Data fusion for ecological studies

Data fusion for ecological studies
Jaime Collazo, Beth Gardner, Dorit Hammerling, Andrea Kostura, David
Miller, Krishna Pacifici, Brian Reich, Susheela Singh, Glenn Stauffer
SAMSI working group
Data fusion for ecological studies
1
Motivation
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Our group focused on developing methods to combine
multiple data sources to estimate species distribution maps.
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These maps are fundamental to ecology, e.g., to study effects
of land use and climate change.
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We apply the methods to jointly model
1. eBirds and SE US breeding-bird survey (BBS) data.
2. eBirds and PA Bird Atlas data.
3. ship and areal surveys of seabirds.
SAMSI working group
Data fusion for ecological studies
2
eBird effort
(c) eBirds sqrt effort
40
40
36
30
20
10
32
−90
SAMSI working group
−80
Data fusion for ecological studies
3
eBird number of observations
(d) ebirds sqrt sample rates
40
3
36
2
1
0
32
−90
SAMSI working group
−80
Data fusion for ecological studies
4
BBS effort
(a) BBS effort
40
150
125
36
100
75
50
32
−90
SAMSI working group
−80
Data fusion for ecological studies
5
BBS sample proportion
(b) BBS sample proportions
40
36
0.2
0.1
0.0
32
−90
SAMSI working group
−80
Data fusion for ecological studies
6
Models
We considered four models:
1. BBS-only
2. Using EB as a covariate to predict BBS
3. Joint model for EB and BBS with shared occupancy
4. Joint model for EB and BBS with multivariate random effects
SAMSI working group
Data fusion for ecological studies
7
Spatial occupancy model for the BBS data
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Let Ni and Yi be the number of sampling occasions and
sightings, respectively, in grid cell i.
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Yi ∼ Binomial(Ni , pi Zi ), where
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Zi = 1 indicates that the species occupies cell i
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Zi = 0 indicates that the species doesn’t occupy cell i.
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pi is the detection probability.
Our objective to estimate Zi in all grid cells.
SAMSI working group
Data fusion for ecological studies
8
Spatial occupancy model for the BBS data
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We use a bivariate spatial model for occupancy and detection.
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Let θ i = (θ0i , θ1i )T be a random effect for site i, with
Zi = I (θ0i > 0) and pi = Φ(θ1i ).
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To model spatial variation in occupancy and detection, and
their relationship use a multivariate CAR model
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Given the random effects at all other sites,
θ i ∼ Normal(ρθ̄ i ,
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I
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1
Σ)
mi
θ̄ i is the mean of θ j over the mi neighboring sites
ρ controls spatial dependence
Σ is the 2 × 2 covariance between occupancy and detection.
SAMSI working group
Data fusion for ecological studies
9
Estimated occupancy (posterior mean of Zi )
(a) Single
40
1.00
0.75
36
0.50
0.25
0.00
32
−90
SAMSI working group
−80
Data fusion for ecological studies
10
Estimated detection (posterior mean of pi )
(a) Single
40
0.20
36
0.15
0.10
0.05
32
−90
SAMSI working group
−80
Data fusion for ecological studies
11
Using EB as a covariate for BBS
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The simplest data fusion method is to use BBS as a covariate
in the prior mean for θ i
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That is, let Xi be an initial estimate of EB abundance or
occupancy at site i.
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E(θji ) = Xi β j .
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We included six constructed covariates.
SAMSI working group
Data fusion for ecological studies
12
Estimated EB abundance (Xi )
eBirds Abundance
40
−0.5
−1.0
36
−1.5
−2.0
32
−90
SAMSI working group
−80
Data fusion for ecological studies
13
Estimated occupancy (posterior mean of Zi )
(b) Covariate
40
1.00
0.75
36
0.50
0.25
0.00
32
−90
SAMSI working group
−80
Data fusion for ecological studies
14
Estimated detection (posterior mean of pi )
(b) Covariate
40
0.20
36
0.15
0.10
0.05
32
−90
SAMSI working group
−80
Data fusion for ecological studies
15
Shared-occupancy model for EB and BBS data
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Let Wi and Ei be the number of sightings and hours of effort
for the EB data in cell i.
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We assume the joint model
Yi ∼ Binomial(Ni , pi Zi ) and Wi ∼ Poisson[Ei (Zi exp(θi2 )+q)].
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Zi = I (θ0i > 0) is the shared occupancy indicator.
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θi2 controls abundance
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q > 0 is the false positive rate
θ i = (θ0i , θ1i , θ2i )T is modeled with an MCAR.
SAMSI working group
Data fusion for ecological studies
16
Estimated occupancy (posterior mean of Zi )
(c) Shared
40
1.00
0.75
36
0.50
0.25
0.00
32
−90
SAMSI working group
−80
Data fusion for ecological studies
17
Correlation model for EB and BBS data
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To be more robust against bias in EB data, we also tried
removing the occupancy indicator from the EB model.
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We assume the joint model
Yi ∼ Binomial(Ni , pi Zi ) and Wi ∼ Poisson[Ei exp(θi2 )].
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θ i = (θ0i , θ1i , θ2i )T is modeled with an MCAR.
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Only the correlation of θ2i and θ0i links the data sources.
SAMSI working group
Data fusion for ecological studies
18
Estimated occupancy (posterior mean of Zi )
(d) Correlation
40
1.00
0.75
36
0.50
0.25
0.00
32
−90
SAMSI working group
−80
Data fusion for ecological studies
19
Model comparisons
Mean squared error and deviance comparing estimates based on
2012 BBS and EB data to the observed 2007-2011 BBS data.
MSE
Deviance
Single
6.43
3714
Covariate
5.98
3692
SAMSI working group
Shared
5.80
3301
Correlation
5.94
3366
Data fusion for ecological studies
20
Application – PA Bird Atlas
breeding bird atlas point counts
Blocks: j = 1, … , J
Points: i = 1, …, I
eBird – block level counts (Wj) and effort (Ej)
Wj ~ Poisson(Ej*λj)
log(λj) = α1 + θ1,j
BBA – number of occasions seen at a point (Yj,i)
p – P(detection|present)
Yj,i ~ binomial(zj,i*p,5)
zj,i ~ Bernouli(ψj)
logit(ψj) = α2 + θ2,j
Θ ~ MCAR
black-throated blue warbler
prairie warbler
Distribution and abundance of seabirds in the
Northwestern mid-Atlantic
Project funded by DOE in preparation for energy development
• Coast off Delaware/Maryland/
Virginia: three Wind Energy
Areas (WEA)
• From April 2012 - April 2014
• Ship board distance sampling
surveys
• 656 km – green lines
• High definition aerial surveys
• 3500 km - red lines
Distance sampling
Observation model
• Detection probability p is declining
function of distance to observer,
𝑝𝑝 = 𝑓𝑓(𝑑𝑑)
• Detection on transect line is perfect
• ‘Half-normal’: 𝑓𝑓 𝑑𝑑 =
𝑑𝑑 2
exp(− 2 )
2𝜎𝜎
Application/Example: Loons
Loons are common in the
study area during the
winter and frequently
observed in both survey
methods.
Loons Boat
996
Aerial
1661