How to Calculate Population Size After One Year Using Birth and Death Rates

Population growth is a fundamental concept in ecology, demography, and experimental biology. Understanding how birth and death rates influence population size over time is essential for researchers and students alike. This article provides a detailed explanation of how to calculate the population size at time $t+1$ for an experimental population, given initial population size and specific birth and death rates.

Understanding Birth and Death Rates

Birth rate and death rate are standard demographic metrics used to describe the rate at which individuals are added to or removed from a population. These rates are typically expressed as the number of births or deaths per 1000 individuals per year:

• Birth rate: Number of live births per 1000 individuals per year.

• Death rate: Number of deaths per 1000 individuals per year.

These rates allow us to compare populations of different sizes and predict future population changes.

Calculating Population Growth

The net increase in population over a period is determined by the difference between the number of births and the number of deaths. The formula is:

$$\text{Net Increase}=\text{Number of Births}-\text{Number of Deaths}$$

To find the population at time $t+1$:

Nt+1=Nt+Net IncreaseNt+1=Nt+Net Increase

where NtNt is the population at time $t$.

Step-by-Step Calculation

Given:

• Population at time $t$ (NtNt): 10,000

• Birth rate: 18 per 1000

• Death rate: 14 per 1000

1. Calculate Number of Births

Number of Births=(181000)×10,000=180Number of Births=(100018)×10,000=180

2. Calculate Number of Deaths

Number of Deaths=(141000)×10,000=140Number of Deaths=(100014)×10,000=140

3. Calculate Net Increase

$$\text{Net Increase}=180-140=40$$

4. Calculate Population at Time $t+1$

Nt+1=10,000+40=10,040Nt+1=10,000+40=10,040

Verification and Alternative Approaches

This method is widely used in population ecology and is consistent with the standard approach to modeling population growth based on birth and death rates. The calculation does not account for migration, which is common in experimental or closed populations unless specified.

Why Is This Calculation Important?

Understanding how to project population size based on birth and death rates is crucial for:

• Experimental biology: Tracking changes in laboratory or field populations.

• Conservation: Estimating future population sizes for endangered species.

• Public health: Predicting disease spread or vaccine impact.

• Urban planning: Forecasting resource needs and infrastructure development.

Population Growth Rate

The population growth rate is the net increase divided by the initial population size, often expressed as a percentage:

Growth Rate (%)=Net IncreaseNt×100=4010,000×100=0.4%Growth Rate (%)=NtNet Increase×100=10,00040×100=0.4%

This low growth rate is typical of many stable or slowly growing populations.

Common Mistakes

• Using the wrong denominator: Always use rates per 1000 for birth and death rates unless specified otherwise.

• Forgetting to subtract deaths: Only adding births or only subtracting deaths will give an incorrect result.

• Including migration: Unless specified, only use natural increase (births minus deaths).

Real-World Context

A population of 10,000 with a birth rate of 18 per 1000 and a death rate of 14 per 1000 is typical for many experimental or natural populations under controlled conditions. The modest net increase reflects a stable or slowly growing population, which is often the goal in experimental settings to avoid overcrowding and resource depletion.

Summary Table

Conclusion

For an experimental population of 10,000 individuals with a birth rate of 18 per 1000 and a death rate of 14 per 1000, the population at time $t+1$ will be 10,040.

Correct answer:
(2) 10,040