Logistic models and the intrinsic growth rate

In summary, in models of exponential growth, the intrinsic growth rate (r) is calculated as the difference between birth rates and death rates. The same applies in the logistic growth model, where the intrinsic growth rate is also determined by birth and death rates. However, in this model, the equation is bounded and more practical in the real world. The values of r and K are assumed to be constant, but in reality, they may change. Additionally, the growth rate is dependent on the value of P(t) and it is assumed that the rate of change of P is solely dependent on P(t). The relationship between r and the maximum growth point of P(t) = K/2 is not clear.
  • #1
thelema418
132
4
In models of exponential growth, we have an intrinsic growth rate (r) that is calculated as the difference of birth rates to death rates.

With the logistic growth model, we also have an intrinsic growth rate (r). How then do birth rates and death rates relate to the intrinsic growth rate in the context of this model? Specifically, if you have a model where you have been given values for r and K, does the birth rate and death rate associated with r occur at a particular time? I'm wondering if this specifically relates to P(t) = K/2 since this is where the maximum growth occurs.

Thanks.
 
Biology news on Phys.org
  • #2
The same applies in logistic model too. The growth rate here is determined the same but condition is just the equation is bounded because it is little bit practical in real world. As far as i know r and K are kept constant theoretically but they have to change but in the equation and importantly we assume that dP/dt is dependent on just P(t) which is fair(correct me if i am wrong). I didn't get what u r saying in the last part.cheers
 

1. What is a logistic model?

A logistic model is a mathematical model used to describe the growth of a population over time. It takes into account limiting factors, such as limited resources, that can slow down the growth rate of a population.

2. How is the intrinsic growth rate calculated in a logistic model?

The intrinsic growth rate, also known as the carrying capacity, is calculated by taking the difference between the maximum growth rate and the growth rate at the current population size. It represents the rate at which a population can grow in the absence of limiting factors.

3. What is the significance of the carrying capacity in a logistic model?

The carrying capacity is an important concept in a logistic model because it represents the maximum number of individuals that can be sustained by the available resources in a given environment. It helps to predict how a population will grow and eventually stabilize over time.

4. Can a population exceed its carrying capacity in a logistic model?

No, a population cannot exceed its carrying capacity in a logistic model. As the population approaches the carrying capacity, the growth rate slows down until it reaches a point of equilibrium. This is known as the logistic growth curve.

5. How are logistic models used in real-world applications?

Logistic models are commonly used in ecology and population biology to study the dynamics of animal and plant populations. They can also be applied in other fields, such as economics and marketing, to predict the growth of a market or consumer base over time.

Similar threads

Replies
2
Views
5K
  • Differential Equations
Replies
7
Views
1K
Replies
4
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
  • General Math
Replies
4
Views
1K
Replies
26
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
2
Views
6K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
985
Back
Top