# Lionfish Invasion: Density-Dependent Population Dynamics

## Visualizing a population growth model

Let’s take a closer look at the continuous-time logistic model. We’ll now explore a new variable, ${r}_{\text{realized}}$, which represents the realized per capita growth rate: the actual growth rate of the population per individual. Unlike the maximum per capita growth rate ${r}_{\text{max}}$, which is a constant, ${r}_{\text{realized}}$ will change as the population grows.

Click on the three points highlighted on the lionfish population growth curve in the graph below. For each point you click, you will get more information about the population growth rates (both the overall growth rate $\frac{dN}{dt}$ and the per capita growth rate ${r}_{\text{realized}}$) at that time. The estimated numbers of lionfish at that time will also appear, separated into two groups: adults and juveniles. The adults, shown in white, are fish that were present at the start of that year. The juveniles, shown in blue, are new fish that were added to the population during that year.