New methods for quantifying macroevolutionary patterns and processes

Abstract This paper documents a series of methodological innovations that are relevant to macroevolutionary studies. The new methods are applied to updated faunal and body mass data sets for North American fossil mammals, documenting several key trends across the late Cretaceous and Cenozoic. The methods are (1) A maximum likelihood formulation of appearance event ordination. The reformulated criterion involves generating a maximally likely hypothesized relative ordering of first and last appearances (i.e., an age range chart). The criterion takes faunal occurrences, stratigraphic relationships, and the sampling probability of individual genera and species into account. (2) A nonparametric temporal interpolation method called “shrink-wrapping” that makes it possible to employ the greatest possible number of tie points without violating monotonicity or allowing abrupt changes in slopes. The new calibration method is used in computing provisional definitions of boundaries among North American land mammal ages. (3) Additional methods for randomized subsampling of faunal lists, one weighting the number of lists that have been drawn by the sum of the square of the number of occurrences in each list, and one further modifying this approach to account for long-term changes in average local species richness. (4) Foote's new equations for instantaneous speciation and extinction rates. The equations are rederived and used to generate time series, confirm that logistic dynamics result from the diversity dependence of speciation but not extinction, and define the median duration of species (i.e., 2.6 m.y. for Eocene–Pleistocene mammals). (5) A method employing the G likelihood ratio statistic that is used to quantify the volatility of changes in the relative proportion of species falling in each of several major taxonomic groups. (6) Univariate measures of body mass distributions based on ordinary moment statistics (mean, standard deviation, skewness, kurtosis). These measures are favored over the method of cenogram analysis. Data are presented showing that even diverse individual fossil collections merely yield a noisy version of the same pattern seen in the overall continental data set. Peaks in speciation rates, extinction rates, proportional volatility, and shifts in body mass distributions occur at different times, suggesting that environmental perturbations do not have simple effects on the biota.

[1]  P. Wagner,et al.  A likelihood approach for evaluating estimates of phylogenetic relationships among fossil taxa , 1998, Paleobiology.

[2]  B. Valkenburgh.  Trophic diversity in past and present guilds of large predatory mammals , 1988 .

[3]  M. Foote.  Origination and extinction components of taxonomic diversity: general problems , 2000, Paleobiology.

[4]  John Alroy,et al.  Appearance event ordination: a new biochronologic method , 1994, Paleobiology.

[5]  John Alroy,et al.  Conjunction among taxonomic distributions and the Miocene mammalian biochronology of the Great Plains , 1992, Paleobiology.

[6]  R. Stucky.  Evolution of land mammal diversity in North America during the Cenozoic , 1990 .

[7]  M. Fortelius,et al.  Molar Tooth Diversity, Disparity, and Ecology in Cenozoic Ungulate Radiations , 1996, Science.

[8]  S. Legendre.  Les communautés de mammifères du paléogène (éocène supérieur et oligocène) d'Europe occidentale : structures, milieux et évolution , 1988 .

[9]  P. Gingerich,et al.  New Species of Batodonoides (Lipotyphla, Geolabididae) from the Early Eocene of Wyoming: Smallest Known Mammal? , 1998 .

[10]  D. Raup,et al.  Mass Extinctions in the Marine Fossil Record , 1982, Science.

[11]  M. Foote.  Origination and extinction components of taxonomic diversity: Paleozoic and post-Paleozoic dynamics , 2000, Paleobiology.

[12]  N. L. Gilinsky,et al.  Probabilities of origination, persistence, and extinction of families of marine invertebrate life , 1991, Paleobiology.

[13]  C. Janis.  Tertiary mammal evolution in the context of changing climates, vegetation, and tectonic events , 1993 .

[14]  S. Wing,et al.  The reciprocal interaction of angiosperm evolution and tetrapod herbivory , 1987 .

[15]  J. Alroy,et al.  Plant and mammal diversity in the Paleocene to early Eocene of the Bighorn Basin , 1995 .

[16]  George Gaylord Simpson,et al.  Classification of mammals : above the species level , 1997 .

[17]  J. Sepkoski,et al.  A kinetic model of Phanerozoic taxonomic diversity. III. Post-Paleozoic families and mass extinctions , 1984, Paleobiology.

[18]  D. Raup.  Species diversity in the Phanerozoic: an interpretation , 1976, Paleobiology.

[19]  P. Gingerich,et al.  MAMMALIAN COMMUNITY RESPONSE TO THE LATEST PALEOCENE THERMAL MAXIMUM : AN ISOTAPHONOMIC STUDY IN THE NORTHERN BIGHORN BASIN, WYOMING , 1998 .

[20]  J. Sepkoski,et al.  A factor analytic description of the Phanerozoic marine fossil record , 1981, Paleobiology.

[21]  K. Crandall,et al.  Phylogeny Estimation and Hypothesis Testing Using Maximum Likelihood , 1997 .

[22]  R. May.  Patterns of species abundance and diversity , 1975 .

[23]  J. Alroy.  Putting North America’s End-Pleistocene Megafaunal Extinction in Context , 1999 .

[24]  P. Gingerich.  New Earliest Wasatchian Mammalian Fauna from the Eocene of Northwestern Wyoming: Composition and Diversity in a Rarely Sampled High-Floodplain Assemblage , 1989 .

[25]  R. Hilborn,et al.  The Ecological Detective: Confronting Models with Data , 1997 .

[26]  J. Alroy,et al.  Global climate change and North American mammalian evolution , 2000, Paleobiology.

[27]  C. W. Harper.  Patterns of diversity, extinction and origination in the Ordovician‐Devonian stropheodontacea , 1996 .

[28]  J. W. Valentine,et al.  Equilibrium Models of Evolutionary Species Diversity and the Number of Empty Niches , 1984, The American Naturalist.

[29]  David M. Raup,et al.  Mathematical models of cladogenesis , 1985, Paleobiology.

[30]  C. Swisher,et al.  Land Mammal High-Resolution Geochronology, Intercontinental Overland Dispersals, Sea Level, Climate and Vicariance , 1995 .

[31]  P H Harvey,et al.  Tempo and mode of evolution revealed from molecular phylogenies. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[32]  David M. Raup,et al.  Taxonomic diversity estimation using rarefaction , 1975, Paleobiology.

[33]  J. Sepkoski,et al.  Alpha, beta, or gamma: where does all the diversity go? , 1988, Paleobiology.

[34]  P. Gingerich.  SIZE VARIABILITY OF THE TEETH IN LIVING MAMMALS AND THE DIAGNOSIS OF CLOSELY RELATED SYMPATRIC FOSSIL SPECIES , 1974 .

[35]  Arnold I. Miller,et al.  Modeling bivalve diversification: the effect of interaction on a macroevolutionary system , 1988, Paleobiology.

[36]  T. Carr,et al.  Dynamics of taxonomic diversity , 1980, Paleobiology.

[37]  P. Markwick.  Crocodilian diversity in space and time: the role of climate in paleoecology and its implication for understanding K/T extinctions , 1998, Paleobiology.

[38]  F. Agterberg,et al.  The RASC method for ranking and scaling of biostratigraphic events , 1999 .

[39]  H. L. Sanders,et al.  Marine Benthic Diversity: A Comparative Study , 1968, The American Naturalist.

[40]  James H. Brown,et al.  Spatial Scaling of Species Composition: Body Masses of North American Land Mammals , 1991, The American Naturalist.

[41]  J. Malcolm,et al.  MAMMALS OF THE RIO JURUÁ AND THE EVOLUTIONARY AND ECOLOGICAL DIVERSIFICATION OF AMAZONIA , 2000 .

[42]  S. Webb,et al.  A History of Savanna Vertebrates in the New World. Part I: North America , 1977 .

[43]  J. Alroy.  The fossil record of North American mammals: evidence for a Paleocene evolutionary radiation. , 1999, Systematic biology.

[44]  J. Alroy.  Constant extinction, constrained diversification, and uncoordinated stasis in North American mammals , 1996 .

[45]  A I Miller,et al.  Calibrating the Ordovician Radiation of marine life: implications for Phanerozoic diversity trends. , 1996, Paleobiology.

[46]  D. Raup.  Cohort analysis of generic survivorship , 1978, Paleobiology.

[47]  B. A. Maurer.  Diversity-dependent species dynamics: incorporating the effects of population-level processes on species dynamics , 1989, Paleobiology.

[48]  K Shinozaki.  Note on the species-area curve , 1963 .

[49]  John Alroy,et al.  Diachrony of mammalian appearance events: Implications for biochronology , 1998 .

[50]  B. Valkenburgh.  Locomotor diversity within past and present guilds of large predatory mammals , 1985 .

[51]  B. G. Murray.  On calculating birth and death rates , 1997 .

[52]  David M. Raup,et al.  Geometric analysis of shell coiling; general problems , 1966 .

[53]  P. Gingerich,et al.  Comparative paleoecology of Paleogene and Neogene mammalian faunas: Trophic structure and composition , 1995 .

[54]  M. Foote.  Temporal variation in extinction risk and temporal scaling of extinction metrics , 1994, Paleobiology.

[55]  R. Stucky.  Review of John Storer, Mammals of the Swift Current Creek Local Fauna (Eocene: Uintan, Saskatchewan) , 1985 .

[56]  K. Beard,et al.  Portrait of a late Paleocene (early Clarkforkian) terrestrial ecosystem; Big Multi Quarry and associated strata, Washakie Basin, southwestern Wyoming , 1998 .

[57]  J. C. Tipper.  Rarefaction and rarefiction—the use and abuse of a method in paleoecology , 1979, Paleobiology.

[58]  J. Alroy.  Cope's rule and the dynamics of body mass evolution in North American fossil mammals. , 1998, Science.

[59]  P. Gingerich,et al.  Comparative paleoecology of Paleogene and Neogene mammalian faunas: body-size structure , 1995 .

[60]  D. Raup,et al.  Periodicity of extinctions in the geologic past. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[61]  J. Sepkoski,et al.  A kinetic model of Phanerozoic taxonomic diversity I. Analysis of marine orders , 1978, Paleobiology.

[62]  Robert K. Colwell,et al.  Estimating terrestrial biodiversity through extrapolation. , 1994, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[63]  D M Raup,et al.  Fossil preservation and the stratigraphic ranges of taxa , 1996, Paleobiology.

[64]  Michael Foote,et al.  Morphological diversity in the evolutionary radiation of Paleozoic and post-Paleozoic crinoids , 1999, Paleobiology.

[65]  J. Jernvall,et al.  The hypocone as a key innovation in mammalian evolution. , 1995, Proceedings of the National Academy of Sciences of the United States of America.