Lab 03 (III): The overshoot deer population model

Submit the lab before June 21st 2024, 20:00

Introduction

Now that we are familiar with the basics of the Kaibab deer herd case, we are now moving towards more complex models. This part is based on two main sources: (1) chapter 21 of the book Modelling the Environment1, (2) a suite of pre-defined models that we will explore and modify in this lab. All pdfs and models are available on moodle. Make sure that you really invest the time and energy needed for the reading as well as for the different models – both elements, in particular the models, are much more complex compared to what you worked with thus far. Be prepared that it will take you some time until you understand the details of the models!

The overarching question of this lab is What is meant by the ‘overshoot’ of the deer population?. To do that, we will examine the models M21.3.mdl, M21.5.mdl, M21-7.mdl, M21-9.mdl, M21-12.mdl and M21-15.mdl and reproduce the simulations that are described in the book chapter. Again: be prepared that this will take you some time. Some of the models will show a warning related to the extrapolation outside the value range of the look-up tables – feel free to either ignore those warnings. Though, if you can think about ways to fix them, feel free to do so.

Question I:

What does the term ‘overshoot’ refer to in the context of our case?

◻️ ‘Overshoot’ refers to a sharp increase in deer populations at first, followed by steady population numbers thereafter.

◻️ ‘Overshoot’ refers to a sharp increase in deer populations at first, followed by moderately increasing population numbers thereafter.

◻️ ‘Overshoot’ refers to a sharp increase in deer populations at first, followed by a collapse of these population numbers.

◻️ ‘Overshoot’ refers to a sharp increase in deer populations at first, followed by moderately decreasing population numbers thereafter.

Exercise I: The concept of fullness.

Focus now on the full model M21-15.mdl in Vensim At first, we want to think about the concept of fullness in the context of bioproductivity (i.e., primary productivity). Run the model, and visualize the two relevant variables related to fullness in the context of bioproductivity. After that, answer the following question:

Question II:

What does the term ‘overshoot’ refer to in the context of our case?

◻️ ‘Fullness’ refers to the phenomenon that in an ecosystem with limited resources and limited available space no additional biomass can be produced.

◻️ ‘Fullness’ is scaled between 0 and 1 and has a linear trajectory.

◻️ ‘Fullness’ is scaled between 0 and 1 and follows normally an S-shaped curve.

◻️ As ‘fullness’ fractions decline, the overall ‘fullness’ effect on bioproductivity also declines.

◻️ As ‘fullness’ fractions decline, the overall ‘fullness’ effect on bioproductivity increases.

◻️ ‘Fullness’ explains how much of an area is covered with vegetation, and how much new biomass can be produced.

Exercise II: Exploring effects of a wolve population on deer populations.

Now, we want to expand the model from above. Specifically, we want to specify the deer’s predator and replace the lookup tables (lookup for predators, lookup for 2nd shape, etc.) by a wolve population model, similar to what you have seen in model M2.mdl of lab 3(II). To do so, replace the lookup tables by a population model for wolves that matches the following criteria:

  1. The births of wolves are determined by the amount of deer killed per predator per year and a factor <1 that develops in a meaningful way across the range of potential deer kills.

  2. Introduce the same ruleset for the deaths of wolves

  3. The factors should be chosen in a way that the model produces an oscillating pattern for both predator and prey stocks. You can achieve this either by try-and-error or through the SyntheSim functionality.

  4. The wolves’ population should start with 150 individuals.

Question III:

Implement the model and provide a screenshot of your implementation. Please also describe how you did it inside the text box (3-4 sentences).

Hint: you can add figures into your text by using ctrl + c and ctrl + v inside the text field

Question IV:

What is the effect of the wolves’ population model in standing biomass and why (2-3 sentences)?

Exercise III: Introducing hunting pressure.

In this last exercise of the lab, we want to explore the impact that hunting wolves has on standing biomass in the system. Do that considering the following criteria:

  1. the number of hunted wolves must be only dependent on the size of the wolves’ population and a hunting rate (which has to be found; see below)

  2. Increase the model’s run time to 100 years.

  3. Find (and report) the maximum rate (rounded, no comma) of annual wolf hunts possible so that the standing biomass does not collapse entirely.

Once you are done, provide the information below.

Question V:

Which hunting rate did you choose?

Question VI:

Provide a screenshot of your implemented model, alongside with a short description (3-4 sentences) of what you did.

  1. Ford, A. (1999). Modelling the Environment (2nd Edition). Island Press. 488 pages↩︎