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Biology
Posted 6 months ago

Imagine you study a population of Florida panthers that have a maximal per capita birth rate of 0.3yr10.3 \mathrm{yr}-1. However, birth rate declines with density with strength 0.005yr10.005 \mathrm{yr}-1 (\#/ha) - 1 . Minimal death rate is 0.1 yr1\mathrm{yr}-1, but it increases with density with the same strength as birth rate declines. Given this information about the components of fitness (sometimes called 'vital rates'), what would you predict for a carrying capacity?
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Answer from Sia
Posted 6 months ago
Answer
The carrying capacity of the environment for the Florida panther population is 40 panthers per hectare.
Solution
a
Define carrying capacity: Carrying capacity is the maximum population size of a species that the environment can sustain indefinitely, given the food, habitat, water, and other necessities available in the environment
b
Set birth rate equal to death rate: At carrying capacity, the birth rate equals the death rate. Let PP be the population density (number of panthers per hectare), then the birth rate as a function of PP is 0.30.005P0.3 - 0.005P and the death rate as a function of PP is 0.1+0.005P0.1 + 0.005P
c
Solve for PP: Set the birth rate equal to the death rate to find the carrying capacity. 0.30.005P=0.1+0.005P 0.3 - 0.005P = 0.1 + 0.005P Solving for PP gives us: 0.2=0.01P 0.2 = 0.01P P=0.20.01=20 P = \frac{0.2}{0.01} = 20 However, since the birth rate and death rate change with the same strength but in opposite directions, we need to account for both changes, effectively doubling the impact of the population density on the rates: P=0.20.005=40 P = \frac{0.2}{0.005} = 40
Key Concept
Carrying capacity is determined by the point at which birth rates equal death rates in a given environment.
Explanation
By setting the adjusted birth rate equal to the adjusted death rate and solving for the population density PP, we can determine the carrying capacity of the environment for the Florida panther population.

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