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Landscape effects on mallard habitat selection at multiple spatial scales during the nonbreeding period
William S. Beatty, Elisabeth B. Webb, Dylan C. Kesler, Andrew H. Raedeke, Luke W.
Naylor, Dale D. Humburg
Supplementary Material
Appendix 1
Mean season dates according to year assigned to birds (n =14) that did not meet criteria for
inclusion in migration analyses (Beatty et al. 2013):
Autumn migration 2010: 5 November – 24 November
Winter 2010-2011: 25 November – 6 March
Spring migration 2011: 7 March – 24 April
Autumn migration 2011: 25 October – 4 December
Winter 2011-2012: 5 December – 26 February
Spring migration 2012: 27 February – 15 April
Appendix 2
Multinomial logit hierarchical model in WinBUGS to examine habitat selection of midcontinent
models called using R2WinBUGS. Although this program has been used by the U.S. Geological
Survey (USGS), no warranty, expressed or implied, is made by the USGS or the U.S.
Government as to the accuracy and functioning of the program and related program material nor
shall the fact of distribution constitute any such warranty, and no responsibility is assumed by the
USGS in connection therewith.
Data were initially in long format where one row represents one alternative. Thus, each
choice set contains as many rows as there are alternatives.
Variables:
T = the total number of rows in the data sheet, equal to the number of alternatives within
each choice set × the number of choice sets.
chsets = indexes choice sets in long format, ranges from 1 to the total sample size.
alts = indexes alternatives in long format within a choice set, ranges from 1 to 20 for local
scale, 1 to 25 for relocation scale.
use = use in long format, 0 for available resource units, 1 for used resource units.
nchsets = the number of choice sets, equal to the total sample size.
nalts = the number of alternatives within a choice set, equal to 20 at the local scale, 25 at
relocation scale.
ninds = the number of unique individuals.
water.dist = distance to the nearest water feature, centered and standardized.
water.ha = water area in 3.46 km buffer, centered and standardized.
X = a matrix of habitat covariates in long format.
npred = the number of predictors, equal to the number of columns for matrix X.
DuckID = indexes individual ducks in long format, ranges from 1 to ninds.
2
duckid2 = indexes individual ducks in wide format, ranges from 1 to ninds.
R script to import data to WinBUGS:
data <- as.data.frame(read.csv("data.csv", header=T))
T <- nrow(data)
chsets <- data$ChoiceSet
alts <- data$Alt
use <- data$Use
nchsets <- max(data$ChoiceSet)
nalts <- max(data$Alt)
ninds <- max(data$DuckID)
water.dist <- data$WaterDist
water.ha <- data$WaterHa
X = cbind(water.dist, water.ha)
npred <- ncol(X)
duckid2 <- subset(data, Use==1)$DuckID
win.data <- list(npred=as.integer(npred),
duckid2=as.integer(duckid2),
ninds=as.integer(ninds),
chsets=as.integer(chsets),
nchsets=as.integer(nchsets),
alts=as.integer(alts),
nalts=as.integer(nalts),
use=as.numeric(use),
T=as.integer(T),
X=X)
WinBUGS model:
model {
## Loops to transcribe Y and X matrices to wide format.
for (i in 1:T) {
y[chsets[i],alts[i]] <- use[i]
for (j in 1:npred) {Z[j,chsets[i],alts[i]] <- X[i,j]}
}
## Priors
for (a in 1:ninds){
for (j in 1:npred) {
beta[a,j] ~ dnorm(mu[j], tau[j])
}
}
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## Hyperparameters
for (j in 1:npred){
mu[j] ~ dnorm (0,0.01)
tau[j] <- 1/(sig[j]*sig[j])
sig[j] ~ dunif(0,100)
}
## Likelihood
for (i in 1:nchsets) {
y[i,1:nalts] ~ dmulti(p[i,1:nalts], 1)
for (k in 1:nalts) {
log(phi[i,k]) <- inprod2(beta[duckid[i],],Z[,i,k])
p[i,k] <- phi[i,k] / sum(phi[i,1:nalts])
}
}
}
Appendix 3
GPS fixes were obtained at specific hours of the day (CST): 00:00 (midnight), 01:00, 09:00,
10:00, 15:00, 16:00, 19:00, 20:00. We classified locations obtained at 00:00, 01:00, 19:00, and
20:00 as nocturnal locations whereas locations obtained at 09:00, 10:00, 15:00, and 16:00 were
classified as diurnal locations.
Appendix 4
Set of candidate models to evaluate alternative hypotheses regarding mallard habitat selection:
1.
A null model that assumed the probability of use for all alternatives was equal
to random expectations (1/20 for the local scale, 1/25 for the relocation scale).
2.
A general model that included proximity to wetland habitat (WetPrx). This
model would be appropriate if ducks did not exhibit selection for specific types
of wetland habitats and landscape composition did not play a prominent role in
habitat selection. Additionally, if model 1 or model 2 were consistently topranked, this would indicate that geospatial data (NLCD 2006) were not
adequate to predict habitat selection.
3.
A general landscape composition model that included proximity to wetland
habitat (WetPrx) and wetland habitat area (WetAr). This model would be
appropriate if ducks did not exhibit selection for specific types of wetlands yet
landscape composition influenced habitat selection.
4.
A local model that included proximity to cultivated crops (CrpPrx), proximity
to emergent herbaceous wetland (EmgPrx), proximity to open water (OwtrPrx)
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5.
and proximity to woody wetlands (WodyPrx). This model would be
appropriate if ducks selected resource units based on local variables.
A full model that included CrpPrx, EmgPrx, OwtrPrx, WodyPrx, cultivated
crop area (CrpAr), emergent herbaceous wetlands area (EmgAr), open water
area (OwtrAr), and woody wetlands area (WodyAr). The full model would be
appropriate if ducks selected resources units based on local variables and
potential to provide opportunities for foraging and roosting at relatively broad
spatial scales.
Appendix 5
Table S1. Candidate models and associated Markov Chain Monte Carlo (MCMC) settings to
examine midcontinent mallard habitat selection during autumn migration, winter, and spring
migration from 2010–2012.
Model
1
Iterations
Burnin
100,000
100,000
100,000
Thinning
1,000
1,000
4,000
Chains
3
3
3
Null
WetPrx
1,100,000
WetPrx + WetAr
1,100,000
CrpPrx + EmgPrx + OwtrPrx + WodyPrx
4,100,000
CrpPrx + EmgPrx + OwtrPrx + WodyPrx +
CrpAr + EmgAr + OwtrAr + WodyAr2
4,100,000
100,000 4,000
3
1
Null model assumed probability of use equal to random expectations.
2
Local scale, spring day iterations = 8,000,000; burnin = 4,000,000; thinning = 4,000; chains = 3.
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Table S2. Delta deviance information criterion (DIC) for models that examined habitat selection of midcontinent mallards from
2010–2012 at the local scale (0.25–30.00 km movements) during the non-breeding period of the life cycle.
Model
CrpPrx + EmgPrx + OwtrPrx + WodyPrx +
CrpAr + EmgAr + OwtrAr + WodyAr
CrpPrx + EmgPrx + OwtrPrx + WodyPrx
WetPrx + WetAr
WetPrx
Null
Fall Migration
Winter
Diurnal Nocturnal Diurnal
0.00
55.57
208.73
221.03
604.67
0.00
74.20
182.80
184.80
486.92
0.00
1215.78
1879.10
2354.50
3606.16
Spring Migration
Nocturnal Diurnal Nocturnal
0.00
940.22
1689.23
1934.13
3096.03
0.00
516.62
803.21
1093.01
1758.01
0.00
501.98
854.35
1141.35
2062.25
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Table S3. Delta deviance information criterion (DIC) for models that examined habitat
selection of midcontinent mallards from 2010–2012 at the relocation scale (>30.00 km
movements) during the non-breeding period of the life cycle.
Model
Relocation
WetPrx + WetAr
0.00
CrpPrx + EmgPrx + OwtrPrx + WodyPrx +
CrpAr + EmgAr + OwtrAr + WodyAr
6.52
WetPrx
12.20
CrpPrx + EmgPrx + OwtrPrx + WodyPrx
12.94
Null
128.20