Methods for Largescale Comparative Risk Analyses

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Methods for Large-scale Comparative Risk Analyses

• Comparative analyses
• More detailed ESU analyses

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Method for Comparative Risk Analyses

• Use only time series of spawner counts (or index
  counts)
• Robust to high levels of sampling error
• Accounts for hatchery fish in counts
• Accounts / tests for trends
• Accounts / tests for density-dependence

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Overview of the Dennis Model
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Underlying Model
where e is lognormal process error
See Dennis et al 1991
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Foundations of the Dennis Model

• Population Counts
• Nt1 comes from Nt
• mean(ln(Ntt/Nt)) increases linearly with lag, t

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

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Need Population Counts Nt1 comes from Nt

• Spawner counts violate this assumption
• Wont work as a surrogate for population count

• Estimate of s2
• Using spawner counts 10000 too high
• Estimate of m
• Using spawner counts 100 too low

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Getting around this problem

• Need a count for which N_t1 comes from N_t
  Living current and future spawners

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S80SS80
S81SS81
S82SS82
S83SS83
S84SS84
OCEAN
DEAD
STREAM
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Estimated Living Current and Future Spawners

• True value

• Estimated value

These are the numbers you see in the running sum
figures.
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Estimating s2
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Estimating m
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How good is the parameter estimation with the
running sum counts?

• Mean percent under-estimation of m
• Spawner
• 50 (robust to sampling error)
• Running sum counts
• 0 (robust to sampling error)
• Mean percent over-estimation of s2
• Spawner
• 3,000 (increases with severe sampling error)
• Running sum counts
• 50 (increases with severe sampling error)