5.4: Artificial Selection
- Page ID
- 143503
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The amount that a phenotype changes in one generation is called the selection response, R. The selection response is dependent on two factors—the narrow-sense heritability and the selection differential, S. The selection differential is a measure of the average superiority of individuals selected to be parents of the next generation.
\[R = h^{2}S\]
The above equation is often called the “breeder’s equation”. It shows the key point that response to selection increases when either the heritability of the trait or the strength of the selection increases.
Articial Selection
Let's consider an a traditional directional selection experiment, where a breeder intends to improve a trait in a population of plants or animals. To do so, the breeder selects individuals from a starting generation whose trait of interest is above some threshold, and those individuals become the parents for the next generation. If the trait is heritable, then there is an increase in the average of that trait:
The breeder's equation, above, can be used to predict how fast the trait will increase. It also demonstrates the two things that can speed up the response to selection (ie, how fast the trait increases):
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Increase the selection differential (S) -- ie, how high the threshold is
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Increased heritability.
Alternately, if the narrow-sense heritability of a complex trait is unknown, we can use an artificial selection experiment to estimate it. Rearranging the breeder's equation, we find:
\[ h^{2} = R / S \]
A low h2 (<0.01) occurs when offspring of the selected parents differ very little from the original population, even though there may be a large difference between the population as a whole and the selected parents. Conversely, a high h2 occurs when progeny of the selected parents differ from the original population almost as much as the selected parents.
What are R and S? The selection differential (S) in each generation is the difference between the mean of the entire original population and the mean of group of individuals selected to form the next generation. In contrast, the response to selection (R) indicates the differences in population means across generations. The value of R is the difference between the mean of the offspring from the selected parents and the mean of the entire original population:
\[S = \bar{T}_{S} - \bar{T}\]
\[R = \bar{T}_{O} - \bar{T}\]
where:
- T = mean of the entire original population
- TS = mean of selected parents
- TO = mean of the offspring of the selected parents
You might intuit that, while artificial selection can be used to improve traits of crops and farm animals, there might be a limit to how far you can go -- and you'd be right. There are two reasons, both with a similar underlying reason: loss of genetic diversity. Through repeated rounds of selection, some alleles are fixed and others are lost. This has two consequences:
- Detrimental alleles are fixed. Called "inbreeding depression," this phenomenon increases the frequency of undesired traits as the desired trait also improves. An example is the common musculoskeletal problems in highly inbred breeds of dogs.
- Alleleic diversity is lost, leading to fewer remaining opportunities for enhancement. We can see this mathematically by remembering the definition of \( h^2 \) -- the proportion of phenotypic diversity that comes from diversity in alleles. As alleleic diversity goes to 0 (in a fully inbred strain), \( h^2 \) also drops to 0 -- and so does the response to selection.
References
Barbour, M.G, J.H. Burk, F.S. Gilliam, W.D. Pitts and M.W. Schwartz. 1999. Terrestrial Plant Ecology. 3rd edition. Benjamin Cummings, San Francisco, CA.
Clausen, J., D.D. Keck, and W. Hiesey. 1940. Experimental studies on the nature of species. I. Effects of varied environments on western North American plants. Carnegie Inst. Wash. Publ. 520.
Clausen, J., D. D. Keck, and W. M. Hiesey. 1948. Experimental studies on the nature of species. III. environmental responses of climactic races of Achillea. Carnegie Inst. Wash. Publi. 581.
Conner, J.K. and D.L. Hartl. 2004. A Primer of Ecological Genetics. Sinauer Associates, Sunderland, MA.
Falconer, D.S., and T.F.C. Mackay. 1996. Introduction to Quantitative Genetics. 4th edition. Longman Publ. Group, San Francisco, CA.
Hallauer, A. R. and J. B. Miranda. 1988. Quantitative Genetics in Maize Breeding. 2nd Edition. Iowa State University Press, Ames, IA.
Hill, W.G. 2005. A century of corn selection. Science 307: 683-684.
Pierce, B. A. 2008. Genetics: A Conceptual Approach. 3rd edition. W.H. Freeman, New York.
Rausher, M.D.. 2005. Example of Clausen, Keck, and Hiesey Experiment, Lecture 1-Lineages, Populations, and Genetic Variation. Online lecture notes from course on Principles of Evolution.
Department of Crop Science, University of Illinois at Urbana-Champaign. Values obtained for protein in the strains selected for oil and the values for oil obtained for the strains selected for protein each generation (1896-2004). 2007.