This document summarizes a presentation on modeling speciation and extinction rates in fossil mammals over time. It describes a database of 282 fossil mammal species found at 347 European sites dating back 25 million years, with dating methods including paleomagnetism and oxygen isotopes. A Bayesian model is developed using MCMC to estimate speciation and extinction times based on species presences at sites, while accounting for dating uncertainties. The model fits speciation and extinction rates as logistic regressions on species and site effects. Results show estimated site dates look reasonable but calibration could be improved. Future work aims to incorporate spatial effects and trait-based "frailty" models to understand drivers of speciation and extinction.

1. Fossil Mammals in Time
(and Space)
Bob O'Hara
BiK-F, Frankfurt am Main, Germany
http://blogs.nature.com/boboh/2012/07/04/ISEC2012

2. Kiitoksia..
Mikael Fortelius
Jussi Eronen
– University of Helsinki

3. I want to play with the
fossil record
Some obvious statistical issues

4. The fossil record has holes
Where are the missing lynx?

5. There's a process here
somewhere
The real distribution?

6. Extinction & Speciation
in the fossil record
• How do they vary?
– can we blame climate change?
• Who dies?
– Related to traits?

7. Bad News
I won't answer either question

8. Good News
There is some progress, and there
might be more before the next ISEC

9. Where I am Now

10. Where I am Now
• Sundvollen
© Andres Lopez-Sepzulcre

11. No, where the research has
got to?
• Got the simple model working
• Starting to puzzle over the full model

12. The problems
• Estimating dates of sites
– many based on fossils, not external data
• Estimating actual extinction and
speciation times
– mark recapture

13. The First Problem
Getting some data

14. A database. Woooo!
http://www.helsinki.fi/science/now/database.html

15. Data
• 282 Species
• 347 locations
– Europe (not Russia)
• Covers last 25m years

16. The Data
Species Date Dating
I II III IV Method
Site 1 1 0 1 0 12-14 C
Site 2 1 1 0 0 12-15 C
Site 3 0 0 0 1 1-3 MN
Site 4 0 1 0 0 5-12 OI
Site 5 0 1 0 1 2-7 MN

17. Independent Dating
• Paleaomagnetic
Bloggy explanation:
http://tinyurl.com/ctskvmx
• Oxygen Isotopes
Wikipedia explains:
http://en.wikipedia.org/wiki/Oxygen_isotope_ratio_cycle
http://en.wikipedia.org/wiki/File:Phanerozoic_Climate_Change.png

18. The Model I: Species
Now 25 mya
Extinction Speciation
U(0, Speciation) U(Extinction, 25)

19. The Model II: Sites
If dating uses
Date independent data
U(min, max)
Now 25 mya
Date
U(0, 25)
If dating uses fossil data

20. The Model III: Observations
Now 25 mya
Pr(Observed|Extant) ~ Species + Site
Logistic regression

21. Estimating
extinction/speciaiotn
Now 25 mya
Pr(Observed|Extant) ~ Species + Site
Logistic regression

22. Model Fitting
model {
• OpenBUGS for(l in 1:NLocations) {
for(s in 1:NSpecies) {
Presences[l,s] ~ dbern(p[l,s])
– MCMC Age[l])
logit(pSTAR[l,s]) <- mu + al.Loc[l] + al.Sp[s]
p[l,s] <- pSTAR[l,s]*step(Age[l]-Extinct[s])*step(Speciate[s]-
}
Age[l] ~ dunif(MinAge[l], MaxAge[l])
al.Loc[l] ~ dnorm(muL,tauLoc)
}
for(s in 1:NSpecies) {
Speciate[s] ~ dunif(Extinct[s], 25)
Extinct[s] ~ dunif(0,Speciate[s])
al.Sp[s] ~ dnorm(muS,tauSp)
}
sdLoc ~ dunif(0,10); tauLoc <- pow(sdLoc,-2)
sdSp ~ dunif(0,10); tauSp <- pow(sdSp,-2)
mu ~ dnorm(0,2)
muL ~ dnorm(0,2)
muS ~ dnorm(0,2)
}

23. Estimated Site Dates
Looks OK
Not good
But no
calibration
Not good
(& doesn't
converge)
Time (mya)

24. Speciation & Extinction
Rates

25. What Next?
• Calibration needs improvement?
– also spatial effects
• Extend the model to look at trait
effects
– frailty models

26. http://blogs.nature.com/boboh/2012/07/04/ISEC2012
Credit: Dr. H.G of Cromer

27. http://blogs.nature.com/boboh/2012/07/04/ISEC2012
But I'm an
effing Bison!
Credit: Dr. H.G of Cromer