Krishna Pacifici Department of Applied Ecology NCSU January 10, 2014 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. 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. What? Many kinds of data Population-level Population size/density Survival Immigration & emigration Presence/absence Community-level Persistence Colonization & extinction Species richness/diversity 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, capturerecapture, occupancy modeling… PURPOSES OF SAMPLING ESTIMATE ATTRIBUTES (PARAMETERS) Abundance/ density Survival Occurrence probability ALLOW LEGITIMATE EXTRAPOLATION FROM DATA TO POPULATIONS PROVIDE MEASURES OF STATISTICAL RELIABILITY SAMPLING NEEDS TO BE ACCURATE– LEADING TO UNBIASED ESTIMATES REPEATABLE– ESTIMATES LEAD TO SIMILAR ANSWERS EFFICIENT– DO NOT WASTE RESOURCES BIAS HOW GOOD “ON AVERAGE” AN ESTIMATE IS CANNOT TELL FROM A SINGLE SAMPLE DEPENDS ON SAMPLING DESIGN, ESTIMATOR, AND ASSUMPTIONS UNBIASED TRUE VALUE SAMPLE ESTIMATE * * * * * * ** AVERAGE ESTIMATE BIASED TRUE VALUE * * * * * SAMPLE ESTIMATE * * BIAS AVERAGE ESTIMATE REPEATABLE (PRECISE) * * * * * * ** SAMPLE ESTIMATE NOT REPEATABLE (IMPRECISE) * * * * * * * * SAMPLE ESTIMATE CAN BE IMPRECISE BUT UNBIASED.. OR * AVERAGE ESTIMATE * * * * * * * TRUE VALUE SAMPLE ESTIMATE PRECISELY BIASED..OR TRUE VALUE * * * * ** * * SAMPLE ESTIMATE AVERAGE ESTIMATE IMPRECISE AND BIASED! AVERAGE ESTIMATE * * * SAMPLE ESTIMATE * * * * TRUE VALUE * ACCURATE=UNBIASED & PRECISE TRUE VALUE SAMPLE ESTIMATE * * * * * * ** AVERAGE ESTIMATE 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 Key Issues Spatial sampling Proper consideration and incorporation of detectability Sampling principles What is the objective? What is the target population? What are the appropriate sampling units? Size, shape, placement Quantities measured Remember Field sampling must be representative of the population of inference Incomplete detection MUST be accounted for in sampling and estimation 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 What is the target population? Population in the NP What are the appropriate sampling units? Quadrats? Point samples? Line transects? Sampling units- nonrandom placement Road 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 OR- redefine the target: Road Sampling units- random placement 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 Stratified sampling 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 Single, unreplicated line 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 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 A valid sampling design Allows valid probability inference about the population Statistical model Allows estimates of precision Replication, independence 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 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 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 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 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 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). 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 Basic Sampling Scheme: Single Season s sites are surveyed, each at k distinct sampling occasions. Species is detected/not detected at each occasion. 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! 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. 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 Timing of repeated surveys Usually conducted as multiple discrete visits (e.g., on different days) Can also use multiple surveys within a single visit Multiple independent observers Potentially introduce heterogeneity into data Single visit to each site vs. multiple visits to each site Rotate observers amongst sites on each day Rotate order each site is sampled within a day Designing occupancy surveys Several important issues to consider: 1. Clear objectives that are explicitly linked to science or management 2. Selection of sampling units Probabilistic sampling design Size of unit relative to species of interest Timing of repeat surveys 3. “closed” Relaxed for lab project Allocation of survey effort 4. Survey all of the sites equal number of times? Getting To Know PRESENCE PRESENCE is software that has been developed to apply these models to collected data. Within PRESENCE you can fit multiple models to your data. PRESENCE stores the results from each model and presents a summary of the results in a model selection table using AIC. PRESENCE The analysis is stored in a project file (created from the File menu). A project consists of 3 files, *.pao, *.pa2 and *.pa2.out *.pao is the data file *.pa2 stores a summary of the models fit to the data *.pa2.out stores the full results for all the models PRESENCE consists of 2 main windows Number crunching window Point and click window When you create a new project, you must specify the data file (if previously created), or input the data to be analysed. Once the data file has been defined and selected, the filename for the project file will be the same as the data file. To enter data specify the number of sites, survey occasions, site-specific and survey-specific (sampling) covariates. Then select the Input Data Form. The No. Occasions/season box is used for multi-season data. You must list the number of surveys per season, separated with a comma. Data can be copied and pasted (via the menus only) from a spreadsheet into each respective tab. You can also enter data directly, or insert from a comma delimited text (.csv) file. Note the number of PRESENCErelated windows now open. Once data has been entered, you must save the data before closing the window! After saving your data and closing the data window, check that the correct data filename appears here. If not then will have to select the file manually. Make sure you click OK before proceeding. The type of analysis to perform is selected from the run menu. After setting up your project, an empty Results Browser window should appear. Make sure you see this before attempting to run any models!