Known Fate Models

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Known Fate Models
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Study Design
Experiments (Assigned Treatments)
Quasi-Experiments (Unassigned Treatments)
Survey Sampling
CMR
Observational Studies (Passive Monitoring)
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Decision Tree
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Known Fate

• Fate is known with certainty
• Do not have to estimate p
• Most often radio-telemetry studies
• Also, nest (egg fish) survival
• Nest survival is a special case
• Interval specific fate or
• DSR

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Assumptions

• Fate of marked individuals is known with
  certainty
• All marked individuals have the same survival
  probability
• Heterogenity
• Fate of marked individuals is independent
• Censoring is independent of fate
• Survival is constant over time
• Relaxed in many models

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Parameters

• True survival probability (S) for a specified
  interval
• Probability that an individual alive at occasion
  i survives to occasion i1
• This is slightly, but importantly different, than
  the true DSR in most nest survival studies
• What happens if occasions are too long?

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Design

• Frequently, a specific (short) time frame
• Post-marking, marked individuals are monitored at
  regular or irregular
• How to make irregular intervals comparable?
• Best if all marked individuals are monitored at
  each occasion
• Clearly defined intervals are easier
• Nest survival module for messy data
• Staggered entry to improve precision of estimates
  for later intervals
• Right censoring of individuals with uncertain
  fate

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Design
-Interval Lengths Can Vary (long enough for
death) -Timing of mortality not needed, but
frequently recorded
Right Censoring
Staggered Entry
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Design

• Monitoring frequency /timing and number of
  releases
• Monitored frequently enough to minimize censoring
  or detect individuals that emigrate from study
  area
• Include demographic class (e.g., gender, age) of
  individuals
• Sample sizes may be reduced through marker
  effects

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Design Sample Size

• Objective Based
• What to consider?
• Precision
• Bias
• Binomial Outcome
• Sampling variance pq/n or np(1-p)

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Design Sample Size

• New technology more frequent monitoring
• More precise estimates when mortality is frequent
  (Johnson 1979)
• Sample size gains may not be as expected
• Observations not independent (Otis and White
  1999)
• More marked individuals than more frequent
  monitoring (Garton et al. 2001, White and Garrott
  1990)
• Population-level inference

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Design Bias
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Design - Bias
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Models

• Smoothed constant survival models (parametric)
• Exponential, Wiebull, and lognormal
• Non-parametric (distribution free)
• Kaplan-Meier
• Step-function updated (at nest occasion) every
  time there is a mortality
• User-specified models

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Models

• Constant solid curved
• KM step
• Smoothed - dashed

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MARK -format

• Live dead
• 1 alive in alive column
• 1 dead in dead column
• 11, 10, but not 01
• Animal can can be temporarily censored from
  population
• e.g., 100011