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, capture- recapture, 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 * * * * * * * * AVERAGE ESTIMATE SAMPLE ESTIMATE

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

REPEATABLE (PRECISE) * * * * * * * SAMPLE ESTIMATE *

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

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

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

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

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

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 (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: h i = 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

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 Model assumptions

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 3. Timing of repeat surveys “closed” Relaxed for lab project 4. Allocation of survey effort 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 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.