Class presentation (2 Oct)

1. Class presentation (2 Oct) • What are the 1-2 most important questions that the paper is trying to answer? • What is the approach used to answer that question? • What are the assumptions, implicit or explicit, underlying the approach? • What does the paper infer (re: point 1) • Which commandment(s) from Houle et al. might the authors have broken? • If any commandments are broken, do you think there inference holds? • How might you improve on the approach to make better inference?

2. Class presentation (2 Oct) Purposes Practice Extracting important information (quickly) Presenting information simply Practical info 10 minutes presentation with 5 minutes for discussion One page summary to be sent around class Postdocs, Let me know if you are doing this • Apply parts of what we have discussed during this course • thinking about assumptions and whether inference might hold. • are models being compared or are we comparing strawman hypotheses. • are the numbers presented appropriate

3. Extinction: Group rates: q

4. Traditional methods for estimating e.g. extinction rates • Face value • Survivorship analyses • Dynamic survivorship (Raup) • Cohort survivorship (Raup) • FreqRat (Raup and Foote) • Within time interval rates (Foote, Alroy) • Sampling standardized rates (Alroy)

5. Extinction: Capture recapture approaches

6. Day 1: catch 10 rats, put tags on them Day 2: catch rats in the same place. 2 had your tags, but 8 didn’t What is the capture probability? 2/10=0.2 How many rats are there in that “place?” 50

7. Motivation • Origination and extinction • Trends, drivers, correlates • Diversity, occupancy • Trends, drivers, correlates • Preservation/sampling is a mostly a nuisance • Incomplete sampling is universal • We can try to account for some sources (e.g. uneven no. of samples, control for facies, mineralogy of groups) • Many unknown factors, heterogeneous

9. 2. CMR Thinking 1 of 25 Encounter or Detection Histories Encounter/detection histories - Series of ones and zeros - Ones are taken as true presences - Two types of zeros - Not sampled - Not sampled or truly absent

10. 2. CMR Thinking Detection probability

11. 2. CMR Thinking Estimated no. taxa

12. 2. CMR Thinking Extinction probability

13. 2. CMR Thinking Extinction probability 16

14. Encounter/Detection Probability

15. 2. CMR Thinking Representing detection/encounter histories Detection probabilities Extinction probabilities eh = 0 0 1 0 1 1 0 0 Pr(eh = 0 0 1 0 1 1 0 0 | initial encounter in interval 3) = CJS model

16. 2. CMR Thinking Representing detection/encounter histories Detection probabilities Extinction probabilities eh = 0 0 1 0 1 1 0 0 Pr(eh = 0 0 1 0 1 1 0 0 | initial encounter in interval 3) = (1-ε3)(1-p4) (1-ε4)p5 (1-ε5)p6 [ε6 + (1-ε6)(1-p7){ε7+(1- ε7)(1- p8)}]

17. 2. CMR Thinking Representing detection/encounter histories Detection probabilities Extinction probabilities eh = 0 0 1 0 1 1 0 0 Pr(eh = 0 0 1 0 1 1 0 0 | initial encounter in interval 3) = (1-ε3)(1-p4) (1-ε4)p5 (1-ε5)p6 [ε6 + (1-ε6)(1-p7){ε7+(1- ε7)(1- p8)}]

18. 2. CMR Thinking Representing detection/encounter histories Detection probabilities Extinction probabilities eh = 0 0 1 0 1 1 0 0 Pr(eh = 0 0 1 0 1 1 0 0 | initial encounter in interval 3) = (1-ε3)(1-p4) (1-ε4)p5 (1-ε5)p6 [ε6 +(1-ε6)(1-p7){ε7+(1- ε7)(1- p8)}]

19. 2. CMR Thinking Representing detection/encounter histories Detection probabilities Extinction probabilities eh = 0 0 1 0 1 1 0 0 Pr(eh = 0 0 1 0 1 1 0 0 | initial encounter in interval 3) = (1-ε3)(1-p4) (1-ε4)p5 (1-ε5)p6 [ε6 +(1-ε6)(1-p7){ε7+(1- ε7)(1- p8)}]

20. 2. CMR Thinking Representing detection/encounter histories Detection probabilities Extinction probabilities eh = 0 0 1 0 1 1 0 0 Pr(eh = 0 0 1 0 1 1 0 0 | initial encounter in interval 3) = (1-ε3)(1-p4) (1-ε4)p5 (1-ε5)p6 [ε6 +(1-ε6)(1-p7){ε7+(1- ε7)(1- p8)}] ”sampling” and vital parameters are both explicit!

21. 3. Likelihood framework We have detection histories – now what? Pr(eh = 0 0 1 0 1 1 0 0) = (1-ε3)(1-p4) (1-ε4)p5 (1-ε5)p6 [ε6 + (1-ε6)(1-p7){ε7+(1- ε7)(1- p8)}]= H1 Likelihood (parameters|data) = H1No. cases H2No. cases HxNo. cases 0001010010 0010001101 0101010100 1001000000 0001010111 0011101000 10 3 4 18 2 1 3 No. cases

22. 3. Likelihood framework Likelihood of Detection histories • Estimate parameters (by maximizing the likelihood) • Estimate uncertainty in parameters • Compare models • e.g. same or different p’s or ε’s • e.g. with or without covariates (important factors that you think might influence p and ε) • AkaikeInformation Criteria, AIC • classical hypothesis testing • extendable to Bayesian approaches • Good statistical properties

23. 4. Assumptions Assumptions of the CJS model • After initial encounters, detection/encounter probabilities are equal for all taxa in the data/group of interest • After initial encounters, extinction probabilities for all taxa are equal • Sampling intervals are short relative to the time over which extinction is to be estimated • The fate of each taxon (with respect to extinction and encounter) is independent of the fate of every other taxon

24. 4. Assumptions Assumptions of the CJS model • After initial encounters, detection/encounter probabilities are equal for all taxa in the data/group of interest • Taxon specific covariates • After initial encounters, extinction probabilities for all taxa are equal • Sampling intervals are short relative to the time over which extinction is to be estimated • The fate of each taxon (with respect to extinction and encounter) is independent of the fate of every other taxon

25. 4. Assumptions Assumptions of the CJS model • After initial encounters, detection/encounter probabilities are equal for all taxa in the data/group of interest • After initial encounters, extinction probabilities for all taxa are equal • Taxon specific covariates • Sampling intervals are short relative to the time over which extinction is to be estimated • The fate of each taxon (with respect to extinction and encounter) is independent of the fate of every other taxon

26. 4. Assumptions Assumptions of the CJS model • After initial encounters, detection/encounter probabilities are equal for all taxa in the data/group of interest • After initial encounters, extinction probabilities for all taxa are equal • Sampling intervals are short relative to the time over which extinction is to be estimated • Simulations show that this is not a big problem • The fate of each taxon (with respect to extinction and encounter) is independent of the fate of every other taxon

27. 4. Assumptions Assumptions of the CJS model • After initial encounters, detection/encounter probabilities are equal for all taxa in the data/group of interest • After initial encounters, extinction probabilities for all taxa are equal • Sampling intervals are short relative to the time over which extinction is to be estimated • The fate of each taxon (with respect to extinction and encounter) is independent of the fate of every other taxon • Corrections for over-dispersion • Co-occurrence analyses

28. 5. Covariate modeling Covariate modeling • A way to include factors or variables that may be important in explaining variation in the parameters (e.g. extinction, sampling) you are interested in • Allows us to compare models with different [or no] covariates (Model comparison and selection) • models to compare • ε(constant)p(time-varying) • ε(time-varying)p(sea-levels)

29. 5. Covariate modeling Covariate modeling via link functions • Taxonspecific covariates • size • minerology • taxonomic group

30. 5. Covariate modeling Covariate modeling via link functions • Time specific covariates • Duration of bin • Sea-level • Temperature

31. 5. Covariate modeling Covariate modeling via link functions

32. 6. MARK

33. MARK demo • Follow supplement from Liow and Nichols • Rexercise3

34. 7. Coda Why Capture-Mark-Recapture (CMR) ? • Detection probability • Separating between - probability of detection (given presence) - probability of the parameters in question (e.g. survivorship, origination, occupancy, immigration) and derived parameters such as species richness/diversity The probability of detection or sampling is sometimes only a nuisance but sometimes interesting in itself. • Covariates can be EASILY included in models for both vital parameters and sampling/detection estimates. • Covariates can be modeled at a variety of levels (e.g. group factors, individual traits, temporal characteristics)

35. References • Reading: Liow, L. H. and J. D. Nichols (2010). Estimating rates and probabilities of origination and extinction using taxonomic occurrence data: Capture-recapture approaches. Short Courses in Paleontology: Quantitative Paleobiology. G. Hunt and J. Alroy, Paleontological Society: 81-99 (plus supplement which will help with the MARK exercise) • Mark Book (Chap 3 most relevant for today’s lecture)http://www.phidot.org/software/mark/docs/book/

36. Assignment • Use the previous data you downloaded and arrange it in a matrix that will be suitable for data analyses in MARK. Using MARK or RMARK run a few reasonable CJS models on the data • Write a short note on your observations

37. bL FL Ft bt Per capita origination and extinction rates Foote, M. 2000. Origination and extinction components of taxonomic diversity: general problems. Paleobiology 26:74-102.