Sampling and Occupancy Estimation

1. Sampling and Occupancy Estimation Krishna Pacifici Department of Applied Ecology NCSU January 10, 2014

2. 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.

3. Why?Clear objectives • How will the data be used to discriminate between scientific hypotheses about a system? • 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.

4. What?Many kinds of data • Population-level • Population size/density • Survival • Immigration & emigration • Presence/absence • Community-level • Persistence • Colonization & extinction • Species richness/diversity

5. 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, capture-recapture, occupancy modeling…

6. PURPOSES OF SAMPLING • ESTIMATE ATTRIBUTES (PARAMETERS) • Abundance/ density • Survival • Occurrence probability • ALLOW LEGITIMATE EXTRAPOLATION FROM DATA TO POPULATIONS • PROVIDE MEASURES OF STATISTICAL RELIABILITY

7. SAMPLING NEEDS TO BE • ACCURATE– LEADING TO UNBIASED ESTIMATES • REPEATABLE– ESTIMATES LEAD TO SIMILAR ANSWERS • EFFICIENT– DO NOT WASTE RESOURCES

8. BIAS • HOW GOOD “ON AVERAGE” AN ESTIMATE IS • CANNOT TELL FROM A SINGLE SAMPLE • DEPENDS ON SAMPLING DESIGN, ESTIMATOR, AND ASSUMPTIONS

9. UNBIASED TRUE VALUE SAMPLE ESTIMATE * * * * * * * * AVERAGE ESTIMATE

10. BIASED TRUE VALUE SAMPLE ESTIMATE * * * * * * * * BIAS AVERAGE ESTIMATE

11. REPEATABLE (PRECISE) SAMPLE ESTIMATE * * * * * * * *

12. NOT REPEATABLE (IMPRECISE) * * * SAMPLE ESTIMATE * * * * *

13. CAN BE IMPRECISE BUT UNBIASED.. OR * AVERAGE ESTIMATE * * SAMPLE ESTIMATE * * * * * TRUE VALUE

14. PRECISELY BIASED..OR TRUE VALUE SAMPLE ESTIMATE * * * * * * * * AVERAGE ESTIMATE

15. IMPRECISE AND BIASED! AVERAGE ESTIMATE * * SAMPLE ESTIMATE * * * * * TRUE VALUE *

16. ACCURATE=UNBIASED & PRECISE TRUE VALUE SAMPLE ESTIMATE * * * * * * * * AVERAGE ESTIMATE

17. HOW DO WE MAKE ESTIMATES ACCURATE ? • KEEP BIAS LOW • SAMPLE TO ADEQUATELY REPRESENT POPULATION • ACCOUNT FOR DETECTION • KEEP VARIANCE LOW • REPLICATION (ADEQUATE SAMPLE SIZE) • STRATIFICATION, RECORDING OF COVARIATES, BLOCKING

18. Key Issues • Spatial sampling • Proper consideration and incorporation of detectability

19. Sampling principles • What is the objective? • What is the target population? • What are the appropriate sampling units? • Size, shape, placement • Quantities measured

20. Remember • Field sampling must be representative of the population of inference • Incomplete detection MUST be accounted for in sampling and estimation

21. Example- Transect sampling to count snakes in Corbett National Park, India

22. 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

23. What is the target population?Population in the NP

24. What are the appropriate sampling units? • Quadrats? • Point samples? • Line transects?

25. Sampling units- nonrandom placement Road

26. Nonrandom placement • Advantages • Easy to lay out • More convenient to sample • Disadvantage • Do not represent other (off road) habitats • Road may attract (or repel) snakes

27. OR- redefine the target: Road

28. Sampling units- random placement

29. Random placement • Advantages • Valid statistical design • Represents study area • Replication allows variance estimation • Disadvantage • May be logistically difficult • Harder to lay out • May not work well in heterogeneous study areas

30. Stratified sampling

31. Stratified sampling • Advantages • Controls for heterogeneous study area • Allows estimation of density by strata • More precise estimate of overall density • Disadvantages • More complex design • May require larger total sample

32. Single, unreplicated line

33. 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

34. 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

35. A valid sampling design • Allows valid probability inference about the population • Statistical model • Allows estimates of precision • Replication, independence

36. 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 • Adaptive sampling • More efficient when populations are distributed “clumpily” • Dual-frame sampling

37. 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

42. 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

43. 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

44. 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

45. 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).

46. 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

47. Basic Sampling Scheme:Single Season • s sites are surveyed, each at k distinct sampling occasions. • Species is detected/not detected at each occasion.

48. 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!

49. 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.

50. 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