Question

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?

1) 1/3
2) 2/3
3) 1
4) 3/2

Answer 1

Option 2.

To find the competition coefficient of houseflies on Teleopsis, the logistic growth equation is modified to include the competing species. With 30,000 houseflies added, the growth rate is zero.

Step-by-step explanation:

To determine the competition coefficient of houseflies on Teleopsis, we need to use the logistic growth equation and the carrying capacity.

Using the provided data, we know the carrying capacity (K) is 40,000 individuals, the growth rate (r) is 0.2 per day, and adding 30,000 houseflies brings the growth rate to zero.

The logistic growth equation in the presence of another competing species is modified as follows:

dN/dt = rN(1 - (N + αP)/K)

Where:

• N is the population size of Teleopsis
• α is the competition coefficient of the houseflies on Teleopsis
• P is the population size of the houseflies

Setting the growth rate to zero (dN/dt = 0) and rearranging the equation gives us:

N + αP = K

Given that the addition of 30,000 houseflies brings growth to zero, we substitute this value into the equation:

20,000 + α(30,000) = 40,000

Solving for α:

α(30,000) = 40,000 - 20,000

α = 20,000 / 30,000

α = 2/3

Thus, the correct option is (2) 2/3.

The competition coefficient is a measure of the per capita effect of houseflies on the growth rate of Teleopsis.