Lecture 13 Family Selection. Bruce Walsh lecture notes Synbreed course version 4 July 2013

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1 Lecture 13 Family Selection Bruce Walsh lecture notes Synbreed course version 4 July

2 Selection in outbred populations If offspring are formed by randomly-mating selected parents, goal of the breeder is to find those parents with the highest breeding values for the trait (or trait index) of interest If h 2 is high, then phenotype is a good predictor of breeding value (A) If h 2 is low, information from relatives very helpful Focus here is on using family information Lots of schemes, esp. for plants More generally, BLUP selection 2

3 Why Family selection? Low heritability High G x E, esp. year-to-year Single phenotypes very poor predictors of A, G. Hence, often grow out relatives in field trails (multiple plots over a range of regions and years -- better sampling of G x E) Other reasons When measuring the trait removes that individual as a potential parents (i.e, meat quality traits) When trait in sex-limited. Use information from sisters to pick best males When single individuals difficult to measures (e.g., forage crops) 3

4 Overview: When to use? When common family effects variance is large, use within-family selection Selection based on within-family components results in less inbreeding vs. schemes with strong btw-family components When G x E is high, use between-family selection Replicate family members over a variety of E s (esp. different uses through remnant seed) Generally speaking, when h 2 is low, use between-family A weighted index (within + between) can always beat individual selection Selection on phenotype a special case of equal weight on within- and between-family components 4

5 Putting together familybased selection schemes Three components are combined to make a particular design Type of family half-, full-sib, nested full/half-sib How sib data is used Between, within, index Relationship between measured sib and individuals serving as parents for the next generation 5

6 Different ways to use sib data for selection Uppermost fraction p chosen, m families each with N sibs 6

7 Choice of scheme has implication on selection intensity 7

8 General approach P 1 P 2 x 1 R 1 R 2 x 2 y Offspring y is the product of parents R 1 and R 2 (the recombination unit) Based on information of sib x i, R i is chosen (the selection unit) 8

9 Overview of different family-selection schemes 9

10 General response The basic idea is that a parent P generates a set of relatives x 1 through x n whose phenotypes are measured (selection unit or group) Based on the performance of the selection group, relatives R i of the best parents are chosen to represent P i in forming the next generation (recombination unit or group) R can be The parent itself Progeny (measured or unmeasured) of the parent, could be half- or full-sibs to the selection group, could also be the seed from selfing the parent Other relatives of P 10

11 Recombination units With within-family (either strict or family deviation) and family index selection, R is a measured sib With between-family selection, MANY options for R Idea is to use part (or all) of family information to pick best families, and then select parents from these families 11

12 Parents P f P m x1... xn Selected group Chooses parents R y Offspring Recombinant Group Parents of next generation (offspring y) Response in next generation Key: The covariance!(x i,y) between a member in the selection group and the offspring is critical to predicting selection response, closely related to!(x i,a Ri ), the cov bwt selection unit and BV of R x 1 Expected response is the average breeding values of the R i. P 1 R 1 y R 2 P 2 x 2 12

13 A) Family Selection R is a measured sib x i = R P B) Sib Selection R is a unmeasured sib P x 1 x i = R x n x 1 x n R y y C) Parental Selection (progeny testing) P = R D) S 1 Seed Selection P R is the selfed progeny (S 1 ) of P x 1 x n y x 1 x n R 13 y

14 Response under general family selection: Selection differential Let x m, x f denote relatives of mother and father Can express in breeder s equation from by extending the definition of heritability 14

15 Response under general family selection: Selection Intensity Recall the accuracy version of the breeder s equation, R = i r ua! A In our context, i is the selection intensity between selection units u is the value of the selection unit A the breeding value in the corresponding member R of the recombination unit,! 2 A the additive variance in the recombination unit The correlation r ua is obtained from standard resemblance between relatives calculations 15

16 Obtaining!(x,y), the selection unit-offspring covariance 16

17 (A) x and R 1 are half-sibs P1 P2 P3 P4 P5 1/2 P1 R x 1 R 2 1/2 1/2 R x 1 y " = 1/16 y 1/2 (B) x and y have a common parent, P 1 1/2 P1 P2 P4 P5 P1 = R 1 x R 2 1/2 x 1/2 y " = 1/8 y 17

18 C) Half-Sib S 1 P2 P1 P4 P5 1/2 P1 1/2 x R 1 y R 2 1/2 Two paths " = 1/16 + 1/16 = 1/8 x 1/2 1/2 R y 1 R D) x and 1 are full-sibs P1 P2 P4 P5 1/2 1/2 R x 1 y R 2 1/2 P1 Two paths " = 1/16 + 1/16 = 1/8 1/2 R x 1 y 1/2 1/2 P2 R x 1 y 1/2 1/2 18

19 Within- vs. Between-family selection Between-family response Within-family response 19

20 Example 1: Between-family where (for x = t,r) x n = x + (1-x)/n Suppose upper 20% saved (-> i = 1.40), while h 2 = 0.1, Var(A) = 100, t = 0.3, n = 10 Under individual selection, R = 10*0.32*1.40 = 4.48 For full sibs, r n = (1-0.5)/10 = 0.55 t n = 0.37, R FS = 10*0.32*0.55/(0.61)*1.40 = This is 90% of the response under individual selection. 20

21 Example 2: Within family where (for x = t,r) x n = x + (1-x)/n Suppose upper 20% saved -> i = 1.40 h 2 = 0.1, Var(A) = 100, t -> 0.3, n = 10 For full sibs, r n = 0.55, t n = 0.37, R FS = 10*0.32*(1-0.55)/(0.84)*1.40 = 2.4. Resulting response is ~ 50% of that under individual selection. 21

22 Response Equations The next few slides summarizes the selection unitoffspring covariance!(x,y) for a number of designs and the variance! 2 (x) of the selection unit These are used in the response equations 22

23 Different designs 23

24 Offspring - selection unit covariances 24

25 Offspring - selection unit covariances (cont) 25

26 Variance in the selection unit 26

27 Response 27

28 Within, Between or Individual selection? Which scheme is best depends on the trait heritability and the intraclass correlation t among sibs Between-family response > individual when Low heritability, small common-family variance 28

29 Within-family response > individual response when Requires low heritability, and a large c. c 2 Var(z) = between family common variance thus accounts for much of the total trait variance 29

30 30

31 31

32 Specific schemes: ear-to-row A common scheme in corn breeding is to plant the seeds from an ear as rows Each row is thus a half-sib family (this is the selection unit) Some seed from ear saved (these form the recombination unit) Suppose total N seeds per ear grown as n p rows of n s sibs in n e environments Family x E interaction 32

33 Modified ear-to-row Lonnquist (1964) proposed this scheme Combines ear-to-row (between family) with selection within row (within-family selection) Plant the seeds from the ear as two sets of rows. One set is several rows over multiple environments. Select best ears based on this performance. Grow out residual seed from these best ears in a single row, then select best from each family within each row. 33

34 Best Best 34

35 Response Total R = R from ear-to-row + R from within-row 35

36 Lush s family index Finally, Lush suggested that an index weighting both within- and between-family values is optimal The optimal weights are given by Ratio of response/individual selection > 1 36

37 Example Consider full sibs (r = 0.5) with intraclass sib correlation of t = 0.6, and n = 10 sibs Index weights Resulting index Increase in response over mass selection (2%) 37

38 38

39 More emphasis on between-family deviations b2 / b More emphasis on within-family deviations Half-sibs n = 2 n = 4 n = 10 n = 25 n = t

40 More emphasis on between-family deviations b2 / b More emphasis on within-family deviations Full-sibs n = 2 n = 4 n = 10 n = 25 n = t 40

41 Relative response of Index/Individual selection Response relative to Mass Selection Half-Sibs n = 2 n = 5 n = Phenotypic correlation t between sibs 41

42 Relative response of Index/Individual selection Response relative to Mass Selection Full Sibs 0.1 n = 2 n = 5 n = Phenotypic correlation t between sibs

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