LIFE214: Interspecific competition

Notes and guiding questions

The work described here is for you to explore in your own time, to help you understand the concepts relating to interspecific competition. For this you will be running simulations based on the Lotka-Volterra interspecific competition model. Through this you will explore how different combinations of intra- and interspecific competition affect the coexistence or exclusion of 2 species competing for a limiting resource.

NOTE: This work is NOT assessed; answers will be released after the practical.

General instructions on how to run the simulations

The file Interspecific competition model.xlsm is an Excel spreadsheet that allows you to simulate several of the classic models of ecological population dynamics that are discussed in this module. To use it:

Download the file and save it somewhere in your home directory

Open the file you saved. Note that the file will only work properly on a Windows computer, using Microsoft Excel.

You may be warned that the file contains “macros” and that these can pose a security risk. You will need to enable macros in order to run the practical. If the Excel window has a yellow stripe above the spreadsheet, as shown below, then click on “enable content

Excel may ask you whether you want to make this file a “Trusted Document”; it’s safe to answer “yes”.

The spreadsheet has different “Worksheets” (selected using the tabs at the bottom of the window) that allow you to simulate different models (colour-coded into groups of related models). To run a model, set the various parameters to appropriate values (as described in the instructions) and click the large grey button:

After a couple of seconds, the output of the model will appear on the ‘Results’ worksheet:

You can now plot the results as a graph, look at the numbers directly, or perform another analysis as you would with any set of numbers in Excel.

Note that the ‘Results’ worksheet is overwritten each time you run the model. We suggest you create a new Excel spreadsheet, and copy to it any model runs you wish to compare or keep.

Interspecific competition model

In the questions that follow we are mostly interested in the long-term (‘steady state’) behaviour of the model – does it show sustained cycles or does it stabilise to a single value? If it stabilises, what value does it end up at (i.e., what is the 'equilibrium'; do both species persist in the long-term etc)? We are less interested in the time it takes to reach that equilibrium, or the exact values it passes through to get there.

As a baseline, use the following parameter values (except when changing them in the following questions):

Questions/tasks

How does changing the per capita growth rates (r1 and r2) affect (1) the positions of the nullclines and (2) the dynamics on the 'Results' sheet?

What does this mean for the effect of those growth rates on the outcome of interspecific competition? Do they matter?

By changing the K and alpha values (α12 and α21), can you create the 4 outcomes of competition from the lecture (Cases 1-4)? Can you interpret these in terms of the relative strength of inter- and intra-specific competition in each case?

Check the dynamics on the Results sheet match what you expect from the nullclines for each Case.

Remember you can add the dynamics from the Results sheet onto the Phase Plot, to overlay them on top of the nullclines (see guidance notes below).

By varying the initial population sizes, check if any of those cases are dependent on initial conditions. Does that match what you expected from the lecture.

What combination of inter- and intra-specific competition give coexistence? Is this affected by the growth rates (r1 or r2) or the initial population sizes?

Guidance on adding data to graphs in Excel

To answer some of the questions it is useful to plot the predator and prey dynamics against each other on the same phase plot as the nullclines. To do this I suggest you follow the following steps:

Run the model by pressing the big grey button on the relevant sheet

Copy the Sp 1 density and Sp 2 density data (columns B and C), excluding the headers from cells B1 and C1. Paste the data into empty cells on the “2 species competition” spreadsheet (eg in columns Q and R).

Right click on the Phase Plot chart on the spreadsheet to bring up the mini-menu and click “Select data…”

This brings up a dialog box – click “Add”, to bring up the “Edit Series dialog box

For the “Series X” values choose the column of ‘Sp 1 densities’ (eg column Q) and for the “Series Y” values choose the column of ‘Sp 2 densities’ (eg column R). When you click ‘OK’ the data should appear on the figure.

Repeat for different runs of the model, pasting the new predator and prey data into new columns on your spreadsheet, and adding the data to the phase plot.