Question

Look carefully at the variables in the equation, remembering that species 1 is the pathogen and species 2 is the probiotic. If the probiotic grows logistically and competes with the pathogen, which of the below equations is correct for the probiotic?

1) dN₂/dt=r2N₂
2) dN₂/dt=r2N₂(1-N₂+a21N1/K2)
3) dN₂/dt=r2N₂(1-N1+a12N₂/K2)
4) dN₂/dt=r2N₂(1-N₂/K2)

Answer 1

The correct equation for the probiotic is dN₂/dt=r₂N₂(1-N₂+a21N₁/K₂). It represents the logistic growth model and considers various factors such as the growth rate, population sizes, and competitive effects.

Step-by-step explanation:

In the equation provided, the correct equation for the probiotic is:

dN₂/dt=r₂N₂(1-N₂+a21N₁/K₂)

This equation represents the logistic growth model, where dN₂/dt represents the rate of change of the probiotic population over time, r₂ is the growth rate of the probiotic, N₂ is the current population size of the probiotic, N₁ represents the population size of the pathogen, a21 is the competitive effect of the pathogen on the probiotic, and K₂ is the carrying capacity of the probiotic population.