**Population growth rate and population rise per capita** (Definitions, formulas and examples)

What do you exactly meant by the word population? It can be defined as a group of individuals of the same species that occupy a particular area over a certain period of time. Population of species in an area is not always constant. Sometimes the population decreases or sometimes it increases. Let us discuss what all are the parameters that allow us to determine whether a population will increase or decrease in size.

**4 major parameters that determine population size are: **

1) Birth rate

2) Death rate/ mortality

3) Immigration (number of people who have been added to a country from other countries permanently)

4) Emigration (number of people who have been permanently moved out from one country to other countries)

Number of individuals in a population increases when: High birth rate and immigration

Number of individuals in a population decreases when: High death rate and emigration

Formula to find **population growth rate** = (Birth rate + Immigration) – (Death rate + emigration)

(Assume that emigration is equal to immigration in particular area overtime for simplifying the equation)

**Birth rate **(Can be designated as B)

**Definition: **Number of new individuals born for every thousand people residing in an area during a particular period of time

Simply we can tell birth rate (B) as 20 births/ year

**Per capita birth rate** (Designated as **b**): Average birth per individual

**How to calculate per capita birth rate?**

**Per capita birth rate** (b) = No of individuals born over time/ population size

**b = B/N** (Can be rewritten as **B = bN**)

Q) Imagine a population of 1000 rabbits in a given forest area. In one year 300 new bunnies were born. Find out the per capita birth rate for 1 year?

In the question it is given that B= 300 and N = 1000

Per capita birth rate = B/N (300/1000) = **0.3**

It means that 0.3 births per individual rabbits per year

(0.3 per capita birth rate is similar to 30 % birth rate. Decimals and percentages are inter changeable)

In the same question if per capita birth rate (b) is given instead of birth rate (B), you have to multiply the per capita birth rate with number of rabbit to get the birth rate (B)

That is** B = b x N** (0.3 X 1000 = 300 bunnies)

** ****Death rate / Mortality **(Can be designated as D)

**Definition: **Number of individuals died for every thousand people residing in an area during a particular period of time

Simply we can tell Death rate (D) as 5 deaths per year

**Per capita death rate** (Designated as **d**): Average death per individual

**How to calculate per capita death rate?**

**Per capita death rate = **No of individuals died over time/ population size

Q) Imagine a population of 1000 rabbits in a given forest area. In one year 100 of them were died. Find out the per capita death rate?

Per capita death rate (d) = D/N (100/1000 = **0.1**)

It means that 0.1 deaths per individual rabbits per year

(0.1 per capita death rate is similar to 10% death rate)

In the same question if per capita death rate (d) is given instead of death rate (D), you have to multiply the per capita death rate with number of rabbit to get the death rate (D)

That is **D = d x N** (0.1X 1000 = 100 rabbits)

(We can compare the birth rate and death rate of different population size using b and d)

**Population growth rate**

- It defines the rate at which a population is growing
- It is expressed on annual or decimal basis
- It is the difference between birth rate (B) and death rate (D)

Change in population size over time interval = Births during time interval – Death during time interval

This relationship can be expressed mathematically as given below

**Population growth rate** (dN/dT) = **B – D** **(Equation 1)**

**Example:** Refer the above question of rabbits

**Population growth rate** = (300 birth per year – 100 death per year)

= 200 rabbits/year

The same equation can be rewritten as,

Population growth rate (dN/dT) = **(b x N) – (d X N) **

**dN/dT = (b – d) N (Equation 2)**

**Population rise per capita** (r) = Birth per capita (b) – death per capita (d)

**r = b – d** ** (Equation 3)**

In a population,

If b>d = r is greater than zero (Indicates that population is increasing)

If b<d = r is less than zero (Indicates that population is decreasing)

If b = d, then r = 0 (Indicates that zero population growth, population remains constant)

Inserting equation 3 into equation 2, we will get **dN/dT = r x N (Equation 4)**

This equation says that we have to multiply per capita rise in population with number of individuals to get the actual population growth rate

**(Important thing to keep in mind: **per capita rate of increase, r is** b – d **not **B – D)**

**Sample question with explanation for better understanding of the concept**

Q) Consider 265 rabbits were living in a small forest area. The rabbit population’s birth rate is 0.341 rabbits/ year and the death rate is 0.296 rabbits/ year. What is the rate of population growth in a year? Is the population is increasing or decreasing?

**Answer: **First of all you have to write what all things are given in the question.

**Per capita birth rate (b) = **0.341 rabbits/ year

**Per capita death rate (d)** = 0.296 rabbits/ year

**Population size (N)** = 265 rabbits

From these values we have to calculate per capita growth rate and population growth rate.

**Per capita growth rate** (r) = b – d

That is** r** = (0.341 – 0.296) = **0.045** (4.5 % increase)

Substitutes the given values in the equation for population growth rate

**Population growth rate** (dN/dT) = **rN**

**dN/dT** = 0.045 x 265 = 11.925 (~ 12 rabbits/ year)

Since r is a positive value, we can say that the rabbit population is increasing. In 1 year rabbit population showed 4.5 % increase. That is 12 more new rabbits were added to the existing population and number of rabbits in the population become 277.

**Additional information**

Equation 1 can also be written as ΔN/Δt = B – D

You already know that B is the number of births in a population during the time interval and D is the number of deaths in a population during a time interval.

N represents population size and t represents time. ΔN is the change in population size and Δt is the time interval (life span or generation time of the species)

(The Greek letter delta (Δ) indicates change, such as change in time.)

ΔN = N2 – N1 (Subtract the starting population size from ending population size)

Δt = t2 – t1 (subtract the starting date or time from ending date or time)