a
To calculate: To find the number of wild-type bacteria that mutates using the given information
a
Answer to Problem 32E
The number of wild-type bacteria that mutate is
Explanation of Solution
Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each wild-type individual produces 2.0 offspring while each mutant produces only 1.0 offspring.
Calculation:
Initially, let there be
Now a fraction 0.2 of wild-type mutate each generation.
Therefore, the number of wild-type bacteria that mutate is
b
To calculate: To find the number of wild-type bacteria and the number of mutants after mutation using the given information
b
Answer to Problem 32E
The number of mutants after mutation is given by
Explanation of Solution
Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each wild-type individual produces 2.0 offspring while each mutant produces only 1.0 offspring.
Calculation:
Now the number of wild type bacteria after mutation is given by
Also, the number of mutants after mutation is given by
c
To calculate: To find the number of wild-type bacteria and the number of mutants after reproduction using the given information
c
Answer to Problem 32E
Therefore, the number of mutants after reproduction shall be
Explanation of Solution
Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each wild-type individual produces 2.0 offspring while each mutant produces only 1.0 offspring.
Calculation:
Now, each wild-type individual produces 2.0 offspring.
Therefore, the number of wild-type bacteria after reproduction is given by
Also, each mutant produces only 1.5 offspring.
Therefore, the number of mutants after reproduction shall be
d
To calculate: To find the total number of bacteria after mutation and reproduction using the given information
d
Answer to Problem 32E
The total number of bacteria after mutation and reproduction is given by
Explanation of Solution
Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each wild-type individual produces 2.0 offspring while each mutant produces only 1.0 offspring.
Calculation:
The total number of bacteria after mutation and reproduction is given by
e
To calculate: To find the fraction of mutants after mutation and reproduction using the given information
e
Answer to Problem 32E
Explanation of Solution
Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each wild-type individual produces 2.0 offspring while each mutant produces only 1.0 offspring.
Calculation:
To find the fraction of mutants after mutation and reproduction, divide the discrete-time dynamical system for
Therefore, we have
f
To calculate: To find the equilibrium using the obtained values
f
Answer to Problem 32E
Explanation of Solution
Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each wild-type individual produces 2.0 offspring while each mutant produces only 1.0 offspring.
Calculation:
Let
To find the equilibrium consider,
Solving the above equation gives,
Therefore,
g
To calculate: To determine and to find whether the equilibrium is stable or not using the obtained information
g
Answer to Problem 32E
The fraction of mutants will end up at about 33.33 percent.
Explanation of Solution
Given information: Suppose that a fraction 0.2 of wild-type mutate each generation, but that each wild-type individual produces 2.0 offspring while each mutant produces only 1.0 offspring.
Calculation:
The cobweb starting from the initial condition is as shown below:
The equilibrium at l/ 3 seems to be stable. The fraction of mutants will end up at about 33.33 percent.
Want to see more full solutions like this?
Chapter 1 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forwardRepeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning