Introduction to Occupancy Models
Key to in-class exercise are in blue
Jan 8, 2016
AEC 501
Nathan J. Hostetter
njhostet@ncsu.edu
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Occupancy
• Abundance often most interesting variable when
analyzing a population
• Occupancy – probability that a site is occupied
• Probability abundance is >0
Detection/non-detection data
• Presence data rise from a two part process
• The species occurs in the region of interest
AND
• The species is discovered by an investigator
• What do absence data tell us?
• The species does not occur at that particular site
OR
• The species was not detected by the investigator
Occupancy studies
• Introduced by MacKenzie et al. 2002 and Tyre et al.
2003
• Allows for collection of data that is less intensive than
those based on abundance estimation
• Use a designed survey method like we discussed
before – simple random, stratified random, systematic,
or double
• Multiple site visits are required to estimate detection
and probability of occurrence
Why occupancy?
• Data to estimate abundance can be difficult to
collect, require more time and effort, might be more
limited in spatial/temporal scope
• Obtaining presence/absence data is
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Usually less intensive
Cheaper
Can cover a larger area or time frame
Might be more practical for certain objectives
Why occupancy?
• Some common reasons and objectives
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Extensive monitoring programs
Distribution (e.g., ranges shifts, invasive species, etc.)
Habitat selection
Meta-population dynamics
Species interactions
Species richness
Occupancy studies
• Key design issues: Replication
• Temporal replication:
• repeat visits to sample units
• Spatial replication:
• randomly selected ‘sites’ or sample units within area of
interest
Model parameters
• Replication allows us to separate state and
observation processes
𝜓𝑖 -probability site i is occupied.
pij -probability of detecting the species in site i at time j,
given species is present.
Blue grosbeak example
• Associated with shrub and field habitats, medium sized trees,
and edges
• Voluntary program to restore high-quality early successional
habitat in Southern Georgia (BQI – bobwhite quail initiative)
• Are grosbeaks more likely to use fields enrolled in BQI program?
Blue grosbeak example
• N = 41 sites (spatial replication)
• K = 3 sample occasions (temporal replication)
• Example data:
Site S1 S2 S3
1
1 1 1
2
1 1 0
3
0 0 0
…
… … …
41
0 1 0
Model assumptions
• Sites are closed to changes in occupancy state between sampling
occasions
• Duration between surveys
• The detection process is independent at each site
• Distance between sites
• Probability of detection is constant across sites and visits or
explained by covariates
• Probability of occupancy is constant across sites or explained by
covariates
Enough talk,
Let’s work through the blue grosbeak example
Introduction to R
Basics and
Occupancy modeling
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Intro to R:
Submitting commands
Commands can be entered one at a time
2+2
[1] 4
2^4
[1] 16
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The R environment
• Script file (File|New script)
• R Console
•Where commands are executed
• Text file
• Save for later use
• Submit command by highlighting
command at pressing “Crtl R”
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R console: Interactive calculations
#Try the following in the script file:
2+2
a <- 2 + 2
#create the object a
a
#returns object a
A
#Nope, case sensitive
b<-2*3
b
a+b
#Use the +, -, *, /, and ^ symbols
# Use “#” to enter comments
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Built in functions
x1 <- c(1,3,5,7)
x1
mean(x1)
[1] 4
sd(x1)
[1] 2.581989
#vector
#Help files
?mean
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Loading and storing data sets
Comma separated variable (CSV)
• Create a CSV file in excel by clicking “save as” and scrolling to “.csv”.
CSV files can be opened in excel, but also in any other text editor.
• Say “C:\Documents\data.csv” is an .csv file. To load a csv file:
dat <- read.csv(“C:\\Documents\\data.csv",header=TRUE)
dat
• ?read.csv
#for further help
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Saving work
• Save your current session in an R workspace as
save.image(“C:\\Documents\\whatever.RData")
• Load a previously saved workspace
File|Load workspace
• Save script file
• Click on script file
• File|Save
Check out Brian Reich’s intro to R at
http://www4.stat.ncsu.edu/~reich/ST590/code/Data
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Intro to Occupancy analysis in R
Blue grosbeak example
• Associated with shrub and field habitats, medium sized trees,
and edges
• Voluntary program to restore high-quality early successional
habitat in Southern Georgia (BQI – bobwhite quail initiative)
• Are grosbeaks more likely to use fields enrolled in BQI program?
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Intro to Occupancy analysis in R
Blue grosbeak example
• 41 fields were surveyed
• Each field visited on 3 occasions during the 2001
breeding season
• A 500 m transect was surveyed on each field
• Data on detection/non-detection
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Load data
Download and save the blgr.csv file from https://www.cals.ncsu.edu/course/zo501/
Use “save link as…”
Open the file and make sure you understand the data
Load blgr.csv (see example on slide 18)
blgr<- read.csv("C:\\My Documents\\blgr.csv", header=TRUE)
head(blgr)
#first 5 rows
#y.1, y.2, y.3 are detection/non-detection surveys
dim(blgr)
#dimensions of the data (how many sites?)
41 sites; there are 41 rows and each row is a site
colSums(blgr)
#sums the columns
#how many fields were enrolled in bqi? 14
#how many fields had blgr detections in during first survey? 18
#what is the naïve occupancy if only the first survey was conducted? 18/41 = 0.44
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Covariates
• Site level covariates
• Data that is site specific but does not change with repeated visits
• e.g., forest cover, percent urban, tree height, on/off road, etc.
• Observation level covariates
• Data that is collected specific to the sample occasion and site
• e.g., time of day, day of year, wind, etc.
What type of covariate is bqi? bqi is a site level covariate. bqi varies
by site, but does not change during repeated visits.
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Occupancy analysis – Unmarked
• Unmarked
• R package
• Fits models of animal abundance and occurrence
• Complete description of unmarked at
https://cran.r-project.org/web/packages/unmarked/unmarked.pdf
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Install Unmarked
install.packages("unmarked") #Only required first time to install
library(unmarked)
#loads package, required each time
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Format data for occupancy analysis in unmarked
Square brackets can be used to select columns
You need to create a file of the observations
ydat <- blgr[,1:3]
#select columns 1 through 3, detection data
Covariates can be separated here or in the unmarkedFrameOccu later
bqi <- blgr[,4]
#select column 4, bqi enrollment
#use built in function to format data
umf <- unmarkedFrameOccu(y=ydat, #Observation data must be named ‘y’
siteCovs=data.frame(bqi=bqi))
#name site covariate bqi
umf
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Occupancy in unmarked
#run occupancy model with no covariates
# occu(~detection ~occupancy)
# ~1 means constant. Here Detection and Occupancy are constant
fm1 <- occu(~ 1 ~ 1, umf )
fm1 #look at the output
#Get the estimates for detection 0.551
backTransform(fm1['det'])
#Get the estimates for occupancy 0.885
#remember, occupancy is our ‘state variable’
backTransform(fm1['state'])
#higher or lower than naïve occupancy? Why? The occupancy
probability (0.885) is higher than naïve occupancy (0.44) because 27it
accounts for imperfect detection (i.e., detection probability is <1.0).
Occupancy in unmarked - Covariates
#effect of bqi
# occu(~detection ~occupancy)
fm2 <- occu(~ 1 ~ bqi, umf )
#Detection is constant and occupancy varies by bqi
fm2
#look at the output
#interpret bqi parameter – BQI was associated with a decrease
in occupancy probability (estimate = -1.39), but it was not significant
(p = 0.3690)
#Get the estimates for detection 0.551
backTransform(fm2['det'])
#Get the estimates for occupancy
backTransform(fm2['state'])
#Nope, backTransform is a bit more complicated when covariates are used.
#see ?backTransform for options if interested
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Occupancy in unmarked – Model comparison
#Compare model support using AIC
fitlist<-fitList(fm1, fm2)
modSel(fitlist)
# I added the Occupancy and Detection columns
Occupancy Detection Name nPars AIC
delta AICwt cumltvWt
~1
~1
172.19 0.00 0.61
0.61
fm1
2
BQI
~1
3
173.12 0.93 0.39
1.00
fm2
• ‘unmarked’ has a built in function to compare models using AIC.
Here is a summary of the default table:
• “nPars” – Number of parameters in the model
• “AIC” – Models with lower AIC have more support.
• “delta” – the AIC difference between each model and the top model.
• AICwt – “Model weight” - the probability that the model is the top model
• cumltvWt – cumulative model weights.
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Summary
• Occupancy (presence/absence)
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Usually less intensive to collect
Often less expensive
Can cover a larger area or time frame
Several important fields in ecology focus on occupancy
Might be more practical for monitoring
• True census is often (always) impossible
• Must account for detection probability
• Requires clear objectives
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Quantity to be estimated
Temporal and spatial scope
Precision
Practical constraints
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EXTRA – Format observation covariates in unmarked
This is a general approach for formatting detections, site covariates, and observation
covariates.
#the file is named data
#observations are ydat
#habitat is a site level covariate in a column named ‘habitat’
#date is an observation level covariate, it was recorded during each survey
#date columns are named: date.1, date.2, date.3
#use unmarkedFrameOccu () to format data
umf <- unmarkedFrameOccu(y=ydat,
#Observation data must be named ‘y’
siteCovs=data.frame(habitat=data$habitat),
#name site covariate habitat
obsCovs=list(date=data[,c("date.1", "date.2", "date.3")])) #name date covariate date
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