Lab 03 (II): The Kaibab deer herd model

Submit the lab before June 20th 2024, 20:00

Introduction

After having worked last week with a simple Lotka-Volterra model and its implementation in Vensim, we are now shifting gears and will work with some more complex models. At the center of the next two weeks are simulations surrounding cycles in predator and prey populations, and we will take the Kaibab examples as our point of departure. We have two readings prepared for this lab, both are book chapters from the book Modelling the Environment¹. Please make sure you read the two chapters carefully before you start the exercise and also revisit the content while you are working on the exercises. Compared to last week, we will provide you with a number pre-configured models. You will have to carefully look at these models and modify them slightly or run simulations. Based on these modifications/simulations we’ll ask you to answer a number of questions.

Exercise I: Understanding a simple model of the Kaibab case

Open the file M1.mdl in Vensim and explore the general structure of the model. What are important stocks and flows? Run the model, either using the run and the SyntheSim functions to see how the two populations develop when modifying the different parameters. Once you have explored a number of different combinations of the simulations, answer the question below.

Question I:

Comparing the basic Lotka-Volterra model that you built last week, with the model M1.mdl provided here: which of the statements below are correct?

◻️ The prey’s interaction term \(b*XY\) does not depend on the deer population \(X\) but only on the predator’s population \(Y\).

◻️ The prey’s population is solely dependent on the initial deer population.

◻️ Like in the Lotka-Volterra model, the predator’s population depends on the prey population.

◻️ Deer densities are an important parameter driving predator’s populations.

◻️ In the Lotka-Volterra model the number of available prey had a stabilizing effect on the predator populations.

◻️ The model M1 reacts more sensitive to changes in initial populations

◻️ When predator’s birth and death rate are in equilibrium, the number of deer remains stable independent from the initial number of deers.

◻️ The initial number of prey available to predators is more important in controlling predator’s numbers that the death rate.

◻️ Both populations remain in a stable equilibrium independently when increasing the number of prey a predator hunts.

Once you have answered this question, move on to model M2.mdl and explore it in the same way you did for the previous model. Again, make sure you examine how the populations change in relation to changing one or more parameters of the model. If you feel that you understand the model well, take a look at the following question.

Question II:

Compared to the model M1.mdland the simple Lotka-Volterra (LV) model which of the following statements are true for model M2.mdl?

◻️ Predator’s birth rates are implemented through clear rules inside the model.

◻️ The size of the Kaibab area remains neglectable.

◻️ The simulation is robust against small parameter changes.

◻️ Predation success is not dependent on deer density.

◻️ Lookup tables are introduced to control birth rates of prey and predators.

◻️ Predator birth and death rates are controlled through lookup tables.

◻️ Predator’s and prey’s numbers are controlling each other, more similar to the LV model.

◻️ Model M2 is oscillating like the LV model but with larger amplitudes.

◻️ Model M2 is oscillating like the LV model but with lower amplitudes.

◻️ Both the model M2 and the LV model have a natural death control of the deer population.

As the last part of this exercise, we want you to have a look at the model M3.mdl. At first, it does look very similar to model M2.mdl but there are some small, yet important differences implemented which result in the two populations to stabilize at the end of the simulation period.

Question III:

What causes the different model behavior of model M3.mdl compared to model M2.mdl (provide 2-3 sentences)?

Exercise II: Introducing stochasticity into the model

Until now, we have dealt with fixed rates of birth and death rates over time. However, one can think that in reality this is too big of a simplification; and this is also discussed in the book chapter. We want to pick up on this discussion in the following exercise. Specifically, we have prepared for you a model RandomNoise.mdl that represents an example of how to introduce random noise into an otherwise constant variable. Make yourself familiar with this structure, and have a look into the documentation of Vensim to better understand the functions used in this model. Once you understood the model, implement this functionality for the variable DeerNetBirthRate in model M2.mdl. Run the simulation and compare the outcome to the outcomes of model M2.mdl without the stochastic component. After that, continue with the following questions:

Question IV:

Provide 2-3 sentences of description on how you set the parameters of the stochastic component, alongside with a visualization of the variable DeerNetBirthRate over the simulation period (you can add figures into your text by using ctrl + c and ctrl + v inside the text field).

Question V:

Provide 2-3 sentences of your thoughts on what might this stochasticity relate to in ecological terms?

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