the logistic population growth model, rN[(K-N)/K], describes a population's growth when an upper limit to growth is assumed. As N approaches (numerically) the value of K, additions to the population
To understand how additions to a population behave as it approaches the carrying capacity (K) based on the logistic population growth model (rN[(K-N)/K]), let's break down the equation and explain each term.
The logistic population growth model is an extension of the exponential growth model, which assumes unlimited resources and unrestricted growth of the population. In reality, most populations face limited resources and environmental constraints, leading to a maximum population size known as the carrying capacity (K).
In the logistic growth model, r represents the intrinsic growth rate of the population. It defines how fast the population would grow in the absence of any limiting factors. The variable N represents the current population size at a given time.
The term (K-N)/K in the equation denotes the available growth potential. It calculates the fraction of the carrying capacity that is still available for population growth. When N is far below K, this ratio is close to 1, indicating that there is significant room for population growth. As N approaches K, the growth potential decreases, approaching 0 as N gets closer to K.
Returning to your question, let's consider what happens to additions to the population as N approaches the value of K.
As N approaches K, the growth potential (K-N)/K decreases because the available resources become scarce relative to the population size. With fewer resources available, the population growth rate slows down.
Additions to the population, which represent the rate at which individuals are being added, also decrease as N approaches K. This occurs because there is less room for new individuals to be accommodated as the population nears its carrying capacity. Therefore, the number of individuals being added to the population decreases as it approaches K.
In summary, additions to the population decrease as N approaches the value of K in the logistic population growth model. This decrease occurs due to diminishing growth potential and limited resources available as the population nears its carrying capacity.