Genetic and Genomic Relationships

Heritability estimation introduction

Phenotypic variance (σ²P) is estimated directly from the population because phenotype can be observed. Narrow-sense heritability equation: h² = σ²A / σ²P where σ²A is additive genetic variance. Additive genetic variance and breeding values (BV/EBV) are estimated using pedigree or genomic information and covariance among relatives.

Covariance among relatives

Parent-offspring covariance = ½σ²A. Grandparent-grandchild covariance = ¼σ²A. kth generation-offspring covariance = (½)^kσ²A. Half-sib covariance = ¼σ²A. Full-sib covariance = ½σ²A + ¼σ²D. Additive genetic variance is estimated from covariance among relatives, so studying genetic resemblance among relatives is essential.

Genetic relationship definition

“Genetic relationship: The proportion of alleles that two individuals have in common because they are members of the same family.”

Pedigree definition and importance

Pedigree provides genetic and record information on an individual animal and its ancestors and is therefore a record of ancestry. Pedigrees always follow the same format and are commonly shown as three-generation pedigrees including sire, dam, paternal grandparents, and maternal grandparents.

Common ancestor definition

“An ancestor common to more than one individual and contribute to their allelic similarity.” Also: “an ancestor common to the parents of an inbred individual.”

Examples of relationship coefficients

Identical twins = 100%. Fraternal twins = 50%. Full sibs = 50%. Parent-offspring = 50%. Half-sibs = 25%. Grandparent-grandchild = 25%. Great-grandparent = 12.5%. First cousins = 12.5%. Great-great grandparent = 6.25%. Second cousins = 3.125%. Third cousins = 0.78%.

Why genetic relationships matter

1. Improve prediction accuracy of breeding values for young animals using information from relatives. 2. Used in BLUP (Best Linear Unbiased Prediction). 3. Help design mating systems to avoid inbreeding depression, explore heterosis/hybrid vigor, and increase genetic diversity in small populations.

Inbreeding definition

“The mating of relatives” or “Matings individuals that are closer in genetic relationship than the average of relationships of the population.”

Consequences of inbreeding

Increases homozygosity, increases expression of deleterious recessive alleles, and causes inbreeding depression (low performance).

Inbreeding coefficient (Fx) definition

“A measure of the level of inbreeding of an individual.” Defined as the probability that both alleles in an individual are identical by descent (IBD), or the probable proportion of loci containing alleles identical by descent. Fx ranges from 0 (no inbreeding) to 1 (maximally inbred). F stands for fixation index because inbreeding increases homozygosity/fixing.

Identical by descent (IBD)

Alleles are identical because they originated from the same common ancestor.

Wright’s coefficient of relationship (Rxy) definition

“A measure of the pedigree relationship.” Defined as the proportion of one individual’s alleles that are identical by descent to alleles of a second individual. Also: “It is the correlation between breeding values of two individuals due to pedigree relationship alone.” Ranges from 0 (unrelated) to 1 (identical twins).

Methods for calculating inbreeding and relationship coefficients

1. Path Method (not much used). 2. Tabular Method. 3. Genomic relationship matrix based on DNA markers.

Rules of the Tabular Method

1. Numerator relationship between X and Y equals the average numerator relationship between X and the parents of Y (or vice versa). 2. Relationship between an individual and itself is 1 + its inbreeding coefficient. 3. An individual’s inbreeding coefficient equals half the numerator relationship between its parents. 4. Wright’s coefficient of relationship between X and Y equals the numerator relationship divided by √[(1+Fx)(1+Fy)].

Steps of the Tabular Method

1. Order animals by birth date so parents come first. 2. Create a square table with animals across top and side. 3. Write parents above each animal. 4. Fill numerator relationships row by row from left to right. 5. Copy row values into columns. 6. Use rules 1–3 for off-diagonal and diagonal elements. 7. Repeat until table is complete.

Important interpretation of diagonal values in the Tabular Method

Diagonal element = 1 + F. Example: if rCC = 1.25, then FC = 1.25 − 1 = 0.25.

How to calculate inbreeding coefficient from the relationship matrix

Fx = rxx − 1 where rxx is the diagonal value for individual x.

How to calculate Wright’s coefficient of relationship

RXY = rxy / √[(1 + FX)(1 + FY)] where rxy is the off-diagonal numerator relationship value.

Example of Wright’s coefficient calculation

Given rXD = 0.8125, FX = 0.25, and FD = 0.25: RXD = 0.8125 / √[(1.25)(1.25)] = 0.6477.

Animal relationship matrix (A matrix)

The matrix containing Wright’s coefficients of relationships among animals based on pedigree information.

Genomic relationship matrix concept

Animals with more similar genotypes are more closely related genetically. DNA marker similarity across SNPs can be used to estimate relationships among animals more accurately than pedigree averages.

Why genomic relationships are more accurate than pedigree relationships

Genomic relationship matrices capture actual genotypes and Mendelian sampling, while pedigree relationships are only averages expected from ancestry.

Mendelian sampling

“The chance factor in distributing half the genetic material from each parent to their offspring.”

Genomic relationship matrix (VanRaden method)

G = ZZ′ / [2Σpi(1 − pi)] where Z is the genotype matrix adjusted by allele frequencies. Genotypes are coded as 0, 1, and 2 for AA, AB, and BB.

Difference between pedigree-based and genomic relationships

Pedigree relationships estimate expected relatedness based on ancestry averages, while genomic relationships measure actual DNA similarity and capture Mendelian sampling.

Reasons to inbreed

1. Increase uniformity. 2. Create pure lines to increase hybrid vigor later. 3. Identify deleterious recessive alleles/genotypes for selection (test mating).

Inbreeding depression

Inbreeding depression means reduced performance caused by increased homozygosity and expression of harmful recessive alleles.

Examples of inbreeding depression in dairy cattle

Increased age at first calving (+0.36 days), reduced productive life (−13.07 days), reduced lifetime milk (−358.41 kg), reduced lifetime fat (−13.17 kg), reduced lifetime protein (−11.41 kg), and reduced net income (−$24.43) for every 1% increase in inbreeding coefficient.

Examples of inbreeding depression in sheep

Reduced fleece weight (−0.017 kg), reduced fertility (−1.4 ewes lambing/100 ewes mated), reduced lamb survival (−2.8 lambs weaned/100 lambs born), and reduced lamb weaning weight (−0.111 kg) for every 1% increase in inbreeding coefficient.

Linebreeding definition

“The mating of individuals within a particular line.” Also: “A mating system designed to maintain a substantial degree of relationship to a highly regarded ancestor or group of ancestors without causing high levels of inbreeding.” It is considered a slow form of inbreeding.

Outbreeding definition

“The mating of unrelated individuals” or matings less related than the population average.

Types of outbreeding

Outcrossing = mating unrelated animals within the same breed. Crossbreeding = crossing two or more breeds. Linecrossing = crossing two inbred lines.

Consequences of outbreeding

Increases heterozygosity, masks deleterious recessive alleles, and increases gene combination value resulting in hybrid vigor/heterosis.

Heterosis (hybrid vigor) definition

Occurs “when the performance of the offspring is greater than the average of the performance of the parents.”

Reasons for outbreeding

1. Avoid harmful recessive disorders. 2. Avoid inbreeding depression. 3. Prevent loss of genetic variance. 4. Increase heterosis. 5. Take advantage of breed complementarity.

Effects improved by heterosis

Fertility, disease resistance, and longevity may improve by 10–30%.

Percent heterosis equation

% Heterosis = [(crossbred average − straightbred average) / straightbred average] × 100.

Heterosis example

If F1 calves average 525 lb and parent breed averages are 450 lb and 550 lb: Pounds of heterosis = 525 − [(450 + 550)/2] = 25 lb. Percent heterosis = 25 / 500 × 100 = 5%.

Breed complementarity

Breed complementarity combines desirable traits from different breeds. Example from slides: Angus tenderness/marbling combined with Charolais size.

True/False high-yield concepts

• Parent-offspring relationship coefficient = 50% TRUE

• Half-sibs share 25% of alleles TRUE

• Inbreeding increases homozygosity TRUE

• Inbreeding depression reduces performance TRUE

• Wright’s coefficient ranges from 0 to 1 TRUE

• Genomic relationships are generally more accurate than pedigree relationships TRUE

• Outbreeding increases heterozygosity TRUE

• Heterosis is a non-additive genetic effect TRUE

• Linebreeding is a slow form of inbreeding TRUE

• Pedigree relationships capture Mendelian sampling FALSE.

Most important conceptual distinction between pedigree and genomic relationships

Pedigree relationships estimate expected relatedness from ancestry, while genomic relationships estimate realized relatedness from actual DNA markers.

Why relationship matrices are important in breeding

They improve breeding value estimation, help manage inbreeding, optimize mating systems, and maximize genetic diversity and heterosis.