Logistic models and the intrinsic growth rate

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SUMMARY

The discussion centers on the relationship between birth rates, death rates, and the intrinsic growth rate (r) within logistic growth models. It establishes that while r is calculated similarly to exponential growth models, the logistic model introduces a carrying capacity (K) that bounds growth. The maximum growth occurs at P(t) = K/2, indicating a specific point where birth and death rates influence r. The conversation emphasizes that while r and K are theoretically constant, they must adapt in practical applications, and the growth rate is dependent on the population size P(t).

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  • Understanding of logistic growth models
  • Familiarity with intrinsic growth rate (r) calculations
  • Knowledge of carrying capacity (K) in population dynamics
  • Basic differential equations related to population growth
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thelema418
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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.
 
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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
 

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