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Estimating Vital Rates

Estimating Vital Rates. Vital rates. BIDE Equation. Indices vs. Estimates. Index A value thought to be related to the parameter of interest Estimate Estimated value of the parameter of interest. When do indices work?. Relationship between index and parameter is known and 1:1

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Estimating Vital Rates

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  1. Estimating Vital Rates

  2. Vital rates • BIDE Equation

  3. Indices vs. Estimates • Index • A value thought to be related to the parameter of interest • Estimate • Estimated value of the parameter of interest

  4. When do indices work? • Relationship between index and parameter is known and 1:1 • Index is collected in a statistically valid, repeatable way • Rarely

  5. Examples of Indices • Lek counts • Roadside counts of ____ (name your favorite species) • Breeding Bird Survey

  6. Bad Reasons to Use an Index • Maintaining past data collection • It’s cheap • Volunteers like to collect them • We don’t know what else to do

  7. Indices vs. Estimates • We, as a profession, can and must do better • Always strive to estimate the parameter of interest • Use an index only as a last resort

  8. Is it an index or estimate? • That depends on the question

  9. Abundance

  10. Abundance: total number of animals • Density: animals per unit area

  11. Census – complete count

  12. Estimate: derived from sampling and an incomplete count • Sampling fraction • Incomplete detection

  13. Sampling Fraction • Proportion of the area selected in a sample • Example: randomly selecting 100 plots out of an area of 10,000 potential plots.

  14. Incomplete Detection • Proportion of animals detected within the area selected to be sampled.

  15. Heuristic Abundance Estimator

  16. Heuristic Abundance Estimator 2 • If a random sample is taken over the “entire” area

  17. Abundance estimate - detection

  18. Abundance Estimate - Detection

  19. Sampling Cows

  20. Environmental Conditions

  21. Does distance matter?

  22. Are all individuals detected equally?

  23. Is p < 1?

  24. Line Transect Sampling • Distribution of animals around a randomly placed line of known width?

  25. Line Transect Sampling

  26. Line transect sampling • How do we estimate p? • A function of frequency of detection by distance

  27. Line Transect Sampling

  28. Line transect sampling

  29. p=blue area/red area

  30. p=blue area/red area Calculus is usefulafter all

  31. Distance Sampling

  32. Distance sampling assumptions • All animals along the line are detected • Detection drops monotonically • Lines placed randomly with respect to the animals • Distances measured accurately • Trigonometry can help • Objects are detected at their initial location

  33. Common pitfalls/recommendations • Animal movement • Measurement error • Heaping • Missing animals on the line • If binning distance smaller bins closer to line • 40 m, 60-80 animals, 15-20 lines

  34. Distance sampling examples • Shipboard whale surveys • Fixed-wing aerial pronghorn surveys • Elephant dung surveys • Helicopter surveys for kangaroos

  35. What if p < 1? • Sightability

  36. Sightability models • Run detection trials on animals in known locations (radio-marked animals) • Fit a model to the trial data • Group size • Cover • Observer • Survey the study area • Apply model results to survey observations

  37. What if p < 1? • Sightability

  38. Sightability Examples • Deer • Elk • Moose

  39. Next: Mark-recapture

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