Draw population growth curve and explain briefly.

Explanation

Population Growth Curves. The growth of population with time shows specific pattern. There are two curves of population growth in nature :-
1. Exponential growth curve
2. Logistic growth curve
1. Exponential Growth Curve.
(i) When the resource availability in the habitat is unlimited , each species has the ability to realise fully its innate potentials and grows in number .
(ii) The population grows in an exponential or geometric fashion .
(iii) The equation for exponential growth is :
dN/dt = (b - d) `xx` N
Let (b-d) = r, then
d N/dt= rN.

Here , N = Populaiton size b = birth rate (per capita) d = death rate (per capita), the decrease or increse in N during a unit time priod t ( dN/dt) will be as per equation.
The r in the equation is called intrinsic rate of natural increase and helps in assessing impacts of any biotic or abiotic factor on population growth .
When we plot N in relation to time , the exponential or geometric growth results in a J - Shaped curve .
We can derive the integral from of the exponential growth equations as :
`N_(t) = N_(0^(e^(n)))`
Where N = population density after time `N_(0)` = population density at time zero r = intrinsic rate f natural increase , e = the base of natural logarithms (2.71828).
Any species growing exponentially under unlimited resource can reach enormous population densities in a short time , e.g., a slow growing animal like elephant could reach enomours numbers in the absence of checks .
(b) Logistic Growth Curve .
(i) No popluation can continue to grow exponetially, as the resource availability becomes limiting at certain points of time .
(ii) Every environment /habitat has resoureea to support a particular maximum number of individuals of a particular species called carrying capacity, (K) for the species in that habitat beyond which there is no increase in the size - density of a population .
(iii) A population showing logistic growth shows sigmoid curve when we plot N in relation to time and such a popluation growth is also called Verhuslt - PearI logistic Growth.
(iv) It is described by the following equation.
`dN//dt = rn [(K-N)/(K)]`
where N = Population density at time t, r = intrinsic rate of natural increase , K = carrying capacity.
(v) The logistic growth model is more realistic in nature because no population can sustain exponential growth as the resourceas are finite and become limiting sooner or late .