Selection Coefficient Simulation

Selection Coefficient Simulation - Evolution by Natural...

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Evolution by Natural Selection: A Mathematical Model This Excel Spreadsheet uses the Hardy-Weinberg Equation to mathematically model evolution by natural selection. 0.01 <- Change this number to change the initial frequency of the dominant allele. 0.01 means it starts at 1% of the gene pool. 0.01 To print the graph, click on the printable graph tab below. To understand how this graph is created, click on "How it works" tab and read that page. Main worksheet contains the actual calculation page. starting p = s = <-- Change this number to change the selection coefficient. The selection coefficient is the advantage the dominant form has over the recessive form. If it's 0.1, then the advantage is 10%. 0 10 20 30 40 50 60 70 80 90 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Evolutionary change due to selection Column B Column D Generations Relative frequency
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0 10 20 30 40 50 60 70 80 90 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Evolutionary change due to selection Column B Column D Generations Relative frequency
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How it works This sheet explains how the main worksheet works. It is protected to prevent accidental changes. Review of Hardy-Weinberg Equation Adapting the Hardy-Weinberg Equation to model selection In this model, selection operates on the ratios calculated by the Hardy-Weinberg Equation. 0.01 0.1 Genotype frequencies after selection generations Total 1 0.0100 0.9900 0.0199 0.9801 0.0001 0.0218 0.9801 1.0020 0.0110 0.9890 2 0.0110 0.9890 0.0218 0.9782 0.0001 0.0239 0.9782 1.0022 0.0120 0.9880 3 0.0120 0.9880 0.0240 0.9760 0.0002 0.0262 0.9760 1.0024 0.0132 0.9868 4 0.0132 0.9868 0.0263 0.9737 0.0002 0.0287 0.9737 1.0026 0.0145 0.9855 5 0.0145 0.9855 0.0288 0.9712 0.0002 0.0315 0.9712 1.0029 0.0159 0.9841 6 0.0159 0.9841 0.0316 0.9684 0.0003 0.0344 0.9684 1.0032 0.0174 0.9826 Generation number for the row q is calculated by 1-p {p^2(1+s) + pq(1+s)} / (new total T) 1 - [{p^2(1+s) + pq(1+s)} / (new total T)] Consider a gene with two alleles R and r. R is dominant, r is recessive. Frequency for R is p , for r is q . Using the Hardy-Weinberg equation, the relative proportion of the RR, Rr, and rr genotypes are p 2 , 2 pq , and q 2 respectively. p 2 + 2 pq + q 2 = 1 Fitness coefficient is s Because R is completely dominant, the fitness for RR and Rr are the same and is 1+ s . The fitness for rr is 1. Instead of the relative proportion being p 2 + 2 pq + q 2 = 1, after selection, the relative proportions are p 2 (1 + s ) + 2 pq (1 + s ) + q 2 The next generation of p can be calculated by counting up the total number of R alleles and dividing by the total number of all alleles (twice the number of individuals because of diploidy.) Next generation p = (2 x RR individuals + Rr individuals) / 2 x (total individuals) Total individual after selection is p 2 (1 + s ) + 2 pq (1 + s ) + q 2 Therefore, new p = (2 x p 2 (1 + s ) + 2 pq (1 + s )) / (2 x ( p 2 (1 + s ) + 2 pq (1 + s ) + q 2 )) = ( p 2(1 + s ) + pq (1 + s )) / ( p 2 (1 + s ) + 2 pq (1 + s ) + q 2 ) This looks daunting, but it is fairly easy to set up the calculations in Excel. Excel can calculate the values for hundreds of generations in an instant! starting p = <-- This is the the starting gene frequency for the dominant allele. 0.01 means it starts at 1% of the gene pool. s = <-- This is the selection coefficient. It is the advantage the dominant form has over the recessive form. If it's 0.1, then the advantage is 10%.
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