Introduction to Quantitative Genetics

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Introduction to Quantitative Genetics

• The branch of genetics concerned with influences
  on , measurement of, relationship among, genetic
  prediction for, and the rate of change in traits
  that are or can be treated as quantitative.

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Introduction to Quantitative Genetics

• Phenotypic Value (P) A measure of performance
  for a trait in an individual- a performance
  record.
• Population Mean The average phenotypic value of
  all individuals on populations.
• Genotypic Value (G) The effect of an
  individuals genes on its performance for a
  trait.
• Environmental Effect The effect that external
  (nongenetic) factors have on animal performance.

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Qualitative versus quantitative traits

• Phenotypes are many (continuous variation ie. not
  observed in classes).
• Affected by several loci in other words genetic
  variability can be explained by action of many
  loci. (Polygenic Model).
• Large environmental effect.
• Ex Growth, milk production, rib eye area, wool
  fiber diameter
• egg production, litter Size

• Phenotypes are few (discrete variation ie,
  observed in categories).
• Affected by 1 or few loci.
• Small or no environmental effect.
• Ex. Color coat, horn development, blood type,
  etc.

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From one Locus to many loci
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Distributions
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Polygenic Model

• Phenotype is determined by several loci for
  quantitative traits.
• P G E
• ( values presented as a deviation from the media
  )
• For Qualitative traits E 0 or very small
• For Quantitative traits G may be very small

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Example PGE
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Inheritance of Quantitative Traits

• Exact genotype is usually unknown.
• Can have many loci each one with different types
  of gene action affecting same trait.
• Additive
• Complete dominance
• Partial dominance
• Over-dominance
• Basic goal of Animal Breeding is still to ?
  frequency of desirable alleles.

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Types of gene action

• Additive no dominance
• Non-additive
• dominance
• complete
• partial
• over-dominance
• epistasis

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additive gene action
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complete dominance
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partial dominance
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positive over-dominance
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negative over-dominance
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Epistasis-interaction between 2 or more loci
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From one Locus to many loci
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Genetic model for quantitative a trait

• Previous, P G E
• Phenotype Genotype Environment
• Let, ? overall population mean. Then
• P ? G E

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Example calf birth weight

• Assumptions
• Controlled by 4 loci.
• No epistasis.
• ? 85 lb.
• Ignore effects of E and sex

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Genetic key (lb)

• AA 10
• Aa 0
• aa -10
• BB 3
• Bb 3
• bb 0

• CC 3
• Cc 5
• cc -2
• DD 4
• Dd 2
• dd -3

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Expected birth weight of AABbccDd?

• P ? G E
• 85 (10 3 - 2 2) E
• 85 13 E
• 98 lb (ignoring E or E average effect on
  the population)

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Quantitative trait

• Influenced by
• several or many loci.
• additive and(or) non-additive gene action.
• Number of genotypic combinations in pop. can be
  large.
• Phenotypic variation can be very large,
  especially when E is large.

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Partitioning of phenotype

• P ? G E
• G A D I additive dominance epistasis
• Thus, P ? A D I E
• Also, E EP ET (permanent temporary E)
• Thus P ? A D I EP ET

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Partition phenotypic variance

• P ? G E
• ? A D I EP ET
• VP VG VE
• VA VD VI VEP VET
• VP VA VD VI VEP VET

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VP VA VD VI VEP VET

• Ability to partition these effects accurately is
  fundamental to genetic improvement of livestock.
• Capacity to estimate the genetic value of an
  individual and consequently predict its breeding
  value!!!

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Heritability

• Heritability (h2) proportion of the phenotypic
  variance that is genetic or in other words,
• Proportion of phenotypic variation in pop. that
  is heritable.
• Only the genetic portion of P is heritable.
• In many cases, only the additive (A) portion of G
  is heritable.

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Heritability in the broad sense
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Heritability in the narrow sense
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h2NS is usually more applicable to livestock.
Why?

• Genes, not genotypes are passed from parent to
  offspring.
• Effect of dominance (D) depends on both members
  of a gene pair.
• Effect of epistasis (I) depends on both members
  of two or more gene pairs.
• Effect of additive (A) depends on individual
  allele.

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Previous example birth wt controlled by 4 loci

• A/a controlled by additive effects.
• B/b by complete dominance.
• C/c by positive overdominance.
• D/d by partial dominance.

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Genetic key (lb)

• AA 10
• Aa 0
• aa -10
• BB 3
• Bb 3
• bb 0

• CC 3
• Cc 5
• cc -2
• DD 4
• Dd 2
• dd -3

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• Animal with genotype AABbccDd.
• One possible gamete AbcD.
• Effect of allele A on offspring is 10 lb
  (relative to allele a) regardless of what allele
  is inherited from other parent.
• Effects of alleles b, c and D depend on which
  alleles are inherited from other parent.

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• At an additive locus, the sum of effects of the
  alleles from each parent equals the genotype
  value in offspring.
• That is not true for a non-additive locus.
• With additive effects, we can say the parents
  will breed true. Offspring performance equals
  the average of parent performance (assuming
  constant E).

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Example 1

• Trait 1 controlled by two loci, both additive.
• AA 30 BB 20
• Aa 0 Bb 0
• aa -30 bb -20
• AAbb ? aaBB ? ? AaBb offspring
• 10 -10 0
• parent avg (0) offspring avg (0)

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Example 2

• Trait 2 partial and complete dominance.
• AA 30 BB 20
• Aa 20 Bb 20
• aa 0 bb 0
• AABB ? aabb ? ? AaBb offspring
• 50 0 40
• parent avg (25) ? offspring avg (40)

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Example 3

• Trait 3 over dominance.
• AA 30 BB 20
• Aa 40 Bb 30
• aa 0 bb 0
• AaBb ? aaBB ? ? AaBb offspring
• 70 20 35
• AaBB 50
• AaBb 70
• aaBB 20
• Aabb 0
• parent avg (45) ? offspring avg (35)

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• Only additive effects are inherited consistently
  in a predictable manner.
• Non-additive effects depend on genotype, not
  individual alleles.
• Thus, we usually use narrow sense h2 for
  livestock.

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Characteristics of h2

• Value ranges from 0 to 1.
• 0 to .25 low
• .25 to .40 moderate
• .40 to 1 high
• Related to the amount of change we can make
  through selection.
• Can make more change when h2 is higher.
• Measures likeness between parent/offspring

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Characteristics of h2

• Varies trait-to-trait.
• Varies pop.-to-pop. for same trait.
• Varies over time.
• Higher when E is small.
• Uniform treatment of animals helps selection.
• Higher for traits controlled primarily by A.

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Rules of Thumb for h2

• Reproductive traits
• Growth milk yield
• Conformation and carcass

• Low h2
• Moderate h2
• High h2

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Rules of Thumb for h2
3
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h2 measures heritable proportion of observed
difference

• Group A cows average 20,000 lb milk
• Group B cows average 17,000 lb milk
• Same environment for both groups.
• Breed all cows to same bull. Assume h2.40
• What is expected difference in milk yield of
  daughters?
• (3000)(.5)(h2) 1500(.4) 600 lb

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Repeatability (rep)

• rep association between 2 or more records on
  same individual.
• (compare to h2 association between parent
  offspring records).
• Only applies to traits with repeatable records
  (e.g., milk yield, litter size, ewes wool
  production).

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• rep proportion of phenotypic variation due to
  all permanent effects (G EP).

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(No Transcript)
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Characteristics of rep

• Varies trait-to-trait.
• Varies pop.-to-pop. for same trait.
• Varies over time.
• Higher when E is small.

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Average milk yield, lb per lactation

• Herd 2
• 17,500
• 18,000
• 17,000
• 17,500

• Year Herd 1
• 1 16,000
• 2 19,000
• 3 15,000
• 4 20,000
• rep much higher in herd 2.

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repeatability

• rep is used to predict an animals own future
  performance (MPPA, PPA).
• h2 is used predict performance of animals
  offspring (EPD, PTA).
• When rep is high, an animals first record is a
  good indicator of subsequent performance.