Genotypic value is not transferred from parent to offspring; genes are.

Need a value that reflects the genes that an individual carries and passes on to it’s offspring

Empirically: An individual’s value based on the mean deviation of its progenyfrom the population mean.

Theoretically: An individual’s value based on the sum of the average effectsof the alleles/genes it carries.

Breeding Value

average effect of An:

n = mean deviation from the population mean of individuals that received An from one parent, if the other parent’s allele chosen randomly

1 = q [ a + d (q – p)]

2 = –p [ a + d (q – p)]

1 = pa + qd - [ a (p – q) + 2dpq ]

population mean.

f (A1) f (A2)

Average Effect of an Allele

Type of Values and Freq Mean value Population Average gamete of gametes of genotypes mean effect of

geneA1A1 A1A2 A2A2

a d -a

A1 p q pa + qd -a(p-q) + 2dpq q[a+d(q-p)] A2 p q -qa + pd -a(p-q) + 2dpq -p[a+d(q-p)]

When there are only two alleles at a locus

A1A1 A1A2+a d

A2A2-a

Average effect of a gene substitution

(a - d) (d + a)

p(a - d) + q(d + a)

= a + d(q - p)

p

Frequency q (A2 orTH2)

0.0 0.3 0.5 0.7 1.0

: TH1 0 9.3 12.5 13.3 10

:TH2 -40 -21.7 -12.5 -5.7 0

4031 251910d = -15; a = 25

Average Effects

Genotype Breeding Value

A1A1

A1A2

A2A2

21 = 2q

1 + 2 = (q - p)

22 = -2p

Theoretically: An individual’s value based on the sum of the average effects of the alleles/genes it carries.

Breeding Values - TH example

A2 or Th2 Pop Mean A1A1 A1A2 A2A2

q = 1.0 150 20 20 0

q = 0.7 158.7 26.6 15.2 -11.4

q = 0.5 167.5 25 0 -25

q = 0.3 178.7 18.6 -24.8 -43.4

q = 0.0 200 0 -80 -80

Sum of average effects across loci

Breeding Value

(A)=

G = A + D

Genotypic Value = Additive effects

of genes + Dominancedeviation

A1A1 A1A2 A2A2

21 1 + 2 22(breeding values)

+B1B1 B1B2 B2B2

21 1 + 2 22(breeding values)

Partitioning the phenotypic value

P = G

P = A1 + D1 + A2 + D2 + I12

phenotypic value of individual

genotypic value of individual

G = A + D

breeding value

dominancedeviation

G = G1 + G2 + I12

interaction

two-locus:

genotypic value

breedingvalue

geno

typi

c va

lue

deviations from population m

ean

d=3/4a, q = 1/4

Pop Mean

Environmental effects on phenotypes

P = A + D

One locus, two alleles

One locus, two alleles + environmental variation

environmentaldeviation

P = A + D + E

Amount of genetic variation in a population depends on# of genotypes, genotypic value, and gene frequencies.

p = 0.5 p = 0.9

A1A1 A1A2 A2A2 A1A1 A1A2 A2A2

0.75

0.50

0.25

0.75

0.50

0.25

Mean Mean

9 10 11 9 10 11

More variation Less variation

Components of phenotypic variation

P = A + D + I + E

VP = VG + VE

Variance partitioning:

totalphenotypic

variance

additivegenetic

variance

dominancegenetic

variance

interaction(epistatic)

geneticvariance

environmentalvariance

VP = VA + VD + VI + VE

.

• Phenotypic variation can be decomposed into additive genetic and other variation• Relative contributions of different sources depend on allele frequencies

V

f (A1)

a = d = 0.07

Genotypic, VG

Additive, VA

Dominance, VD

q = 0.3

443.31

403.62

39.69

q = 0.7

191.24

151.62

39.69

VA = 2pq[a + d (q - p)]2 VD = (2pqd)2

d = -15; a = 25

TH alpha Example

(178.7) (158.7)

Environment and genotype can interact

VP = VA + VD + VI + VE

Different environmental effects across genotypes result in G x E interaction variance

VP = VA + VD + VI + VE + VGxE

genetic xenvironmental

interactionvariance

h2 = VA/Vp

Expresses the extent to which genes are transmitted from parents to offspring

Proportion of total phenotypic variance attributed to variation in breeding values.

Heritability

Resemblance between parents and offspring indicates degree to which a trait is inherited

heritability (narrow sense):

h2 = VA

VP

h2 = bOP

• heritability can also be estimated with offspring–midparent regression

Drosophila wing length

offs

prin

g (O

)

bOP

parental average (P)

Detecting the genetic componentof phenotypic variation

Fraction of variation in parents that is explained by variation in their genes (VA).

19761978 h2 = 0.9

Bill depthin the

Ground Finch

Almost all characteristics in almost all species are genetically variable to some extent.

Heritability is often measured in the lab; estimates are higher than would be expected in nature.