Inbreeding

Inbreeding is sexual reproduction between close biological relatives.

Some recessive alleles decrease the fitness of an individual. Inbreeding depression is the effect on a population when inbreeding spreads such harmful recessive traits. It may happen after a population bottleneck. Various Google searches for inbreeding reveal that the children of close relatives are commonly thought to have brain problems and facial deformities. In the United States, a hillbilly stereotype has emerged referring to inbred, uneducated people living in isolated mountainous regions. However, inbreeding depression is not as dramatic as some people might claim. In fact, the child of a first cousin couple is no worse off than the child of a 41-year-old mother.

In the Bible
The Hebrew Scriptures state that for a time, inbreeding was a common practice. Cain and Seth, for example, married their sisters, who were at the time the only humans on earth of the same age. Prior to the global flood of 1656 AM, there were still few enough defects in the gene pool to make inbreeding acceptable. But by the time of Moses, the human genome had deteriorated so far that humanity faced the threat of inbreeding depression.

So Jehovah gave instructions on how to prevent pedigree collapse, mixed with other prohibitions that apparently target sexual abuse. (Leviticus 18:6-21) Inbreeding-related prohibitions include [6] a "close fleshly relative", [7] father-daugher and mother-son, [9] brother-sister, [10] grandfather-granddaughter, [12-13] aunt-nephew (father's or mother's sister), [14] paternal uncle-niece (father's brother). Prohibitions appearing to target solely VD include [19] women during menstruation, [22] male bisexuality, and [23] sex with other species. Prohibitions involving a marriage include [8] stepmother-stepson (father's wife), [11] parallel stepsiblings (father's wife's daughter), [14] paternal aunt by marriage (father's brother's wife), [15] daughter-in-law (son's wife), [16] sister-in-law (brother's wife), and [20] the wife of one's "associate" or "neighbor" depending on translation. Prohibitions on sequential sex during a lifetime include [17] both a woman and her mother, son, or daughter, and [18] both a woman and her sister.

To a legalist, omissions appear to include a maternal uncle-niece, maternal aunt by marriage, grandmother-grandson, and cross stepsiblings (mother's husband's daughter). But Jews have historically not considered a first cousin to be a "close fleshly relative" (Genesis 24:48-51; Numbers 36:1-11). Inheritance customs may help explain why some of these prohibitions aren't sex-symmetric.

Iceland
Iceland has a surprisingly long lifespan for the amount of inbreeding. It turns out that since the early 19th century, third-cousin marriages produce in fact more offspring than distant marriages. It is conjectured that part of this comes from the tendency of close-knit families in a particular society to eat the foods that the society's members have evolved to process, averting outbreeding depression.

Breeding patterns
It may take dozens of couples to populate a new habitat after a bottleneck, at least until the population has grown to 5,000 individuals. So some societies have evolved complex breeding patterns to ensure that partners in marriage share a common ancestor no closer than a specific generation.

If second cousins are permitted to marry, the minimum population needed to avoid inbreeding is eight. Given four pairs of siblings, one brother and sister each, arranged with their individuals in a Morse-Thue sequence of sexes (MF FM FM MF), the following iteration produces valid couples as long as each couple produces at least one son and one daughter: Pair 1 with 5 to make 1' and 2', 2 with 6 to make 3' and 4', 3 with 7 to make 5' and 6', and 4 with 8 to make 7' and 8'.

All of the third generation are second cousins; they all share the same great-grandparents. But the second generation, which had four distinct grandparents, produced a third generation, also with four distinct grandparents. This pattern can continue indefinitely as long as each pair produces two children, at least one male and one female.
 * Founders: A B C D E F G H
 * Generation 1: I(AE) J(AE) K(BF) L(BF) M(CG) N(CG) O(DH) P(DH)
 * Generation 2: Q(IM)(ACEG) R(IM)(ACEG) S(JN)(ACEG) T(JN)(ACEG) U(KO)(BDFH) V(KO)(BDFH) W(LP)(BDFH) X(LP)(BDFH)
 * Generation 3: 1(QU)(IKMO) 2(QU)(IKMO) 3(RV)(IKMO) 4(RV)(IKMO) 5(SW)(JLNP) 6(SW)(JLNP) 7(TX)(JLNP) 8(TX)(JLNP)

A similar pattern with 16 founders (1 with 9, 2 with 10...) avoids second cousins as well, giving third cousins at each generation.

Apply this to entire populations, not just individuals, and you get something akin to the "skin groups" of Australian Aboriginal kinship. Four skin groups (corresponding to AB, CD, EF, and GH above) guarantee that a couple are no closer than second cousins, and eight guarantee no closer than third cousins.