detectability lab. outline i.brief discussion of modeling, sampling, and inference ii.review and...

Detectability Lab

Outline

I. Brief Discussion of Modeling, Sampling, and Inference

II. Review and Discussion of Detection Probability and Point Count Methods

III. Examples with Data and SoftwareIV. Discussion of Upcoming Lab

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 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

• 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

Habitat A

Habitat B

Random

Habitat A

Habitat B

Stratified Random

Habitat A

Habitat B

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

• Solution– Estimate the probability that birds are detected

( )

p̂

C N̂

N

p̂

ˆWhere: = the population estimate

= the probability that a bird is detected

= number of birds countedC

p̂

Components of Detection

1) Pp = the probability that a bird associated with the point count area is present during the point count

2) Pa = the probability a bird that is present in the point count area is available for detection

3) Pd = the probability a bird that is present and available is actually detected

p̂ = Pp Pa Pd

Hypothetical study area with 10 territories of species A

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.

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.

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.

1

5

3

4

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

• Distance Sampling• Multiple Observers

– Independent observers– Dependent observers– Unreconciled observers

• Time-of-detection• Repeated Visits

– Simple counts or presence/absence

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

Pd

0 50 100meters

1

0.75

0.50

0.25

0

Distance category

Number of observations

0-25m 100

25-50m 89

50-75m 19

75-100m 1

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?

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 Exercise

• The model selection criteria is:

Predictability Score – (2*number of lines)

Reliability Component

Parameter Penalty Component