GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 1

Meetings: Tuesdays and Thursdays, 10:30-12:00, HGS 180

Nature of the course: This course is an introduction to mathematical modeling as applied to problems in paleobiology and evolutionary biology. Topics include: basic probability theory; general approaches to modeling; model comparison using likelihood and other criteria; forward modeling of branching processes; sampling models; and inverse methods. A series of programming exercises and a term project are required. Programming in R or C is recommended, but any language may be used.

Requirements:

1. Short exercises

2. Readings to be assigned

3. Term paper: Original research, relevant to topics covered in course. Publication length and quality. Brief presentation of research.

Prerequisites: Mathematics through first-year calculus; basic computer programming skills (or willingness to learn)

URL for course materials: http://geosci.uchicago.edu/∼foote/MODEL

Reading

General Reference Works Burnham, K.P., and D. R. Anderson. 1998. Model selection and inference: a practical information-theoretic approach. Springer, New York. Edwards, A.W.F. 1992. Likelihood. Johns Hopkins U. Press. Efron, B. and R.J. Tibshirani. 1993. An introduction to the bootstrap. Chapman and Hall, N.Y. Feller, W. 1968 (and other editions). An introduction to probability theory and its applications (two volumes). John Wiley and Sons, N.Y. Gilinsky, N.L., and P.W. Signor, eds. 1991. Analytical paleobiology. Short Courses in Paleontology Number 4. Paleontological Society, Knoxville, Tenn. Gumbel, E.J. 1958. Statistics of extremes. Columbia University Press, N.Y. Press, W.H., S.A. Teukolsky, W.T. Vetterling, B.P. Flannery. 1996. Numerical Recipes in C (2d. ed.). Cambridge U. Press. [See also FORTRAN edition of this text.] Rohlf, F.J., and R.R. Sokal. 1981. Statistical tables (2d. ed.) W.H. Freeman and Co., N.Y. Siegel, S., and N.J. Castellan, Jr. 1988. Nonparametric statistics for the behavioral sciences. McGraw-Hill, N.Y. Sokal, R.R., and F.J. Rohlf. 1981. Biometry (2d. ed.) W.H. Freeman and Co., N.Y. GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 2

Articles Alroy, J., C.R. Marshall, R.K. Bambach, K. Bezusko, M. Foote, F.T. F¨ursich, T.A. Hansen, S.M. Holland, L.C. Ivany, D. Jablonski, D.K. Jacobs, D.C. Jones, M.A. Kosnik, S. Lidgard, S. Low, A.I. Miller, P.M. Novack-Gottshall, T.D. Olszewski, M.E. Patzkowsky, D.M. Raup, K. Roy, J.J. Sepkoski, Jr., M.G. Sommers, P.J. Wagner, and A. Webber. 2001. Effects of sampling standardization on estimates of Phanerozoic marine diversification. Proceedings of the National Academy of Sciences, USA 98:6261-6266. Bookstein, F.L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446-464. Connolly, S.R. and A.I. Miller. 2001a. Joint estimation of sampling and turnover rates from fossil databases: capture-mark-recapture methods revisited. Paleobiology 27:751-767. Connolly, S.R. and A.I. Miller. 2001b. Global Ordovician faunal transitions in the marine benthos: proximate causes. Paleobiology 27:779-785. Connolly, S.R. and A.I. Miller. 2002. Global Ordovician faunal transitions in the marine benthos: ultimate causes. Paleobiology 28:26-40. Foote, M. 1988. Survivorship analysis of Cambrian and Ordovician trilobites. Paleobiology 14:258-271. Foote, M. 1992. Rarefaction analysis of morphological and taxonomic diversity. Paleobiology 18:1-16. Foote, M. 1994. Morphological disparity in Ordovician-Devonian crinoids and the early saturation of morphological space. Paleobiology 20:320-344. Foote, M. 1996. On the probability of ancestors in the fossil record. Paleobiology 22:141-151. Foote, M. 1997. Estimating taxonomic durations and preservation probability. Paleobiology 23:278-300. Foote, M. 2000. Origination and extinction components of taxonomic diversity: general problems. Paleobiology 26 (supplement to No. 4): 74-102. Foote, M. 2001a. Evolutionary rates and the age distributions of living and extinct taxa. Pp. 245-294 in J. B. C. Jackson, S. Lidgard, and F. K. McKinney, eds. Evolutionary patterns: growth form and tempo in the fossil record. University of Chicago Press, Chicago. Foote, M. 2001b. Inferring temporal patterns of preservation, origination, and extinction from taxonomic survivorship analysis. Paleobiology 27:602-630. Foote, M. 2003. Origination and extinction through the Phanerozoic: a new approach. Journal of Geology 111:125-148; erratum p. 752-753. Foote, M. 2005. Pulsed origination and extinction in the marine realm. Paleobiology 31:6-20. Foote, M., and D. M. Raup. 1996. Fossil preservation and the stratigraphic ranges of taxa. Paleobiology 22:121-140. Foote, M., J. P. Hunter, C. M. Janis, and J. J. Sepkoski, Jr. 1999. Evolutionary and preservational constraints on origins of biologic groups: divergence times of eutherian mammals. Science 283:1310-1314 [plus online Technical Comments: Science 285:2031a]. GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 3

Gaines, S.D., and M. W. Denny. 1993. The largest, smallest, highest, lowest, longest, and shortest: extremes in ecology. Ecology 74:1677-1692. Gilinsky, N.L. 1994. Volatility and the Phanerozoic decline of background extinction intensity. Paleobiology 20:445-458. Gilinsky, N.L., and I.J. Good. 1991. Probabilities of origination, persistence, and extinction of families of marine invertebrate life. Paleobiology 17:145-166. Holland, S.M. 1995. The stratigraphic distribution of fossils. Paleobiology 21:92-109. Holland, S.M. 2000. The quality of the fossil record: a sequence-stratigrahpic perspective. Paleobiology 26(suppl. to no. 4):148-168 Holland, S.M. 2003. Confidence limits on fossil ranges that account for facies changes. Paleobiology 29:468-479. Hunt, G. 2004a. Phenotypic variation in fossil samples: modeling the consequences of time-averaging. Paleobiology 30:426-443. Hunt, G. 2004b. Phenotypic variance inflation in fossil samples: an empirical assessment. Paleobiology 30:487-506. Hunt, G., and R. E. Chapman. 2001. Evaluating hypotheses of instar-grouping in arthropods: a maximum likelihood approach. Paleobiology 27:466-484. Magall´on,S., and M. J. Sanderson. 2001. Absolute diversification rates in angiosperm clades. Evolution 55:1762-1780. McConway, K. J., and H. J. Sims. 2004. A likelihood-based method for testing for nonstochastic variation of diversification rates in phylogenies. Evolution 58:12-23. Miller, A.I. and M. Foote. 1996. Calibrating the Ordovician radiation of marine life: implications for Phanerozoic diversity trends. Paleobiology 22:304-309. Miller, A. I., and M. Foote. 2003. Increased longevities of post-Paleozoic marine genera after mass extinctions. Science 302:1030-1032. Nee, S. 2004. Extinct meets extant: simple models in paleontology and molecular phylogenetics. Paleobiology 30:172-178. Patzkowsky, M.E. 1995. A hierarchical branching model of evolutionary radiations. Paleobiology 21:440-460. Przeworski, M., and J. D. Wall. 1998. An evaluation of a hierarchical branching process as a model for species diversification. Paleobiology 24:498-511. Raup, D.M. 1975. Taxonomic diversity estimation using rarefaction. Paleobiology 1:333-342. Raup, D.M. 1978. Cohort analysis of generic survivorship. Paleobiology 4:1-15. Raup, D.M. 1985. Mathematical models of cladogenesis. Paleobiology 11:42-52. Raup, D.M., and R.E. Crick. 1981. Evolution of single characters in the Jurassic ammonite Kosmoceras. Paleobiology 7:200-215. Roopnarine, P.D. 2001. The description and classification of evolutionary mode: a computational approach. Paleobiology 27:446-465. Sims, H.J., and K.J. McConway. 2003. Nonstochastic variation of species-level diversification rates within angiosperms. Evolution 57:460-479. GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 4

Solow, A.R., and W. Smith. 1997. On fossil preservation and the stratigraphic ranges of taxa. Paleobiology 23:271-277. Stanley, S.M., P.W. Signor III, S. Lidgard, A.F. Karr. 1981. Natural clades differ from “random” clades: simulations and analyses. Paleobiology 7:115-127. Tavar´e,S., C. R. Marshall, O. Will, C. Soligo, and R. D. Martin. 2002. Using the fossil record to estimate the age of the last common ancestor of extant primates. Nature 416:726-729.

List of topics (subject to evolve as the course progresses)

1. Jan. 3: Introduction to Probability, 1

Topics: Introduction; probability; sample space; conditional probability; combinatorials; binomial, Poisson, and multinomial distributions

Reading: Efron and Tibshirani, Ch. 3; Feller, vol. I: Ch. I, Ch. II (sections 1-4, 8), Ch. VI

Assignment out: Exercise 1 (due Jan. 12)

2. Jan. 5: Introduction to Probability, 2

Topics: Random variables; Density; distribution; expectation; variance; covariance; waiting times; application to binomial, Poisson, uniform, and exponential distributions; application to novel situations

Reading: Feller, vol. I, Ch. IX (sections 1-5), vol. II, Ch. I (sections 1-7)

3. Jan. 10: Sampling

Topics: Sampling; resampling; rarefaction; bootstrapping; extreme value statistics

Assignment out: Exercise 2 (due Jan. 19)

Reading: Efron and Tibshirani, Ch. 6; Raup (1975); Foote (1992); Foote (1994); Gaines and Denny (1993) GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 5

4. Jan. 12: Introduction to Modeling

Topics: Introduction to modeling; “philosophy” of modeling; deterministic vs. stochastic models; path-dependent models; random walks

Reading: Raup and Crick (1981); Bookstein (1987) [skim]; Hunt (2004a); Roopnarine (2001) [skim]; Hunt (in press); Feller, vol. I, Ch. III [optional]

Assignment in: Exercise 1

5. Jan. 17: Introduction to Likelihood

Topics: Introduction to likelihood; method of maximum support— illustration with binomial, Poisson, exponential, and normal distributions; likelihood ratios, AIC, and model selection—illustration with random walks, differential extinction rates, differential diversification rates, instars (mixture models); analytical vs. numerical solutions

Readings: Edwards, Chs. 1-4, 5 (sections 5.1-5.6), 6 (sections 6.1-6.2); Connolly and Miller (2001a); Hunt and Chapman (2001).

Assignment out: Exercise 3 (due Jan. 26)

6. Jan. 19: Introduction to Branching Models

Topics: Introduction to branching models; pure birth and birth-death models; time-homogenous and type-varying models; analytic approaches vs. simulation; importance of empirical scaling; non-hierarchical vs. hierarchical models; forward vs. inverse problems; examples of forward problems—clade survivorship, multiple origins of life, taxon size and effect on survivorship, improbability of animal phyla with few species, taxonomic rates and volatility in diversity

Readings: Raup (1985); Nee (2004); Gilinsky (1994); Stanley et al. (1981); Miller and Foote 2003)

Assignment in: Exercise 2 GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 6

7. Jan. 24: Inverse Problems with Birth-Death Models

Topics: Introduction to inverse problems; long-term average origination and extinction rates; interval rates

Reading: Gilinsky and Good (1991); Foote (2000); Foote (2001a); selected pages from Principles of Paleontology (3/e).

Assignment out: Exercise 4 (due Feb. 2)

8. Jan. 26: Hierarchical Branching Models, 1

Topics: Hierarchical branching models, with emphasis on inverse problems; alternative risk models

Reading: Raup (1978); Raup (1985); Foote (1988); Foote (2001a); Patzkowsky (1995)

Assignment in: Exercise 3

9. Jan. 31: Hierarchical Branching Models, 2

Topics: Hierarchical branching models, continued.

10. Feb. 2: Sampling Models, 1

Topics: Incorporation of sampling models; time-homogeneous sampling; forward and inverse problems with long-term average rates

Readings: Foote and Raup (1996); Solow and Smith (1997); Foote (1997)

Assignment in: Exercise 4

11. Feb. 7: Sampling Models, 2

Topics: Sampling models, continued GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 7

12. Feb. 9: Sampling Models, 3

Topics: Further applications of sampling models: probability of hidden clade history; probability of ancestors in the fossil record; proportion of monotypic taxa and proportion of species in the largest clade; confidence limits on stratigraphic ranges

Readings: Foote, Hunter, Janis & Sepkoski (1999); Tavar´eet al. (2002); Przeworski and Wall (1998); Foote (1996); Holland (2003)

13. Feb. 14: Sampling Models, 4

Topics: Introduction to time-heterogeneous sampling models; forward modeling; predicting apparent patterns of first and last appearance

Readings: Holland (1995); Holland (2000); Foote (2000)

14. Feb. 16: Inverse Methods and Sampling Models, 1

Topics: Inverse methods with time-varying models—sampling standardization

Readings: Miller and Foote (1996); Alroy et al. (2001); Bush et al. (2004)

15. Feb. 21: Inverse Methods and Sampling Models, 2

Topics: Inverse methods with time-varying models—other approaches

Readings: Foote (2001b); Foote (2003); Connolly and Miller (2001a,b, 2002); Alroy (manuscript).

16. Feb. 23: Further Applications

Topics: Other applications: risk models; pulsed vs. continuous turnover; long-term quiescence in extinction

Readings: Foote (2005) GEOS 33000/EVOL 33000: Winter 2006 Course Outline Page 8

17. Feb. 28: Inference from Extant Taxa

Topics: Rate inference with extant taxa only

Readings: Nee (2001); Nee (2004); Magall´onand Sanderson (2001); Sims and McConway (2003); McConway and Sims (2004)

18. Mar. 2

Student presentations

19. Mar. 7

Student presentations