patch based approaches
DESCRIPTION
Patch based Approaches. A classification of multi-site scenarios. 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) - PowerPoint PPT PresentationTRANSCRIPT
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Patch based Approaches
![Page 2: Patch based Approaches](https://reader031.vdocuments.us/reader031/viewer/2022012914/56814f1d550346895dbcae8e/html5/thumbnails/2.jpg)
A classification of multi-site scenarios
Correlations
in population
Movement rates
Vital rates Essentially none Low to medium
High
Significantly
negative
Separate pops, multiple strongly beneficial
Highly effective
Metapop
Multiple sites, very different habitat
Non different from zero
Separate pops multiple strongly beneficial
Somewhat effective Matapop
Multiple sites
Somewhat different habitat
Significantly
Positive
Separate pops
Multiple not very effective
Ineffective
Metapop
One population
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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 patch’s 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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Area
P(e
xtin
ctio
n )
in p
atch
i e=1
x=0.5
xi
i A
eE
A= area
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Colonization
Arriving migrants
P(c
olon
izat
ion)
in p
atch
i
22
2
yM
MC
i
ii
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6
M= number of migrants
y=1
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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
jij
N
ij
bji pDAM )exp(
Mi= number of migrants
β = per-unit-area migrant production rate
A= patch i area
Scaled by parameter b to allow for nonlinearity
pj= 0 = empty and pj=1 if occupied
α= scaling factor
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Number of migrantsA= area
distance
Num
ber
of m
igra
nts
(M)
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6
A=10
A=20
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The incidence function model
)1( iii
ii CEC
CJ
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
)'
1(
1
2 xii
i
ASe
J
Where e’=ey’ and y’=y/β
jij
N
ij
bji pDAS )exp(
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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
Population Numbers μ σ2 P(ex)
Mowry 70 0.043 0.051 0.06
Faber 29 -0.002 0.041 0.79
Laumeister 33 0 0.051 0.72
Harding et al. 2001
0.06*0.79*0.72=0.034
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Pearson correlation coefficients
Population Mowry Faber
Mowry 1
Faber 0.995 1
Laumiester 0.896 0.938
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The transition matrix
• Determining counts at different sites
nM(t+1)
nF(t+1)
nL(t+1)
=
nM(t)
nF(t)
nL(t)
λMt 0 0
0 λFt 0
0 0 λLt
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The transition matrix
• Determining counts at different sites
nM(t+1)
nF(t+1)
nL(t+1)
=
nM(t)
nF(t)
nL(t)
(1-d)λMt da da
da (1-d)λFt da
da da (1-d)λLt
d=constant probability of an individual dispersing
a=constant probability of an individual arriving
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Effect of correlations
0
0.1
0.2
0.3
0.4
0.5
0.6
1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
Years in the future
Cu
m p
rob
of
(Exti
n)
.
With correlations
Without correlations
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Effect of levels of dispersal
0
0.1
0.2
0.3
0.4
0.5
0.6
1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
Years in the future
Cu
m p
rob
of
(Exti
n)
.
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
0 0 0 f4s4
s1 s2(1-g2) 0 0
0 0 s3g3 s4
0 s2g2 s3(1-g3) 0A=
Seeds
Small juveniles
Large juveniles
Adults
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Vital rates
Site s1 s2 s3 s4 g2 g3 f4
a 0.0173 0.8545 0.9875 0.9692 0.2145 0.1411 33
0.0175 0.0524 0.025 0.0386 0.1304 0.0528 0
b 0.0028 0.6197 0.9645 0.9852 0.1834 0.2466 33
0.0017 0.1924 0.0416 0.0295 0.2135 0.1711 0
c 0.0073 0.767 0.9135 0.9563 0.4376 0.3348 33
0.0057 0.0905 0.0512 0.0361 0.3198 0.071 0
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The multi-site model0 0 0 f4as4a
s1a s2a(1-g2a) 0 0
0 0 s3ag3a s4a
0 s2ag2a s3a(1-g3a) 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 f4bs4b
s1b s2b(1-g2b) 0 0
0 0 s3bg3b s4b
0 s2bg2b s3b(1-g3b) 0
0 0 0 f4c4c
s1c s2c(1-g2c) 0 0
0 0 s3cg3c s4c
0 s2cg2c s3c(1-g3c) 0
G=
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The multi-site model0 0 0 f4as4a(1-m-m)s1a s2a(1-g2a) 0 0
0 0 s3ag3a s4a
0 s2ag2a s3a(1-g3a) 00 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 f4as4a,mBA
0 0 0 0
0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 f4bs4b(1-m-m)
s1b s2b(1-g2b) 0 0
0 0 s3bg3b s4b
0 s2bg2b s3b(1-g3b) 0
0 0 0 f4c4c (1-m-m)s1c s2c(1-g2c) 0 0
0 0 s3cg3c s4c
0 s2cg2c s3c(1-g3c) 0
G=
0 0 0 f4as4a,mcA
0 0 0 f4as4a,mAB
0 0 0 f4as4a,mCB
0 0 0 f4as4a,mAC
0 0 0 f4as4a,mBC