WLF 448: Fish & Wildlife Population Ecology

Fall 2010

DEMOGRAPHIC-BASED POPULATION MODELS

Population Projection Matrix

A population projection matrix is a box that helps keep straight the bookkeeping of projecting population abundances based on survival and fecundity (Mills 2007).

from Mills (2007:136)

Projecting a matrix through time:

    Remember:  Exponential growth model

    Matrix-projection model:

        n(t+1) = M * n(t)

Matrix x Vector multiplication conveniently carries out the required mathematical operations (additions due to births and subtractions due to mortality) to project each age (stage) to the next time step.

    Example:

Adding Stochasticity:

    Deterministic model:  M is the same for each time step

    Stochastic model:  Values in M are different each time step

                Where do we get the different values of M?

Adding Density Dependence:

Metapopulation Models:

• Each population has its own projection matrix
• Individuals can move among populations via dispersal
• Projection matrices (M) can be correlated among populations 

Sensitivity Analysis:

Manual perturbation

References:

Mills, L. S.  2007.  Conservation of wildlife populations: demography, genetics and management.  Blackwell Publishing, Malden, MA.

Revised: November 01, 2010