Homework Help is Here – Start Your Trial Now!
Science
Biology
b) Suppose that we want to model the evolution of the population of a cer- tain type of organisms. Observations indicate that if the population drops below a survival level of 102 individuals, it goes extinct. Moreover, the population growth is limited: the available resources of space and food can sustain at most 10° individuals. We treat the population size P(t) as a continuous function of time. (i) Explain briefly how the following model incorporates the above ob- servations: dP — К(А - Р)(Р — В), k>0, dt where P(t) denotes the population size at time t and B < A. Using the informations given in the text of the question, determine the val- ues of the constants A and B. Can you also determine the value of [2] k?

b) Suppose that we want to model the evolution of the population of a cer- tain type of organisms. Observations indicate that if the population drops below a survival level of 102 individuals, it goes extinct. Moreover, the population growth is limited: the available resources of space and food can sustain at most 10° individuals. We treat the population size P(t) as a continuous function of time. (i) Explain briefly how the following model incorporates the above ob- servations: dP — К(А - Р)(Р — В), k>0, dt where P(t) denotes the population size at time t and B < A. Using the informations given in the text of the question, determine the val- ues of the constants A and B. Can you also determine the value of [2] k?

Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
See similar textbooks
icon
Related questions
Question
(b) Suppose that we want to model the evolution of the population of a cer- tain type of organisms. Observations indicate that if the population drops below a survival level of 10° individuals, it goes extinct. Moreover, the population growth is limited: the available resources of space and food can sustain at most 106 individuals. We treat the population size P(t) as a continuous function of time. (i) Explain briefly how the following model incorporates the above ob- servations: dP — К(А- Р)(Р — В), k>0, dt where P(t) denotes the population size at time t and B < A. Using the informations given in the text of the question, determine the val- ues of the constants A and B. Can you also determine the value of [2] (ii) Suppose that A < P < B. At which value of the population is the [2] k? growth fastest? (c) Perform a linear stability analysis for the model below: dP P(1 – P)e-P*,P > 0. dt Find the equilibrium values and determine their stability. [6]
Transcribed Image Text:(b) Suppose that we want to model the evolution of the population of a cer- tain type of organisms. Observations indicate that if the population drops below a survival level of 10° individuals, it goes extinct. Moreover, the population growth is limited: the available resources of space and food can sustain at most 106 individuals. We treat the population size P(t) as a continuous function of time. (i) Explain briefly how the following model incorporates the above ob- servations: dP — К(А- Р)(Р — В), k>0, dt where P(t) denotes the population size at time t and B < A. Using the informations given in the text of the question, determine the val- ues of the constants A and B. Can you also determine the value of [2] (ii) Suppose that A < P < B. At which value of the population is the [2] k? growth fastest? (c) Perform a linear stability analysis for the model below: dP P(1 – P)e-P*,P > 0. dt Find the equilibrium values and determine their stability. [6]
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Genetic evolution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, biology and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
Biology
ISBN:
9780134580999
Author:
Elaine N. Marieb, Katja N. Hoehn
Publisher:
PEARSON
Biology 2e
Biology 2e
Biology
ISBN:
9781947172517
Author:
Matthew Douglas, Jung Choi, Mary Ann Clark
Publisher:
OpenStax
Anatomy & Physiology
Anatomy & Physiology
Biology
ISBN:
9781259398629
Author:
McKinley, Michael P., O'loughlin, Valerie Dean, Bidle, Theresa Stouter
Publisher:
Mcgraw Hill Education,
Molecular Biology of the Cell (Sixth Edition)
Molecular Biology of the Cell (Sixth Edition)
Biology
ISBN:
9780815344322
Author:
Bruce Alberts, Alexander D. Johnson, Julian Lewis, David Morgan, Martin Raff, Keith Roberts, Peter Walter
Publisher:
W. W. Norton & Company
Laboratory Manual For Human Anatomy & Physiology
Laboratory Manual For Human Anatomy & Physiology
Biology
ISBN:
9781260159363
Author:
Martin, Terry R., Prentice-craver, Cynthia
Publisher:
McGraw-Hill Publishing Co.
Inquiry Into Life (16th Edition)
Inquiry Into Life (16th Edition)
Biology
ISBN:
9781260231700
Author:
Sylvia S. Mader, Michael Windelspecht
Publisher:
McGraw Hill Education
SEE MORE TEXTBOOKS