Homework Sourseplease help Under what conditions do you expect the continu
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Under what conditions do you expect the continuous-time exponential and logistic population growth models to be approximately equal? Provide a biological interpretation of these conditions.
Solution
1) The conditions that expect the continuous-time exponential and logistic population growth models to be approximately equal?
The conditions that expect the continuous-time exponential and logistic population growth models to be approximately equal are the Carrying Capacity (K).
Carrying Capacity: The largest population that can be supported indefinitely, given the resources available in the environment. This is to be happened in the logistic growth. Logistic growth means competition between the individuals of the same species. Logistic growth model is a S-shaped curve.
Where K is a carrying capacity, P is population and T is time.
Logistic growth can be explained in either continuous or discrete fashion.
Discrete Growth:
The logistic equation assumes that the number of individuals in next generation decreases linearly with population size.
That is
Where, Nt+1 refers to the number of individuals in next generation,
Nt refers to the number of individuals in current generation,
Rm refers to the maximum rate of growth,
K is the carrying capacity.
Continuous Growth:
The model of logistic growth in continuous time follows from the assumption that each individual reproduces at a rate that decreases as a linear function of the population size.
That is
Where, rm is the maximum rate of growth,
N is the number of individuals,
K is the carrying capacity.
2) Biological Interpretation
Yeast, a microscopic fungus used to make bread and alcoholic beverages, can produce a classic S-shaped curve when grown in a test tube.The yeast population shows S-curve like above.
1) The conditions that expect the continuous-time exponential and logistic population growth models to be approximately equal?
The conditions that expect the continuous-time exponential and logistic population growth models to be approximately equal are the Carrying Capacity (K).
Carrying Capacity: The largest population that can be supported indefinitely, given the resources available in the environment. This is to be happened in the logistic growth. Logistic growth means competition between the individuals of the same species. Logistic growth model is a S-shaped curve.
Where K is a carrying capacity, P is population and T is time.
Logistic growth can be explained in either continuous or discrete fashion.
Discrete Growth:
The logistic equation assumes that the number of individuals in next generation decreases linearly with population size.
That is
Where, Nt+1 refers to the number of individuals in next generation,
Nt refers to the number of individuals in current generation,
Rm refers to the maximum rate of growth,
K is the carrying capacity.
Continuous Growth:
The model of logistic growth in continuous time follows from the assumption that each individual reproduces at a rate that decreases as a linear function of the population size.
That is
Where, rm is the maximum rate of growth,
N is the number of individuals,
K is the carrying capacity.
2) Biological Interpretation
Yeast, a microscopic fungus used to make bread and alcoholic beverages, can produce a classic S-shaped curve when grown in a test tube.The yeast population shows S-curve like above.
