week 10

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

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

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

Model that does not take chance into effect

models that account for the role of chance

time is measured in discrete steps

time meaner continuously

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

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

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

• Start by formulating a question • Identify the basic ingredients of the model, including • Qualitatively describe the system • Quantitatively describe the system • Analyze the equations

• 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?

Variables (things that change over time) Parameters (constants in the model)

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