Section 3: Equation Components
The “Unused Portion of K”
Notice that the logistic equation looks like the exponential equation multiplied by [1-(N/K)]. This mathematical term is what accounts for the density-dependent population growth rate.
![Lake divided into 50 equally sized squares with each square that can only support one fish on average.](/static/fish-1-48e1a3e703d29449be52c6334eb2b9ee.jpg)
Lake divided into 50 equally sized squares with each square that can only support one fish on average.
Notice that the logistic equation looks like the exponential equation multiplied by [1-(N/K)]. This mathematical term is what accounts for the density-dependent population growth rate.
This gives the per capita growth rate of the population, which is represented as:
The per capita growth rate is mathematically interchangeable with the variable r (realized intrinsic rate of increase). r is the rate of increase at each moment in time. Therefore:
Given this equation for r:
Predict what happens to r as the population reaches K.
If K = 50 and rmax = 0.5, when will r be exactly half of r max? r will be exactly half of rmax when N equals: Number of Fish (N)