### Sampling and Occupancy Estimation

Krishna Pacifici
Department of Applied Ecology
NCSU
January 10, 2014
Designing studies
 Why, what, and how?
 Why collect the data?
 What type of data to collect?
 How should the data be collected in the field and then
analyzed?
 Clear objectives help relate all three components.
Why?
Clear objectives
 How will the data be used to discriminate between
 How the data will be used to make management
decisions?
 For example:
 Determine overall level of occupancy for a species in
particular region.
 Compare the level of occupancy in two different habitat
types within that region.
What?
Many kinds of data
 Population-level
 Population size/density
 Survival
 Immigration & emigration
 Presence/absence
 Community-level
 Persistence
 Colonization & extinction
 Species richness/diversity
How?
Sampling and Modeling
 Interest lies in making inference from a sample to a
population
 Statistics!
 Want it to be repeatable and accurate
 Others should understand what you have done and be
able to replicate
 Many different modeling/analysis approaches
 Distance sampling, multiple observer, capturerecapture, occupancy modeling…
PURPOSES OF SAMPLING
 ESTIMATE ATTRIBUTES (PARAMETERS)
 Abundance/ density
 Survival
 Occurrence probability
 ALLOW LEGITIMATE EXTRAPOLATION FROM
DATA TO POPULATIONS
 PROVIDE MEASURES OF STATISTICAL
RELIABILITY
SAMPLING NEEDS TO BE
 ACCURATE– LEADING TO UNBIASED ESTIMATES
 REPEATABLE– ESTIMATES LEAD TO SIMILAR
 EFFICIENT– DO NOT WASTE RESOURCES
BIAS
 HOW GOOD “ON AVERAGE” AN ESTIMATE IS
 CANNOT TELL FROM A SINGLE SAMPLE
 DEPENDS ON SAMPLING DESIGN, ESTIMATOR,
AND ASSUMPTIONS
UNBIASED
TRUE VALUE
SAMPLE
ESTIMATE
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AVERAGE ESTIMATE
BIASED
TRUE VALUE
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SAMPLE
ESTIMATE
*
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BIAS
AVERAGE ESTIMATE
REPEATABLE (PRECISE)
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* *
**
SAMPLE
ESTIMATE
NOT REPEATABLE (IMPRECISE)
*
*
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*
*
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*
SAMPLE
ESTIMATE
CAN BE IMPRECISE BUT UNBIASED..
OR
*
AVERAGE ESTIMATE
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*
*
*
*
*
*
TRUE VALUE
SAMPLE
ESTIMATE
PRECISELY BIASED..OR
TRUE VALUE
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* *
SAMPLE
ESTIMATE
AVERAGE ESTIMATE
IMPRECISE AND BIASED!
AVERAGE ESTIMATE
*
*
*
SAMPLE
ESTIMATE
*
*
*
*
TRUE VALUE
*
ACCURATE=UNBIASED & PRECISE
TRUE VALUE
SAMPLE
ESTIMATE
*
* * *
* *
**
AVERAGE ESTIMATE
HOW DO WE MAKE ESTIMATES
ACCURATE ?
 KEEP BIAS LOW
POPULATION
 ACCOUNT FOR DETECTION
 KEEP VARIANCE LOW
 STRATIFICATION, RECORDING OF COVARIATES,
BLOCKING
Key Issues
 Spatial sampling
 Proper consideration and incorporation of
detectability
Sampling principles
 What is the objective?
 What is the target population?
 What are the appropriate sampling units?
 Size, shape, placement
 Quantities measured
Remember
 Field sampling must be representative of the
population of inference
 Incomplete detection MUST be accounted for in
sampling and estimation
What is the objective?
 Unbiased estimate of population density of snakes
(e.g., cobras) on Corbett National Park
 Coefficient of variation of estimate < 20%
 As cost efficient as possible
What is the target population?
Population in the NP
What are the appropriate sampling
units?
 Point samples?
 Line transects?
Sampling units- nonrandom
placement
Nonrandom placement
 Easy to lay out
 More convenient to sample
 Do not represent other (off road) habitats
 Road may attract (or repel) snakes
OR- redefine the target:
Sampling units- random placement
Random placement
 Valid statistical design
 Represents study area
 Replication allows variance estimation
 May be logistically difficult
 Harder to lay out
 May not work well in heterogeneous study areas
Stratified sampling
Stratified sampling
 Controls for heterogeneous study area
 Allows estimation of density by strata
 More precise estimate of overall density
 More complex design
 May require larger total sample
Single, unreplicated line
Are these hard “rules” –NO!
 Some violations of assumptions can be OK – and even
necessary (idea of “robustness”)
 These are ideals to strive toward
 Good if you can achieve them
 If you can’t, you can’t– but study results may need
different interpretation
Estimation: from Count Data to
Population (I)
 Geographic variation (can’t look everywhere)
 Frequently counts/observations cannot be conducted
over entire area of interest
 Proper inference requires a spatial sampling design that
permits inference about entire area, based on a sample
A valid sampling design
 Allows valid probability inference about the
population
 Statistical model
 Allows estimates of precision
 Replication, independence
Other Spatial Sampling Designs
 Systematic sampling
 Can approximate random sampling in some cases
 Cluster sampling
 When the biological units come in clusters
 Double sampling
 Very useful for detection calibration
 More efficient when populations are distributed
“clumpily”
 Dual-frame sampling
Estimation: from Count to
Population (II)
 Detectability (can’t see everything in places where you
do look)
 Counts represent some unknown fraction of animals in
sampled area
 Proper inference requires information on detection
probability
Sampling Take Home Messages
 Field sampling must be designed to meet study or
conservation objectives
 Field sampling must be representative of the
population of inference
 Incomplete detection MUST be accounted for in
sampling and estimation
Occupancy Estimation
 Species status = present or absent
 Coarse measure of population status
 Proportion of occupied patches
 Data can be collected efficiently over large spatial and
temporal extents
 Species and community-level dynamics
Occupancy Estimation: Uses
 Surveys of geographic range
 Habitat relationships
 Metapopulation dynamics
 Observed colonization and extinction
 Extensive monitoring programs: 'trends' or changes in
occupancy over time
Species Occurrence
 Conduct “presence-absence” (detection-nondetection)
surveys.
 Estimate what fraction of sites (or area) is occupied by
a species when species is not always detected with
certainty, even when present (p < 1).
 ‘Site’: Arbitrarily defined spatial unit (forest patch of a
specified size) or discrete naturally occurring sampling
units (ponds).
Site occupancy: A solution
 MacKenzie et al. 2002 (Ecology)
 Key design issues: Replication
 Temporal replication: repeat visits to sample units

Replicate visits occur within a relatively short period of time
(e.g., a breeding season)
 Spatial replication: randomly selected ‘sites’ or sample
units within area of interest
Basic Sampling Scheme:
Single Season
 s sites are surveyed, each at k distinct sampling
occasions.
 Species is detected/not detected at each occasion.
Necessary information:
Data summary → Detection histories
 Detection history: Record for each visited site or
sample unit
 1 denotes detection
 0 denotes nondetection
 Example detection history: hi = 1 0 0 1 0
 Denotes 5 visits to the site
 Target species detected during visits 1 and 4
 0 does not necessarily mean the species was absent

Not detected, but could be there!
Model Parameters: Single-Season
Models
-probability site i is occupied.
pij -probability of detecting the species in
site i at time j, given species is
present.
Model assumptions
• Sites are closed to changes in occupancy
state between sampling occasions
• No heterogeneity that cannot be explained
by covariates
• The detection process is independent at
each site
• > 500 meters apart
Timing of repeated surveys
 Usually conducted as multiple discrete visits (e.g., on
different days)
 Can also use multiple surveys within a single visit
 Multiple independent observers
 Potentially introduce heterogeneity into data

Single visit to each site vs. multiple visits to each site
 Rotate observers amongst sites on each day
 Rotate order each site is sampled within a day
Designing occupancy surveys
 Several important issues to consider:
1. Clear objectives that are explicitly linked to science or
management
2. Selection of sampling units


Probabilistic sampling design
Size of unit relative to species of interest
Timing of repeat surveys
3.

“closed”
 Relaxed for lab project
Allocation of survey effort
4.

Survey all of the sites equal number of times?
Getting To Know
PRESENCE
 PRESENCE is software that has been developed to
apply these models to collected data.
 Within PRESENCE you can fit multiple models to your
data.
 PRESENCE stores the results from each model and
presents a summary of the results in a model selection
table using AIC.
PRESENCE
 The analysis is stored in a project file (created from the
 A project consists of 3 files, *.pao, *.pa2 and *.pa2.out



*.pao is the data file
*.pa2 stores a summary of the models fit to the data
*.pa2.out stores the full results for all the models
PRESENCE
consists of 2
main windows
Number crunching
window
Point and click
window
When you create a new
project, you must
specify the data file (if
previously created), or
input the data to be
analysed.
Once the data file has
been defined and
selected, the filename
for the project file will be
the same as the data
file.
To enter data specify the
number of sites, survey
occasions, site-specific
and survey-specific
(sampling) covariates.
Then select the Input
Data Form.
The No.
Occasions/season box is
used for multi-season
data. You must list the
number of surveys per
season, separated with a
comma.
Data can be copied
and pasted (via the
each respective tab.
You can also enter
data directly, or insert
from a comma
delimited text (.csv)
file.
Note the number of PRESENCErelated windows now open.
Once data has been
entered, you must
save the data before
closing the window!
and closing the data
window, check that the
correct data filename
appears here. If not
then will have to select
the file manually.
Make sure you click OK before proceeding.
The type of analysis to perform is selected from the run menu.
After setting up