## PATTERNS OF DIRECT RELATIONSHIP

Direct relatives, as opposed to collateral ones, are our true ancestors and descendants. The best model to illustrate direct relationships is that of a hypothetical tree where both roots and branches are shown. Each time we move back from the nominated person, who is the tree trunk, the ancestors (the roots) double in number. Thus, you have 2 parents, 4 grandparents, 8 great-grandparents and so on. However, after a few generations it will be noticed that some ancestors are repeated in several lines of descent because of inbreeding (see here). As we go further back through the generations this loss of ancestors through duplication increases. Without this compensating reduction you would have the paradox of a future decline in the world population.

The pattern of the descendants (the branches) is different. Some branches are cut short early because of premature death or failure to have children, while others increase exponentially at varying rates. Cross links between branches due to occasional cousin marriages will still continue, but unlike ancestors who actually get fewer in number as we go back, inbreeding will not prevent the number of descendants increasing as we go forward; it will merely reduce the rate.

Although this model is correct for each person depicted, it gives a distorted view of the population as a whole because the trees interconnect and share roots and branches. When you observe all trees simultaneously you see a complicated matrix or network pattern. Regardless of the number of branches of ancestors and descendants, the chains of relationship are quite simple. Going back, the chains consist of parent - grandparent - great-grandparent etc; and going forward you have children - grandchildren - great-grandchildren and so on. As you go from one generation of direct relatives to the next (forward or backward), the coefficient of relationship is halved.

The second paradox about direct relationships is that 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 the probability that the male line remains unbroken in the ancestors is 100%. This illustrates the difference between a priori and a posteriori probability.

Finally, if there is more than one line of descent between two individuals because of inbreeding, direct relationships may be double or even multiple (for examples see here, here and here).

For a complete description of direct relationships see here.