Q.104 A population of rabbits was determined to have a birth rate of 200 and mortality rate of 50
per year. If the initial population size is 4000 individuals, after 2 years of non–interfered
breeding the final population size will be _______________.
Final Answer: Population after 2 years = 25,000 individuals
In this problem, we calculate the population growth of rabbits under
non-interfered breeding conditions, meaning unlimited resources,
no density dependence, and constant per capita birth and death rates.
Given Data
- Birth rate = 200 per 100 individuals per year
- Mortality rate = 50 per 100 individuals per year
- Initial population (N0) = 4000
- Time (t) = 2 years
Step-by-Step Solution
1. Per Capita Rates
Per capita birth rate:
b = 200 / 100 = 2
Per capita mortality rate:
d = 50 / 100 = 0.5
2. Net Growth Rate
Net growth rate (r) is given by:
r = b − d = 2 − 0.5 = 1.5
This corresponds to a 150% increase per year.
Growth Model Used
Since growth is unrestricted and rates are given on a per-year basis,
discrete exponential growth is appropriate:
Nt = N0(1 + r)t
Year-wise Population Calculation
After Year 1
N1 = 4000 × (1 + 1.5) = 4000 × 2.5 = 10,000
After Year 2
N2 = 10,000 × 2.5 = 25,000
✔️ Final population after 2 years = 25,000 rabbits
Why Exponential Growth?
The birth and death rates are given on a per capita basis,
so population increase is proportional to the current population size.
This causes compounding growth, similar to compound interest.
The phrase “non-interfered breeding” implies:
- No density dependence
- No migration
- No resource limitation
Common Incorrect Approaches Explained
- Linear growth: Adding a fixed number each year ignores compounding
- Ignoring compounding: Underestimates or overestimates population
- Continuous model (ert): Gives ~25,949, but discrete model fits annual rates better
Exam Relevance (CSIR NET / GATE)
- Understand difference between per capita and absolute rates
- Choose discrete vs. continuous models correctly
- Frequently tested in Population Ecology
- Final answers are usually rounded to whole numbers
