2014 isec slides
TRANSCRIPT
Spatial occupancy models for
metapopulation viability
analysis
Richard Chandler, Erin Muths, Brent Sigafus, Cecil Schwalbe,
Christopher Jarchow, and Blake Hossack
Motivating questions
(1) What is extinction risk over the next 100
years?
(2) How do hydrology and connectivity a�ect
extinction risk?
(3) What is the best strategy for increasing
viability?
Chandler et al. � Spatial occupancy models 3 / 13
Motivating questions
(1) What is extinction risk over the next 100
years?
(2) How do hydrology and connectivity a�ect
extinction risk?
(3) What is the best strategy for increasing
viability?
Chandler et al. � Spatial occupancy models 3 / 13
Motivating questions
(1) What is extinction risk over the next 100
years?
(2) How do hydrology and connectivity a�ect
extinction risk?
(3) What is the best strategy for increasing
viability?
Chandler et al. � Spatial occupancy models 3 / 13
Motivating data
Year
2007 2008 . . . 2013
Site 1 2 3 1 2 3 . . . 1 2 3
1 0 1 1 0 0 0 . . . 1 0 1
2 0 0 0 0 0 0 . . . 0 0 0
3 � � � 1 1 0 . . . 0 0 1...
......
......
......
......
......
41 0 1 1 0 1 0 . . . 0 0 0
42 � � � � � � . . . � � �...
......
......
......
......
......
273 � � � � � � . . . � � �
Plus, coordinates and covariates for each site
Chandler et al. � Spatial occupancy models 4 / 13
Motivating data
Year
2007 2008 . . . 2013
Site 1 2 3 1 2 3 . . . 1 2 3
1 0 1 1 0 0 0 . . . 1 0 1
2 0 0 0 0 0 0 . . . 0 0 0
3 � � � 1 1 0 . . . 0 0 1...
......
......
......
......
......
41 0 1 1 0 1 0 . . . 0 0 0
42 � � � � � � . . . � � �...
......
......
......
......
......
273 � � � � � � . . . � � �
Plus, coordinates and covariates for each site
Chandler et al. � Spatial occupancy models 4 / 13
Motivating data
Year
2007 2008 . . . 2013
Site 1 2 3 1 2 3 . . . 1 2 3
1 0 1 1 0 0 0 . . . 1 0 1
2 0 0 0 0 0 0 . . . 0 0 0
3 � � � 1 1 0 . . . 0 0 1...
......
......
......
......
......
41 0 1 1 0 1 0 . . . 0 0 0
42 � � � � � � . . . � � �...
......
......
......
......
......
273 � � � � � � . . . � � �
Plus, coordinates and covariates for each site
Chandler et al. � Spatial occupancy models 4 / 13
Metapopulation theory
Basic elements
• Dispersal-based colonization function
• Rescue e�ect• Correlated extinction
Missing elements
• Observation model
MacKenzie et al. (2003) occupancy modelsprovided the latter, but not the former
Chandler et al. � Spatial occupancy models 5 / 13
Metapopulation theory
Basic elements
• Dispersal-based colonization function
• Rescue e�ect• Correlated extinction
Missing elements
• Observation model
MacKenzie et al. (2003) occupancy modelsprovided the latter, but not the former
Chandler et al. � Spatial occupancy models 5 / 13
Metapopulation theory
Basic elements
• Dispersal-based colonization function
• Rescue e�ect• Correlated extinction
Missing elements
• Observation model
MacKenzie et al. (2003) occupancy modelsprovided the latter, but not the former
Chandler et al. � Spatial occupancy models 5 / 13
Standard dynamic occupancy model
Initial occupancy
zi,1 ∼ Bern(ψ)
Colonization and extinction
zi,k ∼ Bern(µi,k)
µi,k = (1− zi,k)γ + zi,k(1− ε)
Detection
yi,j,k ∼ Bern(zi,k × p)
Useful, but doesn't allow formetapopulation extinction
Chandler et al. � Spatial occupancy models 6 / 13
Standard dynamic occupancy model
Initial occupancy
zi,1 ∼ Bern(ψ)
Colonization and extinction
zi,k ∼ Bern(µi,k)
µi,k = (1− zi,k)γ + zi,k(1− ε)
Detection
yi,j,k ∼ Bern(zi,k × p)
Useful, but doesn't allow formetapopulation extinction
Chandler et al. � Spatial occupancy models 6 / 13
A spatial occupancy model
Probability that site i is colonized by ≥ 1 individual from site m
γ(xi,xm) = γ0 exp(−‖xi − xm‖2/(2σ2))zm,k−1
Probability that site i is colonized by ≥ 1 individual from any site
γi,k−1 = 1−
{M∏
m=1
1− γ(xi,xm)
}Hence:
• Metapopulation extinction is possible
• Useful for PVA, connectivity planning
Chandler et al. � Spatial occupancy models 7 / 13
A spatial occupancy model
Probability that site i is colonized by ≥ 1 individual from site m
γ(xi,xm) = γ0 exp(−‖xi − xm‖2/(2σ2))zm,k−1
Probability that site i is colonized by ≥ 1 individual from any site
γi,k−1 = 1−
{M∏
m=1
1− γ(xi,xm)
}
Hence:
• Metapopulation extinction is possible
• Useful for PVA, connectivity planning
Chandler et al. � Spatial occupancy models 7 / 13
A spatial occupancy model
Probability that site i is colonized by ≥ 1 individual from site m
γ(xi,xm) = γ0 exp(−‖xi − xm‖2/(2σ2))zm,k−1
Probability that site i is colonized by ≥ 1 individual from any site
γi,k−1 = 1−
{M∏
m=1
1− γ(xi,xm)
}Hence:
• Metapopulation extinction is possible
• Useful for PVA, connectivity planning
Chandler et al. � Spatial occupancy models 7 / 13
Results � Local extinction and hydroperiod
●
●
●
0.0
0.2
0.4
0.6
0.8
1.0
Loca
l ext
inct
ion
prob
abili
ty (
ε)
Intermittent Semi−permanent Permanent
Chandler et al. � Spatial occupancy models 8 / 13
Results � Colonization and connectivity
2008 2009 2010
2011 2012 2013
2014 2015 2016
2017 2018 2019
2020 2021 2022
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Chandler et al. � Spatial occupancy models 9 / 13
Results � Colonization and connectivity
2008 2009 2010
2011 2012 2013
2014 2015 2016
2017 2018 2019
2020 2021 2022
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Chandler et al. � Spatial occupancy models 9 / 13
Results � Proportion of sites occupied
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2010 2015 2020
0.0
0.2
0.4
0.6
0.8
1.0
Year
Pro
port
ion
of s
ites
occu
pied
2020 2040 2060 2080 21000.
00.
10.
20.
30.
40.
50.
6
Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 10 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10 km
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Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
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0.15
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0.25
0.30
0.35
10 km
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Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10 km
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Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
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10 km
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2020 2040 2060 2080 2100
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Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10 km
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2020 2040 2060 2080 2100
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Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10 km
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2020 2040 2060 2080 2100
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0.6
Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10 km
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2020 2040 2060 2080 2100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10 km
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2020 2040 2060 2080 2100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Extinction risk after new reintroductions
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10 km
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2020 2040 2060 2080 2100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Year
Ext
inct
ion
risk
Chandler et al. � Spatial occupancy models 11 / 13
Future directions
• Abundance-based formulation
• Landscape resistance to movement
• Undiscovered sites
Chandler et al. � Spatial occupancy models 12 / 13
Future directions
• Abundance-based formulation
• Landscape resistance to movement
• Undiscovered sites
Chandler et al. � Spatial occupancy models 12 / 13
Future directions
• Abundance-based formulation
• Landscape resistance to movement
• Undiscovered sites
Chandler et al. � Spatial occupancy models 12 / 13