Multi-site PVA


I.  Introduction to multi-site PVA

    A.  How many sites to rare species occupy?





    B.  What is a metapopulation?



II.  How to approach multi-sites PVAs

    A.  Prerequisites

        1.  First, determine if there is one main ‘source’ or ‘mainland’ population
        2.  If so, then just worry about that one population
        3.  If not, then consider the relative movement rates and population correlations


    B. Data needs

        1. Site specific population data
       
        2. Something about movement between sites

        3. Something about correlation of fates
            -  Assume no negative correlation.
            -  If positive, then reduces insurance created by metapopulation
   




III.  Count-based multi-site PVA

A.  Usually the most useful, as there is the greatest available data

B.  Need:
        - mean, variance, and covariance of population growth rates for local populations
        - movement probabilities

C.  If lots of movement, treat as a single population

D.  If populations are totally independent of one another, then:

    1.  Pglobal = P1 * P2*...Pn

        2.  Can test the importance of saving an additional site





E.  For correlated populations or with limited dispersal, project a matrix






V.  Demographic PVA
A.  Needs
    - demographic rates for each local population
    - class-specific estimates of movement




B.  Models are enlarged versions of basic, population specific matrix models








VI.  Patch occupancy and PVA

A.  Needs
    - Assume modest movement
    - Patch occupancy collected over a sequence of years

B.  Classic metapopulation model by Levins
    -dp/dt = m*p*(1-p) – e*p
    -Equilibrium p is dependent on a balance between colonization and extinction
    -Patches are occupied as long as m>e
    -There are always unoccupied patches, and these are important to the maintenance of the population


C.  The Incidence Function model
   
Mi = βSi

Si = ∑pj exp(-αdij) Aj

    dij is the distance between patch i and patch j

Solve with logistic regression