Patch based Approaches

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Patch based Approaches
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A classification of multi-site scenarios
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Metapopulation models

• Most theoretical metapopulation models assume
  that all populations have identical extinction
  rates, and that they are all equi-distant from
  one another (e.g. Harrison and Quinn 1989)
• But these models are too far removed from
  realities of specific multi-site situations to be
  of practical use for particular species.

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Incidence function models

• Developed by Hanski (1991, 1994)
• Sjögren-Gulve and Ray 1996, Moilanen 1999, 2000
  and Kindvall 2000)

Ilkka Hanski
Atte Moilanen
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The Incidence function model

• Use patterns of patch occupancy over time and
  space (incidence) to estimate
• Ei, the probability of extinction for habitat
  patch i when it is occupied, and
• Ci, the probability that patch i becomes
  colonized when it is occupied
• Taking in account the patchs habitat area,
  habitat quality, distance to other populations,
  and other potentially important characteristics

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The Incidence function model

• We start assuming specific function forms for
  the effects of the causal factors (patch area and
  quality, proximity of other populations, etc) on
  Ei and Ci.

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Extinction
e1 x0.5
A area
P(extinction ) in patch i
Area
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Colonization
M number of migrants
P(colonization) in patch i
y1
Arriving migrants
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The number of migrants

• depends on
• The probability of other patches having extant
  populations, their population sizes (which is
  assumed to be proportional to the area of each
  patch), the rate at which dispersers leave the
  patch, and the distances from each other patch to
  focal patch i.

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The number of migrants
Mi number of migrants ß per-unit-area migrant
production rate A patch i area Scaled by
parameter b to allow for nonlinearity pj 0
empty and pj1 if occupied a scaling factor
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Number of migrants
A area
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The incidence function model
The probability that site i is occupied in any
one site is predicted by
in cases where rescue effects are thought to occur
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The incidence function model

• A snap-shot of the pattern of patch occupancy can
  be used to estimate the parameters governing Ci
  and Ei

However, it means assuming that the occupancy
patterns seen in the field are very near their
equilibrium values
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The incidence function model
Where eey and yy/ß
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Count based Approaches
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Information needed

• Mean population growth rate
• Variance in population growth rate
• Covariance in population growth rate
• Probabilities of movement between populations
• Estimates of density dependence

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The California clapper rail
Harding et al 2001
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The California clapper rail
0.060.790.720.034
Harding et al. 2001
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Pearson correlation coefficients
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The transition matrix

• Determining counts at different sites

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The transition matrix

• Determining counts at different sites

(1-d)?Mt da da

da (1-d)?Ft da
da da (1-d)?Lt
dconstant probability of an individual dispersing
aconstant probability of an individual arriving
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Effect of correlations
With correlations
Without correlations
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Effect of levels of dispersal
20 move
10 move
5 move
none move
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Demographic Approaches
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Coryphantha robbinsorum
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The basic model
Seeds Small juveniles Large juveniles Adults
A
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Vital rates
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The multi-site model
G
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The multi-site model
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0 0 0 f4as4a,mAC
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0 0 0 f4as4a,mBA
0 0 0 f4as4a,mBC
0 0 0 0
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G
0 0 0 0
0 0 0 0
0 0 0 0
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0 0 0 f4as4a,mcA
0 0 0 f4as4a,mCB
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