A laboratory population of fruit flies is growing in a limited resource environment. The carrying capacity ( K ) of the environment is 1000 flies, and the intrinsic rate of natural increase ( r ) for the population is 0.12 per day. What will be the population growth rate ( dN dt ) when the current population density ( N ) is 500 flies?

Step-by-step solution

According to the Verhulst-Pearl logistic growth model, the population growth rate is given by the equation: dN dt = rN ( K-N K ) Given: Intrinsic rate of natural increase ( r ) = 0.12 per day Current population density ( N ) = 500 Carrying capacity ( K ) = 1000 Substituting the values into the equation: dN dt = 0.12 500 ( 1000 - 500 1000 ) dN dt = 60 ( 500 1000 ) dN dt = 60 0.5 = 30 The population growth rate is 30 flies per day. Note: A value of 60 would imply exponential growth (ignoring carrying capacity), while