Cha7: Evil Humans harvesting a Fish population Flashcards
Word Model: A fish population in a large region of the ocean has not been harvested before. Therefore, we observe an equilibrium at the ecosystem’s carrying capacity. We start to apply a harvesting system, where the harvested amount per unit time is proportional to the size of the population. What type of Harvesting is this?
What’s the math behind it and when do we have a stable fish population ?
Stock-Dependent Harvesting H= h*N
Math Model:
dN/dt = r * N * (1 – N/C) – h * N
Equilibria: dN/dt = 0
0 = r * N * (1 – N/C) – h * N
h * N = r * N * (1 – N/C) —> h= r*(1- N/C)
Draw the fish population CLD but this time, taking harvesting ( pop depenedent into consideration)
Compare the pop growth at harvest rate = 0.5 and Harvest rate= 0.05
Compare the pop growth at harvest rate = 0.5 and Harvest rate= 0.05
Word Model: A fish population in a large region of the ocean has not been harvested before. Thus, we observe an equilibrium at the ecosystem’s carrying capacity. We start to apply a harvesting system where the amount harvested per year is constant, and independent from the population size. Typical: Fishing with sonar systems.
How is this harvesting type called and what is the maths behind ?
This is Harvesting constant amounts
Math Model
dN/dt = r * N * (1 – N/C) – m
m: Harvest amount [t/year]
Equilibria:
0 = r * N * (1 – N/C) – m
0 = r * N – r/C * N² – m
- This is a quadratic equation in N
Such equations have up to two solutions.
How can we test for stability in a model ? and specifically in this fish model ?
We disturb the equilibrium either by iontroducing:
First test: “Death Shock” – we have a sudden break in of the population, say, due a fish disease. Assume 500 t of fish are dying in addition to normal in year 20.
Deaths = Fish * Death Rate + 500 * PULSE(20, 1)
Contrary: “Birth Shock”
Births = Fish * Birth Rate + 500 * PULSE(20, 1)
