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Detectability Lab. Outline. Brief Discussion of Modeling, Sampling, and Inference Review and Discussion of Detection Probability and Point Count Methods Examples with Data and Software Discussion of Upcoming Lab . Biological Modeling and Inference.

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outline
Outline
  • Brief Discussion of Modeling, Sampling, and Inference
  • Review and Discussion of Detection Probability and Point Count Methods
  • Examples with Data and Software
  • Discussion of Upcoming Lab
biological modeling and inference
Biological Modeling and Inference
  • We want to understand the world in meaningful and often predictive ways.
  • Models – representations of reality
  • Often we seek the most parsimonious model.

Conceptual

Verbal

Mathematical

Statistical

Physical

Mechanical

biological modeling and inference4
Biological Modeling and Inference
  • Models should be made with clear goals in mind.
  • In order to make inference, models should be confronted with data.
  • Inference – decisions
    • test hypotheses
    • model selection
    • model evaluation
sampling
Sampling
  • Process of gathering data for inference.
  • Why sample instead of census?
  • Sampling must be done in the context of study objectives.
  • Common sampling regimes include:
    • Systematic
    • Random
    • Stratified Random
systematic
Systematic

Habitat B

Habitat A

random
Random

Habitat B

Habitat A

stratified random
Stratified Random

Habitat B

Habitat A

point counts
Point Counts
  • Point count
    • very common and simple sampling method
    • number of birds seen or heard (C)
  • What is the relationship between C and the bird population (N)?

C = N

C = a constant but unknown fraction of N

point counts and detection probability
Point Counts and Detection Probability
  • Solution
    • Estimate the probability that birds are detected ( )

ˆ

N

Where:

= the population estimate

= number of birds counted

= the probability that a bird is detected

components of detection
Components of Detection
  • Pp = the probability that a bird associated with the point count area is present during the point count
  • Pa = the probability a bird that is present in the point count area is available for detection
  • Pd = the probability a bird that is present and available is actually detected

= Pp Pa Pd

slide13

In any given 5 minute period, this species only uses 25% of its territory on average. The yellow area represents the portion of each territory that is occupied in this example.

slide14

In any given 5 minute period, species A has a 70% chance of being available (singing). Therefore 3 out the 10 birds shown here are not available to be counted.

slide15

Given that a bird is available, the average observer has a 71% chance of detecting it. Therefore, only 5 of the 7 available birds would be counted. The available, but undetected birds are shown in light grey.

slide16

1

4

5

3

2

Therefore, 5 sampling scenarios exist for species A with 5 minute point counts:

1) Point count is located where there is no bird.

2) Point count contains bird territory, but not the bird.

3) Point count contains bird, but bird is not singing and therefore available for detection.

4) Point count contains singing bird, but it is not detected.

5) Point count contains singing bird which is detected.

methods that account for the detection process
Methods That Account for the Detection Process
  • Distance Sampling
  • Multiple Observers
    • Independent observers
    • Dependent observers
    • Unreconciled observers
  • Time-of-detection
  • Repeated Visits
    • Simple counts or presence/absence
distance methods

Pd

Distance Methods
  • Distance to individual birds is measured or estimated
  • Sometimes distance categories are used (e.g., 0-25, 25-50, 50-100m, etc.)
  • Data are aggregated from point counts

1

0.75

0.50

0.25

0

0 50 100

meters

distance methods19
Distance Methods
  • Critical Assumptions
    • Detection probability = 1 when distance = 0
    • Distances are measured accurately
    • Birds do not move in response to the observer prior to detection
  • What do you think?
multiple observers
Multiple Observers
  • Independent Observers
    • Observers sample same locations simultaneously and independently
    • Match observations when the point count is over
    • Matched observations, together with observations unique to each observer, provide information about each observers unique detection probability
    • Pd only
multiple observers21
Multiple Observers

N

Observer 1

Observer 2

…after matching

multiple observers22
Multiple Observers
  • Critical Assumptions
    • Observers do not influence each other’s detections
    • No matching errors
    • The sample area is closed to bird movements
    • For each observer, individual birds are not double-counted and multiple birds are not lumped into one
  • What do you think?
time of detection
Time-of-Detection
  • Similar to capture-recapture methods
  • Point counts are divided into several intervals (e.g., 10min count split into 4 2.5min intervals)
  • Once a bird is detected, it is “tracked” during the remaining intervals
  • PaPd only
time of detection24
Time-of-Detection

Bobwhite

Interval 1 (0-2.5min)

Interval 2 (2.5-5min)

Interval 3 (5-7.5min)

Interval 4 (7.5-10min)

Bobwhite detection history = 1111

Grasshopper Sparrow detection history = 0101

Grasshopper Sparrow

time of detection25
Time-of-Detection
  • Critical Assumptions
    • The sample area is closed to bird movements
    • Birds are tracked accurately from interval to intervals
    • Individual birds are not double-counted and multiple birds are not lumped into one
  • What do you think?
repeated visits counts
Repeated Visits (Counts)
  • Multiple visits are made to conduct point counts
  • Birds are counted at each visit
  • Site history is generated
  • PpPaPd
repeated visits counts27
Repeated Visits (Counts)

Visit 1

Visit 2

Visit 3

Bluebird

Bluebird

Bluebird

Bluebird

Bluebird

Site History = 3,0,2

repeated visits counts28
Repeated Visits (Counts)
  • Critical Assumptions
    • Individual birds are not double-counted or lumped within a visit
    • Each individual associated with the sample area has a > 0 chance of being present at each visit
    • Each visit is independent of the others
  • What do you think?
slide29

What if you didn’t need to know how many birds where at a location (i.e., abundance)?What if all you needed to know was if the species was there (i.e., presence/absence or occupancy)?

repeated visits presence absence
Repeated Visits (Presence/Absence)
  • Multiple visits are made to conduct surveys
  • Presence/absence is recorded at each visit
  • Site history is generated
  • = the probability that at least one individual is detected
repeated visits presence absence31
Repeated Visits (Presence/Absence)

Visit 1

Visit 2

Visit 3

Bluebird

Bluebird

Bluebird

Bluebird

Bluebird

Site History = 1,0,1

repeated visits presence absence32
Repeated Visits (Presence/Absence)
  • Critical Assumptions
    • Occupancy status of each sample location is constant across all visits
    • The sample area is closed to bird movements within a visit
    • Each visit is independent of the others
  • What do you think?
occupancy example
Occupancy Example
  • Objective: Determine occupancy rate for Whispering Pine Hawk (it prefers pine forests)
  • Study area description
    • 50% loblolly, 50% Virginia pine
  • Previous studies suggest no preference of one pine species over another, but you think detectability may be less in Virginia pine stands
  • What models could you use to resolve this dilemma?
occupancy example35
Occupancy Example
  • Sampling scenario
    • 100 point count locations
    • Stratified random design
    • Each count visited 3 times within 2 weeks
model selection exercise
Model Selection Exercise
  • Get into groups of 2
  • You will be presented with an image of a northern cardinal
  • Your task is to model that image with a pencil or pen drawing
  • Your drawing will be scored from 0-100 based on how likely the judge thinks others will recognize it as a cardinal
  • Your drawing will be penalized for the number of lines used to draw the cardinal
model selection exercise37
Model Selection Exercise
  • The model selection criteria is:

Predictability Score – (2*number of lines)

Reliability Component

Parameter Penalty Component

all bird radio experiments
All Bird Radio Experiments

Black-throated green warbler

Hooded warbler

Acadian Flycatcher

Yellow-throated warbler

Black-and-white warbler

Black-throated blue warbler

Scarlet tanager

Ovenbird

Acadian Flycatcher

Black-throated blue warbler

Hooded warbler

all bird radio experiments39
All Bird Radio Experiments

Black-throated green warbler

Hooded warbler

Acadian Flycatcher

Yellow-throated warbler

Black-and-white warbler

Black-throated blue warbler

Scarlet tanager

Ovenbird

Black-throated green warbler

Acadian Flycatcher

Black-and-white warbler

Observer 1

Observer 2

Black-throated blue warbler

Hooded warbler

Hooded warbler

Acadian Flycatcher

Black-throated blue warbler

Black-and-white warbler

Black-throated blue warbler

Black-and-white warbler

Black-and-white warbler

Scarlet tanager

Black-throated green warbler

Black-throated blue warbler

Hooded warbler

Black-throated green warbler

all bird radio experiments40
All Bird Radio Experiments

Observer 1

Observer 2

Hooded warbler

Acadian Flycatcher

Black-throated blue warbler

Black-and-white warbler

Black-throated blue warbler

Black-and-white warbler

Black-and-white warbler

Scarlet tanager

Black-throated green warbler

Black-throated blue warbler

Hooded warbler

Black-throated green warbler

2 Black-throated Blue Warblers

1 Black-throated Blue Warbler

1 Match

repeated visits counts41
Repeated Visits (Counts)
  • One important caveat…
    • the abundance estimate doesn’t have a clear interpretation, especially with regard to area
where do i find presence
Where do I find PRESENCE?

http://www.mbr-pwrc.usgs.gov/software/doc/presence/presence.html