 # Population Growth

Population growth is one of the major concerns of the present world as human population is not a static factor. Rather, it is growing at a very alarming rate. In spite of the increasing world population, the resources of the earth remain constant. Thus, the ability to maintain sustainable development is becoming a major challenge to mankind today. The fluctuations in the population in a given area are influenced by four major factors, which include the following:

• Natality – It is the number of births in a given period of time in a population
• Mortality – It is defined as the number of deaths that takes place in a population at a given period of time.
• Immigration – It is defined as the number of individuals which come from another population and add to the population in consideration during a period of time.
• Emigration – It is defined as the number of individuals from a population who leave the habitat and go to a different habitat at a given period of time.

Thus, it is clearly visible, that Natality (N) and Immigration (I) add to a population thus increasing population whereas, Mortality (M) and Emigration (E) decrease the population. The population density (Pt) at a given point of time can be given as:

Pt =P0 + (N + I) – (M + E)

where, P0 is the initial population density.

We have two growth models which describe the basic growth trend in a population. These are:

1. Exponential growth – In an ideal condition where there is unlimited supply of food and resources, the population growth will follow an exponential order. Consider a population of size N and birth rate be represented as b, death rate as Rate of change of N can be given by the equation

dN/dt = (b-d) x N

If, (b – d) = r,

dN/dt = rN

Where, r = intrinsic rate of natural increase

This equation can be represented with a graph which has a J shaped curve. According to calculus

Nt=N0ert

Where, Nt = Population density at time t

N0= Population density at time zero

r = intrinsic rate of natural increase

e = base of natural logarithms

1. Logistic growth – This model defines the concept of ‘survival of the fittest’. Thus, it considers the fact that resources in nature are exhaustible. The term ‘Carrying capacity’ defines the limit of the resources beyond which it cannot support any number of organisms. Let this carrying capacity be represented as K.

The availability of limited resources cannot show an exponential growth. As a result, the graph will have a lag phase, followed by an exponential phase, then a declining phase and finally an asymptote. This is called Verhulst-Pearl Logistic Growth and is represented by the following equation:

dN/dt = rN((K-N)/K)