The total number of inhabitants of a specific area like city, country or any other location is termed to be population.
Different patterns of population growth
In a population, some organisms are born, some die, some immigrate while some emigrate. These four processes are known as natality, mortality, immigration and emigration respectively.
Natality is the number of births in the population that are added to the initial density during a given period.
Mortality is the number of deaths in the population during a given period.
Immigration is the number of individuals of the same species that come into a particular habitat from elsewhere during a given period.
Emigration is the number of individuals of a population who leave a particular habitat and go elsewhere during a given period.
Factors affecting the size of a population
Populations of all organisms on planet earth are dynamic as they are constantly changing due to their interactions with various biotic and abiotic factors.
Natality and immigration result in an increase in population density.
Mortality and emigration result in a decrease in population density.
In the flow diagram, N is the population density at time t.
Density at time t+1 can be calculated as shown.
Although the number of births and deaths greatly influence population density, immigration and emigration assume importance.
Real life examples
If a newly formed habitat is colonised by great egret birds, the immigration of the egrets has a greater significance in determining the population density rather than the natality in this population.
If most of these birds fly to another wetland, then the emigration of these birds has a significant contribution to determining population density rather than deaths in this population.
Thus, populations grow through births and immigration and decline through deaths and emigration.
Growth is the most fundamental, dynamic feature exhibited by populations.
Population growth exhibits two patterns namely, exponential growth and logistic growth.
When resources available to the individuals in a population are unlimited, there is a tendency of the individuals to grow exponentially or in a geometric manner.
This behaviour was observed by Charles Darwin while he was developing his theory of natural selection. He also showed that a slow-growing animal, such as the elephant, could also reach enormous numbers if resources such as food and space were inexhaustible.
Let’s take the example of the Pistia plant. When it is introduced in a water body, due to unlimited food and space, these plants grow exponentially and cover the entire water body in a matter of a few days.
Now, to determine the population growth pattern of the Pistia plant, we plot various readings of population density against time.
On plotting the readings, you will notice a J-shaped curve, which shows two phases – a lag phase followed by an acceleration phase.
Moreover, with the basic knowledge of calculus, you can derive the integral form of the exponential growth using the equation as shown.
Thus, an exponential growth pattern is seen when resources are unlimited.
Considering the population size as ‘N’, birth rates as ‘b’ and death rates as ‘d’, the increase or decrease in population size during a unit time period t is as shown. The difference between the birth and death rates provides the value of r or the ‘intrinsic rate of natural increase’. Intrinsic rate of natural increase is a very important parameter for measuring the impact of biotic or abiotic factors on population growth.
The intrinsic rate of natural increase is a measure of the inherent potential of a population to grow.
Did you know that the value of r for the Norway rat is 0.015 and for the flour beetle is 0.12?
These numbers indicate that the rate at which the population size of the flour beetle increases is greater compared to the Norway rat.
When resources are limited, the population growth pattern is logistic. There is always competition between individuals for limited resources and finally the fittest individuals survive and reproduce.
Keeping this fact in mind, the governments of many countries have introduced various restraints to limit human population growth.
In fact, in nature, a given habitat has sufficient resources to support a maximum number of individuals, beyond which no further growth is possible.
This maximum capacity or limit is called the carrying capacity of the species in that habitat, which is denoted by the letter ‘K’.
Let us consider the population growth pattern of the Mandarin duck in this wetland. For this, we plot various readings of population density against time.
On plotting the readings, you will notice an S-shaped curve or a sigmoid curve. From the graph, you can see that for a population growing in a habitat with limited resources, there are three phases – initially a lag phase, followed by phases of acceleration and deceleration and finally, an asymptote, when the population density reaches the carrying capacity.
The logistic growth is also known as Verhulst-Pearl Logistic Growth after the scientists Pierre Francois Verhulst and Raymond Pearl and is
described by the equation as shown. In nature, as the resources available for growth are limited, the logistic growth model is considered a more realistic one.Thus, we can say that population density is dynamic and the growth of the population is dependent on the resources available.