Explanation Given: Initially 40 % of the snail have characteristic B and after 5 generations population increases to 80 % also assume a = 2 and b = 1 . Calculation: Hybrid selection model is given by: d y d t = k y ( 1 − y ) ( a − b y ) , where y represents the portion of population that has certain characteristic and t represents the time measured in generations. By given value of a and b , the equation becomes, d y d t = k y ( 1 − y ) ( 2 − y ) This gives, d y y ( 1 − y ) ( 2 − y ) = k d t This differential equation is of variable separable form f ( y ) d y = g ( x ) d x . Now, integrate ∫ d y y ( 1 − y ) ( 2 − y ) = ∫ k d t with the use of maple, Input: ∫ d y y ( 1 − y ) ( 2 − y ) = ∫ k d t Output: Simplify further to get, y ( 2 − y ) ( 1 − y ) 2 = c e 2 k t So, the general solution is y ( 2 − y ) ( 1 − y ) 2 = c e 2 k t , where c is constant of integration. Now use first condition t = 0 , y = 0.4 , c = 0.4 ( 2 − 0.4 ) ( 1 − 0.4 ) 2 = 0

Calculus: Early Transcendental Functions

7th Edition

ISBN: 9781337552516

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 6.3, Problem 64E

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To calculate: The percent of population that will have the characteristics B using the hybrid selection model with initially 40% of the snail have characteristic B and after 5 generations population increases to 80% also assume a=2 and b=1.

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Chapter 6.3, Problem 63E

Chapter 6.3, Problem 65E

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The percent of population that will have the characteristics B using the hybrid selection model with initially 40 % of the snail have characteristic B and after 5 generations population increases to 80 % also assume a = 2 and b = 1 .

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To calculate: The percent of population that will have the characteristics B using the hybrid selection model with initially 40% of the snail have characteristic B and after 5 generations population increases to 80% also assume a=2 and b=1.

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