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
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)
}
