Chapter 2

Question 1

What is the equation for exponential growth rate?

Answer 1

dA/dt = c * A
c = relative growth rate (1/time)
A = state (amount)

Question 2

What are the assumptions of an exponential model?

Answer 2

• Homogeneous population
• Instantaneous growth
• No competition for resources
• Constant effect of abiotic environment (the value of c is not dependent on any other factors. This assumed lack of intraspecific competition and the assumed absence of variation in the abiotic environment implies that the exponential model will only be relevant in real-world systems for short periods of time, when
  population numbers are low.)

Question 3

What is the equation for logistic growth rate?

Answer 3

dA/dt = c * A * (1 - A/A_max)

A_max = max possible pop size
(1 - A/A_max) = density dependent reduction factor

Question 4

What is the logistic growth rate equation (solving for A_t)?

Answer 4

A_t = A_max / (1 + K * e ^ -c * t)
K = carrying capacity constant

Question 5

What are the assumptions of logistic growth in 2 interacting populations?

Answer 5

• Two interacting populations
• Instantaneous growth
• Competition for resources
• Effects in abiotic environment
  modelled in a homogeneous mixed
  vessel

Question 6

What is a Forrester diagram?

Answer 6

Suitable to visualise all details of the model, including all required parameters, auxillary variables and information flows that explain what is needed for every equation in the model

Question 7

What is a state flow diagram?

Answer 7

Conceptual model for communication with the public

Question 8

What is the notation for state flow diagrams?

Answer 8

Rectangles = state variables
Arrows = processes / flows
Parallelograms = input / output / other

Question 9

What are the steps to making a Forrester diagram?

Answer 9

1. Identify the state variables (var of extention not intensity)
2. identify how they change (components that increase or decrease the amount)
3. Add dotted lines to connect information that is needed

Question 10

How to design a conceptual model (state flow model)?

Answer 10

1. Identify states (rectangles)
2. Identify processes that change states (arrows)
3. Some processes influence other processes (arrow influences arrow)
4. Translate diagram into mathematical equations

Question 11

What is the difference between Forrester and State flow models?

Answer 11

Forrester: for modellers
* detailed, directly linked to equations in the model
* can be used to fully derive equations
* differentiation between rates and auxiliary
equations
* all parameters are shown and named

State-flow models: for general communication
* Overview of states, processes and flows
* Can be drawn from equations but vice versa is not easy due to missing information