# Lionfish Invasion: Density-Dependent Population Dynamics

## Calculating lionfish population growth each year

Using what is known about lionfish in the Bahamas, let’s model their population growth each year from 2004 to 2014. To do this, we’ll use a discrete-time logistic model to project changes in the population over time periods of one year ($\mathrm{\Delta }t=1$) each. We can write the population size at the start of a year as ${N}_{t}$. The population size at the end of that year, or start of the next year, will be ${N}_{t+1}$.

Over each year, our model will estimate the change in population size, in terms of the number of .

The table below lists the values calculated from the model for each year. The first row, for the year 2004, is completed for you. Click on any cell in the first row with data to see how the values were calculated.

Fill in the next three rows of this table to determine the population size (${N}_{t}$) after each year. Enter your calculated values in order from left to right starting with the first empty cell in the row for 2005. Round your calculations to 2 decimal places and hit enter to move to the next cell. If the calculation is incorrect, you will receive an alert and you can modify your answer. If the answer is correct, you will not be able to change your response. As you complete each row, the population sizes you calculated will appear on the graph below.

Use the following values for the lionfish population to complete your calculations.