How does increasing the average lifespan affect the deer population trajectory if the birth rate stays the same?

Conditions

• The birth fraction parameter remains unchanged.
• The lifespan parameter is increased.
• The model follows the equation $Deaths = Deer / Lifespan$.

Reasoning, step by step

1. Recall the death rate equation: $Deaths = Deer / Lifespan$.
2. Observe that increasing Lifespan in the denominator reduces the value of Deaths for a given Deer stock.
3. Compare the new death rate to the constant birth rate ($Births = Deer \cdot Birth\_fraction$).
4. Determine that $Births > Deaths$ after the lifespan increase.
5. Conclude that the net rate of change ($Births - Deaths$) is positive.
6. Predict that the population will grow exponentially over time.

Example

In the video, changing the lifespan from 5 to 10 years halves the death rate coefficient from 0.2 to 0.1. With the birth rate staying at 0.2, the population grows, shown by an upward-curving graph in Run 2.

Common misconceptions

• Believing that a longer lifespan immediately increases the population count without considering rates.
• Thinking that the birth rate adjusts automatically to the new lifespan.
• Assuming the population will stabilize at a new higher level rather than growing exponentially in this simple model.

Watch the explanation

Explore next

• What happens to the population if the birth fraction is decreased?
• Why does the population decline when births are less than deaths?
• How does this simple model differ from a more complex ecological model?