class: center, middle, inverse, title-slide # Variability in response ### Jinliang Yang ### Nov. 11th, 2020 --- # Improvement of response `\begin{align*} & R = \frac{i h^2\sigma_P}{L} \\ \end{align*}` The form of the breeder's equation allows us to clearly see how to maximize response to selection per unit of time. ### 1. Reduce the generation interval ### 2. Increase the heritability of the trait ### 3. Increase the selection intensity ### 4. Increase additive genetic variance --- # Measuring response to selection Response selection of two populations of broilers. - One population was selected for __high__ 56-day body weight. - One population was selected for __low__ 56-day body weight. .pull-left[ <div align="center"> <img src="poultry.jpg" height=200> </div> ] -- .pull-right[ <div align="center"> <img src="longterm.png" height=250> </div> ] -- #### Causes of response variability to selection? -- 1. Genetic drift 2. Sampling error in estimating the generation mean 3. Differences in selection differential 4. Environmental factors --- # Measuring response to selection .pull-left[ <div align="center"> <img src="longterm.png" height=250> </div> ] .pull-right[ #### Causes of response variability: 1. Genetic drift 2. Sampling error in estimating the generation mean 3. Differences in selection differential 4. Environmental factors ] ### How to separate these effects? -- 1. Maintain an unselected control population 2. Practice divergent selection 3. Or carry out replicated, parallel selection programs --- # Breeder's equation ### The complex version `\begin{align*} & R = \frac{i h^2\sigma_P}{L} \\ \end{align*}` -- ### The simple version `\begin{align*} & R = h^2 S \\ \end{align*}` -- The heritability, therefore `\begin{align*} & h^2 = R/S \\ \end{align*}` --- # Realized heritability .pull-left[ `\begin{align*} & h_R^2 = R/S\\ \end{align*}` Shows how the response is related to the selection differential ] -- .pull-right[ ```r S <- c(5, 6, 5, 6, 6, 10) R <- c(3, 2, 1, 3, 2, 3) df <- data.frame(s=cumsum(S), r=cumsum(R)) library(ggplot2) ggplot(df, aes(x=s, y=r)) + geom_point(color='red', size = 4) + geom_smooth(method=lm, color='#2C3E50') ``` ``` ## `geom_smooth()` using formula 'y ~ x' ``` <img src="Ch11-c2_files/figure-html/unnamed-chunk-1-1.png" width="80%" style="display: block; margin: auto;" /> ] --- # Realized heritability .pull-left[ `\begin{align*} & h_R^2 = R/S\\ \end{align*}` Shows how the response is related to the selection differential - The selection differential are summed across the generations plotted against the cumulative response. - The slope of the regression line fitted to the points is equal to the average value of R/S. ] .pull-right[ ```r S <- c(5, 6, 5, 6, 6, 10) R <- c(3, 2, 1, 3, 2, 3) df <- data.frame(s=cumsum(S), r=cumsum(R)) library(ggplot2) ggplot(df, aes(x=s, y=r)) + geom_point(color='red', size = 4) + geom_smooth(method=lm, color='#2C3E50') ``` ``` ## `geom_smooth()` using formula 'y ~ x' ``` <img src="Ch11-c2_files/figure-html/unnamed-chunk-2-1.png" width="80%" style="display: block; margin: auto;" /> ] --- # Realized heritability `\begin{align*} & h_R^2 = R/S\\ \end{align*}` ### Be cautious: 1. Reduces response to selection after first generation for high heritability traits (__Bulmer effect__) -- - For complex traits, each allele carries a small effect. Therefore, allele frequencies changes are gradual and change in variance through changes in individual allele frequency is slow. -- - However, what is known as the __Bulmer effect__ immediately changes the variance of complex traits subjected to one generation of selection. --- # Realized heritability `\begin{align*} & h_R^2 = R/S\\ \end{align*}` ### Be cautious: 1. Reduces response to selection after first generation for high heritability traits (__Bulmer effect__) 2. Systematic changes in environment or inbreeding depression will affect response. - comparison with control line can adjust for these effects. -- 3. Random drift affect response. - the magnitude of random drift can be assessed by replicated selection. --- # Points to cover in the review: ### Novelty - What are the main claims of the paper and how significant are they? - How novel is the work? Are the conclusions worth knowing? - Is this paper important in its discipline? - Are the claims properly placed in the context of the previous literature? ### Quality - Do the data and analyses support the authors’ claims? - Is the stated purpose achieved throughout the paper? - Would additional work improve the manuscript? - Is the experimentation design appropriate for the purpose of the study? --- # Points to cover in the review: ### Clarity - Evaluate clarity, style and readability of the paper to scientists in the field. - Would you recommend the author seek the service of a professional science writer? ### Reproduciblity - Are original data (and/or code) deposited in appropriate repositories? - Are details of the methodology sufficient to allow the experiments to be reproduced?