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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
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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.
. a1 = 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 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 = 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 pa
Average Effects Frequency q (A2 orTHa2) 0.00.30.50.7 1.0 : THa1 0 9.3 12.5 13.3 10 :THa2 -40 -21.7 -12.5 -5.7 0 4031 251910 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 2a1 = 2qa A1A1 A1A2 A2A2 a1 + a2 = (q - p)a 2a2 = -2pa
Breeding Values - THa example A2 or Tha2 Pop MeanA1A1A1A2A2A2 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) 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
breeding value deviations from population mean phenotypic value of individual genotypic value of individual genotypic value breeding value genotypic value dominance deviation G = A + D G = G1 + G2 + I12 two-locus: interaction Partitioning the phenotypic value P = G Pop Mean P = A1 + D1 + A2 + D2 + I12 d=3/4a, q = 1/4
One locus, two alleles P = A + D One locus, two alleles + environmental variation P = A + D + E environmental deviation Environmental effects on phenotypes
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 10 10 11 9 11 9 A1A1 A1A2 A2A2 A1A1 A1A2 A2A2 Mean Mean
a = d = 0.07 V . VP = VA + VD + VI + VE f (A1) total phenotypic variance additive genetic variance dominance genetic variance interaction (epistatic) genetic variance environmental variance Components of phenotypic variation P = A + D + I + E Variance partitioning: VP = VG + VE • Phenotypic variation can be decomposed into additive genetic and other variation • Relative contributions of different sources depend on allele frequencies
VA = 2pq[a + d (q - p)]2 VD = (2pqd)2 TH alpha Example q = 0.7 191.24 151.62 39.69 q = 0.3 443.31 403.62 39.69 Genotypic, VG Additive, VA Dominance, VD d = -15; a = 25 (178.7) (158.7)
Different environmental effects across genotypes result in G x E interaction variance VP = VA + VD + VI + VE + VGxE genetic x environmental interaction variance Environment and genotype can interact 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
Drosophila wing length heritability (narrow sense): parental average (P) VA VP h2 = offspring (O) h2 = bOP bOP Detecting the genetic component of phenotypic variation Resemblance between parents and offspring indicates degree to which a trait is inherited 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.