Quantitative genetics

Differential survival/reproduction = Evolution Darwin’s tenets: Heritable variation + Differential survival/reproduction = Evolution Measuring heritability -Darwins 2 tenets – heritable variation + differences in survival/reprod success = evol -imagine popln with continuous variation among indiv in some trait eg. human height -normally distributed bell curve -is height heritable? -what fraction of the variation in height among indiv is due to variation in their genes, and what fraction due to variation in their environment?

Heritability = 0 Heritability = 1

Phenotypic variation: total variation in a trait (VP) Genetic variation: variation among individuals due to variation in their genes (VG) Environmental variation: variation among individuals due to variation in their environments (VE) -heritability – fraction due to variation in genes -phenotypic variation = Vp – total variation in a trait -genetic variation= Vg – variation among indiv due to variation in their genes -environmental variation=Ve – variation due to environment -heritability = Vg/Vp = Vg/Vg+Ve -this is broad sense heritability – degree of genetic determination

Broad sense heritability: fraction of the total variation in a trait that is due to variation in genes Heritability = VP VG VG + VE = Phenotypic variation: VP Genetic variation: VG Environmental variation: VE

Biological parents Foster parents estimating heritability from parents & offspring -if variation is due to genes, offspring will resemble their parents -check by making scatterplot -2 parents, so use mid-parent value, if 2+ offspring use mid-offspring value -if no variation due to genes, regression = 0 -if offspring strongly resemble parents, regression = 1 -most traits somewhere between Biological parents Foster parents

Genetic variation: variation among individuals due to variation in their genes (VG) Additive variation: variation among individuals due to the additive effects of genes (VA) Dominance variation: variation among individuals due to gene interactions such as dominance (VD) -variation due to genes & environment -slope is estimate of heritability -narrow sense heritability = h^2 VA + VD VG =

Genetic variation: VG Phenotypic variation: VP Narrow sense heritability: a measure of the (additive) genetic variation in a trait Heritability, h2 = VP VA VA + VD + VE = narrow sense vs broad sense heritability -additive genetic variation = Va – variation among individuals due to additive effects of genes -dominance genetic variation= Vd – variation among indiv due to gene interactions such as dominance -total genetic variation = Vg = Va + Vd -broad sense heritability = Vg/Vp -narrow sense heritability = h^2 = Va/Vp = Va/Va + Vd + Ve -almost always mean narrow sense -recall offspring can resemble parents for reasons other than genes -eg similar diets, similar exercise regimes etc -need to ensure no correlation between parental and offspring environs -could use twin studies if raised apart Genetic variation: VG Phenotypic variation: VP Additive variation: VA Environmental variation: VE Dominance variation: VD

Selection differential: difference between the mean of the selected individuals and the mean of the population (S) measuring differential survival/reprod success -measuring strength of selectin -can then combine with heritability to predict evol’ary change in response to selectin -indiv with some values of a trait survive at higher rates or product more offspring than indiv with other values of a trait -to measure strength of selection, note who survies and reproduces and who fails to do so -then quantify the difference between the winners and losers in the trait of interest -mouse example -bred indiv with 1/3 longst tails for 18 generations -measure mean tail length of breeders & of popln -difference = selection differential =S

P: average midparent value for the entire population Evolutionary response: predicted response of the population to selection (R) R = h2 S Slope = h2 = S O* - O P* - P R = predicting evol’ary response to selection -predicted evolary response to selection = R R=h^2 S h^2 = heritability, S = selection differential P = mean midparent value for entire popln P* = mean of 10 largest midparent values P* - P = S, selection differential O = mean midoffspring values for the entire popln O* = mean mid offspring value for 10 parents with ihgest midparent vlues O* - O = R, evol’ary response, if selected 10 largest parents as breeders Slope = O*-O/P*-P = R/S = h^2 P: average midparent value for the entire population P*: average midparent value for the selected individuals O: average midoffspring value for the entire population O*: average midoffspring value for the selected individuals

R S Slope = h2 = -so R=h^2 S -i) can estimate how much of the variation is due to variation in genes -ii) quantify the strength of selection that results from differences in survival/reprod -iii) combine these to predict how much of the popln will change from 1 generation to the next