Modelling population dynamics and density Flashcards
Why are we interested in population dynamics? Give 2 examples.
- Pest control
2. Conservation biology
What type of error is increased in simple models?
Approximation error.
What is approximation error?
Discrepancy between the exact value and an approximation of it.
What is the benefit of using a complex model and why?
They are a good fit to current data because they consider many parameters.
Why are complex models not good for predicting future values?
They are too specific.
What type of error is increased in complex models?
Estimation error.
What are the 2 types of model?
- Non-overlapping
2. Overlapping
What is a non-overlapping model? Give an example.
One that uses discrete time. The Ricker equation is a non-overlapping model.
What do we use models for in population dynamics?
To predict future densities of populations.
Give the Ricker equation. Explain each term.
N(t+1) = N(t)exp[r(1-Nt/k)]
N(t) = density at time t exp = exponential function r = net fecundity (births-deaths) k = carrying capacity
What is carrying capacity?
The maximum theoretical density an environment could sustain based on current resources.
If a population is at carrying capacity what kind of state is it in?
Equilibrium.
If population size = k, is there growth in the population? Why, why not?
No, because the population is at equilibrium.
If ‘r’ is positive, do we expect growth? Why, why not?
Yes, because births are greater than deaths.
High levels of ‘r’ produce oscillations in density. What is a 2-point limit cycle?
The population fluctuates between 2 points.
Just changing levels of ‘r’, and nothing else, causes large fluctuations in density. True or false?
True.
In a 2-point limit cycle, is k ever reached?
No.
What is a 4-point limit cycle?
The population fluctuates between 4 points.
Are levels of ‘r’ higher in a 2 or 4-point limit cycle?
4-point limit cycle.
Define chaos.
Extreme sensitivity to the initial conditions.
What happens in chaotic conditions?
There are random oscillations.
What causes chaos and why?
Extreme levels of r - if many individuals all produce offspring at the same time there is severe competition for resources and space, thus the population will fluctuate from high to very low levels as individuals that are outcompeted die off.
Chaos is common in nature. True of false?
False.
Give an example of chaos.
Measles outbreak.
Define a phase space.
Essentially the space in a graph, whereby the axes describe the state of a physical system.
Define an attractor.
A coordinate in the phase space.
In stable populations, are the attractors in a phase space single points or a series of points?
Single points.
What is cobwebbing?
A technique that (no one understands) for visualising the solution to a discrete time model, by comparing it to a graph in which there is exponential growth (it is bullshit).
What is an overlapping model? Give an example.
One that uses continuous time. The Logistic equation is an over-lapping model.
Give the Logistic equation. Explain all the terms.
dN/dt = rN(1-N/k)
N = density t = time r = net fecundity k = carrying capacity
If dN/dt = 0, what does that mean about the population?
There is no growth (density does not change over time).
According to the Logistic equation of dN/dt = rN(1-N/k), if dN/dt = 0, what must rN(1-N/k) equal?
Also 0.
If rN(1-N/k) = 0 there are 2 possibilities. What are they?
- rN = 0, which means there must be no individuals in the population to reproduce.
- (1-N/k) = 0, which must mean than N = k, and 1 - k/k must equal 0.
