The BIDE Model

Applied Population Dynamics

WILD 5700/7700

BIDE model

Today’s class


  1. A few definitions
  2. Modeling 101
  3. The BIDE model

Definitions

Population dynamics: The study of spatial and temporal variation in population size and structure


Population: Individuals of the same species occuring in the same geographic region


Population size and structure

  • Size: Abundance
  • Structure: Distribution of individuals among age groups, sexes, habitat patches, etc…

Models and science

A model is an abstraction of reality that describes the relationship between two or more variables.

Models help us…

  • Describe complex natural systems in
    a manageable way

  • Formalize and evaluate hypotheses

  • Predict future outcomes

  • …all while accounting for uncertainty

Island Scrub Jay

Island Scrub Jay density

Models and science

But don’t models require assumptions?

Yes. We have to simplify, so we have to make assumptions. We do this all the time.


image “All models are wrong, but some are useful.” G.E.P. Box (1987)

Model validation


Putting the model to the test

  • How well does it predict?

  • Will your results hold up in court?

  • Can your results be replicated/reproduced?

NASA climate models

Types of models

  • Conceptual
  • Physical
  • Graphical
  • Mathematical
  • Statistical

The BIDE model

\[N_{t+1} = N_t + B_t + I_t - D_t - E_t\]

\(N_t\): population size (state variable) at time \(t\)
\(B_t\): births
\(I_t\): immigrants
\(D_t\): deaths
\(E_t\): emigrants

The BIDE model

\[N_{t+1} = N_t + B_t + I_t - D_t - E_t\] As written, this model implies the following:

  • \(B\), \(I\), \(D\), and \(E\) are not rates, they are the number of events at time \(t\).

  • The model is deterministic, not stochastic

  • Time is discrete, not continuous

In reality, things are more complicated, and interest lies in understanding the factors influencing each process.

The BIDE model

Group exercise


Split into groups of 4–6 students.


Come up with a list of at least 5 factors that influence the four demographic variables: B, I, D, and E.


Be prepared to explain which demographic variables are influenced by each factor.

Assignment


Read the first 3 pages of Chapter 3 in Conroy and Carroll.


Expect a quiz next time we meet.