Applied Animal Breeding

Animal breeding is the application of genetic principles to improve farm-animal populations for the traits people value: more milk, faster or leaner growth, better fertility, disease resistance and resilience. The breeder’s task is to identify the genetically superior animals and choose which become parents, so that each generation is, on average, better than the last. Everything starts from a clearly stated breeding goal, the traits to improve and their relative economic weights.

The work then repeats a four-step breeder’s cycle: record phenotypes, estimate each candidate’s genetic merit, select the best as parents, and mate them to produce the next generation. Robert Bakewell pioneered systematic selection and progeny testing in the eighteenth century; Mendel (1865) supplied the genetic mechanism; and Jay Lush, from 1945, built the quantitative methods, heritability, breeding values and selection theory, that this course teaches.

A little history shows how hard-won this logic was. Robert Bakewell (1725–1790) was the first to breed systematically, keeping careful records, progeny-testing his bulls and rams by hiring them out and judging them on their offspring, and rearing the progeny under common conditions so comparisons were fair. Mendel (1865) later supplied the mechanism of inheritance, and from 1945 Jay Lush fused Mendelian genetics with statistics into the quantitative methods used today. The modern lesson is that a breeding goal must be economic and balanced: chasing a single headline trait (peak milk, maximum growth) usually drags down fertility, health or longevity, so the goal weights several traits by their value to the production system before any animal is selected.

Traits fall into two broad classes. Qualitative traits (coat colour, horned or polled) are controlled by one or a few genes, fall into distinct categories and are little affected by environment. Quantitative traits (milk yield, growth rate, litter size) are controlled by many genes plus the environment, vary continuously and are the main target of selection. A few are threshold traits: an underlying continuous liability expressed as a yes/no outcome such as calving difficulty or survival.

Economically important traits differ by species and system: in dairy cattle, milk volume and composition (fat, protein), fertility, udder health (mastitis) and longevity; in beef cattle, growth rate, feed efficiency, carcass yield and calving ease; in sheep, reproduction rate, growth, and wool or meat quality. Because animals are kept in different herds, years and seasons, raw records are not comparable. They must first be standardised, corrected for fixed environmental effects such as parity, age, season and lactation length, so that the genetic signal is not confounded with management.

Standardisation is done with explicit correction factors. A young first-lactation cow is not genetically inferior to a mature cow; she is simply younger, so records are scaled to a common mature-equivalent and to a fixed lactation length (commonly 305 days). Season, parity, herd, year and management group are likewise removed, because each is an environmental effect that would otherwise masquerade as genetic merit. Threshold traits need special handling: calving difficulty or survival are recorded as categories (easy/hard, alive/dead) but are assumed to sit on an unobserved continuous liability scale, so an animal’s genetic risk can still be estimated though the outcome is yes-or-no. Getting measurement and standardisation right is unglamorous but decisive, since every later estimate of heritability and breeding value is only as good as the records feeding it.

Selection works only because animals vary. An individual’s phenotype is P = G + E: a genotypic value plus an environmental deviation. The genotypic value itself splits into an additive part (the average effect of alleles, transmissible to offspring), a dominance part (interaction of alleles at a locus) and an epistatic part (interaction between loci). Only the additive part is reliably passed on, which is why it is the currency of selection.

At the population level the same logic partitions variance: V_P = V_A + V_D + V_I + V_E. Genetic variation arises from recombination, the independent assortment of chromosomes, mutation and chromosomal change; environmental variation comes from feeding, climate, health and management. A further complication is genotype-by-environment interaction (G×E): the best genotype in one environment is not always the best in another, so an animal selected under high input may not excel under harsh tropical conditions, a central concern for African breeding programmes.

It is worth separating the genetic components further, because they behave differently under selection. The additive variance is what passes reliably from parent to offspring and is the part that responds to selection within a breed. The dominance and epistatic components, interactions within and between loci, do not transmit predictably, but they are exactly what crossbreeding exploits through heterosis. New genetic variation enters a population only through recombination and the independent assortment of chromosomes (reshuffling existing alleles each generation) and, more slowly, through mutation; selection and drift remove it. This is why a breeder treats additive variance as a finite, precious resource: it fuels genetic gain, and once eroded by intense selection in a small population it is not quickly replaced.

The additive part can be defined precisely through the average effect of an allele: the mean deviation from the population mean shown by offspring that receive that allele. An animal’s breeding value is the sum of the average effects of the alleles it carries, and equals twice the mean deviation of its progeny under random mating. The genotypic value of any single genotype then splits into this breeding value plus a dominance deviation, the within-locus interaction that is not transmitted: for a locus with genotypes A1A1, A1A2, A2A2 the heterozygote’s breeding value is exactly the average of the two homozygotes, while any departure of its genotypic value from that average is dominance. This is why selection moves a population only through breeding values, and why crossbreeding, which exploits dominance, gives a one-generation boost that does not accumulate.

Heritability in the narrow sense, h² = V_A / V_P, is the fraction of phenotypic variation that is additive genetic, and therefore the fraction that responds to selection. It runs from 0 to 1. A useful rule of thumb from the course materials: h² < 0.1 is very low, 0.1–0.2 low, 0.2–0.4 medium and > 0.4 high. Reproduction traits are usually low, growth traits moderate, and conformation or some milk-composition traits high. The higher the heritability, the more an animal’s own phenotype reveals its breeding value.

Repeatability (R) applies to traits measured more than once per animal (successive lactations, litters). It is the proportion of variance due to permanent differences between animals: R = (V_G + V_Ep) / V_P, the ratio of genetic plus permanent-environmental variance to total. Repeatability is always at least as large as heritability and sets an upper limit on it. A high repeatability means one record already predicts future performance well, so few records are needed; a low one means you should average several records before judging an animal.

The course materials give repeatability a precise working meaning: it is the fraction of the differences in a single record that are likely to reappear in the animal’s future records, equivalently the ratio of the variance of producing ability to total phenotypic variance. Because it captures permanent genetic and permanent environmental effects, it is always at least as large as heritability and sets a ceiling on it. Its practical value is prediction: a high repeatability means an animal’s first lactation already forecasts later ones well, so culling and selection can be done early on a single record; a low repeatability means one record is unreliable and several should be averaged before judging the animal. Heritability and repeatability together therefore tell the breeder both how much progress selection can make and how many records are needed to act safely.

Heritability is not assumed but estimated from the resemblance between relatives. Because relatives share a known fraction of their additive genes, theory predicts the phenotypic correlation between them: about ¼h² between half-sibs, ½h² between full-sibs, and ½h² between parent and offspring, while the regression of offspring on the mid-parent is h² itself. Measuring these correlations in real data and inverting the formulae yields the heritability. A revealing check is to compare estimates: if the full-sib figure implies a much higher h² than the half-sib figure, the excess is a common-environment component (c²), typically the shared maternal or litter environment, since full-sib correlation is ½h² + c². Recognising c² prevents heritability from being overstated, a frequent error when only full-sib or dam-offspring data are used.

The expected genetic gain from one round of selection is captured by the breeder’s equation:

where R is response, i the selection intensity (how extreme the selected group is, in standard-deviation units; selecting fewer animals raises i), r the accuracy of selection (correlation between the estimated and true breeding value), σ_A the additive genetic standard deviation (the variation available), and L the generation interval (average age of parents when their replacements are born). To breed faster you increase intensity or accuracy, preserve genetic variation, or shorten the generation interval, and these levers trade off against one another.

How accurately we rank candidates depends on the information source. Mass (individual) selection uses the animal’s own record, simple and effective for highly heritable traits expressed in both sexes. Family selection and the use of relatives’ records help for low-heritability traits. Progeny testing, judging a sire by the mean of his offspring, gives the highest accuracy for traits of low heritability or expressed in one sex (milk, egg production), but lengthens the generation interval; the materials note that as many as 30 offspring per sire may be needed for very low-heritability traits. When several traits matter at once, they are combined into a selection index rather than selected one at a time.

The same equation can be written R = h² · S, where S is the selection differential, how far the selected parents exceed the herd average; multiplying the herd’s superiority by the heritability gives the part actually inherited. When several traits matter at once there are three strategies of increasing efficiency. Tandem selection improves one trait at a time and is slow. Independent culling levels set a minimum standard for each trait and reject any animal that fails one, simple, but it can discard an animal that is outstanding overall. The selection index combines all traits into a single economically weighted score and is the most efficient, because strength in one trait can compensate for a modest value in another. The materials add a quantitative rule of thumb for progeny testing: for traits of very low heritability, as many as 30 recorded offspring per sire may be needed to estimate his breeding value reliably.

A breeding value (BV) is the additive genetic merit of an animal, twice the average deviation of its offspring from the population mean, because a parent passes on a sample of half its genes. We never observe a BV directly; we estimate it (an EBV) from records on the animal’s own performance, its pedigree, its progeny, and correlated traits, weighting each source by how much information it carries.

The classical tool for combining sources is the selection index: a weighted sum of records, with weights chosen to maximise the correlation between the index and the true breeding value (it is the best linear prediction, BLP). Its weakness is that it assumes the records are already corrected for environmental effects and that those effects are known without error, rarely true in field data with unbalanced herds, years and management.

BLUP (best linear unbiased prediction) removes that weakness. In the mixed-model equation y = Xb + Zu + e, it estimates the fixed environmental effects (b) and predicts the random breeding values (u) simultaneously, using the relationship matrix A so that information flows between relatives across the whole pedigree. BLUP therefore corrects for unequal environments, accounts for non-random mating and selection, and ranks all animals on one comparable scale, which is why it underpins national genetic evaluations. Each animal’s BV also contains a Mendelian-sampling term, its deviation from the parental average, the reason full sibs differ in merit.

The accuracy of any breeding value depends on how much information stands behind it and how heritable the trait is. An animal’s own single record gives accuracy equal to the square root of the heritability; adding repeated records, records on parents and sibs, and above all on progeny raises it, which is why a heavily progeny-tested sire can reach an accuracy approaching one. Every estimated breeding value also contains a Mendelian-sampling term, the animal’s own deviation from the average of its two parents, caused by the particular sample of alleles it inherited; this is why full sibs differ in merit and why an elite pair can still produce an ordinary calf. BLUP estimates all of this jointly across the whole pedigree, putting young and old animals, different herds and different years on one comparable scale, the property that national evaluations and genomic selection both build on.

Selection decides which animals breed; the mating system decides which with which. Options range from random mating, through positive and negative assortative mating (like-with-like or unlike-with-unlike for a trait), to the two pure-breeding strategies: inbreeding (mating relatives) and outbreeding / crossbreeding (mating unrelated animals or different breeds). Crossbreeding exploits heterosis (hybrid vigour) and breed complementarity; inbreeding concentrates desired genes and exposes recessives but carries costs.

The inbreeding coefficient F is the probability that the two alleles at a locus are identical by descent. From a pedigree it is computed by the path method:

summing over every common ancestor A, where n₁ and n₂ are the numbers of generations from each parent back to A, and F_A is that ancestor’s own inbreeding.

Inbreeding accumulates fastest in small populations. Its rate per generation depends on the effective population size N_e:

so using too few sires, the usual bottleneck, drives N_e down and inbreeding up, eroding fitness through inbreeding depression (lower fertility, survival and growth). Managing genetic gain and genetic diversity together, by limiting the rate of inbreeding while selecting, is essential, and is exactly the concern carried into the genomic-selection course.

Crossbreeding is the mirror image of inbreeding and is widely used in the tropics. Mating unrelated breeds produces heterosis (hybrid vigour), offspring that exceed the parental average especially for fitness traits such as fertility and survival, and lets breeders combine the strengths of two breeds, for example a hardy local dam line with an improved sire line. Structured systems (rotational crossing to keep heterosis in the cows, or terminal crossing for uniform slaughter generations) make this repeatable. Inbreeding depression works the other way: as inbreeding raises homozygosity it exposes deleterious recessive alleles and removes the heterozygosity that fitness traits depend on, lowering fertility, survival and growth. Because the rate of inbreeding is governed by effective population size, and the usual bottleneck is the number of sires (N_e ≈ 4N_mN_f/(N_m+N_f), dominated by the scarcer sex), spreading matings across more sires is the simplest way to keep diversity alive.

For real multi-generation pedigrees the path method becomes unwieldy, so inbreeding and relationship are computed by the tabular method: a relationship matrix is built row by row in birth order, each animal’s relationship to the others derived from the average of its two parents’ relationships, and its inbreeding read directly as half the relationship between its sire and dam. This is the same additive-relationship matrix that drives BLUP, which is why pedigree recording underpins both inbreeding control and genetic evaluation. Inbreeding depression is, to a good approximation, linear in F: each one-percent rise in inbreeding lowers fitness traits by a roughly constant amount, so capping the rate of inbreeding protects the herd. Populations are structured as a breeding pyramid, a small nucleus of elite recorded animals at the top, multiplier herds below, and commercial producers at the base, so that genetic progress made in the nucleus flows downward while gene flow and exchange of sires keep the effective population size, and therefore diversity, large enough.

Glossary