Quantitative characters

Transcription

1 Quantitative characters Joe Felsenstein GENOME 453, Autumn 015 Quantitative characters p.1/38

2 A random mating population with two genes having alleles each, at equal frequencies, symmetrically affecting a quantitative character ab ab Ab 3 1 AB AB 3 1 Ab 3 1 ab ab Quantitative characters p./38

3 Quantitative characters p.3/38

4 Quantitative characters p.4/38

5 The distribution of the genotypes and the quantitative character before artificial selection AAbb AaBb Aabb aabb AABb aabb AabB AAbB aabb aabb AaBB aabb aabb aabb aabb AABB Quantitative characters p.5/38

6 An imaginary quantitative character with 4 loci The character is a sum of effects including interaction and environmental effects: starting value 1 + AA Aa aa two loci that add up CC Cc cc 0 3 DD Dd dd + BB Bb bb plus two that interact plus an environmental effect What kind of distribution will this lead to when gene frequencies at the four loci are p A = 0.4, p B = 0.5, p C = 0.3, and p D = 0.6? Quantitative characters p.6/38

7 frequency The resulting distribution Phenotype Quantitative characters p.7/38

8 A similar distribution in a 5-locus character 100 random individuals: Gene frequencies A B C D E Phenotype: Number of copies of these alleles. No environmental effects Quantitative characters p.8/38

9 Distributions of quantitative characters Quantitative characters p.9/38

10 Quantitative characters p.10/38

11 Quantitative characters p.11/38

12 Recall this distribution The distribution of the genotypes and the quantitative character before artificial selection Before selection frequency of A = 0.5 AAbb AaBb Mean phenotype of population =.0 frequency of B = 0.5 Aabb aabb AABb aabb AabB AAbB aabb aabb AaBB aabb aabb aabb aabb AABB Quantitative characters p.1/38

13 Truncation selection The distributions after artificial selection which saves only those individuals at or above Before selection frequency of A = 0.5 AAbb AaBb Mean phenotype of survivors =.545 frequency of B = 0.5 aabb AABb After selection: AabB AAbB frequency of A = 14/ = aabb AaBB frequency of B = 14/ = aabb aabb AABB Quantitative characters p.13/38

14 Offspring of truncation selection In fact, the offspring will have this distribution: Mean phenotype of offspring =.545 (484 copies in all) Quantitative characters p.14/38

15 Effect of truncation selection on one locus With a larger number of loci, focusing just on one locus phenotype Quantitative characters p.15/38

16 Effect of truncation selection on one locus With a larger number of loci, focusing just on one locus Aa aa AA phenotype Quantitative characters p.16/38

17 Effect of truncation selection on one locus The distribution of offspring at this locus Aa AA aa phenotype Quantitative characters p.17/38

18 Heritability ( assuming genes are additive and environments are independent) Variance of a character = V T V = V + V + V T A D E Environmental variance Dominance variance Additive genetic variance Total variance heritability = h = V A V T heritability in effect measures the fraction of variations that are passed on to the next generation, undisrupted by Mendelian segregation Quantitative characters p.18/38

19 Heritabilities in a real-life example Quantitative characters p.19/38

20 Response to artificial selection R = h S h = heritability truncation point discard these breed from these mean of newborns S mean of those who we breed from h S mean of newborns in next generation Quantitative characters p.0/38

21 # of individuals Response to artificial selection Population mean Mean of selected individuals 1000 lbs 1100 lbs If heritability = 0.4 weight S = selection differential = mean of selected individuals population mean = 100 lbs R = gain = h S = 40 lbs This is the expected gain in one generation Quantitative characters p.1/38

22 Some features of artificial selection experiments a selection limit? selection up mean phenotype replicate lines selection down control line relaxation of selection reverse selection generations Quantitative characters p./38

23 Body weight in mice Quantitative characters p.3/38

24 Tooth decay in rats Quantitative characters p.4/38

25 White blood cell counts Quantitative characters p.5/38

26 Chicken legs Quantitative characters p.6/38

27 Thorax bristles in Drosophila Quantitative characters p.7/38

28 Abdominal bristles in Drisophila Quantitative characters p.8/38

29 Dobzhansky s glass maze Quantitative characters p.9/38

30 Artificial selection on geotaxis Quantitative characters p.30/38

31 Artifical selection on phototaxis Quantitative characters p.31/38

32 Ken Weber s inebriometer diagram photograph Quantitative characters p.3/38

33 The Illinois corn selection experiment (oil content) Quantitative characters p.33/38

34 Quantitative characters p.34/38

35 The Illinois corn selection experiment (protein, oil) Stephen P. Moose, John W. Dudley and Torbert R. Rocheford Maize selection passes the century mark: a unique resource for 1st century genomics. Trends in Plant Science 9 (7): Quantitative characters p.35/38

36 Frequency Hermon Bumpus s 1896 sparrows lengths length Histogram of female total lengths in millimeters Quantitative characters p.36/38

37 Frequency Sparrow survival data length Histogram of total lengths of females, and those that survived Quantitative characters p.37/38

38 fitness Least squares fit of estimated fitnesses total length of female (mm) Fraction of surviving females, and estimate of (quadratic) fitness curve Quantitative characters p.38/38