Models of Population Growth - Practice Questions & MCQ

• Resource (food and space) availability is obviously essential for the unimpeded growth of a population.
• Ideally, when resources in the habitat are unlimited, each species has the ability to fully realise its innate potential to grow in number, as Darwin observed while developing his theory of natural selection.
• Then the population grows in an exponential or geometric fashion.
• The increase or decrease in population density (N) at a unit time period (t) is calculated as (dN/dt).
• If in a population of size N, the birth rates are represented as b and death rates as d, then the increase or decrease in N during a unit time period t (dN/dt) will be:
  

           Let ( b- d) = r then, 

• The r in this equation is called the ‘intrinsic rate of natural increase’ and is a very important parameter chosen for assessing impacts of any biotic or abiotic factor on population growth.
• The above equation describes the exponential or geometric growth pattern of a population. and results in a J-shaped curve when we plot N in relation to time. 
• the integral form of the exponential growth equation can be derived as:

Where,
= Population density after time t
=  Population density at time zero
 =  intrinsic rate of natural increase
 = the base of natural logarithms (2.71828)

• Any species growing exponentially under unlimited resource conditions can reach enormous population densities in a short time. 
• Darwin showed how even a slow growing animal like an elephant could reach enormous numbers in the absence of checks.

• No population of any species in nature has at its disposal unlimited resources to permit exponential growth. 
• This leads to competition between individuals for limited resources.
• Eventually, the ‘fittest’ individual will survive and reproduce. 
• In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible. 
• This limit is known as nature’s carrying capacity (K) for that species in that habitat.
• A population growing in a habitat with limited resources shows 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 as follows:
  

Where,
N = Population density at time t
r  =  Intrinsic rate of natural increase
K = Carrying capacity

• Since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic one.