heritable diversity feb ! gene 8840 biol 8990

Transcription

1 heritable diversity feb ! gene 8840 biol 8990 D. Gordon E. Robertson - photo from Wikipedia

2 HERITABILITY DEPENDS ON CONTEXT heritability: how well does parent predict offspring phenotype? how much genetic variation is associated with trait variation? how will that variation be used to respond to change in context? Tigriopus californicus

3 Predic5ng range shi9s: do popula5ons vary with respect to tolerance to TEMPERATURE? A B Temperature I II La%tude I II Both popula%ons persist Both popula%ons go ex%nct Pop. II could persist with gene flow from I Sanford & Kelly 2011

4 Predic5ng ex5nc5on risk A B Temperature Plas%city or adapta%on? I II I II La%tude do they have enough variation among individuals to survive as a population?

5 response can equal move, adapt, acclimate, or die here we focus on adapt the response to a selective force requires genetic variation for that trait this is heritability: the degree to which individuals harbor specific genetic information that is associated with a trait, and how variable that information is response = heritability x selection

6 R=h 2 S breeder s equation h 2 = R / S, where R is response to selection, S is selection differential S is difference in trait mean of selected parents and population as a whole

7 What is the scope for adapta%on? Selec%on experiments: Heat stress ~50% mortality pairs/ popula%on survivors reproduce! Repeat for 10 genera5ons Genera5on 5me ~4 wks

8 SELECTION from 4 populations ( hot, warm, cool, cold ), select in lab for the individuals that continue to be active at hotter temperatures RESPONSE evaluate how far we can move the LT50* from the natural populations *LT50: Lethal Temperature for 50% of individuals

9 selection so in this case, trait under selection is threshold temperature - what temperature is lethal we know the mean trait for the populations from the LT50 experiments but following each round of selection, you know the individuals survived, but you don t know the trait - only that it is higher than what exposed to now it gets kind of hairy in this case

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12 proportion dead logistic curve the cumulative distribution function of mortality temperature

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14 eek! basically you know the selection temperature; the intensity is proportion dead (the vertical line); the distribution lets you get mean, variance of the dead as well as the survivors

15 the simpler approach Phenotype (P) = Genotype (G) + Environment (E) Var(P) = Var(G) + Var(E) + 2*covariance(G,E) in a planned experiment (common garden), no E variance, so heritability: H 2 = Var(G)/Var(P), broad-sense heritability, includes ALL genetic contributions even dominance and epistasis

16 narrow-sense heritability excludes dominance and epistatic effects, so only additive variance (Var (A)) h 2 = Var(A) / Var(P) breeders equation R = h 2 * S only works with narrow-sense so if you know selection differential S (difference in mean trait between population, and selected individuals) and you observe Response, h 2 = R/S

17 linear regression parent trait v. offspring: slope ~ h 2 Narrow-sense-heritability estimates (h 2 ) are based on the squared regression coefficient of the random effect

18 next 3 slides borrowed from Alan Rogers lectures adapted from Freeman & Herron textbook

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21 is it clear why Morgan Kelly s study required more complicated mathematics? (a) mass selection rather than parent-offspring (b) unclear Selection differential, S is it clear that non-additive allele x allele and gene x gene interactions will complicate matters? this takes us towards multi-locus selection and response!

22 what is G?!

23 linear algebra a = b x c is algebra, variables and their relationship is linear algebra, each item is a vector of numbers, and their relationship 2-d vector (matrix) eqn. from above (2-trait Breeder s) written as algebra

24 variances and covariances G11,G22 are genetic variance for trait 1, trait 2 G12,G21 are genetic covariance between traits no covariance positive covariance

25 draw an ellipse around the points and their relationships no covariance (line slope 0) covariance (line slope >0)

26 tness landscape (topography) when covariance, evolution moves quicker along long axis so NOT straight to optimum. may never get there! again thanks to