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 Breeding Value Empirically: An individual’s value based on the mean deviation of its progeny from the population mean. Theoretically: An individual’s value based on the sum of the average effects of the alleles/genes it carries.

Average Effect of an Allele Type of Values and Freq Mean value Population Average gamete of gametes of genotypes mean effect of gene A1A1 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)] average effect of An: an = mean deviation from the population mean of individuals that received An from one parent, if the other parent’s allele chosen randomly a1 = pa + qd - [ a (p – q) + 2dpq ] population mean . f (A1) f (A2) a1 = q [ a + d (q – p)] a2 = –p [ a + d (q – p)]

When there are only two alleles at a locus Average effect of a gene substitution A1A1 A1A2 A2A2 +a d -a (a - d) (d + a) p(a - d) + q(d + a) a = a + d(q - p) a pa

Average Effects Frequency q (A2 orTHa2) 0.0 0.3 0.5 0.7 1.0 0.0 0.3 0.5 0.7 1.0 : THa1 0 9.3 12.5 13.3 10 : THa2 -40 -21.7 -12.5 -5.7 0   40 31 25 19 10 d = -15; a = 25

Theoretically: An individual’s value based on the sum of the average effects of the alleles/genes it carries. Genotype Breeding Value A1A1 A1A2 A2A2 2a1 = 2qa a1 + a2 = (q - p)a 2a2 = -2pa

Breeding Values - THa example A2 or Tha2 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

= = + (A) G = A + D Sum of average effects across loci + Breeding Value (A) A1A1 A1A2 A2A2 2a1 a1 + a2 2a2 B1B1 B1B2 B2B2 2a1 a1 + a2 2a2 + (breeding values) (breeding values) G = A + D = + Genotypic Value Additive effects of genes Dominance deviation

Partitioning the phenotypic value genotypic value breeding value deviations from population mean phenotypic value of individual genotypic value G = A + D breeding value dominance deviation P = G Pop Mean G = G1 + G2 + I12 interaction two-locus: P = A1 + D1 + A2 + D2 + I12 d=3/4a, q = 1/4

Environmental effects on phenotypes P = A + D One locus, two alleles One locus, two alleles + environmental variation environmental deviation P = A + D + E

Amount of genetic variation in a population depends on # of genotypes, genotypic value, and gene frequencies. More variation Less variation 0.75 0.75 p = 0.5 p = 0.9 0.50 0.50 0.25 0.25 9 10 11 9 10 11 A1A1 A1A2 A2A2 A1A1 A1A2 A2A2 Mean Mean

Components of phenotypic variation f (A1) a = d = 0.07 P = A + D + I + E Variance partitioning: VP = VG + VE VP = VA + VD + VI + VE . total phenotypic variance additive genetic dominance interaction (epistatic) environmental • Phenotypic variation can be decomposed into additive genetic and other variation • Relative contributions of different sources depend on allele frequencies

TH alpha Example VA = 2pq[a + d (q - p)]2 VD = (2pqd)2 q = 0.3 443.31 403.62 39.69 q = 0.7 191.24 151.62 39.69 Genotypic, VG Additive, VA Dominance, VD d = -15; a = 25 (178.7) (158.7)

Environment and genotype can interact Different environmental effects across genotypes result in G x E interaction variance VP = VA + VD + VI + VE + VGxE genetic x environmental interaction variance VP = VA + VD + VI + VE

Heritability h2 = VA/Vp Proportion of total phenotypic variance attributed to variation in breeding values. Expresses the extent to which genes are transmitted from parents to offspring

Detecting the genetic component of phenotypic variation Resemblance between parents and offspring indicates degree to which a trait is inherited Drosophila wing length offspring (O) bOP parental average (P) heritability (narrow sense): h2 = VA VP h2 = bOP Fraction of variation in parents that is explained by variation in their genes (VA). • heritability can also be estimated with offspring–midparent regression

Bill depth in the Ground Finch 1976 h2 = 0.9 1978

Heritability is often measured in the lab; estimates are higher than would be expected in nature. Almost all characteristics in almost all species are genetically variable to some extent.