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 ...
Upcoming SlideShare
Loading in …5
×

Accounting for uncertainty when estimating Pleistocene megafauna extinction times

1,267 views
1,133 views

Published on

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.

Published in: Education, Technology
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
1,267
On SlideShare
0
From Embeds
0
Number of Embeds
5
Actions
Shares
0
Downloads
7
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

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 />

×