Introduction to Population Growth

Population growth is one of the main concerns of this world because the human population isn't a static factor. Rather, it's growing at a really alarming rate. In spite of the increasing world population, the resources of the world remain constant. Thus, the power to take care of sustainable development is becoming a serious challenge to mankind today.

Human increase is the increase in the number of people in a particular area. There has been a decrease in the death rate over the past 200 years due to the changes in public health and sanitation. The advent of antibiotics and vaccines has led to a decrease in the chances of infections in humans. Urbanization and advancements in agriculture have also led to a rise in population.

Factors that Influence Population Fluctuation

The fluctuations within the population during a given area are influenced by four major factors, which include the following:

Natality – it's the number of births during a given period of your time during 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's defined to be the number of people who come from another population and increase the population in consideration during a period of time.

Emigration – it's defined as the number of people from a population who leave the habitat and attend a special habitat at a given period of time.

Thus, it's clearly visible that the two factors Natality (N) and Immigration (I) increase a population, thus increasing population whereas, Mortality (M) and Emigration (E) decrease the population. The population density (Pt) at a given point of time is often given as:

Pt =P0 + (N + I) – (M + E)

Where P0 is the initial population density.

We Have Two Growth Models Which Describe the Essential Growth Trend During a Population. These Are

Exponential Growth

In a perfect condition where there's a vast supply of food and resources, the increase will follow an exponential order. Consider a population of size N and birth rate represented as b, death rate as d, Rate of change of N are often 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 is often represented with a graph that features 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

Logistic Growth

This model defines the concept of ‘survival of the fittest’. Thus, it considers the very fact that resources in nature are exhaustible. 

The limit of resources beyond which it cannot support any number of organisms can be defined as the carrying capacity. The carrying capacity can be represented as K.

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

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