Download Occupancy Modeling

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Occupancy
Modeling
Chloe Boynton & Kristen Walters
February 22, 2017
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Why choose occupancy modeling
for population dynamics?
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Occupancy modeling: a tool to estimate true populations
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Can use occupancy (presence/absence) data to look at
population growth (λ)
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The ability to estimate populations often confounded by
the inability to accurately count species
 Occupancy modeling can be used to get more accurate
estimates
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Able to use occupancy modeling to look at species
distributions
 Multiple season/year data can show how these
distributions are changing over time
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Parameters of Interest: Occupancy
 The
proportion of area, patches or sample units
that is occupied
 ie. a species presence
ψ: probability that a randomly selected site or
sampling unit in an area of interest is occupied
by a species
ψ = x/s
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Parameters of Interest: Detection
Detection Probability (Pj): the probability of
detecting the species during the jth survey,
given it is present
 considered an a priori expectation that a
particular site will be occupied by the species as
determined by some underlying process
Proportion: realization of that process
The distinction becomes important when a large
portion of the population of interest is sampled
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Why use occupancy?
 Presence/absence
data is easier to sample and
collect than abundance, especially for rare
species
 Requires less effort and is less expensive to
collect
 Can
be used to study both single species and
multiple species
 For
monitoring it can used as a metric reflecting
the current state of the population
+ Occupancy can be used for:
 Metapopulation
 Incidence
functions
 Distribution
 Animal
dynamics (patch occupancy models)
and range
invasions
 Disease
dynamics
 Long-term
monitoring
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Geographic Range
 Area
of occurrence: the set of grid cells that contain
at least one individual when a grid is superimposed
on the area containing all individuals of a species
(but may contain cells with no individuals)
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Habitat Relationships
 Use
presence/absence data to determine habitat
variables that describe sites occupied by species (or
not)
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Use habitat variables to which a species responds
and then develop habitat models or predict
abundance/occupancy
 Majority
of habitat studies based on occupancy have
been directed at conservation and management
 False-absences
need to be considered
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Occupancy data
 Presence-absence
data: estimation of
occupancy rates and associated dynamics that
are fundamental for habitat model and metapopulation studies
 Whether
a “patch” or site is occupied by one or
more individuals of a population or species
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Occupancy data
Unit of interest: the extent of occurrence or area
of occupancy
Example: for pond dwelling amphibians, the pond
is the unit of interest
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Occupancy data
Unit of interest: the extent of occurrence or area
of occupancy
Example: for a terrestrial animal being studied
units may be defined as 1,000 hectare blocks
within a national park
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2 critical factors when sampling animal
populations:
 Spatial
variation
 Investigators select a
sample of locations to
survey
 Detectability
 Even
in surveyed
areas, animals and
whole species can go
undetected
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Occupancy data: Non-detection
 Non-detection
does not equate to species absence
 Bias: sites
may be visited but no animals detected
therefore producing false negatives
 “False-absence”
 Failure
to account for imperfect detectability will
result in:
Underestimates of site occupancy
 Biased estimates of local colonization and extinction
probabilities and turnover rates
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 Therefore
need to incorporate detection as a
parameter into occupancy models
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Occupancy Sampling Protocol
 No
restrictions on sampling approaches
 Can include: visual observations of animals,
captures of animals in traps or mist nets,
observations of animal tracks, detection of animal
vocalizations, camera traps
 Survey
produces a list of surveyed sites that are:
 “Occupied” (species detected)
 “Unoccupied” (species not detected)
 Counts
of occupied sites are used to compute the
proportion of occupied sites among all sites visited
 Estimate of occupancy
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Data Collection
 Data
is collected by visiting a number of sites and
recording whether individuals of interest are present
(recorded as 1) or not present (0)
 Important
to repeat surveys over a small time frame
 Occupation
probability: calculated as the
proportion of sites that are occupied
 Extinction
probability: calculated as the proportion
of occupied sites at time t, not occupied at time t+1.
 Results
can be confounded by detection error
 Recorded ‘absence’ may be a ‘non-detection’ of
available individuals and not true absence
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Data Collection: Detection Error
 Detection
probability (p):
 Factors other than abundance may influence
detection probability
 Individual animals may be more visible or
detectable in one habitat than another
 Potential for misleading inference about true
relationship between occupancy and habitat
 If
detection probability can be calculated, then
unbiased estimators of occupancy, extinction
and colonization can be derived
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Data Collection: Detection Error
Detection Error Solutions:
1.
Dealing with false-absences by visiting sites
multiple times to avoid missing a species
2.
Statistically address the issue by incorporating
detection parameters into occupancy models
Best Case Scenario: incorporate BOTH collection
of additional information (visiting site multiple
times) into sampling protocol and utilizing
models that incorporate detection probabilities
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+ The Issue with Detection and
Occupancy Probability
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Wildlife species are rarely detected with 100% accuracy
The issue: the measure of occupancy (presence/absence at
a set of sites) is confounded with the detectability of the
species
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Detectability (p) can vary among study sites
 Can be related to site and survey level parameters:
temperature, precipitation
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Due to variation in detectability presence/absence data
cannot be simply analyzed
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Inferences of site characteristics on occupancy will be
hard to discern reliably
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The Solution: Occupancy Models
 Occupancy
models created to solve
problems of imperfect detectability
 Occupancy
models use information from
repeated observations at each site to estimate
detectability
 Occupancy
relates only to site characteristics
(habitat variables)
+ The Solution: Occupancy Models
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Necessary information for occupancy models:
 Record of whether a species was detected or not
detected during each survey of each site (detection
histories)
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Can convert detection histories to mathematical
statements
 Product of all the mathematical statements forms the
model likelihood for the observed data
 Maximum likelihood techniques are then used to
estimate model parameters.
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Parameter estimates (occupancy or detectability) can
be related to various site and survey characteristics
using the logistic equation or logit-link function in a
generalized linear model
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Occupancy Models
Example for constructing an occupancy model:
 Collect
survey data at time that might influence the
“detection model” (weather, temperature, wind
speed)
 Collect
data that related to the overall probability of
a species being present at that site
Detection Probability : lets you estimate what short
term factors (variables that differ between visits),
influence detectability
Occupancy Probability: can infer about the
correlates of the species presence once you account
for imperfect detection
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Detection Histories
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Detection histories are a record of whether or not the target
species was detected on each survey of each site
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Example 1) 30 sites each sampled four times within a season
Survey 1 Survey 2 Survey 3 Survey 4
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
Site 1
1
0
0
1
Site 2
0
0
0
0
Site 3
1
1
0
0
Site ..30
0
0
0
0
Target species detected at Site 1 during first and last survey
occasion: 1001
Site was occupied (ψ), and the species was detected on first and
last surveys ( p1 and p4) and not detected on the second and
third surveys
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Detection Histories
Example 1)
Survey 1 Survey 2 Survey 3 Survey 4
Site 1
1
0
0
1
 We
can write the probability of this detection
history as:
Pr(Hi = 1001) = ψ × p1 (1 – p2 )(1 – p3 ) p4
+ Detection Histories
Example 1)
Survey 1 Survey 2 Survey 3 Survey 4
Site 2
0
0
0
0
Site ..30 0
0
0
0
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Sites 2 and 30 represent a case where the target species was
never detected (detection history = 0000)
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These sites could either be unoccupied, which
mathematically is (1-ψ), or they could be occupied, but we
never detected the target species, which mathematically is:
ψ(1- p1 )(1- p2 )(1- p3 )(1- p4 ) or ψΠ 4 j=1 (1 – pj )
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Thus, we can write the probability of detection history (0000)
as:
Pr(H i = 0000) = ψΠ 4 j=1 (1 – pj ) + (1-ψ)
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Detection Histories
 Mathematical
statements of all detection
histories are combined into model likelihood,
such as:
L(ψ, p H 1 ,…, H 30) =Π 30 i=1 Pr(Hi )
 Product
of math equations forms the model
likelihood for the observed data
 Maximum
likelihood techniques are then used to
estimate model parameters (for each detection
history)
+ Occupancy Estimation
Assumptions underlying occupancy estimation:
1.
Occupancy state is “closed”
2.
Sites are independent
3.
No explained heterogeneity in occupancy
4.
No unexplained heterogeneity in detectability
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Occupancy Estimation
Example 2) Survey and occupancy/detection
probability (salamander data):
A
number of ponds may be visited (surveyed) to
assess the occupancy of a salamander species
 These
surveys take place during a short period during
the breeding season when ponds (sites) are assumed
to be occupied
 Each
pond is visited once a day for five days (or
alternatively five locations within a pond could be
sampled) and whether any salamanders are present at
each pond is recorded.
+ Occupancy Estimation
Example 2) Survey and occupancy/detection probability
(salamander data):
 Data
from each pond (i) can take the form of an
‘encounter history’ such as: 01010
Occupancy Estimation: since salamanders were
detected at least once, we assume the site was occupied
across all five sampling occasions, but not detected on
sampling occasions 1, 3, 5
we denote ψ as occupancy probability and p as
detection probability we can designate the likelihood
for the salamander example as:
 If
ψi(1− p1)p2(1− p3)p4(1− p5).
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Occupancy Estimation
Example 2) Survey and occupancy/detection probability
(salamander data):
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If salamander pond is visited 3 years in a row:
0100
0000
1011
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Occupancy rates for all three years are calculated as well as
extinction and colonization between years
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In year two no salamanders were detected
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
Could represent an extinction between year 1 and 2 or series of non
detections during year 2
Advantage of estimating the extinction and colonization rates for
sites is that the temporal dynamics of patch occupancy are
available, providing more information than just occupancy rate
through time
+ Occupancy Estimation: Species
Interactions
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Occupancy models have been extended to investigate whether
the occupancy of one species influences the occupancy of a
second species
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The paper by Royle and Nichols (2003) investigates the
relationship between ‘patch’ or ‘site’ level detection probabilities
and individual detection probabilities
ps: site-level detection probability
pi: individual detection probability
n: number of individuals
1−ps =(1−pi)n
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If a site-level detection probability can be obtained and an
individual detection probability can be modeled, a latent
estimate of abundance can be obtained from presence/absence
data
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Occupancy data: Multiple species
 Each
species is considered independently
 Data
can also be used to address possible
interactions between species
 Can
classify studies as
either static patterns of
occupancy or
occupancy dynamics
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Occupancy data: Multiple Species
Static studies null models to deduce occupancy
patterns under a null hypothesis of
independence or no interactions
 Need to estimate occupancy for each species
at each location separately
Dynamic studies use occupancy data taken at
multiple time steps
 Need detection probability to draw
inferences about rates of extinction and
colonization
 General approach is to incorporate detection
probability based on aggregation of species
+ Dynamic Occupancy Models
Example 3) Population Dynamics of Migratory
Songbirds
 Estimated
populations of birds in various rates of
decline
4 population parameters:
1.Detection probability
2. Occupancy probability
3. Persistence probability
4. Colonization probability
+ Dynamic Occupancy Models
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R-Code and package ‘unmarked’
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Unmarked: an R Package for Fitting Hierarchical Models
of Wildlife Occurrence and Abundance -Ian Fiske, R.
Chandler