A population of spotted deer in a nature reserve has a carrying capacity of 1000 individuals. Currently, the population size is 600 . If the per-capita birth rate is 0.15 per year and the per-capita death rate is 0.05 per year, what is the current rate of change of population density ( dN dt )?

Step-by-step solution

Given: Carrying capacity ( K ) = 1000 Current population size ( N ) = 600 Per-capita birth rate ( b ) = 0.15 Per-capita death rate ( d ) = 0.05 The intrinsic rate of natural increase ( r ) is calculated as: r = b - d r = 0.15 - 0.05 = 0.10 Since the nature reserve has limited resources (a carrying capacity), the population follows logistic growth. The equation for logistic growth is: dN dt = rN ( K - N K ) Substituting the values: dN dt = 0.10 600 ( 1000 - 600 1000 ) dN dt = 60 ( 400 1000 ) dN dt = 60 0.4 = 24 The