GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 1. Tuesdays and Thursdays, 10:30-11:50, HGS 180 except February 11th

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1 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 1 Meetings: Tuesdays and Thursdays, 10:30-11:50, HGS 180 except February 11th 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; student-led discussions 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: foote/model/2010 Reading General Reference Works [*=copy available in HGS 228] Burnham, K.P., and D. R. Anderson Model selection and inference: a practical information-theoretic approach. Springer, New York. Burnham, K.P., and D. R. Anderson Model selection and multimodel inference: a practical information-theoretic approach. Springer, New York. *Edwards, A.W.F Likelihood. Johns Hopkins U. Press. *Efron, B. and R.J. Tibshirani An introduction to the bootstrap. Chapman and Hall, N.Y. *Feller, W (and other editions). An introduction to probability theory and its applications (two volumes). John Wiley and Sons, N.Y. *Foote, M. and A. I. Miller Principles of paleontology, third edition. W.H. Freeman, N.Y. *Gilinsky, N.L., and P.W. Signor, eds Analytical paleobiology. Short Courses in Paleontology Number 4. Paleontological Society, Knoxville, Tenn. Gumbel, E.J Statistics of extremes. Columbia University Press, N.Y.

2 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 2 Press, W.H., S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Numerical Recipes in C (2d. ed.). Cambridge U. Press. [See also FORTRAN edition of this text.] Rohlf, F.J., and R.R. Sokal Statistical tables (2d. ed.) W.H. Freeman and Co., N.Y. Siegel, S., and N.J. Castellan, Jr Nonparametric statistics for the behavioral sciences. McGraw-Hill, N.Y. Sokal, R.R., and F.J. Rohlf Biometry (2d. ed.) W.H. Freeman and Co., N.Y. Articles Alroy, J., C.R. Marshall, R.K. Bambach, K. Bezusko, M. Foote, F.T. Fürsich, 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 Effects of sampling standardization on estimates of Phanerozoic marine diversification. Proceedings of the National Academy of Sciences, USA 98: Anderson, S Patterns of faunal evolution. Quarterly Review of Biology 49: Baumiller, T.K Survivoship analysis of Paleozoic Crinoidea: Effect of filter morphology on evolutionary rates. Paleobiology 19: Benton, M.J., M.A. Wills, and R. Hitchin Quality of the fossil record through time. Nature 403: Bininda-Emonds, O.R.P., M. Cardillo, K.E. Jones, R.D.E. McPhee, R.M.D. Beck, R. Grenyer, S.A. Price, R.A. Vos, J.L. Gittleman, and A. Purvis The delayed rise of present-day mammals. Nature 446: Bookstein, F.L Random walk and the existence of evolutionary rates. Paleobiology 13: Bush, A.M., and R.K. Bambach Did alpha diversity increase during the Phanerozoic? Lifting the veils of taphonomic, latitudinal, and environmental biases. Journal of Geology 112: Bush, A.M., M.J. Markey, and C.R. Marshall Removing bias from diversity curves: the effects of spatially organized biodiversity on sampling-standardization. Paleobiology 30: Charlesworth, B Some quantitative methods for studying evolutionary patterns in single characters. Paleobiology 10: Cheetham, A.H Tempo of evolution in a Neogene bryozoan: Rates of morphologic change within and across species boundaries. Paleobiology 12: Clyde, W. C., and P. D. Gingerich Rates of evolution in the dentition of Early Eocene Cantius: Comparison of size and shape. Paleobiology 20: 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: Connolly, S.R. and A.I. Miller. 2001b. Global Ordovician faunal transitions in the marine benthos: proximate causes. Paleobiology 27: Connolly, S.R. and A.I. Miller Global Ordovician faunal transitions in the marine benthos: ultimate causes. Paleobiology 28:26-40.

3 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 3 Cooper, R.A., P.A. Maxwell, J.S. Crampton, A.G. Beu, C.M. Jones, and B.A. Marshall Completeness of the fossil record: Estimating losses due to small body size. Geology 34: Crisp, M. D., and L. G. Cook Explosive radiation or cryptic mass extinction? Interpreting signatures in molecular phylogenies. Evolution 63: Dial, K. P., and J. M. Marzluff Nonrandom diversification within taxonomic assemblages. Systematic Zoology 38: Foote, M Survivorship analysis of Cambrian and Ordovician trilobites. Paleobiology 14: Foote, M Rarefaction analysis of morphological and taxonomic diversity. Paleobiology 18:1-16. Foote, M Morphological disparity in Ordovician-Devonian crinoids and the early saturation of morphological space. Paleobiology 20: Foote, M On the probability of ancestors in the fossil record. Paleobiology 22: Foote, M Estimating taxonomic durations and preservation probability. Paleobiology 23: Foote, M Origination and extinction components of taxonomic diversity: general problems. Paleobiology 26 (supplement to No. 4): Foote, M. 2001a. Evolutionary rates and the age distributions of living and extinct taxa. Pp 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: Foote, M. 2001c. Estimating the completeness of the fossil record. Pp in D. E. G. Briggs and P. R. Crowther, eds. Paleobiology II. Blackwell Scientific, Oxford. Foote, M Origination and extinction through the Phanerozoic: a new approach. Journal of Geology 111: ; erratum p Foote, M Pulsed origination and extinction in the marine realm. Paleobiology 31:6-20. Foote, M. 2007a. Extinction and quiescence in marine animal genera. Paleobiology 33: Foote, M. 2007b. Symmetric waxing and waning of marine invertebrate genera. Paleobiology 33: Foote, M., and D. M. Raup Fossil preservation and the stratigraphic ranges of taxa. Paleobiology 22: Foote, M., J. S. Crampton, A. G. Beu, B. A. Marshall, R. A. Cooper, P. A. Maxwell, and I. Matcham Rise and fall of species occupancy in Cenozoic fossil mollusks. Science 318: Foote, M., J. P. Hunter, C. M. Janis, and J. J. Sepkoski, Jr Evolutionary and preservational constraints on origins of biologic groups: divergence times of eutherian

4 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 4 mammals. Science 283: [plus online Technical Comments: Science 285:2031a]. Gaines, S.D., and M. W. Denny The largest, smallest, highest, lowest, longest, and shortest: extremes in ecology. Ecology 74: Gilinsky, N.L Volatility and the Phanerozoic decline of background extinction intensity. Paleobiology 20: Gilinsky, N.L., and I.J. Good Probabilities of origination, persistence, and extinction of families of marine invertebrate life. Paleobiology 17: Gingerich, P.D Quantification and comparison of evolutionary rates. American Journal of Science 293-A: Gingerich, P.D Rates of evolution on the time scale of the evolutionary process. Genetica : Gould, S.J., N.L. Gilinsky, and R.Z. German Asymmetry of lineages and the direction of evolutionary time. Science 236: Hannisdal, B Phenotypic evolution in the fossil record: numerical experiments. Journal of Geology 114: Hannisdal, B Inferring phenotypic evolution in the fossil record by Bayesian inversion. Paleobiology 33: Harnik, P.G Unveiling rare diversity by integrating museum, literature, and field data. Paleobiology 35: Harvey, P.H., R.M. May, and S. Nee Phylogenies without fossils. Evolution 48: Hey, J Using phylogenetic trees to study speciation and extinction. Evolution 46: Holland, S.M The stratigraphic distribution of fossils. Paleobiology 21: Holland, S.M The quality of the fossil record: a sequence-stratigrahpic perspective. Paleobiology 26(suppl. to no. 4): Holland, S.M Confidence limits on fossil ranges that account for facies changes. Paleobiology 29: Hunt, G. 2004a. Phenotypic variation in fossil samples: modeling the consequences of time-averaging. Paleobiology 30: Hunt, G. 2004b. Phenotypic variance inflation in fossil samples: an empirical assessment. Paleobiology 30: Hunt, G Fitting and comparing models of phyletic evolution: random walks and beyond. Paleobiology 32: Hunt, G The relative importance of directional change, random walks, and stasis in the evolution of fossil lineages. PNAS 104: Hunt, G Gradual or pulsed evolution: when should punctuational explanations be preferred? Paleobiology 34: Hunt, G., M. A. Bell, and M. P. Travis Evolution toward a new adaptive optimum: phenotypic evolution in a fossil stickleback lineage. Evolution 62: Hunt, G., and R. E. Chapman Evaluating hypotheses of instar-grouping in arthropods: a maximum likelihood approach. Paleobiology 27:

5 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 5 Jablonski, D., K. Roy, J.W. Valentine, R.M. Price, and P.S. Anderson The impact of the Pull of the Recent on the history of marine diversity. Science 300: Janevsky, G.A., and T.K. Baumiller Evidence for extinction selectivity throughout the marine invertebrate fossil record. Paleobiology 35: Jin, Y.G., Y. Wang, W. Wang, Q.H. Shang, C.Q. Cao, and D.H. Erwin Pattern of marine mass extinction near the Permian-Triassic boundary in South China. Science 289: Kendall, D. G. On the generalized birth-death process. Annals of Mathematical Statistics 19:1-15. Kiessling, W., and M. Aberhan Environmental determinants of marine benthic biodiversity dynamics through TriassicJurassic time. Paleobiology 33: Kowalewski, M., W. Kiessling, M. Aberhan, F. T. Fürsich, D. Scarponi, S.L.B. Wood, and A.P. Hoffmeister Ecological, taxonomic, and taphonomic components of the post-paleozoic increase in sample-level species diversity of marine benthos. Paleobiology 32: Krug, A. Z., D. Jablonski, and J. W. Valentine Speciesgenus ratios reect a global history of diversication and range expansion in marine bivalves Proc. Roy. Soc. Lond. B 275: Krug, A. Z., D. Jablonski, and J. W. Valentine Signature of the end-cretaceous mass extinction in the modern biota. Science 323: Lane, A., C.M. Janis, and J.J. Sepkoski Jr Estimating paleodiversities: a test of the taxic and phylogeneitc methods. Paleobiology 31: Magallón, S., and M. J. Sanderson Absolute diversification rates in angiosperm clades. Evolution 55: Marshall, C.R Confidence intervals on stratigraphic ranges. Paleobiology 16:1-10. Marshall, C.R Confidence intervals on stratigraphic ranges with nonrandom distributions of fossil horizons. Paleobiology 23: Marshall, C.R., and P.D. Ward Sudden and gradual molluscan extinctions in the latest Cretaceous of western European Tethys. Science 274: McConway, K. J., and H. J. Sims A likelihood-based method for testing for nonstochastic variation of diversification rates in phylogenies. Evolution 58: McCormick, T., and R. A. Fortey The Ordovician trilobite Carolinites, a test case for microevolution in a macrofossil lineage. Palaeontology 45: McKinney, M.L Extinction selectivity among lower taxa: gradational patterns and rarefaction error in extinction estimates. Paleobiology 21: Miller, A.I. and M. Foote Calibrating the Ordovician radiation of marine life: implications for Phanerozoic diversity trends. Paleobiology 22: Miller, A. I., and M. Foote Increased longevities of post-paleozoic marine genera after mass extinctions. Science 302: Nee, S Inferring speciation rates from phylogenies. Evolution 55: Nee, S Extinct meets extant: simple models in paleontology and molecular phylogenetics. Paleobiology 30:

6 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 6 Nee, S Birth-death models in macroevolution. Annual Review of Ecology, Evolution, and Systematics 47:1-17. Nee, S., R.M. May, and P.H. Harvey The reconstructed evolutionary process. Phil. Trans. Roy. Soc. London B 344: Nee, S., E. C. Holmes, R. M. May, and P. H. Harvey Extinction rates can be estimated from molecular phylogenies. Phil. Trans. Roy. Soc. London B 344: Patzkowsky, M.E A hierarchical branching model of evolutionary radiations. Paleobiology 21: Payne, J.L., and S. Finnegan The effect of geographic range on extinction risk during background and mass extinction. PNAS USA 104: Pearson, P.N Speciation and extinction asymmetries in paleontological phylogenies: evidence for evolutionary progress. Paleobiology 24: Pease, C.M Lyellian curves and mean taxonomic durations. Paleobiology 13: Peters, S.E Geologic constraints on the macroevolutionary history of marine animals. PNAS USA 102: Peters, S.E. 2006a. Macrostratigraphy of North America. Journal of Geology 114: Peters, S.E. 2006b. Genus extinction, origination, and the durations of sedimentary hiatuses. Paleobiology 32: Peters, S. E Environmental determinants of extinction selectivity in the fossil record. Nature 454: Peters, S.E., and M. Foote Biodiversity in the Phanerozoic: a reinterpretation. Paleobiology 27: Peters, S.E., and M. Foote Determinants of extinction in the fossil record. Nature 416: Powell, M.G., and M. Kowalewski Increase in evenness and sampled alpha diversity through the Phanerozoic: Comparison of early Paleozoic and Cenozoic marine fossil assemblages. Geology 30: Przeworski, M., and J. D. Wall An evaluation of a hierarchical branching process as a model for species diversification. Paleobiology 24: Quental, T. B., and C. R. Marshall Extinction during evolutionary radiations: Reconciling the fossil record with molecular phylogenies. Evolution 63: Raup, D.M Taxonomic diversity during the Phanerozoic. Science 177: Raup, D.M Taxonomic diversity estimation using rarefaction. Paleobiology 1: Raup, D.M. 1976a. Species diversity in the Phanerozoic: a tabulation. Paleobiology 2: Raup, D.M. 1976b. Species diversity in the Phanerozoic: an interpretation. Paleobiology 2: Raup, D.M Cohort analysis of generic survivorship. Paleobiology 4:1-15. Raup, D. M Size of the Permo-Triassic bottleneck and its evolutionary implications. Science 4415: Raup, D. M On the early origins of major biologic groups. Paleobiology 9:

7 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 7 Raup, D.M Mathematical models of cladogenesis. Paleobiology 11: Raup, D.M., and R.E. Crick Evolution of single characters in the Jurassic ammonite Kosmoceras. Paleobiology 7: Raup, D.M., S.J. Gould, T.J.M. Schopf, and D.S. Simberloff Stochastic models of phylogeny and the evolution of diversity. Journal of Geology 81: Rabosky, D. L., and I. J. Lovette Explosive evolutionary radiations: decreasing speciation or increasing extinction through time? Evolution 62: Ricklefs, R. E Estimating diversification rates from phylogenetic information. Trends. Ecol. Evol. 22: Roopnarine, P.D The description and classification of evolutionary mode: a computational approach. Paleobiology 27: Roopnarine, P.D Analysis of rates of morphological evolution. Annual Review of Ecology, Evolution and Systematics 34: Roopnarine, P.D., G. Byars, and P. Fitzgerald Anagenetic evolution, stratophenetic patterns, and random walk models. Paleobiology 25: Sepkoski, J.J., Jr A kinetic model of Phanerozoic taxonomic diversity. I. Analysis of marine orders. Paleobiology 4: Sepkoski, J.J., Jr A kinetic model of Phanerozoic taxonomic diversity. II. Early Phanerozoic families and multiple equilibria. Paleobiology 5: Sepkoski, J.J., Jr A kinetic model of Phanerozoic taxonomic diversity. III. Post-Paleozoic families and mass extinctions. Paleobiology 10: Sepkoski, J.J., Jr Population biology models in macroevolution. Pp in Gilinsky and Signor. Sepkoski, J.J., Jr. F. K. McKinney, and S. Lidgard Competitive displacement among post-paleozoic cyclostome and cheilostome bryozoans. Paleobiology 26:7-18. Sheets, H.D., and C.E. Mitchell Why the null matters: statistical tests, random walks, and evolution. Genetica : Sims, H.J., and K.J. McConway Nonstochastic variation of species-level diversification rates within angiosperms. Evolution 57: Smith, A.B Large-scale heterogeneity of the fossil record: implications for Phanerozoic biodiversity studies. Phil. Trans. Roy. Soc. London B 356: Solow, A.R Estimation of stratigraphic ranges when fossil finds are not randomly distributed. Paleobiology 29: Solow, A.R., and W. Smith On fossil preservation and the stratigraphic ranges of taxa. Paleobiology 23: Solow, A.R., and W. K. Smith Testing for a mass extinction without selecting taxa. Paleobiology 26: Stanley, S.M., W.O. Addicott, and K. Chinzei Lyellian curves in paleontology: possibilities and limitations. Geology 8: Stanley, S.M., P.W. Signor III, S. Lidgard, A.F. Karr Natural clades differ from random clades: simulations and analyses. Paleobiology 7:

8 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 8 Strathmann, R. R. and M. Slatkin The improbability of animal phyla with few species. Paleobiology 9: Strauss, D., and P.M. Sadler Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology 21: Tavaré, S., C. R. Marshall, O. Will, C. Soligo, and R. D. Martin Using the fossil record to estimate the age of the last common ancestor of extant primates. Nature 416: Wagner, P. J., M. A. Kosnik, and S. Lidgard Abundance distributions imply elevated complexity of post-paleozoic marine ecosystems. Science 314: Wang, S.C., and P. Dodson Estimating the diversity of dinosaurs. PNAS USA 103: Wills, J. C., and G. U. Yule Some statistics of evolution and geographical distribution in plants and animals, and their significance. Nature 109: Wills, M.A Fossil ghost ranges are most common in some of the oldest and some of the youngest strata. Proc. Roy. Soc. Lond. B 274: Yule, G. U A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S. Phil. Trans. R. Soc. Lond. B. 213: Zink, R.M., and J.B. Slowinski Evidence from molecular systematics for decreased avian diversification in the Pleistocene epoch. Proc. Natl. Acad. Sci. USA 92: List of topics (subject to evolve as the course progresses) 1. Jan. 5: Introduction to Probability, I 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. 14) 2. Jan. 7: Introduction to Probability, II 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. 12: Sampling

9 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 9 Topics: Sampling; resampling; rarefaction; bootstrapping; extreme value statistics Assignment out: Exercise 2 (due Jan. 21) Reading: Efron and Tibshirani, Ch. 6; Raup (1975); Foote (1992); Foote (1994); Gaines and Denny (1993) 4. Jan. 14: 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]; Feller, vol. I, Ch. III [optional] Assignment in: Exercise 1 5. Jan. 19: 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; rudimentary Bayesian analysis Readings: Edwards, Chs. 1-4, 5 (sections ), 6 (sections ); Payne and Finnegan 2007; Hunt and Chapman (2001). Assignment out: Exercise 3 (due Jan. 28) 6. Jan. 21: Introduction to Branching Models Topics: Introduction to branching models; pure birth and birth-death models; time-homogenous and time-varying models; analytic approaches vs. simulation; importance of empirical scaling; forward vs. inverse problems Readings: Raup (1985); Nee (2006); Stanley et al. (1981); Sepkoski 1991; Foote and Miller 2007, sections Assignment in: Exercise 2

10 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page Jan. 26: Applications of Basic Branching Models, I: Long-term average origination and extinction rates; some case studies applying models All read: Foote and Miller 2007, section 7.2 Individual papers: Raup 1978; Foote 1988; Baumiller 1993; Patzkowsky 1995; Gilinsky and Good 1991; Stanley et al. 1980; Pease 1987; Gilinsky 1994; Raup et al. 1973; Gould et al. 1987; Foote 2007b 8. Jan. 28: Applications of Basic Branching Models, II: Further case studies All read: Raup 1985; Nee 2006 Individual papers: Raup 1983; Miller and Foote 2003; Sepkoski 1984; Sepkoski, McKinney, and Lidgard 2000; Strathmann and Slatkin 1983; Pearson 1998; Krug et al Assignment in: Exercise 3 9. Feb. 2: Inferring rates from living taxa, I All read: Foote 2001a; Nee 2006; Ricklefs 2007 Individual papers: Hey 1992; Magallon and Sanderson 2001; Sims and McConway 2003; McConway and Sims 2004 Further reading: Harvey et al. 1994; Nee et al. 1994a,b 10. Feb. 4: Inferring rates from living taxa, II All read: Rabosky and Lovette 2008 Individual papers: Bininda-Emonds et al. 2007; Zink and Slowinski 1995; Crisp and Cook 2009; Quental and Marshall Feb. 9: Modeling stratophenetic series All read: Foote and Miller 2007, sections 7.1, 7.3, 7.4; Gingerich 2001; review readings from topic 4.

11 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 11 Individual papers: Hunt 2006; Hunt 2007; Hunt 2008; Hunt et al. 2008; Hannisdal 2007; Clyde and Gingerich 1994; Cheetham 1986 Further reading: Roopnarine 2003; Gingerich 1993; Charlesworth 1984; Hunt 2004b; Sheets and Mitchell 2001; Roopnarine et al. 1999; McCormick and Fortey 2002; Hannisdal 2006; [Feb. 11: No meeting] 12. Feb. 16: Models of incomplete sampling, I: overview and estimation of sampling rates All read: Foote 2000; Foote 2001c; Benton et al. 2000; Foote and Miller 2007, section 1.3 Individual papers: Wills 2007; Lane et al. 2005; Foote and Raup 1996; Foote 1997; Solow and Smith 1997; Crampton et al. 2006a; Cooper et al. 2006; Foote and Sepkoski Feb. 18: Models of incomplete sampling, II: confidence intervals on stratigraphic ranges; other applications All read: Strauss and Sadler 1989; Marshall 1990 Individual papers: Marshall and Ward 1996; Jin et al. 2000; Solow and Smith 2000; Marshall 1997; Solow 2003; Holland 2003; Foote et al. 1999; Tavaré et al. 2002; Foote 1996; Wang and Dodson 2006; Wagner et al Feb. 23: Models of incomplete sampling, III: Introduction to time-varying models All read: Foote 2000; Foote and Miller 2007, chapter 6 (esp. section 6.4); Holland 2000; Holland 1995 [optional] Individual papers: 2006b; Peters 2008 Peters and Foote 2002; Peters 2006a; Peters 2005; Peters 15. Feb. 25: Inverse methods with time-varying sampling models: numerical parameter estimation All read: Foote 2001b

12 GEOS 36501/EVOL 33001: Mathematical Modeling (Winter 2010) Course Outline Page 12 Individual papers: Connolly and Miller 2001a,b, 2002; Foote 2003; Foote 2005; Foote 2007a 16. Mar. 2: Taxon size-frequency distributions All read: Raup 1975; Raup 1979; Patzkowsky 1995; Anderson 1974 [esp.324 ff.] Individual papers: Krug et al. 2008; Dial and Marzluff 1989; Harnik 2009; Przeworski and Wall 1998; McKinney 1995; Janevsky and Baumiller Mar Mar. 9 Student presentations Student presentations