1. Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA
2. Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Correspondence to: Peter Huybers¹ Correspondence and requests for materials should be addressed to P.H. (Email: phuybers@whoi.edu).

The 100,000-year timescale in the glacial/interglacial cycles of the late Pleistocene epoch (the past 700,000 years) is commonly attributed to control by variations in the Earth's orbit¹. This hypothesis has inspired models that depend on the Earth's obliquity ( 40,000 yr; 40 kyr), orbital eccentricity ( 100 kyr) and precessional ( 20 kyr) fluctuations^{2, 3, 4, 5}, with the emphasis usually on eccentricity and precessional forcing. According to a contrasting hypothesis, the glacial cycles arise primarily because of random internal climate variability^{6, 7, 8}. Taking these two perspectives together, there are currently more than thirty different models of the seven late-Pleistocene glacial cycles⁹. Here we present a statistical test of the orbital forcing hypothesis, focusing on the rapid deglaciation events known as terminations^{10, 11}. According to our analysis, the null hypothesis that glacial terminations are independent of obliquity can be rejected at the 5% significance level, whereas the corresponding null hypotheses for eccentricity and precession cannot be rejected. The simplest inference consistent with the test results is that the ice sheets terminated every second or third obliquity cycle at times of high obliquity, similar to the original proposal by Milankovitch¹². We also present simple stochastic and deterministic models that describe the timing of the late-Pleistocene glacial terminations purely in terms of obliquity forcing.

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