Quantifying Risk using Population Count Time Series

1
Quantifying Risk using Population Count Time
Series

• Estimating rates of decline
• Robust risk metrics

2
Why is it hard to detect trends?
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The good news

• Strong theoretical foundations the analysis of
  age-structured (think salmon) fluctuating
  populations at low densities
• Tuljapurkar 1989
• Dennis et al 1991
• Statistical distributions and behaviors are known

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The basic idea
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Predictors

• Whats the best predictor of where the population
  will be in x years?
• Mean
• What determines the variability of future
  trajectories?
• Variance

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Behaviors

• average of ln(Ntt/Nt) decreases linearly with
  lag, t

• variance of ln(Ntt/Nt) increases linearly with
  lag, t

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Summary

• Population time series are a bit like
  coin-flipping
• Two of the most basic attributes of population
  growth are its
• long-term year-to-year mean
• long-term year-to-year variance

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The bad news

• Existing parameter estimation methods dont work
  for salmon data

• WE HAVE
• Stage-specific counts
• Count error
• personnel bias
• visibility
• changing methods
• Age perturbations
• Hatchery fish added

• OLD METHODS WANT
• Count of total population
• No sampling error
• Stable age structure

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Development of new methods

• Holmes, E. E. 2000. Estimating risks in declining
  populations with poor data (in review)
• McClure, M., Holmes, E. and B. Sanderson. A
  standardized quantitative risk assessment for
  salmonids in the Columbia River Basin (in prep.)
• CRI 2000. A standardized quantitative risk
  assessment for salmonids in the Columbia River
  Basin. www.nwfsc.noaa.gov/cri

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Overview of the new methods
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Testing using stochastic life cycle models
(matrix models)
eggs
year 1
year 2
year 3
year 4
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Results old methods
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Results new methods
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Summary

• New methods have been developed to cope with
  sampling error and stage specific counts
• Lambda, the median rate of decline, is very well
  estimated and estimate is quite insensitive to
  sampling error (best predictor of risk)
• New methods estimate variance better to an order
  of magnitude, but still sensitive to sampling
  error
• Consequently, probabilities of decline (or
  extinction are more sensitive to sampling error
  than lambda)