What are models used for?
- Testing verbal intuition (is it logical?)
- Generating new predictions
- Guiding experimental designs
- Establishing formal links between cause & effect
What are dynamic models?
Describe how a variable – or a system of variables – changes over time.
What do dynamic models describe?
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
What is a Deterministic model?
Model that does not take chance into effect
stochastic models what are they?
models that account for the role of chance
discrete models defintion?
time is measured in discrete steps
continuous models defintion?
time meaner continuously
What is pseudo-deterministically?
Stochastic models can behave “pseudo-deterministically” when deterministic processes are strong (e.g., strong natural selection vs. weak genetic drift)
When are Continuous and discrete time models similar?
Continuous and discrete time models have similar dynamics when rates of change are slow.
When do Continuous and discrete time models diverge?
Continuous and discrete models can diverge dramatically when the “jumps” in discrete time models are large.
Steps in Constructing an analyzing dynamical models?
- Start by formulating a question
- Identify the basic ingredients of the model, including
- Qualitatively describe the system
- Quantitatively describe the system
- Analyze the equations
parts of formulating a question?
- 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?
basic ingredients of the model?
Variables (things that change over time)
Parameters (constants in the model)
Qualitatively describe the system
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
