Class 12 Biology Organisms and Populations | Population |

**Population**

A group of individuals living in a geographical area who can interbreed and share or compete for similar resources is called a population.

A population has certain attributes such as birth rates and death rates and in a population these rates refer to per capita births and deaths, respectively.

The rates are expressed as increase or decrease in number of the members of the population. For example-

- If in a pond there are 20 lotus plants last year and through reproduction 8 new plants are added, taking the current population to 28, the birth rate is calculated as 8/20 = 0.4 offspring per lotus per year.
- If 4 individuals in a laboratory population of 40 fruitflies died in a week, the death rate in the population during that period is 4/40 = 0.1 individuals per fruitfly per week.

Another attribute characteristic of a population is sex ratio.

An individual is either a male or a female but a population has a sex ratio.

A population at any given time is composed of individuals of different ages.

If the age distribution is plotted for the population, the resulting structure is called an age pyramid.

The shape of the pyramids reflects the growth status of the population whether it is growing or stable or declining.

Population size is more technically called population density, designated as N.

Population density can be measured by

- Counting the number.
- Percent cover.
- Pug marks and fecal pellets for tiger census.

__Population growth __

The size of a population keeps changing in time, depending on various factors including food availability, predation pressure and reduce weather.

The density of a population in a given habitat during a given period, fluctuates due to changes in four basic processes which are-

- Natality refers to the number of births during a given period in the population that are added to the initial density.
- Mortality is the number of deaths in the population during a given period.
- Immigration is the number of individuals of the same species that have come into the habitat from elsewhere during the time period under consideration.
- Emigration is the number of individuals of the population who left the habitat and gone elsewhere during the time period under consideration.

If N is the population density at time t, then its density at time t +1 is N_{t+1} = N_{t}+ [(B + I) – (D + E)], where

B= number of births

I= number of immigrants

D= number of deaths

E= number of emigrants

N= population density

t= time period.

Fig. four basic processes which fluctuates population density

**Growth models : Exponential growth**

When resources in the habitat are unlimited, each species grow in number and reach enormous population density in a short time.

If in a population of size N, the per capita birth rates and per capita death rates are represented as b and d respectively, then the increase or decrease in N during a unit time period t (dN/dt) will be dN/dt = (b – d) × N

Let (b–d) = r, then

dN/dt = rN

The r in this equation is called the ‘**intrinsic rate of natural increase’.**

The integral form of the exponential growth equation as N_{t} = N_{0}e^{rt}, where

N_{t}= Population density after time t

N_{0 }= Population density at time zero

r = intrinsic rate of natural increase

e = the base of natural logarithms (2.71828).

**Growth models : Logistic growth**

When the resources in the habitat are finite, it limits the growth of the species.

A population growing in a habitat with limited resources show initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity.

This type of population growth is called **Verhulst-Pearl Logistic Growth**and is described by the following equation:

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

N = Population density at time t

r = Intrinsic rate of natural increase

K = Carrying capacity

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