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.

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