week 10

Question 1

What are models used for?

Answer 1

• Testing verbal intuition (is it logical?)
• Generating new predictions
• Guiding experimental designs
• Establishing formal links between cause & effect

Question 2

What are dynamic models?

Answer 2

Describe how a variable – or a system of variables – changes over time.

Question 3

What do dynamic models describe?

Answer 3

Can describe changes in cells, tissues, individuals, populations, and species assemblages, e.g.:
• Diffusion throughout a cell
• Cancer spread within an individual
• Gene freq. change in a population
• Species competition

Question 4

What is a Deterministic model?

Answer 4

Model that does not take chance into effect

Question 5

stochastic models what are they?

Answer 5

models that account for the role of chance

Question 6

discrete models defintion?

Answer 6

time is measured in discrete steps

Question 7

continuous models defintion?

Answer 7

time meaner continuously

Question 8

What is pseudo-deterministically?

Answer 8

Stochastic models can behave “pseudo-deterministically” when deterministic processes are strong (e.g., strong natural selection vs. weak genetic drift)

Question 9

When are Continuous and discrete time models similar?

Answer 9

Continuous and discrete time models have similar dynamics when rates of change are slow.

Question 10

When do Continuous and discrete time models diverge?

Answer 10

Continuous and discrete models can diverge dramatically when the “jumps” in discrete time models are large.

Question 11

Steps in Constructing an analyzing dynamical models?

Answer 11

1. Start by formulating a question
2. Identify the basic ingredients of the model, including
3. Qualitatively describe the system
4. Quantitatively describe the system
5. Analyze the equations

Question 12

parts of formulating a question?

Answer 12

• What conditions promote growth or decline of a population?
• What is the timescale or rate of population size change?
• When should we expect populations to be stable/unstable?

Question 13

basic ingredients of the model?

Answer 13

Variables (things that change over time)

Parameters (constants in the model)

Question 14

Qualitatively describe the system

Answer 14

If order of events is important, use a discrete-time model
• Construct a life-cycle diagram of the events:
Recursion equations of discrete-time models