Designing a Field Project

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Designing a Field Project

• Michael J. Conroy

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PURPOSES OF SAMPLING

• ESTIMATE ATTRIBUTES (PARAMETERS)
• Abundance/ density
• Survival
• Home range size
• ALLOW LEGITIMATE EXTRAPOLATION FROM DATA TO
  POPULATIONS
• PROVIDE MEASURES OF STATISTICAL RELIABILITY

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SAMPLING NEEDS TO BE

• ACCURATE LEADING TO UNBIASED ESTIMATES
• REPEATABLE ESTIMATES LEAD TO SIMILAR ANSWERS
• EFFICIENT DO NOT WASTE RESOURCES

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BIAS

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

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UNBIASED
TRUE VALUE
SAMPLE ESTIMATE








AVERAGE ESTIMATE
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BIASED
TRUE VALUE
SAMPLE ESTIMATE








BIAS
AVERAGE ESTIMATE
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REPEATABLE (PRECISE)
SAMPLE ESTIMATE








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NOT REPEATABLE (IMPRECISE)



SAMPLE ESTIMATE





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CAN BE IMPRECISE BUT UNBIASED.. OR

AVERAGE ESTIMATE


SAMPLE ESTIMATE





TRUE VALUE
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PRECISELY BIASED..OR
TRUE VALUE
SAMPLE ESTIMATE








AVERAGE ESTIMATE
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IMPRECISE AND BIASED!
AVERAGE ESTIMATE


SAMPLE ESTIMATE






TRUE VALUE
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ACCURATEUNBIASED PRECISE
TRUE VALUE
SAMPLE ESTIMATE








AVERAGE ESTIMATE
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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

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Key Issues

• Spatial sampling
• Proper consideration and incorporation of
  detectability

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Sampling principles

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

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Remember

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

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Example- Pheasants in Corbett National Park
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What is the objective?

• Unbiased estimate of population density of
  pheasants on Corbett National Park
• Coefficient of variation of estimate lt 20
• As cost efficient as possible

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What is the target population?Population in CNP
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What are the appropriate sampling units?

• Quadrats?
• Point samples?
• Line transects?

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Sampling units- nonrandom placement
Road
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Nonrandom placement

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

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OR- redefine the target
Road
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Sampling units- random placement
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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

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Stratified sampling
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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

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Single, unreplicated line
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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 cant, you cant but study results may
  need different interpretation

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Estimation from Count Data to Population (I)

• Geographic variation (cant 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

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A valid sampling design

• Allows valid probability inference about the
  population
• Statistical model
• Allows estimates of precision
• Replication, independence

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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

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Remember

• Incomplete detection MUST be accounted for in
  sampling and estimation

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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

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Flushed 2 pheasants from quadrat but there were
4!
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Detectability Conceptual Basis

• N abundance
• C count statistic
• p detection probability P(member of N appears
  in C)

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Detectability Inference

• Inferences about N require inferences about p

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Above example p0.5

• If you know p you can get N (for the sample unit)

• If you ignore p then C 2 is biased
• Usually we have to collect other data to estimate
  p!

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Abundance estimation

• Distance sampling
• Mark-recapture
• Multiple observers
• Independent
• Dependent
• Temporal removal
• Marked subsample
• Sighting probability models
• Bounded counts

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I(ndices)!
I
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INDICES

• Assumed relationship of index to N
• Usually assumed linear through zero
• Assumed homogeneous over time,space
• Practically never tested!

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Linear index
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Nonlinear index
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Indices Assume Equal Detectability (p)!

• Over time (this sample and next sample)
• But observers change, conditions change!
• Over space
• Conditions may differ (e.g., differ amounts of
  cover)

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Nonhomogeneous index
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Indices Assume Equal Detectability!

• N1 abundance for area 1 4
• N2 abundance for area 2 8
• p1 detection for area 1 0.50
• p2 detection for area 2 0.25
• C1 4 X .50 2
• C2 8 X .25 2
• Index says N1 N2 !
• \

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Indices Assume Equal Detectability (p)!

• Heterogeneous detection can mask real differences
• Heterogeneous detection can reveal false
  differences
• You cant possibly know without estimating p or
  at least testing for heterogeneity!

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Uncalibrated indices

• Are unsound scientifically
• Cannot be made sound by standardisation!

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Double sampling

• Large sample provides biased estimate of
  abundance
• Smaller (calibration) sample provides unbiased
  (or less biased) estimate

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Aerial survey of elephants
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Aerial surveys

• Effective for covering large expanse of terrain
• Known to undercount elephants by ???
• Calibrate with counts by ground observers

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Double survey design
Aerial only
Aerial ground
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Estimation

• Aerial survey estimate 40 elephants
• Double survey estimate of p 20 air/ 30
  ground0.67
• Revised survey estimate 40/0.67 60

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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