When looking at descendants, the probability that the male line will continue indefinitely becomes smaller and smaller as we go forward in time. But if we look back in time to our ancestors, the probability that the male line remains unbroken is 100%. This illustrates the difference in probability before and after the event. If G is the proband in Figure 5, he could theoretically trace his male line ancestors back to the beginning of sexual reproduction, but his male line descendants end with J♂ since his grandchildren are all females.

Figure 5 Broken Male Line

This situation applies equally to the female line. The only difference is that unlike the male line, the female line is not identified by the same surname, except for some illegitimate births. However, the female line is characterised by each member having copies of the same mitochondria, just as the male line members all have identical Y chromosomes. This latter aspect is illustrated in Figure 6.

The above paradox has implications for the long-term survival of titled aristocratic families. Very few of the hereditary peerages existing in 1066 have survived to the present day because succession depended on producing a male heir each generation. In the past, the numbers in the hereditary upper chamber were kept fairly constant by new peerages being created to replace the defunct ones. More recently, to prevent peerages dying out, females have been allowed to inherit some titles. e,g. Earl Mountbatten's elder daughter was allowed to become a countess. This, rather belatedly, follows the system used by the monarchy, where a successor has to be found regardless of gender. However, although females can inherit, in the absence of males, males still have priority over females.

Figure 6 Y Chromosome and Mitochondrial Inheritance

Prior to gen. 7 only the two relevant lines are shown, since gen.0 would contain 2048 individuals.

One of the great uncertainties of genealogy is whether the hereditary principle has always been strictly adhered to in the past. Because DNA testing was not available, it is quite likely that illegitimacy or the substitution of new-born babies, has broken several lines of male descent, or even lines of descent in general. In any society it has always been easier to identify a baby's true mother than its true father, so that tracing ancestors through the female line is usually more accurate.

In the case of the royal houses of Europe, where spouses have mainly been chosen from other royal families, the occasional mistake was often corrected later when the direct line was restored through another branch of the family. Although the Norman dynasty replaced the Saxons, the Saxon lineage re-entered the English monarchy when Matilda became Henry I's queen. Henry I was William the Conqueror's son. Matilda was the great-granddaughter of Edmund Ironside, who was the Saxon king of England in 1016 and a descendant of Alfred the Great. Matilda also had links with the Scottish royal family since her mother, Margaret, granddaughter of Edmund Ironside, and her father, Malcolm III, were king and queen of Scotland.

At the present time, an unexpected outcome of DNA testing and other forms of genetic analysis, such as the identification of blood groups, for quite innocent purposes, is that it has stirred up a can of worms by exposing false paternity and thereby disrupting whole families. On the other hand it does allow false claims of relationship to be dismissed, but should be used with discretion when the disclosure of information is not essential.