1. Inferences About Animal Populations

2. Why Estimate Population Attributes? Science Understand ecological systems Learn stuff Management/Conservation Apply decision-theoretic approaches Make smart decisions

3. Key Component of Science: Confront Predictions with Data Make predictions from hypotheses/models. Observe/estimate: System dynamics System state Confrontation: Predictions vs. Observations Ask whether observations correspond to predictions (single-hypothesis). Use correspondence between observations and predictions to help discriminate among hypotheses (multiple-hypothesis).

4. Getting the Data Use design that imposes, or takes advantage of, a manipulation of some sort. Manipulative experimentation (randomization, replication, controls). Constrained design study (lacks one of the 3 features above, e.g., impact studies). No manipulation - observational study. Prospective (confrontation with predictions from a priori hypotheses). Retrospective (a posteriori story-telling).

5. Getting the Data

6. Opinions About Retrospective Story-telling Claims: 1.It is easy to view a time series of abundance estimates and build a story about the stochastic process that generated it. 2.It is foolish to place much confidence in such a story. Phaedrus’ Law: “The number of rational hypotheses that can explain any given phenomenon is infinite.” (Pirsig 1974, Zen and the Art of Motorcycle Maintenance)

8. Pattern-based Predictions: Basic Idea Different processes of interest should yield different patterns, so estimation of pattern can be used to discriminate among competing hypotheses. Spatial pattern frequently used as basis for inference in ecology about process.

9. Inferring Process from Pattern: Ecological Examples Spatial variation in density or occupancy: inferences about habitat suitability. Single-species incidence functions: inference about local extinction, colonization, and their determinants (e.g., area, isolation). Multi-species incidence functions: inferences about “assembly rules” (competition).

10. Inferring Process from Pattern: Opinion Conclusions about underlying processes based upon observed pattern may be misleading (e.g., Clinchy et al. 2002). Much stronger inferences result from observing changes in the system over time.

11. Use of Estimation in Science Primary purpose: Confrontation of predictions with data/observations. Strength of inference: Manipulative experiment > Impact study > Observational study. Strength of inference for observational studies: Prospective (a priori hypotheses) > Retrospective (a posteriori stories). Strength of inference about processes: Estimation of dynamics > Estimation of patterns.

12. Management/Conservation Key Elements Objective(s): what do you want to achieve. Management alternatives: stuff you can do. Model(s) of system response to management actions (for prediction). Measures of model credibility. Monitoring program to estimate system state and other relevant variables.

13. Useful Management Objectives Should articulate the desired management outcome for the system over some time frame maximize harvest over 100 years maintain N>1000 for minimal cost for next 20 years maximize irrigation per year with constraint of wetland occupancy > 30% Trend detection is not a useful management objective no reference to desired state of the system May have to include conservation and economic goals

14. Adaptive Management: Process Use dynamic optimization to select management action based on: 1) objectives 2) available actions 3) estimated state of system 4) models and their measures of credibility Selected action drives system to new state, identified via monitoring program. Compare estimated and predicted system state to update measures of model credibility. Return to first step.

15. Adaptive Management: Process Model 1 Management Action Predicted Outcome Model 2 A B X1X1 Y1Y1 A B X2X2 Y2Y2

16. Adaptive Management: Process Model 1 Management Action Predicted Outcome Model 2 A B X1X1 Y1Y1 A B X2X2 Y2Y2

17. Role of Monitoring in Management Determine system state for state-dependent decisions. Determine system state to assess degree to which management objectives are achieved. Determine system state for comparison with model-based predictions to learn about system dynamics (i.e., do science). Should not be viewed as a stand-alone activity.

18. Toy Example Rare pond breeding frog (Hyla kiwii) present in a wetland that provides water for irrigation to local farms. How do we manage water use with regards to persistence of frog population?

19. Toy Example Decision matrix indicating amount of water that can be used for irrigation in a given year depending on current level of frog occupancy and water level in wetland.

20. Surveillance Monitoring Monitor population until a problem is identified. e.g., ‘significant’ downward trend is detected. Once detected, management takes action to address problem. However, because of inherent variation in monitoring data, statistical procedures will generally have low power. May be too late for the system by the time sufficient data has been collected.

21. Surveillance Monitoring & Science “Biology, with its vast informational detail and complexity, is a ‘high-information’ field, where years and decades can easily be wasted on the usual type of ‘low-information’ observations and experiments if one does not think carefully in advance about what the most important and conclusive experiments would be.” (Platt 1964)

22. Surveillance Monitoring Surveillance monitoring sometimes represents a form of intellectual displacement behavior. Easier to suggest collection of data than to think hard about the most relevant data to collect for science or management. At cynical worst, surveillance monitoring represents a political delaying tactic. “We must collect more information before we can act.”

23. Surveillance Monitoring Regardless of motivation, it’s likely to be inefficient for addressing many scientific and management problems. Monitoring systems in a car do not make it automatically perform in the desired manner…

24. What Quantities to Estimate? 3 Levels of Inference Individual – single species State variable: Abundance Vital rates: Pr(survival, reproduction, movement) Population – single species State variable: Proportion patches occupied Vital rates: Pr(local extinction/colonization) Community – multiple species State variable: Species richness Vital rates: rates of extinction and colonization

25. What State Variables (& Vital Rates) to Estimate? Depends On: Objectives. Science: what hypotheses are to be addressed? Management/conservation: what are the objectives and available actions? Geographic and temporal scale. Effort available. Required effort: species richness, species occurrence < abundance

26. How to Estimate? Basic Sampling Issues Detectability Counts represent some unknown fraction of animals in sampled area Proper inference requires information on detection probability Geographic variation Frequently 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, and/or Provides good opportunity for discriminating among competing hypotheses

27. Spatial Sampling Designs Simple random sampling. Stratified random sampling. Systematic sampling. Cluster sampling. Double sampling. Adaptive sampling. Unequal probability sampling.

28. Spatial Sampling Designs How results can be generalised depends on sampling designs. Methods may be need to be modified in some instances.

29. Detectability: Monitoring Based on Some Sort of Count Ungulates seen while walking a line transect. Tigers detected with camera-traps. Birds heard at point count. Small mammals captured on trapping grid. Bobwhite quail harvested during hunting season. Kangaroos observed while flying aerial transect.

38. Detectability: Conceptual Basis N = abundance or number of occupied units or species in community C = count statistic p = detection probability; Pr(member of N appears in C )

39. Detectability: Inference Inferences about N require inferences about p.

40. Indices Assume Equal Detectability N i = abundance for time/place i p i = detection probability for i C i = count statistic for i

41. Indices: Dealing with Variation in Detectability Standardization (variation sources that we can identify and control). Covariates (variation sources that we can identify and measure and that are independent of the quantity of interest). Prayer (variation sources that we cannot identify, control or measure). CONCLUSION: ESTIMATE DETECTABILITY!

42. Animal Abundance: Estimation and Modeling Traditional monitoring foci: Variation over time: trend. Variation over space or species: relative abundance. Many estimation methods (e.g., Seber 1982, Williams et al. 2002). Each estimation method is simply a way to estimate detection probability for the specific count statistic of interest. Final step is always:

43. Observation-based Count Statistics: Detectability Distance sampling. Double sampling. Marked subsets. Multiple observers (dependent, independent). Sighting probability modelling. Temporal removal modelling.

44. Capture-based Count Statistics: Detectability Closed-population capture-recapture models. Open-population capture-recapture models. Removal models (constant and variable effort). Trapping webs with distance sampling. Change-in-ratio models.

45. Rate Parameters Relevant to Changes in Abundance Population growth rate. Survival rate, harvest rate. Reproductive rate (young per breeding adult). Breeding probability. Movement rate. Process variance. Relationships with predictor variables.

46. Species Richness and Community Dynamics Species detection/nondetection: spatial or temporal replicates. Estimate and model species richness. Replicated species detection/nondetection over multiple years. Estimate and model local rates of extinction and colonization. Applications: Forest bird community dynamics. Amphibian monitoring.

47. 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).

48. Modeling Occupancy Dynamics Estimate time-specific rates of: Occupancy Local extinction Local colonization Model these quantities as functions of relevant covariates, e.g.: Patch size Patch isolation Management actions Environmental or habitat variables

49. Recommendations: Why Estimate Pop Attributes? Estimation efforts are most useful when integrated into efforts to do science or management. Not a useful stand-alone activity. Role of estimation in science. Comparison of data with model predictions is used to discriminate among competing models/hypotheses. Role of monitoring in management - determine system state for: State-specific decisions. Assessing success of management relative to objectives Discrimination among competing models/hypotheses.

50. Recommendations: What to Estimate? Decision should be based on overall program objectives (i.e., determined by the scientific or management context). Decision should consider required scale and effort. Reasonable state variables. Species richness Species occurrence Abundance

51. Recommendations: How to Estimate Pop Attributes? Detectability Counts represent some unknown fraction of animals in sampled area. Proper inference requires information on detection probability. Geographic variation 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, or provides good opportunity for discriminating among competing hypotheses.