Breeding Bird Survey and West Nile Virus

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Breeding Bird Survey and West Nile Virus

• Guide Shannon LaDeau
• Team Maggie, Rich, Nat, Hu, Aparna

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The story so far

• The West Nile virus was first seen in NY in 1999.
  
• Many birds were found dead, and a lot of them
  tested positive for the presence of West Nile.
• The effect of this disease on bird populations
  has not been quantified.

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The question..

• Has West Nile virus caused bird populations to
  decline?
• Problem 1 We cannot conduct an experiment to
  answer this question.
• Problem 2 Data on bird mortality are difficult
  to collect.
• Problem 3 This process occurs over a large
  temporal and spatial scale and may be masked by
  other sources of variation, both internal to the
  population and otherwise.

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One solution

• Breeding Bird Survey (BBS) data.
• Birds are counted along 25-mile routes each year
  in spring.
• There are 3700 routes across continental US and
  Canada.
• Qualified volunteer observers perform the
  surveys.
• YAY!!

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YAY???
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More challenges..
The number of routes surveyed varies through the
study period

• The bird counts are not corrected for observer
  ability.
• The number of routes surveyed has been increasing
  the past 20 years.
• (a) This leads to a lot of missing data.
• (b) It might appear that the bird populations are
  declining.

Number of Routes Surveyed
Year
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More solutions

• Throw out routes with too many missing years of
  information, or
• Throw out years with too many routes that were
  not surveyed.
• BUT - Why waste the data?
• Alternative Use MCMC to fill in the unobserved
  years/routes! ?

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A population model to describe the variability in
counts
counts poisson(mu) muI,j,k observeri
route j year k observer normal(0,
tau.ob) route normal (0, tau.rt) year normal
(0, tau.yr) each tau gamma (0.001,0.001)
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Uh-oh Two approaches to predicting unobserved
data

• Idea - Model the counts as a function of the
  observer, the route and the year of observation.
• More options
• Routes are spatially independent.
• Routes have spatially correlated error.
• Which is better?

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Population model to predict counts at BBS survey
routes for American Crow
Box plot of MCMC predictions Red circles are
observed data
Count per route
Year
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A cross-validation approach

• Randomly assign 10 of the bird counts as
  unmeasured.
• Predict these counts using MCMC compare against
  the observed values.

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Is there a West Nile signal?

• Reminder West Nile virus was first reported in
  1999.
• We want to know if there is evidence that
  population trends changed at this time.
• We can use change point analysis to identify the
  most likely period that shows a change in trend.
• This assumes
• (1) a single change point.
• (2) linear slope on either side of change point.
• (3) lines intersecting at the change point.
• Prediction If West Nile virus has had
  catastrophic effects, the change point should
  occur later than1999.

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Doodle of the change-point models

• Yi dnorm(mui, tau)
• mui lt- alpha betaJ (xi - x.change)
• where J is 1 if Xi gt x.change and 2 o/w.
• tau dgamma(0.001, 0.001)
• alpha dnorm(0.0,1.0E-6)
• betaj dnorm(0.0,1.0E-6)
• sigma lt- 1 / sqrt(tau)
• x.change dunif(1980, 2005)

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American Crow
House Finch
Eastern Bluebird
Black-capped Chickadee
Blue Jay
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Change points
House Finch

Crow and Bluebird
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Mid WN arrival region
Early WN arrival region
Late WN arrival region
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Summary

• Two of five species showed distinct change points
  coincident with the arrival of West Nile virus.
• The change point for American crows appears to be
  earlier in regions where West Nile arrived first.