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Accounting for uncertainty when estimating Pleistocene megafauna extinction times<br />Corey J. A. Bradshaw1,2, Barry W. B...
<ul><li>extinction must be inferred from record of sightings/collections
when a species becomes increasingly rare before extinction, might persist unseen for many years
so the time of last sighting often poor estimate of extinction date</li></ul>x<br />x<br />x<br />x<br />x<br />x<br />x<b...
<ul><li>optimal linear estimation
joint distribution of k same Weibull form regardless of parent distribution
estimated extinction time q
L: symmetric k×k matrix
n: Estimated shape parameter of joint Weibull distribution of k</li></ul>CI<br />q<br />x<br />x<br />x<br />x<br />x<br /...
<ul><li>maximum likelihood to account for radio carbon dating error
assume true ages U independent/uniformly distributed over (b1,g1) where b1 = extinction date
PDF of Xj:</li></ul>b1<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />present<br />past...
<ul><li>but... previous sighting rate important
length of period since last sighting informative
given previous sighting rate(n/tn), probability of next sighting
where p drops below threshold with increasing T-tn, TE inferred</li></ul>TE<br />x<br />x<br />x<br />x<br />x<br />x<br /...
<ul><li>but... TE depends on number of samples in ‘final’ period
declining influence of dates within time since last sighting
sequentially recalculated TE, weighting by cumulative distance from T1</li></ul>T1<br />TE<br />x<br />x<br />x<br />x<br ...
<ul><li>but... TE depends on number of samples in ‘final’ period
declining influence of dates within time since last sighting
sequentially recalculated TE, weighting by cumulative distance from T1</li></ul>T1<br />TE<br />x<br />x<br />x<br />x<br ...
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Accounting for uncertainty when estimating Pleistocene megafauna extinction times

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This week's topic was Accounting for uncertainty when estimating Pleistocene megafauna extinction times and was presented by Corey Bradshow Director of Ecological Modelling here at the Environment Institute.

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Accounting for uncertainty when estimating Pleistocene megafauna extinction times

  1. 1. Accounting for uncertainty when estimating Pleistocene megafauna extinction times<br />Corey J. A. Bradshaw1,2, Barry W. Brook1, Chris S. M. Turney3, Alan Cooper1,4<br />1THE ENVIRONMENT INSTITUTE, University of Adelaide; 2South Australian Research & Development Institute; 3School of Geography, University of Exeter; 4Australian Centre for Ancient DNA<br />
  2. 2. <ul><li>extinction must be inferred from record of sightings/collections
  3. 3. when a species becomes increasingly rare before extinction, might persist unseen for many years
  4. 4. so the time of last sighting often poor estimate of extinction date</li></ul>x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />?<br />?<br />present<br />past<br />Roberts & Solow 2003 Nature 426:245<br />
  5. 5. <ul><li>optimal linear estimation
  6. 6. joint distribution of k same Weibull form regardless of parent distribution
  7. 7. estimated extinction time q
  8. 8. L: symmetric k×k matrix
  9. 9. n: Estimated shape parameter of joint Weibull distribution of k</li></ul>CI<br />q<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />present<br />past<br />Roberts & Solow 2003 Nature 426:245<br />
  10. 10.
  11. 11. <ul><li>maximum likelihood to account for radio carbon dating error
  12. 12. assume true ages U independent/uniformly distributed over (b1,g1) where b1 = extinction date
  13. 13. PDF of Xj:</li></ul>b1<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />present<br />past<br />Solow et al. 2006 PNAS 103:7351<br />
  14. 14. <ul><li>but... previous sighting rate important
  15. 15. length of period since last sighting informative
  16. 16. given previous sighting rate(n/tn), probability of next sighting
  17. 17. where p drops below threshold with increasing T-tn, TE inferred</li></ul>TE<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />present<br />past<br />McInerny et al. 2006 ConservBiol20:562<br />
  18. 18. <ul><li>but... TE depends on number of samples in ‘final’ period
  19. 19. declining influence of dates within time since last sighting
  20. 20. sequentially recalculated TE, weighting by cumulative distance from T1</li></ul>T1<br />TE<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />present<br />past<br />
  21. 21.
  22. 22. <ul><li>but... TE depends on number of samples in ‘final’ period
  23. 23. declining influence of dates within time since last sighting
  24. 24. sequentially recalculated TE, weighting by cumulative distance from T1</li></ul>T1<br />TE<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />present<br />past<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br />x<br /><ul><li>now simply combine methods with Gaussian resampler within carbon date errors for each record</li></li></ul><li><ul><li>now simply combine methods with Gaussian resampler within carbon date errors for each record</li></li></ul><li>exponential<br />‘true’<br />extinction<br />linear<br />sigmoidal<br />logarithmic<br />uniform<br />
  25. 25. uniform<br />linear<br />sigmoidal<br />exponential<br />logarithmic<br />
  26. 26.
  27. 27.
  28. 28. Glacials, Interglacials, Stadials and Interstadials<br />stadial<br />interstadial<br />Interglacial<br />Glacial<br />Interglacial<br />
  29. 29. Extracting An Ice Core<br />
  30. 30. Annual Layers In Ice Core<br />
  31. 31. Cariaco Basin Bathymetry<br /><ul><li>water exchange with the open Caribbean Sea is restricted
  32. 32. intense seasonal productivity and high sedimentation rate
  33. 33. anoxic below 300 m
  34. 34. limited bioturbation (post-depositional mixing of sediments by marine life)</li></li></ul><li>
  35. 35. Mw-rs ~ -83+ 0.98 × AMS<br />
  36. 36.
  37. 37. Interstadials – OXCAL wPDFs<br />extinctions - unconstrained<br />P(rand overlap = 0.12)<br />combined ext/app P(rand overlap) = 0.13<br />extinctions - constrained<br />P(rand overlap) = 0.09<br />
  38. 38. Interstadials – OXCAL raw dates<br />extinctions - raw dates<br />P(rand overlap = 0.06)<br />combined ext/app P(rand overlap) = 0.11<br />appearances – raw dates<br />
  39. 39. Stadials – OXCAL raw dates<br />extinctions - raw dates<br />P(rand overlap = 0.46)<br />combined ext/app P(rand overlap) = 0.27<br />

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