What is meant by growth models?

$\Rightarrow$ Growth model shows the specific and predictable pattern of growth of population with time.

Growth of population takes place according to availability of food, habit condition and presence of other biotic and abiotic factors.

There are two main types of models:

$(a)$ Exponential Growth : This kind of growth occurs when food and space is available in sufficient amount.

When resources in the habitat are unlimited, each species has the ability to realise fully its innate potential to grow in number.

- The population grows in an exponential or geometric fashion.

If in a population of size $\mathrm{N}$, the birth rates as represented as ' $\mathrm{b}$ ' and death rate as 'd'.

$\Rightarrow \quad$ Then increase and decrease in $\mathrm{N}$ during unit period time 't' will be $\mathrm{dN} / \mathrm{dt}=(\mathrm{b}-\mathrm{d}) \times \mathrm{N}$

Let $(b-d)=r$, then $\mathrm{dN} / \mathrm{dt}=\mathrm{rN}$

Then, the $r$ in this equation is called 'intrinsic rate of natural increase' and is a very important parameter chosen for assessing impacts of any biotic or abiotic factor on population growth.

To give some idea about the magnitude of $\mathrm{r}$ values, for the Norway rat the $\mathrm{r}$ is $0.015$, and for the flour beetle it is $0.12$.

In $1981$ , the $\mathrm{r}$ value for human population in India was $0.0205$.

The above equation describes the exponential or geometric growth pattern of a population and results in a J-shaped curve when we plot $\mathrm{N}$ in relation to time.

If you are familiar with basic calculus, you can derive the integral form of the exponential growth equation as

$\mathrm{N}_{\mathrm{t}}=\mathrm{N}_{0} \mathrm{e}^{\mathrm{rt}}$

$where\mathrm{N}_{1}=Population\; density\; after\; time \;\mathrm{t}$

${l}\mathrm{N}_{0}=\text { Population density at time zero }$

$\mathrm{r}=\text { intrinsic rate of natural increase }$

$\mathrm{e}=\text { the base of natural logarithms }(2.71828)$

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 elephant could reach enormous numbers in the absence of checks.

$(b)$ Logistic Growth : No population of any species in nature has 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.

The governments of many countries have also realised this fact and introduced various restraints with a view to limit human population growth.

In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible.