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The Willwood Formation of the Bighorn Basin (Wyoming, USA) is a thick succession of upper Paleocene and lower Eocene fl uvial-fl oodplain sandstones and mudstones. Reddish paleosols, formed on the fl oodplain mudstones, alternate rhythmically on various scales with heterolithic intervals of small-channel sandstones and mudstones showing weak pedogenesis. Spectral analysis of redness in the Willwood successions at Polecat Bench and Red Butte reveals signifi cant spectral peaks corresponding to cycle thicknesses of ~8 and ~3 m. The ~8 m cycle refl ects distinct clusters of 3-5 paleosols. Age constraints show that the period of this cycle closely matches the ~21 k.y. climatic precession cycle. The ~3 m cycle corresponds to individual paleosols, with a period of 7-8 k.y. This period is similar to millennial-scale sub-Milankovitch cycles found in marine and lacustrine successions of Pliocene-Pleistocene age. Precession and millennial-scale climate variations probably affected paleosol development through cyclic changes from predominantly overbank to predominantly channel-avulsion deposition, with the latter periodically halting soil formation because of high sediment accumulation. A new age model was developed for the Paleocene-Eocene carbon isotope excursion (CIE) at Polecat Bench, based on the precessional origin of paleosol clusters. The main body of the CIE spans ~5.5 precession cycles, or ~115 k.y., and the recovery tail of the CIE spans 2 precession cycles, or ~42 k.y. This outcome is consistent with, and independently confi rms, recent estimates of CIE duration based on deep-sea cores.

Mammals are among the fastest-radiating groups, being charac terized by a mean species lifespan of the order of 2.5 million years Changes in organisms occur on a variety of temporal scales. Four basic temporal scales (tiers) have been recognized: the ecological timescale; the Milankovitch timescale of precession (the wobbling of the Earth's axis, �21 kyr periodicity), obliquity (tilt of the Earth's axis, 41 kyr periodicity) and eccentricity (the orbit around the Sun, � 100 and �400 kyr periodicity); the million-year timescale of species extinctions and originations; and the ultra-long timescale of mass extinctions and major taxonomic replacements9. Although the main processes controlling the fi rst tier (climate change and competition), the second tier (climate-forced distributional vari ation)3,9,IO and the fourth tier (catastrophic perturbations of the Earth's biosphere) are reasonably well defi ned, the mechanisms underlying third-tier processes are not well ill1derstood. Mammals have featured importantly in discussions on the processes pertaining to this tier2-7• Because their mean species duration is estimated at 2.3-2.6 Myr (refs 1, 2), primary (20-400kyr) Milankovitch vari ations cannot be held responsible for mammal speciation and extinction4,9,lo. It has been suggested that amplitude changes of climatic oscillations could have played a part in explaining turn over3,1O, but until now no efforts have been made systematically to compare such amplitude variations with turnover in long and well dated records.We compiled a data set of more than 200 rodent assemblages from Central Spain (see Supplementary Notes and Supplementary Ta ble 1) and analysed it in terms of turnover. The record is exceptionally long (22 Myr) , largely continuous, dense and well dated. We focused on rodents, because screen sieving allows the collection of large amounts of easily identifi able dental elements. The studied fossils originate from fl uvio-Iacustrine sections in the Madrid, Calatayud-Daroca and Te ruel basins, and amount to over 80,000 isolated molars, which were identifi ed at the species and lineage level (132 lineages, pseudo extinctions ignored). All studied localities are positioned in strati graphic sections, a large number of which have been tied to the geomagnetic polarity timescale by first-order correlations. The complete temporal sequence was calibrated to the new astronomi cally tuned timescale for the Neogene11 (Supplementary Fig. 1). The use of this new timescale is of crucial importance because it allows a direct comparison -with time series of the Earth's orbital parameters outlined above.Randomization procedures were used to capture uncertainties in the ages oflocalities (by the generation of a series of equally probable age models) and of fi rst and last rodent appearances, resulting in 1,000 equally probable time series. Sample size effects on the presence or absence of rodents were observed to be fairly small and were further reduced by inferring lineage presence on a range-through basis and by excluding...

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The Milankovitch theory of climate change is widely accepted, but the registration of the climate changes in the stratigraphic record and their use in building high-resolution astronomically tuned timescales has been disputed due to the complex and fragmentary nature of the stratigraphic record. However, results of time series analysis and consistency with independent magnetobiostratigraphic and/or radio-isotopic age models show that Milankovitch cycles are recorded not only in deep marine and lacustrine successions, but also in ice cores and speleothems, and in eolian and fluvial successions. Integrated stratigraphic studies further provide evidence for continuous sedimentation at Milankovitch time scales (10 4 years up to 10 6 years). This combined approach also shows that strict application of statistical confidence limits in spectral analysis to verify astronomical forcing in climate proxy records is not fully justified and may lead to false negatives. This is in contrast to recent claims that failure to apply strict statistical standards can lead to false positives in the search for periodic signals. Finally, and contrary to the argument that