How to Calculate Per Capita Death Rate from Bird Population Growth and Birth Rate

Population biology relies on understanding how births and deaths influence population size over time. For ecologists and conservationists, calculating per capita birth and death rates is essential for predicting population trends, assessing species health, and developing management strategies. This article demonstrates how to use annual population growth data and the per capita birth rate to determine the per capita death rate in a bird population.

Understanding Population Growth and Rates

Population growth is the change in the number of individuals in a population over a specific period. This change is primarily driven by births and deaths, with migration sometimes playing a role in open systems. For many bird populations, especially in stable or closed environments, migration can be ignored, so the focus is on birth and death rates.

Per Capita Birth and Death Rates

• Per capita birth rate: The average number of offspring produced per individual per time period (e.g., per year).

• Per capita death rate: The average number of deaths per individual per time period.

These rates are fundamental in population models and are often expressed as:

b=Number of birthsInitial populationb=Initial populationNumber of birthsd=Number of deathsInitial populationd=Initial populationNumber of deaths

where $b$ is the per capita birth rate and $d$ is the per capita death rate.

Calculating Population Change

The change in population size over a period can be described by:

N1=N0+(b×N0)−(d×N0)N1=N0+(b×N0)−(d×N0)

where:

• N0N0: Initial population size

• N1N1: Final population size

• $b$: Per capita birth rate

• $d$: Per capita death rate

This equation can be rearranged to solve for the per capita death rate:

N1−N0=(b−d)×N0N1−N0=(b−d)×N0N1−N0N0=b−dN0N1−N0=b−dd=b−N1−N0N0d=b−N0N1−N0

Applying the Formula to the Bird Population

Given:

• Initial population (N0N0): 600

• Final population (N1N1): 645

• Per capita birth rate ($b$): 0.125

Calculate the population change:

N1−N0=645−600=45N1−N0=645−600=45

Calculate the per capita rate of increase:

N1−N0N0=45600=0.075N0N1−N0=60045=0.075

Now, use the relationship between birth and death rates:

d=b−N1−N0N0d=b−N0N1−N0$$d=0.125-0.075=0.05$$

Why This Calculation Matters

Understanding per capita death rates is crucial for:

• Population monitoring: Tracking changes in bird populations for conservation or management.

• Predicting trends: Estimating future population sizes based on current birth and death rates.

• Assessing health: Evaluating whether a population is stable, increasing, or declining, and identifying potential threats.

Real-World Example

Suppose you are monitoring a population of songbirds in a protected area. By recording the number of birds at the start and end of the breeding season and estimating the number of fledglings produced, you can calculate the per capita birth and death rates. This information helps you assess the population’s health and the effectiveness of conservation measures.

Common Mistakes

• Confusing per capita rates with total rates: Always divide by the initial population to get per capita values.

• Ignoring initial population size: Forgetting to use the initial population in calculations can lead to incorrect rates.

• Miscounting time intervals: Ensure the rates correspond to the same time period (e.g., per year).

Summary Table

Conclusion

For a bird population that increased from 600 to 645 in one year with a per capita birth rate of 0.125, the per capita death rate is:

$$d=0.05$$

Correct answer:
(3) 0.05