LAISHA Explains
Animal science and veterinary

Breeding systems: inbreeding and crossbreeding

Livestock mating systems: inbreeding, line breeding, outcrossing, grading up, crossbreeding, rotations and composites, with inbreeding sums.

Exam essential5 min readUpdated
On this page
  1. Two families of mating systems
  2. Inbreeding
  3. Managing inbreeding with genomics
  4. Crossbreeding
  5. Key points
  6. What the exams ask
  7. Questions people ask
  8. Sources
  9. Related on Laisha
  10. Discussion

Selection decides which animals become parents; the mating system decides which parents are paired. Mating related animals, intentionally or simply because few males are available, concentrates genes and makes a line uniform, but it also exposes harmful recessive genes and depresses fertility and survival. Mating unrelated animals, and especially different breeds, restores vigour and combines strengths. Livestock breeders, from smallholders using a village bull to global poultry companies, use both, deliberately or not.

Mating systems, inbreeding and crossbreeding are core topics in animal breeding and genetics exams.

Two families of mating systems

  • Inbreeding: mating animals more closely related than the average of the population.
  • Close breeding: parent × offspring, full sibs, half sibs.
  • Line breeding: mild inbreeding aimed at keeping a high relationship to an outstanding ancestor.
  • Outbreeding: mating animals less closely related than average.
  • Outcrossing: unrelated animals of the same breed.
  • Crossbreeding: animals of different breeds.
  • Grading up: repeated crossing of local females to purebred males of an improved breed, so that after five or six generations the offspring are nearly purebred.
  • Species crosses, such as the mule (horse × donkey) and cattle × yak hybrids.

Inbreeding

Inbreeding increases homozygosity: an inbred animal is more likely to carry two copies of the same allele inherited from a common ancestor. Sewall Wright defined the coefficient of inbreeding (F) in 1922 as the probability that two alleles at a locus are identical by descent.

Pedigree of an animal X whose sire S and dam D are half-siblings sharing the common ancestor A; the path S to A to D has one step on each side, so the inbreeding coefficient of X is one half raised to the power of one plus one plus one, which is one eighth or 12.5 per cent; for a full-sib mating with two common ancestors it is 25 per cent Acommon ancestorSsireDdamXoffspring n₁ = 1n₂ = 1 Wright's coefficient of inbreeding F = Σ (½)n₁+n₂+1 × (1 + F of A) Half sibs: (½)3 = 1/8 = 12.5% Full sibs: 2 × (½)3 = 25% Parent × offspring: (½)2 = 25% First cousins: 2 × (½)5 = 6.25% assuming ancestors are not inbred
Calculating the inbreeding coefficient from a pedigree. Each path through a common ancestor contributes (½) raised to the number of individuals in the path.Diagram: Laisha, original.

Effects of inbreeding:

  • Inbreeding depression: reduced fertility, survival, growth and disease resistance; fitness traits suffer most. In dairy cattle, each 1 per cent rise in inbreeding typically reduces lifetime milk yield and fertility slightly.
  • Uncovering recessive defects, such as bovine leukocyte adhesion deficiency, complex vertebral malformation, and many breed-specific disorders.
  • Uniformity and prepotency of inbred lines, useful for producing lines to cross.

In closed populations, inbreeding rises over generations. The rate of inbreeding per generation with Nm males and Nf females used as parents is approximately:

Rate of inbreeding
ΔF = 1 ⁄ (8Nm) + 1 ⁄ (8Nf)

So the number of males usually limits genetic diversity. Modern dairy breeds, despite millions of cows, have small effective population sizes because few bulls sire most calves through AI.

Managing inbreeding with genomics

DNA markers now measure inbreeding directly. Runs of homozygosity, long stretches of the genome where both copies are identical, reveal inbreeding that pedigrees miss, including from distant common ancestors. Breeders use optimum contribution selection, which chooses parents to maximise genetic gain while limiting the rise in average relationship, and mating software that avoids pairing animals that share recessive defects or high relationship. Carrier tests for known defects let breeders keep valuable animals while avoiding affected offspring.

Crossbreeding

Crossbreeding exploits:

  • Heterosis (hybrid vigour): crossbred offspring performing better than the average of their parent breeds, especially for fertility, survival and longevity, the traits most hurt by inbreeding.
  • Breed complementarity: combining the strengths of different breeds, such as a hardy, adapted dam breed with a fast-growing sire breed.

Crossbreeding systems

  • Terminal crosses: F1 females of two breeds mated to a third, terminal sire breed, with all offspring sold for meat, as in pig and sheep production.
  • Rotational crosses: females are mated to sires of two or three breeds in rotation. A two-breed rotation retains about 67 per cent of maximum heterosis in the long run, and a three-breed rotation about 86 per cent.
  • Composite (synthetic) breeds: several breeds combined and then bred among themselves, retaining part of the heterosis without needing separate purebred herds, as in Santa Gertrudis and Brangus cattle and many modern poultry and pig lines.
  • In the tropics, crossing local zebu or indigenous breeds with high-producing temperate breeds has greatly raised milk yields, but high exotic proportions often struggle with heat, disease and poor feed, so intermediate crosses are often best.
Worked example

Inbreeding and rate of inbreeding

From a pedigree. An animal's sire and dam are half siblings with one common ancestor, who is not inbred. Each side of the path has one generation (n1 = n2 = 1):

  • F = (½)1+1+1 = (½)3 = 0.125 (12.5 per cent).
  • For full siblings, there are two common ancestors (both grandparents): F = 2 × (½)3 = 0.25.

In a herd. A village herd uses 2 bulls and 100 cows each generation:

  • ΔF = 1 ÷ (8 × 2) + 1 ÷ (8 × 100) = 0.0625 + 0.00125 ≈ 0.064 (6.4 per cent per generation).
  • Using 10 bulls: ΔF = 1 ÷ 80 + 0.00125 ≈ 0.014 (1.4 per cent).

Rotating or exchanging bulls between villages, or using AI from many sires, keeps inbreeding low and protects fertility.

Key points

  • Inbreeding mates relatives (close breeding, line breeding); outbreeding mates unrelated animals (outcrossing, crossbreeding, grading up, species crosses).
  • Wright's F = Σ (½) raised to (n1 + n2 + 1), times (1 + FA); half sibs 12.5 per cent, full sibs 25 per cent.
  • Inbreeding depression mainly harms fertility, survival and fitness; it uncovers recessive defects.
  • ΔF ≈ 1 ÷ 8Nm + 1 ÷ 8Nf: few sires drive inbreeding.
  • Crossbreeding exploits heterosis and complementarity; rotations retain about 67 per cent (two breeds) or 86 per cent (three breeds) of heterosis.

What the exams ask

  • School-leaving and entrance papers: definitions of inbreeding, outbreeding, crossbreeding and grading up.
  • Degree and research-fellowship entrances: coefficient of inbreeding from pedigrees, inbreeding depression, rate of inbreeding, heterosis, and crossbreeding systems.
  • Veterinary and professional examinations: designing breeding programmes for smallholders, managing inbreeding with AI, and choosing crossbreeding systems for tropical conditions.

Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.

Questions people ask

Is all inbreeding bad?

Mild, planned inbreeding can fix desirable traits and is used to create lines for crossing. Unplanned or high inbreeding in commercial herds usually reduces fertility and survival.

Why do crossbred cows often have better fertility?

Fertility and survival show the most heterosis, because they suffered most from inbreeding within breeds. Crossing restores heterozygosity at many genes.

Why not cross every local cow with a high-yielding exotic breed?

Pure or high-grade exotic animals often need better feed, housing and health care than smallholders can provide, and may suffer in heat. Moderate crosses often give the best balance of yield and hardiness.

Sources

  1. Falconer, D. S. and Mackay, T. F. C. Introduction to Quantitative Genetics, 4th edition. Longman, 1996. Chapters 3 and 14.
  2. Wright, S. "Coefficients of inbreeding and relationship." American Naturalist 56, 330–338 (1922).
  3. Bourdon, R. M. Understanding Animal Breeding, 2nd edition. Prentice Hall, 2000.
  4. Gregory, K. E. and Cundiff, L. V. "Crossbreeding in beef cattle: evaluation of systems." Journal of Animal Science 51, 1224–1242 (1980).
  5. Leroy, G. "Inbreeding depression in livestock species: review and meta-analysis." Animal Genetics 45, 618–628 (2014).

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