Incidence function model

1
Incidence function model

• For each patch, need to know area, distance to
  all other patches
• Extinction and colonization are patch specific
• Extinction depends on patch area

2
Colonization

• Colonization probability is saturating function
  of number of immigrants
• Immigrants are more likely to come from large,
  close populations

3
Probability of occupancy (incidence function)

• At equilibrium, so some
  algebra reveals

4
Parameter estimation

• Data consists of annual surveys of presence or
  absence of species in every habitat patch
• Single survey fit incidence function to observed
  occupancy using nonlinear logistic regression
• Multiple surveys fit extinction colonization
  functions to observed extinctions colonizations
  using nonlinear logistic regression

5
Simulating the metapopulation

• For each patch, calculate Ei and Ci(t)
• For each occupied patch, draw random number
  (uniform on 0,1) to compare with Ei
• If extinction occurs, draw another random number
  to compare with Ci(t) rescue effect
• For each unoccupied patch, draw random number to
  compare with Ci(t)
• Update patch status

6
Glanville fritillary metapopulation
7
Habitat loss metapopulation extinction