1. Introduction to Occupancy Models Key to in-class exercise are in blue
Jan 8, 2016 AEC 501
Nathan J. Hostetter

2. Occupancy
Abundance often most interesting variable when analyzing a population
Occupancy – probability that a site is occupied
Probability abundance is >0

3. 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

4. Occupancy studies
Introduced by MacKenzie et al and Tyre et al
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

5. 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
Usually less intensive
Cheaper
Can cover a larger area or time frame
Might be more practical for certain objectives

6. Why occupancy? Some common reasons and objectives
Extensive monitoring programs
Distribution (e.g., ranges shifts, invasive species, etc.)
Habitat selection
Meta-population dynamics
Species interactions
Species richness

7. 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

8. Model parameters
Replication allows us to separate state and observation processes
𝜓 𝑖 -probability site i is occupied.
pij -probability of detecting the species in site i at time j, given species is present.

9. 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?

10. Blue grosbeak example N = 41 sites (spatial replication)
K = 3 sample occasions (temporal replication)
Example data:
Site S1 S2 S3 1 2 3 … 41

11. 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

12. Enough talk, Let’s work through the blue grosbeak example

13. Introduction to R Basics and Occupancy modeling

14. Intro to R: Submitting commands
Commands can be entered one at a time 2+2 [1] 4 2^4 [1] 16

15. The R environment Script file (File|New script) R Console Text file
Save for later use
Submit command by highlighting command at pressing “Crtl R”
R Console
Where commands are executed

16. R console: Interactive calculations
#Try the following in the script file: 2+2 a < #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

17. Built in functions
x1 <- c(1,3,5,7) #vector x1 mean(x1) [1] 4 sd(x1) [1] #Help files ?mean

18. 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

19. 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

20. 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?

21. Intro to Occupancy analysis in R
Blue grosbeak example
41 fields were surveyed
Each field visited on 3 occasions during the breeding season
A 500 m transect was surveyed on each field
Data on detection/non-detection

22. Load data
Download and save the blgr.csv file from 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

23. Covariates Site level covariates Observation 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.

24. Occupancy analysis – Unmarked
R package
Fits models of animal abundance and occurrence
Complete description of unmarked at

25. Install Unmarked
install.packages("unmarked") #Only required first time to install library(unmarked) #loads package, required each time

26. 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

27. 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 backTransform(fm1['det']) #Get the estimates for occupancy #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 it accounts for imperfect detection (i.e., detection probability is <1.0).

28. 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 = )
#Get the estimates for detection
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

29. Occupancy in unmarked – Model comparison
#Compare model support using AIC
fitlist<-fitList(fm1, fm2)
modSel(fitlist)
# I added the Occupancy and Detection columns
‘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.
Occupancy
Detection
Name
nPars
AIC
delta
AICwt
cumltvWt ~1
fm1 2
172.19
0.00
0.61
BQI
fm2 3
173.12
0.93
0.39
1.00

30. Summary Occupancy (presence/absence)
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
Quantity to be estimated
Temporal and spatial scope
Precision
Practical constraints

31. 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