PowerPoint Presentation

Sampling and Occupancy EstimationKrishna PacificiDepartment of Applied EcologyNCSUJanuary 10, 2014Designing studiesWhy, 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 objectivesHow 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 dataPopulation-levelPopulation size/densitySurvivalImmigration & emigrationPresence/absence

Community-levelPersistenceColonization & extinctionSpecies richness/diversityHow?Sampling and ModelingInterest lies in making inference from a sample to a populationStatistics!Want it to be repeatable and accurateOthers should understand what you have done and be able to replicateMany different modeling/analysis approachesDistance sampling, multiple observer, capture-recapture, occupancy modeling

PURPOSES OF SAMPLINGESTIMATE ATTRIBUTES (PARAMETERS)Abundance/ densitySurvivalOccurrence probabilityALLOW LEGITIMATE EXTRAPOLATION FROM DATA TO POPULATIONS

PROVIDE MEASURES OF STATISTICAL RELIABILITYSAMPLING NEEDS TO BEACCURATE LEADING TO UNBIASED ESTIMATES

REPEATABLE ESTIMATES LEAD TO SIMILAR ANSWERS

EFFICIENT DO NOT WASTE RESOURCESBIASHOW GOOD ON AVERAGE AN ESTIMATE IS

CANNOT TELL FROM A SINGLE SAMPLE

DEPENDS ON SAMPLING DESIGN, ESTIMATOR, AND ASSUMPTIONSUNBIASEDTRUE VALUE********AVERAGE ESTIMATESAMPLE ESTIMATEBIASEDTRUE VALUE********AVERAGE ESTIMATESAMPLE ESTIMATEBIASREPEATABLE (PRECISE)*******SAMPLE ESTIMATE*NOT REPEATABLE (IMPRECISE)*******SAMPLE ESTIMATE*CAN BE IMPRECISE BUT UNBIASED.. OR*******SAMPLE ESTIMATE*AVERAGE ESTIMATETRUE VALUEPRECISELY BIASED..ORTRUE VALUE********AVERAGE ESTIMATESAMPLE ESTIMATEIMPRECISE AND BIASED!*******SAMPLE ESTIMATE*AVERAGE ESTIMATETRUE VALUEACCURATE=UNBIASED & PRECISETRUE VALUE********AVERAGE ESTIMATESAMPLE ESTIMATEHOW DO WE MAKE ESTIMATES ACCURATE ?KEEP BIAS LOWSAMPLE TO ADEQUATELY REPRESENT POPULATIONACCOUNT FOR DETECTIONKEEP VARIANCE LOWREPLICATION (ADEQUATE SAMPLE SIZE)STRATIFICATION, RECORDING OF COVARIATES, BLOCKING

Key IssuesSpatial sampling

Proper consideration and incorporation of detectabilitySampling principlesWhat is the objective?

What is the target population?

What are the appropriate sampling units?Size, shape, placementQuantities measuredRememberField sampling must be representative of the population of inferenceIncomplete detection MUST be accounted for in sampling and estimationExample- Transect sampling to count snakes in Corbett National Park, IndiaWhat 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 placementRoadNonrandom placementAdvantagesEasy to lay outMore convenient to sampleDisadvantageDo not represent other (off road) habitatsRoad may attract (or repel) snakesOR- redefine the target:RoadSampling units- random placementRandom placementAdvantagesValid statistical designRepresents study areaReplication allows variance estimationDisadvantageMay be logistically difficultHarder to lay outMay not work well in heterogeneous study areasStratified sampling

Stratified sampling

AdvantagesControls for heterogeneous study areaAllows estimation of density by strataMore precise estimate of overall densityDisadvantagesMore complex designMay require larger total sampleSingle, unreplicated lineAre these hard rules NO!Some violations of assumptions can be OK and even necessary (idea of robustness)

These are ideals to strive towardGood if you can achieve themIf you cant, you cant but study results may need different interpretationEstimation: from Count Data to Population (I)Geographic variation (cant look everywhere)Frequently counts/observations cannot be conducted over entire area of interestProper inference requires a spatial sampling design that permits inference about entire area, based on a sample

A valid sampling designAllows valid probability inference about the populationStatistical model

Allows estimates of precisionReplication, independence Other Spatial Sampling DesignsSystematic samplingCan approximate random sampling in some casesCluster samplingWhen the biological units come in clustersDouble samplingVery useful for detection calibrationAdaptive samplingMore efficient when populations are distributed clumpilyDual-frame sampling

Estimation: from Count to Population (II)Detectability (cant 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

38Statistical uncertaintySpatial not observing every siteDetection not observing every individual

41Sampling Take Home MessagesField sampling must be designed to meet study or conservation objectivesField sampling must be representative of the population of inferenceIncomplete detection MUST be accounted for in sampling and estimationOccupancy EstimationSpecies status = present or absent

Coarse measure of population statusProportion of occupied patches

Data can be collected efficiently over large spatial and temporal extentsSpecies and community-level dynamics

Occupancy Estimation: UsesSurveys of geographic range Habitat relationships Metapopulation dynamicsObserved colonization and extinction Extensive monitoring programs: 'trends' or changes in occupancy over time44Species OccurrenceConduct 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).

45Site occupancy: A solutionMacKenzie 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

46Basic Sampling Scheme:Single Seasons sites are surveyed, each at k distinct sampling occasions.

Species is detected/not detected at each occasion.47Necessary information: Data summary Detection historiesDetection history: Record for each visited site or sample unit1 denotes detection0 denotes nondetectionExample detection history: hi = 1 0 0 1 0Denotes 5 visits to the siteTarget species detected during visits 1 and 40 does not necessarily mean the species was absentNot detected, but could be there!Model Parameters: Single-Season Models49Sites are closed to changes in occupancy state between sampling occasionsNo heterogeneity that cannot be explained by covariates The detection process is independent at each site> 500 meters apart

Model assumptions50Timing of repeated surveysUsually conducted as multiple discrete visits (e.g., on different days)Can also use multiple surveys within a single visitMultiple independent observersPotentially introduce heterogeneity into dataSingle visit to each site vs. multiple visits to each siteRotate observers amongst sites on each day Rotate order each site is sampled within a dayDesigning occupancy surveysSeveral important issues to consider:Clear objectives that are explicitly linked to science or managementSelection of sampling unitsProbabilistic sampling designSize of unit relative to species of interestTiming of repeat surveysclosed Relaxed for lab projectAllocation of survey effortSurvey all of the sites equal number of times?

Program PRESENCEGetting To KnowPRESENCEPRESENCE 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.PRESENCEThe 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 windowsNumber crunching windowPoint 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 PRESENCE-related 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.

After setting up your project, an empty Results Browser window should appear.

Make sure you see this before attempting to run any models!The type of analysis to perform is selected from the run menu.