Data fusion for ecological studies

Transcription

1 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

2 Motivation Our group focused on developing methods to combine multiple data sources to estimate species distribution maps. These maps are fundamental to ecology, e.g., to study effects of land use and climate change. 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

3 ebird effort (c) ebirds sqrt effort SAMSI working group Data fusion for ecological studies 3

4 ebird number of observations (d) ebirds sqrt sample rates SAMSI working group Data fusion for ecological studies 4

5 BBS effort (a) BBS effort SAMSI working group Data fusion for ecological studies 5

6 BBS sample proportion (b) BBS sample proportions SAMSI working group Data fusion for ecological studies 6

7 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

8 Spatial occupancy model for the BBS data Let N i and Y i be the number of sampling occasions and sightings, respectively, in grid cell i. Y i Binomial(N i, p i Z i ), where Z i = 1 indicates that the species occupies cell i Z i = 0 indicates that the species doesn t occupy cell i. pi is the detection probability. Our objective to estimate Z i in all grid cells. SAMSI working group Data fusion for ecological studies 8

9 Spatial occupancy model for the BBS data We use a bivariate spatial model for occupancy and detection. Let θ i = (θ 0i, θ 1i ) T be a random effect for site i, with Z i = I (θ 0i > 0) and p i = Φ(θ 1i ). To model spatial variation in occupancy and detection, and their relationship use a multivariate CAR model Given the random effects at all other sites, θ i Normal(ρ θ i, 1 m i Σ) θi is the mean of θ j over the m i 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

10 Estimated occupancy (posterior mean of Z i ) (a) Single SAMSI working group Data fusion for ecological studies 10

11 Estimated detection (posterior mean of p i ) (a) Single SAMSI working group Data fusion for ecological studies 11

12 Using EB as a covariate for BBS The simplest data fusion method is to use BBS as a covariate in the prior mean for θ i That is, let X i be an initial estimate of EB abundance or occupancy at site i. E(θ ji ) = X i β j. We included six constructed covariates. SAMSI working group Data fusion for ecological studies 12

13 Estimated EB abundance (X i ) ebirds Abundance SAMSI working group Data fusion for ecological studies 13

14 Estimated occupancy (posterior mean of Z i ) (b) Covariate SAMSI working group Data fusion for ecological studies 14

15 Estimated detection (posterior mean of p i ) (b) Covariate SAMSI working group Data fusion for ecological studies 15

16 Shared-occupancy model for EB and BBS data Let W i and E i be the number of sightings and hours of effort for the EB data in cell i. We assume the joint model Y i Binomial(N i, p i Z i ) and W i Poisson[E i (Z i exp(θ i2 )+q)]. Z i = I (θ 0i > 0) is the shared occupancy indicator. θ i2 controls abundance q > 0 is the false positive rate θ i = (θ 0i, θ 1i, θ 2i ) T is modeled with an MCAR. SAMSI working group Data fusion for ecological studies 16

17 Estimated occupancy (posterior mean of Z i ) (c) Shared SAMSI working group Data fusion for ecological studies 17

18 Correlation model for EB and BBS data To be more robust against bias in EB data, we also tried removing the occupancy indicator from the EB model. We assume the joint model Y i Binomial(N i, p i Z i ) and W i Poisson[E i exp(θ i2 )]. θ i = (θ 0i, θ 1i, θ 2i ) T is modeled with an MCAR. Only the correlation of θ 2i and θ 0i links the data sources. SAMSI working group Data fusion for ecological studies 18

19 Estimated occupancy (posterior mean of Z i ) (d) Correlation SAMSI working group Data fusion for ecological studies 19

20 Model comparisons Mean squared error and deviance comparing estimates based on 2012 BBS and EB data to the observed BBS data. Single Covariate Shared Correlation MSE Deviance SAMSI working group Data fusion for ecological studies 20

21 Application PA Bird Atlas

22 breeding bird atlas point counts

23 Blocks: j = 1,, J Points: i = 1,, I ebird block level counts (W j ) and effort (E j ) W j ~ Poisson(E j* λ j ) log(λ j ) = α 1 + θ 1,j BBA number of occasions seen at a point (Y j,i ) p P(detection present) Y j,i ~ binomial(z j,i *p,5) z j,i ~ Bernouli(ψ j ) logit(ψ j ) = α 2 + θ 2,j Θ ~ MCAR

24 black-throated blue warbler

25 prairie warbler

26 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 April 2014 Ship board distance sampling surveys 656 km green lines High definition aerial surveys 3500 km - red lines

27 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 = exp( dd2 2σσ 2)

28 Application/Example: Loons Loons are common in the study area during the winter and frequently observed in both survey methods. Loons Boat Aerial

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