The diversity of life on Earth is controlled by hierarchical processes that interact over wide ranges of timescales¹. Here, we consider the megaclimate regime² at scales ≥1 million years (Myr). We focus on determining the domains of ‘wandering’ stochastic Earth system processes (‘Court Jester’³) and stabilizing biotic interactions that induce diversity dependence of fluctuations in macroevolutionary rates (‘Red Queen’⁴). Using state-of-the-art multiscale Haar and cross-Haar fluctuation analyses, we analysed the global genus-level Phanerozoic marine animal Paleobiology Database record of extinction rates (E), origination rates (O) and diversity (D) as well as sea water palaeotemperatures (T). Over the entire observed range from several million years to several hundred million years, we found that the fluctuations of T, E and O showed time-scaling behaviour. The megaclimate was characterized by positive scaling exponents—it is therefore apparently unstable. E and O are also scaling but with negative exponents—stable behaviour that is biotically mediated. For D, there were two regimes with a crossover at critical timescale \(\Delta {t}_{{\rm{trans}}}\) ≈ 40 Myr. For shorter timescales, D exhibited nearly the same positive scaling as the megaclimate palaeotemperatures, whereas for longer timescales it tracks the scaling of macroevolutionary rates. At scales of at least \(\Delta {t}_{{\rm{trans}}}\) there is onset of diversity dependence of E and O, probably enabled by mixing and synchronization (globalization) of the biota by geodispersal (‘Geo-Red Queen’).

地球上生命的多样性是由等级过程控制的，这些过程在很宽的时间尺度范围内相互作用¹。在这里，我们考虑≥ 100 万年 (Myr) 尺度的大气候状况^{2 。}我们专注于确定“漫游”随机地球系统过程（“宫廷小丑” ³）的领域，并稳定生物相互作用，这些相互作用会引起宏观进化率波动的多样性依赖性（“红皇后” ⁴）。使用最先进的多尺度 Haar 和交叉 Haar 波动分析，我们分析了全球属级显生宙海洋动物古生物学数据库记录的灭绝率 ( E )、起源率 ( O ) 和多样性 ( D )) 以及海水古温度 ( T )。在从几百万年到几亿年的整个观测范围内，我们发现T、E和O的波动表现出时间尺度的行为。大气候的特征是正比例指数——因此它显然是不稳定的。E和O也在缩放，但具有负指数——生物介导的稳定行为。对于D，有两种制度在关键时间尺度上有交叉\(\Delta {t}_{{\rm{trans}}}\)  ≈ 40 Myr。对于更短的时间尺度，D表现出与大气候古温度几乎相同的正缩放，而对于更长的时间尺度，它跟踪宏观进化速率的缩放。在至少\(\Delta {t}_{{\rm{trans}}}\)的尺度上， E和O开始出现多样性依赖性，这可能是通过地理分散（ 'Geo-Red Queen'）。