Quantitative genetics Genes & Quantitative Traits A continuum of phenotypic variation Environmental variance

Important quantitative traits in humans: Infant growth rate Adult weight Blood pressure Serum cholesterol Length in life IQ

I. Genes & Quantitative Traits Quantitative traits = Complex traits, w/ many factors affecting the trait the phenotypes in a population differ in quantity rather than type Phenotypes are distributed on a continuous scale, or their underlying genetic determination is assumed to be. e.g. three loci are important in the number of flowers that will develop in a plant, each locus has two alleles, thus there are 33 = 27 different genotypes, many different genotypes may have the same average phenotype, or because of environmental variation two individuals with the same genotype may not have the same phenotype. Genetic architecture = a description of all the genetic and environmental factors that affect the trait, along with the magnitudes of their individual effects and the magnitudes of interactions among the traits

Quantitative traits For many traits –– the genetic basis is not known precisely Such complex genetic traits are known as quantitative traits Anatomical Height, weight, pigmentation physiological Metabolic rates, running speed, tolerance behavioral I.Q., mating calls, memory, tropism diseases Diabetes, hypertension, arthritis, obesity

1 locus: 2 loci: Several loci: Polygenic! Multiple gene hypothesis Additive, because each allele adds a certain amount to the phenotype Several loci: Polygenic!

Quantitative traits influenced by alleles of two or more genes & the environment Genetic Factors – alternative genotypes for several genes height – 5 genes, 3 possible genotypes for each gene (AA, Aa, aa) so – 35 = 243 genotypes! Calculating the # of polygenes contributing to a phenotype= if the ratio of F2 individuals resemble either of the two extreme parental types, n = 1/4n Environmental Factors – conditions that are favorable or unfavorable for the development of the trait n Extreme phenotype Distinct phenotype classes 1 ¼ 3 2 1/16 5 1/64 7 4 1/256 9

Polygenic trait: eg. Skin color – 3 genes involved. Each dominant allele is favorable for the expression of the trait and adds one unit to the phenotype

population affected by both environmental and genotypic variance Population affected by genotypic variance

Polygenic inheritance creates overlaps between genotypes and phenotypes. Also affected by the environment, i.e. sunlight, soil conditions, pH… Situation in which height is controlled by more than one gene – the overlap is minor when the environment does not cause much variation

Crosses between strains that differ in collora length: Mean collora length close to midpoint of 2 parents F2, unchanged, but there is an increase in variation Nicotiana logiflora

Results of crosses between strains of Nicotiana that differ in corolla length- Frequency distribution different for parents and offspring… Difference between the two lines is genetic, but the variation among individuals within each line is a result of environmental variation and developmental noise… Offspring don’t sort out into discrete 1:2:1 ratios, there is much more individual variation within each generation of offspring

Quantitative trait categories Continuous traits Traits vary continuously from one extreme to another Height, weight, pigmentation, I.Q., memory, tropism Meristic traits Phenotype determined by counting Fingerprint skin ridges, # kernels on corn, eggs laid Threshold traits Have only a few classes, but effected by many genes/ environment Parthenogeneisis, adult diabetes, schizophrenia

II. Quantitative traits – continuum of phenotypic variation Frequency distribution Trait is divided arbitrarily into a number of discrete categories Normal distribution curve A distribution for an infinite sample in which the trait of interest varies in symmetrical way around an average value Statistical methods used to evaluate the distribution quantitatively

Statistical distribution: Statistical measures -mean (average) -variance (s2, spread of the distribution) -standard deviation ( s2 ) -covariance (degree of variation between 2 variables within a group) -correlation (compare 2 variables to see if they are related)

Mom’s weight Offsprings’weight X-X Y-Y (X-X)(Y-Y) 570 568 -26 -30 780 572 560 -24 -38 912 599 642 3 44 132 602 580 6 -18 -108 631 586 35 -12 -420 603 7 308 632 34 102 625 29 -522 584 605 -84 575 585 -21 -13 273 X = 596 Y = 598 Sum = 1373

CoV(X,Y) = ∑ [(X – X)(Y – Y)] SDX = 21.1 SDY = 30.5 CoV(X,Y) = ∑ [(X – X)(Y – Y)] N – 1 = 1373 10–1 = 152.6 Correlation coefficient (r) r(X,Y) = CoV(X,Y) SDX SDY r = 0.237 r indicates how two factors vary in relation to each other, +1 = perfect correlation, 0 = no detectable correlation, >0 indicates the factors vary in opposite ways to each other

Positive correlation between body length and tail length in individual snakes, indicated by this scatter diagram Is genetics the cause of this positive association between these two traits? Could the environment affect both traits in the same manner?

III. Environmental variance Variation in the phenotype caused by differences in environment among individuals (VE) σ2e Genotype and environment can interact (G-E interaction) VP = VG + VE + VG x E Certain genotypes are preferentially associated with certain environments σ2p = σ2e + σ2g Phenotypic variance of a genetically uniform population, provides an estimate of σ2e Phenotypic variance of a genetically heterogenous population, which provides an estimate of σ2e + σ2g

Eye diameter measurements after a cross between two homozygous strains of cave dwelling fish, reared in the same environment: F1: σ2e = 0.057 F2: σ2p = σ2e + σ2g = 0.563 σ2g = 0.563 – 0.057 = 0.506 Hence, the genotypic variance is much greater than the environmental variance Reduced eye size and pigmentation in a cave dwelling Astyanax, compared with the surface dwelling relative…

A. Heritability of a trait Is the observed variation in the character influenced by genes at all? What is the role that genes play in the phenotypic differences between individuals or groups? If genes are involved, then biological relatives should resemble one another more than unrelated individuals do (positive correlation) CONCORDANT = in twins, if both or neither express a trait DISCORDANT = in twins, if one expresses trait, and the other doesn’t Heritability = the amount of phenotypic variation within a group of individuals that is due to genetic factors If all the phenotypic variation in a group were due to genetic variation, then the heritability would = 1. if all the variation is due to environment, then the heritability would = 0 Familial vs. heritable

Testing heritability in experimental organisms: Crosses are performed within two populations of individuals selected from extremes… if the phenotypic distributions of the two groups are significantly different, then the trait is heritable-

Estimating H2 H2 = broad sense heritability – contribution of the genotypic variance to the total phenotypic variance: H2 = VG/VP Crossing homozygote lines, and measuring the phenotypic variance within each heterozygous genotype Twin studies, monozygotic v. dizigotic

B. Twin studies Trait MZ DZ Blood type 1.0 .66 Eye color .99 .28 Monozygotic (identical), dizygotic (fraternal) Concordance: if both have a trait, if the trait is completely controlled by genes, concordance should be 1.0 in MZ, 0.5 in DZ Degree of difference between concordance in MZ v. DZ, the greater the difference, the greater the heritability (must be used w/caution) Trait MZ DZ Blood type 1.0 .66 Eye color .99 .28 Hair color .89 .22 Handness (L/R) .79 .77 Tuberculosis .53 Down syndrome .72 .33 Manic-depression .80 .20 Epilepsy .15 Cleft lip .42 .05

Fingerprint ridge data: Narrow sense heritability – proportion of variance due to genetic variance alone. hN2 = robs/rexp For siblings, rexp = 0.5, for identical twins = 1 Relationship N robs h2 Parent-child 810 0.48 0.96 Parent-parent 200 0.05 --- Sib-sib 642 0.50 1.00 Identical twins 80 0.95 Fraternal twins 92 0.49 0.98 Avg.h2 0.97

arch loop whorl

Problems with twin studies: G-E interaction Sharing of embryonic membranes Similarity in the treatment of identical twins Different sexes