1. Detectability Lab

2. 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 Software IV.Discussion of Upcoming Lab

3. 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

4. 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

5. 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

6. Systematic Habitat A Habitat B

7. Random Habitat A Habitat B

8. Stratified Random Habitat A Habitat B

9. 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

10. Point Counts and Detection Probability Solution – Estimate the probability that birds are detected ( ) N ˆ Where: = the population estimate = the probability that a bird is detected = number of birds counted

11. Components of Detection 1)P p = the probability that a bird associated with the point count area is present during the point count 2)P a = the probability a bird that is present in the point count area is available for detection 3)P d = the probability a bird that is present and available is actually detected = P p P a P d

12. Hypothetical study area with 10 territories of species A

13. 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.

14. 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.

15. 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.

16. 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.

17. 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

19. 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 PdPd 0 50 100 meters 1 0.75 0.50 0.25 0 Distance category Number of observations 0-25m100 25-50m89 50-75m19 75-100m1

20. 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?

21. 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

22. Model Selection Exercise The model selection criteria is: Predictability Score – (2*number of lines) Reliability Component Parameter Penalty Component