Inbreeding

Introduction to Inbreeding

Inbreeding refers to the mating of genetically related individuals. While mathematically everyone is inbred to some extent, the genetic and medical significance is most pronounced in cases involving close relatives, such as cousins or closer. Inbreeding is a central concept in population genetics, affecting genotype frequencies and providing insight into human cultural practices and genetic diversity.

• Paradox of Ancestry: The exponential model of ancestry (2n) quickly leads to more ancestors than the world population, illustrating the inevitability of shared ancestors and inbreeding.

• Genealogy and Pedigrees: Pedigrees visually represent relationships and can reveal loops indicating inbreeding.

• Hardy–Weinberg Equilibrium: Assumes random mating; inbreeding violates this assumption, increasing homozygosity.

Quantifying Inbreeding

Genealogies and Inbreeding

Genealogical diagrams are essential for understanding common ancestry and inbreeding. Inbreeding is indicated by a loop in the pedigree, where an individual can trace a path back to a common ancestor and return via a different line.

• Pedigree Symbols: Squares represent males, circles represent females; lines indicate mating and descent.

• Inbreeding Loop: A loop in the pedigree signifies inbreeding.

Types of Inbreeding

Different types of inbreeding are classified by the degree of relationship between mates.

• Close Inbreeding: Includes parent–child, full sib, half sib, uncle–niece, aunt–nephew matings.

• Cousin Marriages: First cousins share grandparents, second cousins share great-grandparents, etc.

• Variations: First cousins once removed, half first cousins (one shared grandparent), double first cousins (all four grandparents shared).

The Inbreeding Coefficient (F)

The inbreeding coefficient (F) quantifies the probability that an individual has two alleles at a locus that are identical by descent (inherited from a common ancestor).

• Identity by Descent vs. Identity by State: Identity by descent means alleles are inherited from a common ancestor; identity by state means alleles are identical but not from a common ancestor.

• Calculation: For a loop with i ancestors (excluding the inbred individual),

• Multiple Common Ancestors: (sum over all loops/common ancestors)

• Inbred Common Ancestor: where is the inbreeding coefficient of the ancestor.

Table: Inbreeding Coefficients for Different Types of Mating

Mean Inbreeding Coefficient

The mean inbreeding coefficient for a population is calculated as the weighted average of inbreeding coefficients across all marriages:

• Formula: where is the number of marriages in each category, is the inbreeding coefficient for that category.

Table: Example Calculation (Shiiba, Japan)

Mean inbreeding coefficient:

Population Genetics and Inbreeding

Impact on Genotype Frequencies

Inbreeding alters genotype frequencies but does not change allele frequencies. It increases the frequency of homozygotes and decreases the frequency of heterozygotes compared to Hardy–Weinberg equilibrium.

• Genotype Frequencies Under Inbreeding:

  • Expected frequency of AA:

  • Expected frequency of Aa:

  • Expected frequency of aa:

• Hardy–Weinberg Equilibrium: When , frequencies reduce to , , .

Table: Genotype Frequencies Under Inbreeding

Why Inbreeding Does Not Change Allele Frequencies

Inbreeding is not an evolutionary force because it does not directly alter allele frequencies. The allele frequency in the next generation remains unchanged:

• Formula:

• Substituting inbreeding genotype frequencies,

Medical Impact of Inbreeding

Inbreeding increases the probability of homozygosity, especially for rare recessive alleles, leading to higher prevalence of genetic disorders. Studies show increased congenital defects and prereproductive mortality in offspring of consanguineous marriages.

• Example: For a recessive allele with , frequency of homozygotes under Hardy–Weinberg is ; under first cousin mating (), (over seven times higher).

Inbreeding in Human Populations

Rates of Inbreeding

Mean inbreeding coefficients in humans range from near zero to about 0.05, with significant variation due to cultural, religious, and demographic factors.

• Incest vs. Inbreeding: Incest refers to mating between first-degree relatives (parent–child, siblings), almost universally taboo.

• Cultural Variation: Some cultures prefer cousin marriage; others prohibit it. Religious and legal restrictions vary globally.

Genealogical Studies

Genealogical data are used to compute inbreeding coefficients and analyze mating patterns.

• Case Study: Romany of Wales – High prevalence of recessive disorders; mean inbreeding coefficient (adjusted to ).

• Case Study: Ramah Navajo – Clan exogamy reduces inbreeding; most inbreeding from remote consanguinity; (increased to with more data).

Surname Analysis and Isonymy

Surname (isonymy) analysis estimates inbreeding from marriage records by noting frequency of same-surname marriages.

• Formula: where is the frequency of isonymous marriages.

• Limitations: Multiple surname origins, spelling changes, adoptions, and time depth can affect accuracy.

Random and Nonrandom Components of Inbreeding

Total inbreeding () can be partitioned into random () and nonrandom () components:

• Random Inbreeding: Expected by chance due to small population size.

• Nonrandom Inbreeding: Due to preferences or avoidance of consanguineous marriage.

• Formulas:

Table: Example Surname Data (Hutterites)

Random marital isonymy: ; random inbreeding component:

Potential-Mates Analysis

Potential-mates analysis uses computer simulations to pair individuals based on realistic criteria (age, sex, family) and computes random and observed inbreeding coefficients. This method provides more precise analysis of mating behavior and inbreeding components.

Table: Components of Inbreeding (Sanday, Orkney Islands)

Summary

• Inbreeding is the mating of genetically related individuals, inevitable to some degree in all populations.

• The inbreeding coefficient (F) measures the probability of identity by descent; calculated from genealogical data.

• Inbreeding increases homozygosity, decreases heterozygosity, but does not change allele frequencies.

• Medical consequences include increased prevalence of recessive genetic disorders.

• Cultural, religious, and demographic factors influence rates and patterns of inbreeding in human populations.

• Surname analysis and potential-mates analysis are unique methods for studying inbreeding in humans.

• Total inbreeding can be partitioned into random (due to population size) and nonrandom (due to mating preferences) components.

Additional info: These notes expand on the original content by providing definitions, formulas, and context for key concepts, and by recreating tables for clarity and completeness.