men, have identified mostly single nucleotide substitutions, along with a small number of insertions, deletions, and at least one transposable element (Alu) insertion. As with mtDNA, the most divergent Y-chromosome sequences were found in African populations.
- The estimated date for the most recent common male ancestor, popularly termed “Y-chromosome Adam,” is approximately 59,000 years ago.
- The estimated date for the expansion of the male lineage out of Africa is approximately 44,000 years ago.
Both these estimates carry wide confidence intervals. There is no theoretical requirement for “Adam” and “Eve” to have lived at the same time or in the same place, since the mtDNA and Y-chromosome lineages are inherited completely independently of one another, and historical patterns of migration may have differed between men and women.
5. A Mathematical Model of the Coalescence Process
A simple theoretical model can describe how coalescence time depends on population size. Consider a population of constant size, containing N breeding females, all assumed to be equally fit and therefore equally likely to have produced any given offspring. Under these assumptions:
- Any individual in the present generation is equally likely to have descended from any one of the N individuals in the previous generation.
- If two individuals are chosen at random from the present generation, the probability that they share the same mother (i.e., coalesce in the immediately preceding generation) is 1/N, and the probability that they do not is 1 − 1/N.
5.1 Probability Distribution of Coalescence Time
The probability that the most recent common ancestor of two randomly chosen individuals lived exactly T generations ago is given by:
P(T) = (1 − 1/N)^(T−1) × (1/N)
This expression reflects the requirement that the two lineages must have had different mothers for the first (T − 1) generations, and then coalesce by sharing the same mother in generation T.
For large N, this discrete distribution can be closely approximated by a continuous exponential distribution:
P(T) ≈ (1/N) × e^(−T/N)
5.2 Mean Coalescence Times
- The mean time to coalescence for any two randomly chosen individuals is N generations.
- The mean time until all N individuals in the population coalesce to a single common ancestor is approximately 2N generations.
This theoretical result explains why, for a population of constant size, the expected age of the most recent common ancestor scales directly with population size.
6. Coalescence and Autosomal Genes
The simple genealogical tree model described above applies directly to uniparentally inherited, non-recombining sequences such as mtDNA and the Y chromosome. Most genes, however, are located on the autosomes (non-sex chromosomes) and are inherited from both parents:
- For an autosomal gene in a population of size N, there are 2N copies of the gene (two per individual).
- Autosomal chromosomes undergo recombination, typically experiencing one or two crossover events per chromosome pair per generation.
Because of recombination, it is not possible to draw a single genealogical tree for an entire chromosome, since different regions of the same chromosome may be inherited from different ancestors due to crossing over. However, if attention is restricted to a single gene on an autosome, the simple tree model remains approximately valid, because the probability of a crossover event occurring within the boundaries of a single gene is usually very small (since any one gene occupies only a small fraction of the whole chromosome).
Where sequence data are available from multiple individuals for a given gene, coalescence theory can be applied to estimate the probability that recombination events have occurred at specific points within the sequence. If a gene contains more than one segregating (variable) site, recombination between these sites can generate new combinations of variants that were not previously present in the population. However, when the focus of analysis is restricted to the spread of a single point mutation through a population, the presence or absence of recombination elsewhere in the gene does not affect the coalescence calculation for that single site.
Conclusion
Genealogical trees provide a conceptual and mathematical framework for tracing the ancestry of genes back to a common origin, a process termed coalescence. Uniparentally inherited, non-recombining markers such as mitochondrial DNA and the Y chromosome allow this process to be studied directly in humans, leading to the identification of “mitochondrial Eve” and “Y-chromosome Adam” as the most recent common ancestors of all present-day mtDNA and Y-chromosome lineages, respectively, and providing strong support for the “out of Africa” model of human origins. The mathematical theory of coalescence shows that, for a population of constant size N, the expected time to a common ancestor for two individuals is N generations, and for the whole population is approximately 2N generations. While this simple model applies directly to non-recombining sequences, it can still be usefully extended to individual genes on recombining autosomal chromosomes, since recombination within a single gene is a comparatively rare event.
