A population of Teleopsis (a stalk-eyed fly) with 20,000 individuals and a carrying capacity of 40,000 follows the logistic growth equation. Its growth rate under ideal low-density conditions is 0.2 per day. The addition of 30,000 houseflies is enough to bring the population growth of Teleopsis to zero. What is the competition coefficient of the effect of the housefly on Teleopsis?

Question

Tigger

Biology

15 November, 15:21

A population of Teleopsis (a stalk-eyed fly) with 20,000 individuals and a carrying capacity of 40,000 follows the logistic growth equation. Its growth rate under ideal low-density conditions is 0.2 per day. The addition of 30,000 houseflies is enough to bring the population growth of Teleopsis to zero. What is the competition coefficient of the effect of the housefly on Teleopsis?

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Answers (1)

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Tianna Larsen · Answer 1

The correct answer is 2/3.

Explanation:

In the given question, alpha (α) is the competition coefficient, and a differential calculus logistic equation is used in order to solve the question.

dN/dT = rN1 (K - N1 - αN2) / K

Here, alpha is the competition coefficient

K is the carrying capacity, and N is the population size.

Now, setting dN/dT = 0 we get,

= rN1 (K - N1 - αN2) / K = 0

= 0.2 * 20000 (40000 - 20000 - α30000) / 40000 = 0

= 20000 - 30000α / 10000 = 0

= 30000α = 20000

= α = 20000 / 30000

= α = 2/3