Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?

The correct answer is \(\dfrac{dN}{dt} = rN\left(\dfrac{K-N}{K}\right)\)dN/dt=rN(K−N)K[Math Processing Error]dN/dt=rN(K−N)KdN/dt=rN(K−N)K dN/dt=rN(K−N)K

Explanation:

Verhulst-Pearl logistic growth, also simply known as logistic growth, is a model of population growth that describes how a population grows more slowly as it approaches its carrying capacity. 

A population growing in a habitat with limited resources show initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity.

A plot of N in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst-Pearl Logistic Growth.

• Ideally if the resources in a habitat are unlimited, the population shows exponential growth pattern.
• But resources are not available to any species population in unlimited amount. Thus, the species compete for the available resources to survive.
• This competition for the limited resources restricts the exponential or unlimited growth of any population.
• Any given habitat can only provide resources to support a maximum possible number, beyond which it further growth of population is not possible. This is known as the carrying capacity (K) for a particular species in a habitat.

Logistic growth is represented as: \({dN \over dt} = rN({K-N\over K})\)

where,

• N = Population Density at time t
• K = Carrying Capacity,
• \(r \) = Intrinsic rate of natural increase
• \(dN \over dt\) = Rate of change of population density.
• 'r' value denotes the difference between the per capita birth and death (b-d).
• The environmental resistance is represented in the equation as \(({K-N\over K})\).