Models in ESA part 2

Question 1

What are states (stocks)?

Answer 1

• States is a quantity which is measurable at a particular point of time
• It represents “state of the system “ and often it is the focus of analysis
• dynamic models: states change over time ( accumulates or decreases)
• starts with an initial value

Question 2

What are rates?

Answer 2

• The presence of a rate indicates the movement of material
• Changes in states occur via rates
• Quantity which is measured with reference to a period of time
• Can be dependent on state and on exogenous factors

Question 3

What is rule of 72?

Answer 3

Also called rule of 69 or rule of 70. It is used to calculate doubling time or half-life ( growth rate ( in %) x (doubling time) = 72 ( decay rate (in %)) * (half life) = 72

Question 4

What is the basis of numerical integration?

Answer 4

• Numerical integration is an iterative approach: The states summarise where you stand today, the rates are the actions to change the system to a new state tomorrow
• statet+deltat = statet + deltat * ratet
• deltat -> time step of your model (also called delta timer)
• in numerical integration it is assumed that the rate of change of state variable is constant during the time step

Question 5

What is the difference between analytical analysis and numerical integration?

Answer 5

• analytical analysis
  
  • based on solving differential equations
  • exact answer
  • but only possible for simple differential equations
• numerical integration
  
  • time slicing approach
  • not exact
  • many iterations
  • initial conditions should be known

Question 6

What is logistic growth?

Answer 6

In logistic growth a populations per capita growth rate gets smaller and smaller as population size approaches a maximum ( the carrying capacity) resulting from limited resources in the environment, e.g. fish stock or growth of a forest

Question 7

What is the difference between discrete and continuous growth?

Answer 7

• Discrete growth events occur in discrete units of time ( no overlap of generations), e.g. if an organism only breeds during a certain time of the year Equation: Nt = N0 ( 1+r)t
• Continuous growth events occur continuously, e.g. if a population breeds during the whole year ( e.g. humans). Equation: Nt = N0 et*r
• With r = growth rate, Nt = population at time t, and N0 = population at time 0