Modelling population dynamics and density

Question 1

Why are we interested in population dynamics? Give 2 examples.

Answer 1

1. Pest control

2. Conservation biology

Question 2

What type of error is increased in simple models?

Answer 2

Approximation error.

Question 3

What is approximation error?

Answer 3

Discrepancy between the exact value and an approximation of it.

Question 4

What is the benefit of using a complex model and why?

Answer 4

They are a good fit to current data because they consider many parameters.

Question 5

Why are complex models not good for predicting future values?

Answer 5

They are too specific.

Question 6

What type of error is increased in complex models?

Answer 6

Estimation error.

Question 7

What are the 2 types of model?

Answer 7

1. Non-overlapping

2. Overlapping

Question 8

What is a non-overlapping model? Give an example.

Answer 8

One that uses discrete time. The Ricker equation is a non-overlapping model.

Question 9

What do we use models for in population dynamics?

Answer 9

To predict future densities of populations.

Question 10

Give the Ricker equation. Explain each term.

Answer 10

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

Question 11

What is carrying capacity?

Answer 11

The maximum theoretical density an environment could sustain based on current resources.

Question 12

If a population is at carrying capacity what kind of state is it in?

Answer 12

Equilibrium.

Question 13

If population size = k, is there growth in the population? Why, why not?

Answer 13

No, because the population is at equilibrium.

Question 14

If ‘r’ is positive, do we expect growth? Why, why not?

Answer 14

Yes, because births are greater than deaths.

Question 15

High levels of ‘r’ produce oscillations in density. What is a 2-point limit cycle?

Answer 15

The population fluctuates between 2 points.

Question 16

Just changing levels of ‘r’, and nothing else, causes large fluctuations in density. True or false?

Answer 16

True.

Question 17

In a 2-point limit cycle, is k ever reached?

Answer 17

No.

Question 18

What is a 4-point limit cycle?

Answer 18

The population fluctuates between 4 points.

Question 19

Are levels of ‘r’ higher in a 2 or 4-point limit cycle?

Answer 19

4-point limit cycle.

Question 20

Define chaos.

Answer 20

Extreme sensitivity to the initial conditions.

Question 21

What happens in chaotic conditions?

Answer 21

There are random oscillations.

Question 22

What causes chaos and why?

Answer 22

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.

Question 23

Chaos is common in nature. True of false?

Answer 23

False.

Question 24

Give an example of chaos.

Answer 24

Measles outbreak.

Question 25

Define a phase space.

Answer 25

Essentially the space in a graph, whereby the axes describe the state of a physical system.

Question 26

Define an attractor.

Answer 26

A coordinate in the phase space.

Question 27

In stable populations, are the attractors in a phase space single points or a series of points?

Answer 27

Single points.

Question 28

What is cobwebbing?

Answer 28

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).

Question 29

What is an overlapping model? Give an example.

Answer 29

One that uses continuous time. The Logistic equation is an over-lapping model.

Question 30

Give the Logistic equation. Explain all the terms.

Answer 30

dN/dt = rN(1-N/k)

N = density
t = time
r = net fecundity
k = carrying capacity

Question 31

If dN/dt = 0, what does that mean about the population?

Answer 31

There is no growth (density does not change over time).

Question 32

According to the Logistic equation of dN/dt = rN(1-N/k), if dN/dt = 0, what must rN(1-N/k) equal?

Answer 32

Also 0.

Question 33

If rN(1-N/k) = 0 there are 2 possibilities. What are they?

Answer 33

1. rN = 0, which means there must be no individuals in the population to reproduce.
2. (1-N/k) = 0, which must mean than N = k, and 1 - k/k must equal 0.