Landscape dynamics and the Phanerozoic diversification of the biosphere
景观动力学和生物圈的显生宙多样化

The diversity of marine and terrestrial life was assembled over the Phanerozoic eon through complex interplays between biotic controls and abiotic controls^3,4 that are still unclear, although biodiversity patterns over time are fairly well identified from the fossil record^2,5 and mounting evidence from phylogenetics^6,7. Although both continents and oceans, in the most recent stages of the Phanerozoic, host more species than ever, the monotonic increase of diversity over time in the terrestrial realm¹ contrasts with the more complex evolution of diversity in the oceans⁸. Besides the ‘big five’ mass extinctions⁹, turning points in their progressions also became iconic: Darwin referred to the advent of flowering plants in continents as an abominable mystery; Vermeij¹⁰ coined the term Cenozoic marine revolution. Another enduring puzzle is the late expansion of land plants compared to marine life that rapidly diversified 100 million years earlier. Although the joint effects of biotic and abiotic factors are probably required to explain the biodiversity patterns in time³ and space¹¹, a wealth of possible mechanisms have been examined independently. Within this variety, truly independent potential abiotic forcings might have been overlooked, although they are not many and ultimately refer to the physical environment, which couples climatic or geological forcings, suggesting that biodiversity trends could be more comparable for marine and terrestrial life.
海洋和陆地生物的多样性是在显生宙通过生物控制和非生物控制之间复杂的相互作用而形成的^{3 , 4} ，目前尚不清楚，尽管从化石记录^{2 , 5和越来越多的证据中可以很好地识别出随时间变化的生物多样性模式2 , 5 。}系统发育学^{6 , 7} .尽管大陆和海洋在显生宙的最新阶段拥有比以往更多的物种，但陆地领域¹多样性随时间的单调增加与海洋⁸中更复杂的多样性演化形成鲜明对比。除了“五大”大规模灭绝⁹之外，其进程中的转折点也成为标志性的：达尔文将大陆上开花植物的出现称为一个令人厌恶的谜团； Vermeij ¹⁰创造了“新生代海洋革命”一词。另一个持久的谜题是，与一亿年前迅速多样化的海洋生物相比，陆地植物的扩张较晚。尽管可能需要生物和非生物因素的共同影响来解释时间³和空间^{11 的}生物多样性模式，但已经独立研究了大量可能的机制。在这种多样性中，真正独立的潜在非生物强迫可能被忽视，尽管它们并不多，并且最终指的是与气候或地质强迫相结合的物理环境，这表明海洋和陆地生物的生物多样性趋势可能更具可比性。

Continental drift sets the distribution of landmasses at the surface of the Earth during the Phanerozoic. The changing palaeogeography in turns influences the atmospheric circulation. Both plate tectonics and climate are critical to the development of marine and terrestrial life, by setting the latitude and hours of daylight, temperatures or hydrological cycles. Although these processes are undoubtedly primordial, they do not account for the dynamic evolution of the surface of the Earth, which should not be regarded as a series of stationary configurations. Reliefs are changing over time and mass transfers are crucial to the expansion of life: both on the continents and in the oceans, nutrient availability is determined by landscape dynamics. Understanding the impact of nutrient fluxes thus requires a comprehensive quantitative approach that we develop herein, leaving aside the role of truly biotic processes.
大陆漂移决定了显生宙期间地球表面陆地的分布。古地理的变化反过来又影响着大气环流。板块构造和气候通过设定纬度和日照时间、温度或水文循环，对海洋和陆地生命的发展至关重要。尽管这些过程无疑是原始的，但它们并不能解释地球表面的动态演化，地球表面不应被视为一系列静止配置。地形随着时间的推移而变化，物质转移对于生命的扩展至关重要：无论是在大陆还是在海洋，养分的可用性都由景观动态决定。因此，了解养分通量的影响需要我们在本文中开发的全面的定量方法，而忽略真正的生物过程的作用。

Here we propose a new method to quantify the global-scale physiographic changes over the Phanerozoic eon, applying the landscape evolution model goSPL^12,13 to a series of global-scale palaeo-elevation reconstructions, consistently tied to a plate tectonic model¹⁴ and to a series of palaeoclimatic reconstructions¹⁵ (Fig. 1). Our approach allows us to jointly quantify the tectonic uplift at long wavelengths and the high-resolution dissection of the landscape (Methods and Extended Data Figs. 1 and 2). Model outputs, including high-resolution topography, continental erosion and sedimentation rates, drainage networks and sediment and freshwater yields to the oceans (all datasets released online¹⁶), allow estimation of the impacts of surface processes on the physiography of the Earth throughout the entire Phanerozoic (Fig. 1). Sensitivity tests using alternative climatic and tectonic models (Methods) point to spatial variations and differences in the magnitude of erosion rates although global temporal trends remain mostly insensitive (Extended Data Fig. 6a,c).
在这里，我们提出了一种量化显生宙期间全球尺度地貌变化的新方法，将景观演化模型 goSPL ^{12 、 13}应用于一系列全球尺度古海拔重建，始终与板块构造模型¹⁴和一系列古气候重建¹⁵ （图1 ）。我们的方法使我们能够联合量化长波长的构造隆起和地形的高分辨率解剖（方法和扩展数据图1和图 2 ）。模型输出，包括高分辨率地形、大陆侵蚀和沉积率、排水网络以及海洋的沉积物和淡水产量（所有数据集在线发布¹⁶ ），可以估计整个地球表面过程对地球地貌的影响。显生宙（图1 ）。使用替代气候和构造模型（方法）进行的敏感性测试指出了空间变化和侵蚀率大小的差异，尽管全球时间趋势仍然大多不敏感（扩展数据图6a，c ）。

a, goSPL^12,13 simulations showing high-resolution palaeo-landscape, heterogeneous landforms and drainage networks, under the influence of surface processes, at 155 Ma and 11 Ma. b, Erosion and sedimentation rates; positive values correspond to deposition in endorheic basins and depressions, and negative ones to erosion across mountain ranges and along major river upstream channels, at 155 Ma and 11 Ma. c, Total endorheic sediment coverage since 540 Ma (in red) with cumulative mean erosion rates on continents (blue), and instantaneous global net sediment flux to the ocean for specific time intervals (purple).
a 、goSPL ^{12、13模拟}显示了 155 Ma 和 11 Ma 受地表过程影响的高分辨率古地貌、异质地貌和排水网络。 b 、侵蚀和沉积速率；正值对应于内流盆地和洼地的沉积，负值对应于 155 Ma 和 11 Ma 处的山脉和主要河流上游河道的侵蚀。 c ，自 540 Ma 以来的总内流沉积物覆盖范围（红色）以及大陆的累积平均侵蚀率（蓝色），以及特定时间间隔内流入海洋的瞬时全球净沉积物通量（紫色）。

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Surface processes are first calibrated using modern estimates of average global erosion rates^17,18 and suspended sediment flux^19,20 (Methods). Then, propagating this parameterization in past times yields temporal trends in bulk sediment transfer (Fig. 2a) that can be tied to continental elevations and surface runoff (that is, precipitation minus evapotranspiration; Extended Data Fig. 6a). Two phases of sustained fast erosion separated by a quieter period mark the long-term Phanerozoic evolution. The Palaeozoic phase relates to an increase in continental runoff from the Silurian period to the Carboniferous period, and to higher reliefs until the assembly of Pangaea during Permian times. Lower continental elevations and more arid conditions prevailed until Pangaea breakup after the Triassic period. During this period, up to 30% of eroded materials were trapped in the terrestrial domain (Fig. 2a). The Meso-Cenozoic phase of erosion, from the Jurassic period onwards, is marked by a more than twofold increase in erosion flux, fostered by higher runoff and by the rising reliefs of the Cenozoic mountain belts. During that phase, most of the sediments are directly transferred to the ocean (continental deposition decreases to about 13% of the erosion flux). Several peaks in erosion flux, coinciding with major orogenic episodes, overprint the low-frequency Phanerozoic trend (Fig. 2a).
首先使用对全球平均侵蚀^率17、18和悬浮沉积物通量^19、20的现代估计来校准地表过程（方法）。然后，在过去传播这种参数化会产生大量沉积物转移的时间趋势（图2a ），该趋势可以与大陆海拔和地表径流（即降水减去蒸散量；扩展数据图6a ）联系起来。持续快速侵蚀的两个阶段被一个较安静的时期分隔开，标志着显生宙的长期演化。古生代阶段与从志留纪到石炭纪大陆径流的增加有关，并且与二叠纪时期盘古大陆聚集之前的较高地势有关。大陆海拔较低，气候更加干旱，直到三叠纪后盘古大陆分裂为止。在此期间，高达30%的侵蚀物质被困在陆地区域（图2a ）。从侏罗纪时期开始，中新生代侵蚀阶段的特点是侵蚀通量增加两倍以上，这是由于较高的径流和新生代山脉地势的上升而促进的。在此阶段，大部分沉积物直接转移到海洋（大陆沉积物减少至侵蚀通量的 13% 左右）。侵蚀通量的几个峰值与主要造山活动同时发生，印证了低频显生宙趋势（图2a ）。

a, Simulated global erosion flux, net sediment flux delivered to the ocean and endorheic sedimentation flux; and major orogenic episodes for the Phanerozoic (CAMP, Central Atlantic Magmatic Province). b, Global changes in total continental area, and in modelled endorheic basin area. Cm, Cambrian; O, Ordovician; S, Silurian; D, Devonian; Carb, Carboniferous; P, Permian; Tr, Triassic; J, Jurassic; K, Cretaceous; Pg, Palaeogene; Ng, Neogene.
a ，模拟的全球侵蚀通量、输送到海洋的净沉积物通量和内流沉积通量；以及显生宙的主要造山活动（CAMP，大西洋中部岩浆省）。 b ，大陆总面积和模拟内流盆地面积的全球变化。厘米，寒武纪； O，奥陶系； S，志留纪； D，泥盆纪；碳水化合物，石炭系； P，二叠纪； Tr，三叠纪； J，侏罗纪； K，白垩纪； Pg，古近纪；吴，尼奥金。

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By redistributing sediments eroded from the continental reliefs to the oceans, rivers are crucial players in biochemical cycles. However, before extrapolating the model results towards such considerations in deep time, we confront our model predictions with available independent data. First, the geography of model-predicted modern river outlets and watersheds conforms with actual ones (Extended Data Fig. 3). Likewise, the predicted water discharge and sediment yield for the largest modern rivers compare to current ones¹³. As an example, our predictions of the Amazon River discharge and sediment flux are respectively well within the estimated range (6,591 to 7,570 km³ yr⁻¹)²⁰ and only about 4% below the sediment production rate inferred from cosmogenic nuclide analysis (about 610 Mt yr⁻¹)²¹. Our model faithfully accounts for the discharge–area scaling relationship between water and sediment flux at the present day²², and throughout the entire Phanerozoic (Extended Data Fig. 3). Predicted trends of sediment flux compare reasonably well with observations¹⁷, although more closely during the Meso-Cenozoic for which the record is more accurate (Extended Data Fig. 6c). Water and sedimentary fluxes are remarkably anticorrelated over time to the average area of the watersheds (Extended Data Fig. 3c), indicating that large sediment yields are primarily due to small basins characteristic of the heterogeneous landscapes found in tectonically dynamic regions. This is well exemplified by the sharp increase in average drainage basin areas about 240 million years ago (Ma) related to the development of the low-relief landmasses of Pangaea, which closely matches a major decrease in sediment and water flux. Following Pangaea breakup after 200 Ma, water and sediment flux resume owing to wetter climates and an overall increase in mean elevation range under renewed plate tectonic activity. We also predict that about 25% of the surface of present-day landmasses is covered by endorheic catchments (Fig. 2b), in agreement with earlier estimates²³. Additionally, we corroborate the model-predicted sediment flux using the strontium isotopic ratio of seawater for the Phanerozoic, and with a sensitivity analysis based on different palaeo-elevation and palaeoclimate reconstructions (Methods).
通过将大陆地貌侵蚀的沉积物重新分配到海洋，河流在生物化学循环中发挥着至关重要的作用。然而，在深度推断模型结果以考虑这些因素之前，我们用可用的独立数据来面对我们的模型预测。首先，模型预测的现代河流入海口和流域的地理与实际相符（扩展数据图3 ）。同样，最大的现代河流的预测水流量和沉积物产量与现有河流的流量和沉积物产量进行了比较¹³ 。例如，我们对亚马逊河流量和沉积物通量的预测分别完全在估计范围内（6,591 至 7,570 km ³ yr ^-1 ） ²⁰ ，仅比宇宙成因核素分析推断的沉积物生产率（约 610山 yr ^-1 ) ²¹ 。我们的模型忠实地解释了当今²²以及整个显生宙的水和沉积物通量之间的排放面积比例关系（扩展数据图3 ）。沉积物通量的预测趋势与观测结果相当好¹⁷ ，尽管在中新生代期间更接近，其记录更准确（扩展数据图6c ）。随着时间的推移，水和沉积通量与流域的平均面积呈显着反相关（扩展数据图3c ），表明大量沉积物产量主要是由于构造动态区域中发现的异质景观的小盆地特征。 大约2.4亿年前（Ma）平均流域面积急剧增加就是一个很好的例子，这与盘古大陆低地势陆地的发展有关，这与沉积物和水通量的大幅减少密切相关。 200 Ma 后盘古大陆分裂后，由于气候湿润以及板块构造活动更新导致平均海拔范围总体增加，水和沉积物通量恢复。我们还预测，当今陆地约 25% 的表面被内流流域覆盖（图2b ），这与之前的估计一致²³ 。此外，我们使用显生宙海水的锶同位素比，并根据不同的古海拔和古气候重建进行敏感性分析，证实了模型预测的沉积物通量（方法）。

Owing to their quantitative nature, our model predictions provide unprecedented tools to assess the role that physiographic changes might have played in the long-term evolution of the biosphere. During the Phanerozoic, the evolution of the marine biodiversity, derived from palaeontological data^2,5,24, exhibits three major phases (Fig. 3). Following the emergence of the primitive Cambrian fauna, an initial phase of rapid diversification of the Palaeozoic fauna (between the Ordovician and Silurian periods) plateaued up to the Permian period. After a period of lower diversity over the Triassic, marine faunas monotonically diversified and radiated (Extended Data Fig. 10a).
由于其定量性质，我们的模型预测提供了前所未有的工具来评估地理学变化在生物圈长期演化中可能发挥的作用。在显生宙，根据古生物学数据^{2 , 5 , 24} ，海洋生物多样性的演化呈现出三个主要阶段（图3 ）。随着原始寒武纪动物群的出现，古生代动物群快速多样化的初始阶段（奥陶纪和志留纪之间）稳定到二叠纪。经过三叠纪多样性较低的时期后，海洋动物群单调多样化和辐射（扩展数据图10a ）。

Predicted trend in net sediment flux to the ocean (purple curve) and diversity of Cambrian, Palaeozoic and modern marine families (black line indicates total marine families, and Cambrian, Palaeozoic and modern faunas are delimited by white lines, all derived from Sepkoski’s compendium²; http://strata.geology.wisc.edu/jack/). The Pearson coefficient of 0.88 indicates a strong positive correlation between the two variables. The Cambrian explosion and Great Ordovician Biodiversification Event (GOBE), as well as the big five mass extinction events⁹, are indicated.
海洋净沉积物通量的预测趋势（紫色曲线）以及寒武纪、古生代和现代海洋科的多样性（黑线表示海洋科总数，寒武纪、古生代和现代动物区系由白线界定，全部来自Sepkoski的纲要² ； http://strata.geology.wisc.edu/jack/ ）。 Pearson 系数为 0.88，表明两个变量之间存在很强的正相关性。指出了寒武纪大爆发和奥陶纪生物多样性大事件（GOBE），以及五次大灭绝事件⁹ 。

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Among the forcings that control the biodiversity, nutrient availability is regarded as one of the most influential environmental drivers because it directly acts on primary productivity within the trophic zone required to sustain marine life^4,24,25 and diversity^26,27. As nutrient intake by the oceans is primarily related to river runoff, higher erosion rates during orogenic episodes have been proposed as a crucial extrinsic forcing^24,25,28. Yet inferences between nutrient flux and erosion are to our knowledge only qualitatively assessed, either from the geochemical trends—often matching marine genera to the equivocal ⁸⁷Sr/⁸⁶Sr isotopic ratio of seawater—or by deriving first-order empirical relationships between mountain elevations and sediment flux from major rivers. Our direct quantification of these fluxes over time permits us to alleviate the biases associated with the interpretation of the ⁸⁷Sr/⁸⁶Sr ratio of seawater (see Methods) or caused by the default assumption²³ of a linear transfer function between elevation and sediment transport. For example, downstream sediment storage in endorheic basins or reduced precipitation due to orographic shadowing curbs the sediment yield to the oceans, and conversely, small exorheic basins might enhance transport in mid-elevation regions²⁹.
在控制生物多样性的因素中，养分可用性被认为是最有影响力的环境驱动因素之一，因为它直接影响维持海洋生物^{4 , 24 , 25}和多样性^{26 , 27}所需的营养区内的初级生产力。由于海洋的养分摄入主要与河流径流有关，因此造山期较高的侵蚀率被认为是一个关键的外在强迫^{24 , 25 , 28} 。然而，据我们所知，养分通量和侵蚀之间的推论仅是定性评估，要么根据地球化学趋势（通常将海洋属与海水中模棱两可的⁸⁷ Sr/ ⁸⁶ Sr 同位素比相匹配），要么通过推导山脉海拔和侵蚀之间的一阶经验关系。主要河流的沉积物通量。我们对这些通量随时间变化的直接量化使我们能够减轻与海水⁸⁷ Sr/ ⁸⁶ Sr 比率解释相关的偏差（参见方法）或由海拔和沉积物运输之间的线性传递函数的默认假设²³引起的偏差。例如，内流盆地的下游沉积物储存或由于地形阴影而减少的降水量限制了向海洋的沉积物产量，相反，小型外流盆地可能会增强中海拔地区的运输²⁹ 。

The reconstructed net sediment flux to the ocean and the total number of marine families are strongly correlated (Pearson coefficient 0.88) and sediment flux variation markedly matches the three main phases that span the Phanerozoic eon (Fig. 3 and Extended Data Fig. 10a). This suggests that nutrient availability is a prime control on marine diversity, providing an explanation for the observed Palaeozoic plateau—as opposed to a continuous increase—and for the Mesozoic marine revolution¹⁰ that sparked biodiversification until the present day, but also for the low-diversity period of Pangaea, when endorheic basins suddenly sequestered a vast amount of sediments over the continents, depriving oceans of about 30% of the nutrient source (Figs. 1c and 2a). The time lag between the Great Ordovician Biodiversification Event and the predicted increase in Palaeozoic sediment fluxes (Fig. 3) could be explained either by uncertainties in the reconstructions of the climate and tectonics, or by the overwhelming effect of climate cooling³⁰.
重建的海洋净沉积物通量与海洋科总数密切相关（皮尔逊系数0.88），沉积物通量变化与跨越显生宙的三个主要阶段显着匹配（图3和扩展数据图10a ）。这表明营养物质的可用性是对海洋多样性的主要控制因素，为观察到的古生代高原（而不是持续增加）和中生代海洋革命¹⁰提供了解释，这场革命至今引发了生物多样性，而且也解释了低盘古大陆多样性时期，内陆盆地突然封存了大陆上的大量沉积物，剥夺了海洋约30%的营养源（图1和2）。 1c和2a )。奥陶纪大生物多样性事件与预测的古生代沉积物通量增加之间的时间滞后（图3 ）可以用气候和构造重建的不确定性来解释，也可以用气候变冷的压倒性影响来解释³⁰ 。

Mass extinctions are inescapable attributes of the marine diversity curve⁹, which can also be partially matched to the high-frequency variations in the predicted sediment yield to the oceans. Among the big five extinction events, the most pronounced one, during the end-Permian, is associated with the largest drop in sediment flux (Fig. 3). Besides the end-Ordovician and end-Triassic crises, mass extinction events occurred in the aftermath (about 2 to 15 Myr) of important reductions in the net sediment flux (Fig. 3), caused by either major declines in precipitation rates (Late Devonian) or elevation and palaeogeography (end-Permian), or both (end-Cretaceous; Extended Data Fig. 6a). Conversely, intensified hydrological conditions and weathering, and increases in nutrient discharge, are often considered as major drivers of oceanic anoxia³¹ and possibly extinction³². Although some congruences between specific Mesozoic anoxic events³³ and peaks in predicted net sediment flux to the ocean can be found in our model, here instead, we posit that sediment shortage—and not excess—more efficiently acts as an essential undermining mechanism before the impact of the compounding processes that ultimately triggered the episodes of mass extinctions (for example, sea-level fluctuations, rapid climatic changes, volcanism and bolide impacts) during Phanerozoic history, as referred to in the press-pulse framework³⁴.
大规模灭绝是海洋多样性曲线⁹不可避免的属性，它也可以部分地与预测的海洋沉积物产量的高频变化相匹配。在五次大灭绝事件中，二叠纪末期最明显的一次与沉积物通量的最大下降有关（图3 ）。除了奥陶纪末期和三叠纪末期的危机外，大规模灭绝事件还发生在净沉积物通量大幅减少之后（约 2 至 15 Myr）（图3 ），这是由降水率大幅下降（晚泥盆世）引起的。 ）或海拔和古地理（二叠纪末期），或两者（白垩纪末期；扩展数据图6a ）。相反，水文条件和风化的加剧以及养分排放的增加通常被认为是海洋缺氧³¹和可能的灭绝³²的主要驱动因素。尽管在我们的模型中可以发现特定中生代缺氧事件³³与预测的海洋净沉积物通量峰值之间的一些一致性，但在这里，我们认为沉积物短缺（而不是过量）更有效地在影响之前充当了重要的破坏机制显生宙历史中最终引发大规模灭绝事件（例如，海平面波动、快速气候变化、火山活动和火流星撞击）的复合过程，如所提到的到压力脉冲框架³⁴中。

The identified relationship between marine biodiversity and predicted ocean sedimentary flux could be a direct consequence of the incompleteness and spatial heterogeneity of the fossil record. Many have already raised the issue of preservation bias in the marine palaeobiological record^8,35,36. If so, the calculated strong correlation would represent an original tool to deconstruct biodiversity curves³⁷, and computed sediment flux could be used to find under-explored regions with high preservation potentials from the spatiotemporal distribution of simulated palaeo-rivers (Extended Data Fig. 9a). While acknowledging the possibilities for biases in the fossil record^2,5,24, we suggest that the carrying capacity for biodiversity of the oceans is extensively contingent on sedimentary flux and, therefore, on the physiographic evolution of continents. This supports earlier claims that abiotic factors (either environmental^38,39 or related to continental fragmentation and reassembly^40,41) control speciation and extinction rates. The recently proposed diversity hotspots hypothesis¹¹ posits that stability in environmental conditions and high continental fragmentation drove the global marine diversity to levels rarely approaching ecological saturation. Our results accordingly support the idea that tectonically driven shifts in palaeogeographies (that is, creation and destruction of geological barriers) and global ocean–atmospheric circulation ultimately affect sediment transport, which in turn modulates the carrying capacity for marine diversity. Our method offers an independent alternative to existing approaches evaluating long-term trends in nutrient flux^24,25,28; a natural avenue will be to account for the variable lithologies of eroded continental rocks over time and space (for example, large igneous provinces, and continental and volcanic arcs) to precisely quantify the chemical nature of the transferred nutrients (such as silica or phosphorus) that may foster or hinder the development of certain species and trigger evolutionary innovations.
海洋生物多样性与预测的海洋沉积通量之间已确定的关系可能是化石记录的不完整性和空间异质性的直接结果。许多人已经提出了海洋古生物学记录中保存偏差的问题^{8 , 35 , 36} 。如果是这样，计算出的强相关性将代表解构生物多样性曲线的原始工具³⁷ ，并且计算出的沉积物通量可用于从模拟古河流的时空分布中寻找具有高保存潜力的未开发区域（扩展数据图9a） ）。在承认化石记录^{2 , 5 , 24}中可能存在偏差的同时，我们认为海洋生物多样性的承载能力在很大程度上取决于沉积通量，因此也取决于大陆的地貌演化。这支持了早期的主张，即非生物因素（环境因素^{38 、 39}或与大陆分裂和重组相关的因素^{40 、 41} ）控制物种形成和灭绝速率。最近提出的多样性热点假说¹¹认为，环境条件的稳定性和大陆的高度破碎化将全球海洋多样性推向了很少接近生态饱和的水平。 因此，我们的结果支持了这样的观点，即构造驱动的古地理变化（即地质屏障的产生和破坏）和全球海洋-大气环流最终影响沉积物运输，进而调节海洋多样性的承载能力。我们的方法为评估养分通量长期趋势的现有方法提供了独立的替代^{方案24、25、28 ；}一个自然的途径是考虑受侵蚀的大陆岩石随时间和空间变化的岩性（例如，大型火成岩省以及大陆和火山弧），以精确量化转移的营养物（例如二氧化硅或磷）的化学性质这可能会促进或阻碍某些物种的发展并引发进化创新。

Along the same lines, we reappraise the diversification of terrestrial life during the Phanerozoic eon, except that we focus on land plants whose role as primary producers limits the impact of uncontrolled feedback interactions within the trophic chain. For that purpose, we test the possible impact of physiographic changes on vascular plants, by taking as predictors the sedimentary flux onto continents, the gradual spreading of the sediment cover over landmasses and the physiographic diversity of the landscape (Methods).
同样，我们重新评估了显生宙时期陆地生物的多样化，只不过我们关注的是陆地植物，它们作为初级生产者的作用限制了营养链内不受控制的反馈相互作用的影响。为此，我们通过将大陆上的沉积通量、陆地上沉积物覆盖的逐渐扩散以及景观的地貌多样性作为预测因子，测试地貌变化对维管束植物可能产生的影响（方法）。

At first order, the diversification of land plants¹ shows a roughly monotonic increase in the number of species from the Carboniferous onwards (Fig. 4a). Our model results indicate that the sediments accumulated in endorheic basins but that the flux was uneven through time. Owing to the model integration period, the sediment cover is null when the simulation starts, but this does not suggest that no sediment accumulated before the Cambrian period. We however reason that former soft sediments would have turned into barren hard rocks by 450 Ma owing to the limited sediment storage on continents during the Palaeozoic era (Fig. 2a). Sediment flux rapidly rose during the Mesozoic and Cenozoic eras. The good correlation between the sediment flux on continents and the bulk diversity of terrestrial plants (Pearson coefficient 0.67) already suggests that diversification is limited by sediment availability at any time. Moreover, endorheic sediments were mostly preserved after their deposition, thereby increasing the total continental surface covered by sediments (Figs. 1c and 4a). The correlation markedly improves (Pearson coefficient 0.91 (Fig. 4a) and up to 0.96 when limited to the gymnosperms and angiosperms (Extended Data Fig. 10b)) when considering instead that it is the spatial coverage of sediments cumulated over time that limits diversification, by replacing the bare rocks of the substratum with a soil that provides nutrients and moisture to the more specialized plant species that develop over time. Sediment cover is a necessary but non-unique condition for the development of terrestrial plants⁴², and for soil and sediment cover to have an effect of diversification, life is required to co-evolve^6,42. However, after the inception of life, our results suggest that it is the sediment cover that sets the carrying capacity.
在一级，陆地植物¹的多样化显示出从石炭纪开始物种数量大致单调增加（图4a ）。我们的模型结果表明，沉积物在内流盆地中积累，但通量随时间变化不均匀。由于模型积分周期的原因，模拟开始时沉积物覆盖为空，但这并不表明寒武纪之前没有沉积物堆积。然而，我们推断，由于古生代大陆沉积物储存量有限，到450 Ma，以前的软沉积物将变成贫瘠的硬岩（图2a ）。中生代和新生代沉积物通量迅速增加。大陆沉积物通量与陆地植物总体多样性之间的良好相关性（皮尔逊系数 0.67）已经表明，多样化在任何时候都受到沉积物可用性的限制。此外，内流沉积物在沉积后大多被保存下来，从而增加了沉积物覆盖的大陆总面积（图1c和图4a ）。当考虑到沉积物随时间累积的空间覆盖范围限制了多样化时，相关性显着改善（皮尔逊系数为 0.91（图4a ），当仅限于裸子植物和被子植物时高达 0.96（扩展数据图10b ）），通过用土壤取代底层的裸露岩石，为随着时间的推移而发展的更专业的植物物种提供营养和水分。 沉积物覆盖是陆生植物发育的必要但非唯一的条件⁴² ，而土壤和沉积物覆盖要发挥多样化作用，需要生命共同进化^{6 , 42} 。然而，在生命诞生之后，我们的研究结果表明，是沉积物覆盖决定了承载能力。

a, Predicted cumulative area covered by sediments (red curve) and diversity of tracheophyte species throughout the Phanerozoic¹ (green curves). The Pearson coefficient of 0.91 indicates a strong positive correlation between the two main curves. b, Top: temporal distribution of the physiographic diversity index (P_DIV; Methods) with lower (Q1; 25%), median (Q2) and upper (Q3; 75%) quartiles. Probability density function (PDF) is used to estimate the likelihood of having a specific P_DIV for each time interval. Bottom: temporal evolution of the physiographic variety index (P_VAR given by the interquartile range of P_DIV (Q3–Q1). c, Multivariate regression analysis (ordinary least squares (OLS) regression curve) carried out on normalized cumulative area covered by sediments (S_COV) and physiographic variety (P_VAR) gives a strong statistically significant relationship (P value < 2.2 × 10⁻¹⁶). The resulting regression equation is defined by 0.019 + 0.27P_VAR + 0.61S_COV. Analysis of variance shows a high dependence of plant diversity dynamics on these abiotic parameters (R² ≈ 0.9). Botanical icons by Rebecca Horwitt, available at full size and open access from https://sites.psu.edu/rhorwitt/.
a ，预测的沉积物覆盖累积面积（红色曲线）和整个显生宙¹气管植物物种的多样性（绿色曲线）。皮尔逊系数 0.91 表明两条主曲线之间存在很强的正相关性。 b ，上图：地理学多样性指数（ P _DIV ；方法）的时间分布，具有下四分位数（Q1；25%）、中四分位数（Q2）和上四分位数（Q3；75%）。概率密度函数 (PDF) 用于估计每个时间间隔具有特定P _DIV的可能性。底部：自然地理品种指数的时间演变（ P _VAR由P _DIV ( Q 3– Q 1) 的四分位数范围给出。c，对归一化累积覆盖面积进行的多元回归分析（普通最小二乘 (OLS) 回归曲线）沉积物 ( S _COV ) 和地貌变化 ( P _VAR ) 给出了很强的统计显着关系 ( P值 < 2.2 × 10 ^-16 ) 所得到的回归方程由下式定义。 0.019 + 0.27 P _VAR + ^0.61 S _COV 。方差分析显示植物多样性动态对这些非生物参数的高度依赖性（Rebecca Horwitt 的植物图标），可从https://获取完整尺寸和开放获取。 site.psu.edu/rhorwitt/ 。

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A further incentive to diversification comes from the increasing physiographic variety of the landscape (Fig. 4b) since the Carboniferous. Whereas the mean physiographic diversity (P_DIV; Methods) varies only moderately throughout the Phanerozoic eon, the physiographic variety (P_VAR; Methods) varies strongly. From the Triassic to the Cretaceous period, and during the Cretaceous and Cenozoic, the variety of the landscape increases at times when the overall rate of diversification accordingly increased (Fig. 4). By offering new habitats, periods of increased topographic heterogeneity have been identified as drivers of diversification at the regional scale^43,44; our results qualify this observation and indicate that the impact is in fact global, but also that it is the variety of the landscape—from low and high diversity—that promotes the overall diversification of terrestrial plants (Fig. 4c).
自石炭纪以来，多样化的进一步激励来自于地貌多样性的增加（图4b ）。虽然平均地理学多样性（ P _DIV ；方法）在整个显生宙中变化不大，但地理学多样性（ P _VAR ；方法）却变化很大。从三叠纪到白垩纪，以及白垩纪和新生代，地貌的多样性有时会增加，总体多样化率也相应增加（图4 ）。通过提供新的栖息地，地形异质性增加的时期已被确定为区域规模多样化的驱动因素^{43 , 44} ；我们的结果证实了这一观察结果，并表明影响实际上是全球性的，而且景观的多样性（从低多样性到高多样性）促进了陆地植物的整体多样化（图4c ）。

More insights can be gained by scrutinizing the evolution at genus level (Fig. 4a). During the early Palaeozoic era, continents covered less than 20% of the Earth surface with restricted endorheic basins (about 17% of emerged lands; Fig. 2b) and sparse continental deposition, hampering both soil production by physical and chemical weathering and preservation. Irrespective of climatic or biological factors, these poor edaphic conditions are suitable only for non-vascular plants that inhabit a variety of substrates (including bare rock) and access nutrients directly from meteoric waters and leachate^4,7. Early vascular plants radiated during the Devonian period, with the development of arborescent species and seed plants^4,6. Our reconstructions show that at that time, the increased global sediment flux (Fig. 2a) was not stored in endorheic basins (Fig. 4a), and that the physiographic variety was low (Fig. 4b). The low diversification of early vascular plants on land was thus driven only by species adaptation and climatic forcing rather than by geomorphological changes^45,46. This is corroborated by the increasing tolerance of plants to water stress and seasonality⁴⁷ associated with the colonization of diverse environments^6,48 at that time, feeding back on the landforms they live on⁶.
通过仔细观察属水平的进化可以获得更多的见解（图4a ）。在古生代早期，大陆覆盖了不到20%的地球表面，内流盆地有限（约占露出土地的17%；图2b ），大陆沉积稀疏，物理和化学风化和保存都阻碍了土壤的生产。无论气候或生物因素如何，这些不良的土壤条件仅适合栖息于各种基质（包括裸露岩石）并直接从大气水和渗滤液中获取养分的非维管植物^{4 , 7} 。早期的维管束植物在泥盆纪时期辐射出来，伴随着树状植物和种子植物的发展^{4 , 6} 。我们的重建表明，当时全球增加的沉积物通量（图2a ）并未储存在内流盆地中（图4a ），并且地貌多样性较低（图4b ）。因此，陆地上早期维管束植物的低多样性仅是由物种适应和气候强迫驱动的，而不是由地貌变化驱动的^{45 , 46} 。植物对水胁迫和季节性的耐受性不断增强⁴⁷与当时不同环境的殖民化^{6 、 48}相关，并反馈到它们所生活的地貌⁶ ，证实了这一点。

The diversity of land plants steeply increased only during the Late Devonian epoch with the rapid rise of pteridophytes and gymnosperms, but diversity quickly plateaued until the mid-Permian. As the total sediment coverage of landmasses stalled during that period (Fig. 4a) despite sustained erosion flux (Fig. 2a), we suggest that the diversity of terrestrial plants was further hampered by the limited expanse of favourable edaphic conditions.
仅在泥盆纪晚期，随着蕨类植物和裸子植物的迅速崛起，陆地植物的多样性才急剧增加，但多样性很快就趋于稳定，直到二叠纪中期。尽管侵蚀通量持续存在（图2a ），但在此期间陆地的总沉积物覆盖率却停滞不前（图4a ），我们认为陆地植物的多样性因有限的有利土壤条件而进一步受到阻碍。

Over the Permian and Triassic, pteridophytes were superseded by gymnosperms that further radiated (Fig. 4a). At that time, the Pangaea supercontinent gathered more emerged lands than at any other time in the Phanerozoic (Fig. 2b). Sediment-covered surface areas also rapidly increased owing to the development of large endorheic basins (up to 20% of the continental surface; Fig. 2b), fed by a sustained flux of sediments from the high relief of the widespread circum-Pangaean orogenies⁴⁹ (Fig. 4a). The massive development of these reliefs is also associated with an increase of physiographic variety (Fig. 4b). The emergence of these conditions, which would favour the diversification of deep-rooting plants across a diverse range of physiographic environments, coincided with the development of gymnosperms (Fig. 4) that dominated terrestrial floras by the end of the Triassic⁴.
在二叠纪和三叠纪，蕨类植物被进一步辐射的裸子植物所取代（图4a ）。当时，盘古大陆超大陆聚集了比显生宙任何时期都多的涌现陆地（图2b ）。由于大型内流盆地（占大陆表面的 20%；图2b ）的发展，沉积物覆盖的表面积也迅速增加，这些盆地受到来自广泛的环盘古造山带高地势的沉积物的持续流动⁴⁹ （图4a ）。这些地貌的大规模发展也与地貌多样性的增加有关（图4b ）。这些条件的出现，有利于深根植物在不同的自然地理环境中的多样化，与^三叠纪末期主导陆地植物区系的裸子植物的发展相一致（图4 ）。

Gymnosperm diversity continued to rise during the early phases of Pangaea breakup before levelling off during the Jurassic and Cretaceous, along with a decrease in both continental deposition flux (Fig. 2a) and physiographic variety (Fig. 4b), as well as a relatively steady sediment coverage (Fig. 4a), which all restrained the favourable rejuvenation of continental surfaces. Gymnosperms were superseded by angiosperms that diversified at unprecedented rates at least from the Cretaceous onwards (Fig. 4a and Extended Data Fig. 10b), although the timing remains largely controversial^50,51. Common explanations invoke their efficient cross-pollination strategies and high growth rates^52,53. Yet the period was also marked by extensive orogenic phases in North and South America and Eurasia (Fig. 2a). At that time, erosion resumed in the reliefs along with renewed endorheic deposition in the lowlands, and the overall physiographic variety further increased (Fig. 4b). The new diverse niches that developed in this heterogeneous topography, along with quickly expanding, nutrient-rich continental surfaces, could have promoted the fast radiation of angiosperms.
裸子植物多样性在盘古大陆分裂的早期持续上升，然后在侏罗纪和白垩纪趋于平稳，同时大陆沉积通量（图2a ）和地貌多样性（图4b ）均减少，并且相对稳定。沉积物覆盖（图4a ），这些都限制了大陆表面的有利更新。裸子植物被被子植物所取代，至少从白垩纪开始，被子植物以前所未有的速度多样化（图4a和扩展数据图10b ），尽管时间仍然存在很大争议^{50 , 51} 。常见的解释是其高效的异花授粉策略和高增长率^{52 , 53} 。然而，这一时期的标志还包括北美、南美和欧亚大陆广泛的造山期（图2a ）。此时，地貌中的侵蚀重新开始，低地内流沉积又重新出现，总体地貌多样性进一步增加（图4b ）。在这种异质地形中形成的新的多样化生态位，以及快速扩张、营养丰富的大陆表面，可能促进了被子植物的快速辐射。

Our study shows a remarkable congruence between the Phanerozoic landscape dynamics and the diversification of both marine life and terrestrial life. Earlier work already identified elements of this, but the analyses remained fragmentary^{25,53,54,55,56}, considering isolated pieces of the environmental puzzle: climatic, geological or biotic. Here we suggest that the evolution of continental physiography—as set by the interplay between the geosphere and the atmosphere—determines nutrient availability, and that it is a crucial limiting factor in both the marine realm and terrestrial realm, as important as intrinsic biotic processes^9,10,53, or extrinsic processes such as the climatic control⁴⁶ or plate tectonics⁴¹. In the oceans, riverine sedimentary flux directly sets nutrient availability for primary productivity. In continents, nutrient availability is tuned by endorheism, by rerouting the sedimentary flux and gradually varnishing their surfaces with a sedimentary cover, which facilitates the development of more specialized species. The relative effects of physiographic diversity and erosion rates on diversification are difficult to discriminate, but we suggest that the variety of the physiography further adjusts the effect of endorheism by tessellating the landscape.
我们的研究表明显生宙地貌动态与海洋生物和陆地生物的多样化之间存在显着的一致性。早期的工作已经确定了其中的要素，但考虑到环境难题的孤立部分：气候、地质或生物，分析仍然不完整^{25 , 53 , 54 , 55 , 56} 。在这里，我们认为，大陆地貌的演化（由地圈和大气之间的相互作用决定）决定了养分的可用性，并且它是海洋领域和陆地领域的一个关键限制因素，与内在的生物过程一样重要^{9 、 10、53} ，或外部过程，例如气候控制⁴⁶或板块构造⁴¹ 。在海洋中，河流沉积通量直接决定初级生产力的养分可用性。在大陆上，营养物质的可用性是通过内吸作用来调整的，通过改变沉积通量并逐渐用沉积覆盖物覆盖其表面，这有利于更专业的物种的发展。地貌多样性和侵蚀率对多样化的相对影响很难区分，但我们建议地貌多样性通过细分景观进一步调整内吸作用的影响。

The modality of sediment routing implies that diversification is simultaneously detachment limited (the sediment flux should be enough to sustain diversification) and transport limited (sediment storage in continents may, in an extreme case, starve marine life while instead feeding terrestrial life, or vice versa). The Phanerozoic trends of marine and terrestrial diversity highlight these regimes: marine diversity directly scales with sediment flux and is thus dominantly detachment limited. Land plant diversity is instead transport limited: its onset occurred much later than that of marine diversity and exploded only once endorheism efficiently resurfaced continents with sediments. Overall, physiographic changes determine the carrying capacity of both the oceans and the continents.
沉积物路径的模式意味着多样化同时受到分离限制（沉积物通量应足以维持多样化）和运输限制（在极端情况下，大陆沉积物储存可能会导致海洋生物挨饿，而反而喂养陆地生物，反之亦然） ）。海洋和陆地多样性的显生宙趋势突出了这些规律：海洋多样性直接随沉积物通量变化，因此主要受到脱离限制。相反，陆地植物多样性受到运输的限制：它的出现比海洋多样性晚得多，并且只有在内吸作用有效地用沉积物重新覆盖大陆时才爆发。总体而言，地貌变化决定了海洋和大陆的承载能力。

We anticipate that these findings, together with the released sets of physiographic descriptors at a high spatial resolution for the past 540 Myr (ref. ¹⁶), will invite more quantitative reappraisal of the interactions between the solid Earth and the atmosphere, hydrosphere and biosphere. For instance, our current approach conveniently reduced the problem to the temporal dimension by extracting spatially averaged metrics but ignores the spatialization of diversification events. A thorough palaeogeographical analysis of diversification events⁵⁶ in both continents and oceans is now permitted thanks to these reconstructions. Sensitivity tests, which illustrate how denudation rates scale with climate reconstructions and endorheic sediment storage is chiefly controlled by palaeo-elevation reconstructions, will allow further testing of our hypothesis.
我们预计这些发现，连同已发布的过去 540 迈尔高空间分辨率的地理学描述符集（参考文献¹⁶ ），将引发对固体地球与大气、水圈和生物圈之间相互作用的更多定量重新评估。例如，我们当前的方法通过提取空间平均指标，方便地将问题减少到时间维度，但忽略了多样化事件的空间化。由于这些重建，现在可以对大陆和海洋的多样化事件⁵⁶进行彻底的古地理分析。敏感性测试说明了剥蚀率如何随气候重建而变化，以及内流沉积物储存主要由古海拔重建控制，这将有助于进一步检验我们的假设。

Global landscape model 全球景观模型

Here we use goSPL^12,13, an open-source scalable parallel numerical model that simulates landscape and sedimentary basin evolution at the global scale (resolution about 5 km). It accounts for river incision and soil creep, both considered as the main drivers of long-term physiographic changes. goSPL also tracks eroded sediments from source to sink considering alluvial and marine deposition, sediment compaction and porosity change, and could be used to reconstruct basin stratigraphic records. To evaluate these processes on landscape dynamics, different forcing conditions could be imposed from spatially and temporally varying tectonics (both horizontal and vertical displacements) to multiple climatic histories (for example, precipitation patterns and sea-level fluctuations). The model’s main equation, the continuity of mass, has the following common form:
在这里，我们使用 goSPL ^{12 、 13} ，这是一个开源可扩展并行数值模型，可以模拟全球尺度的景观和沉积盆地演化（分辨率约为 5 km）。它解释了河流切割和土壤蠕变，两者都被认为是长期地貌变化的主要驱动因素。 goSPL 还考虑冲积和海洋沉积、沉积物压实和孔隙度变化来跟踪从源头到汇的侵蚀沉积物，并可用于重建盆地​​地层记录。为了评估这些景观动力学过程，可以从空间和时间变化的构造（水平和垂直位移）到多种气候历史（例如降水模式和海平面波动）施加不同的强迫条件。该模型的主要方程，即质量的连续性，具有以下常见形式：

for which changes in surface elevation z with time t depend on tectonic forcing U (rock uplift rate, in metres per year), hillslope processes for which κ is the diffusion coefficient (set to 0.5 m² yr⁻¹)⁵⁷ and fluvial processes defined using the stream power law. m and n are dimensionless empirical constants (set to 0.5 and 1), ε is a precipitation-independent component of erodibility (set to 4.0 × 10⁻⁷ yr⁻¹ on the basis of the choice of m), and PA is the water flux combining upstream total area (A) and local runoff (P) obtained from palaeoclimate mean annual precipitation minus evapotranspiration⁵⁷. In our formulation, the weathering impact of runoff and its role on river incision enhancement is incorporated by scaling the erodibility coefficient with local mean annual runoff rate with a prefactor d (a positive exponent estimated from field-based relationships⁵⁸ and set to 0.42). It follows from equation (1) that deposition in flat plains or along gentle slopes is null. However, it simulates continental deposition in depressions and endorheic basins.
其中地表高程z随时间t 的变化取决于构造强迫U （岩石抬升率，以米/年为单位）、山坡过程（其中κ为扩散系数（设置为 0.5 m ² yr ^-1 ） ⁵⁷和定义的河流过程）使用流幂律。 m和n是无量纲经验常数（设置为 0.5 和 1）， ε是侵蚀性的与降水无关的分量（根据m的选择设置为 4.0 × 10 ^-7 yr ^-1 ）， PA是水通量结合了上游总面积（ A ）和从古气候平均年降水量减去蒸散量中获得的当地径流（ P ） ⁵⁷ 。在我们的公式中，径流的风化影响及其对河流切入增强的作用是通过将侵蚀系数与当地平均年径流率和前因子d （根据基于现场的关系估计的正指数⁵⁸并设置为 0.42）进行缩放来合并的。由式( 1 )可知，平原或缓坡的沉积为零。然而，它模拟了凹陷和内流盆地的大陆沉积。

In goSPL, erosion occurring in upstream catchments is linked to basin sedimentation through a multiple-flow-direction algorithm that routes both water and sediment flux towards multiple downstream nodes, preventing the locking of erosion pathways along a single direction and helping the distribution of the corresponding flux in downstream regions. To solve the flow discharge globally (PA), we use a parallel implicit drainage area (IDA) method^59,60 in a Eulerian reference frame, expressed in the form of a sparse matrix composed of diagonal terms set to unity and off-diagonal terms corresponding to the immediate neighbours of each vertex composing the spherical mesh. The solution of the IDA algorithm is obtained using the Richardson solver with block Jacobian preconditioning⁵⁹, both available in PETSc⁶¹. Continental erosion and sediment transport solutions follow a similar approach⁶⁰. Some of the main advantages of goSPL lie in its design of implicit and parallel solutions of its constitutive equations⁶⁰, making it possible to increase the model stability even with large time steps, and to scale the simulation run time over hundreds of CPUs.
在 goSPL 中，上游流域发生的侵蚀通过多流向算法与盆地沉积联系起来，该算法将水和沉积物通量引向多个下游节点，防止侵蚀路径沿单一方向锁定，并帮助分配相应的侵蚀路径。下游地区的流量。为了求解全局流量（ PA ），我们在欧拉参考系中使用并行隐式排水面积（IDA）方法^{59 , 60} ，以稀疏矩阵的形式表示，该矩阵由设置为统一的对角项和非对角项组成对应于组成球形网格的每个顶点的直接邻居。 IDA 算法的解是使用具有块雅可比预处理^{59 的}Richardson 解算器获得的，两者均在 PETSc ⁶¹中可用。大陆侵蚀和沉积物输送解决方案遵循类似的方法⁶⁰ 。 goSPL 的一些主要优点在于其本构方程⁶⁰的隐式和并行解的设计，使得即使在大时间步长的情况下也可以提高模型稳定性，并且可以在数百个 CPU 上扩展模拟运行时间。

Palaeo-elevation and precipitation forcing
古海拔和降水强迫

To reconstruct the past physiography, goSPL relies on time-evolving boundary conditions—climatic and palaeogeographic—that are used to compute the interplay between the solid Earth and the climate. To reconstruct high-resolution palaeo-elevations throughout the Phanerozoic, we use a series of 108 maps from the PALEOMAP palaeogeographic atlas¹⁴ ranging from the Holocene epoch to the Cambrian–Precambrian boundary (541 Ma). These palaeo-maps are defined at approximately 5-Myr intervals, and each of them is represented as a regular grid with a resolution of 0.1° × 0.1° (approximately 10-km cell width at the Equator). These palaeogeographic maps were initially based on information related to lithofacies and palaeoenvironmental datasets⁶² and supplemented and refined for more than 40 years with regional palaeogeographic atlases^14,63. We acknowledge that these maps bear some uncertainties and controversial aspects. For example, the very early Andean rise to their modern elevations consequently precociously lowers the predicted bulk sediment flux during the Neogene period while diversification continues to increase (Figs. 3 and 4). It is worth noting that even though the PALEOMAP dataset forms the basis of this study, from a methodology standpoint, other datasets^64,65,66 could be used.
为了重建过去的地貌，goSPL 依赖于随时间演变的边界条件（气候和古地理），这些条件用于计算固体地球和气候之间的相互作用。为了重建整个显生宙的高分辨率古海拔，我们使用了 PALEOMAP 古地理图集¹⁴中的一系列 108 张地图，范围从全新世到寒武纪-前寒武纪边界（541 Ma）。这些古地图以大约 5 密尔的间隔定义，每张都表示为分辨率为 0.1° × 0.1° 的规则网格（赤道处的单元宽度约为 10 公里）。这些古地理地图最初基于与岩相和古环境数据集相关的信息⁶² ，并经过 40 多年的区域古地理地图集^{14 、 63}的补充和完善。我们承认这些地图存在一些不确定性和有争议的方面。例如，很早的安第斯山脉上升到现代海拔，因此提前降低了新近纪时期预测的大量沉积物通量，同时多样化继续增加（图3和图4 ）。值得注意的是，尽管 PALEOMAP 数据集构成了本研究的基础，但从方法论的角度来看，也可以使用其他数据集^{64 、 65 、 66} 。

To simulate riverine processes, the palaeo-precipitation dataset used was generated using a variant, HadCM3BL-M2.1aD (ref. ¹⁵), of the coupled atmosphere–ocean–vegetation Hadley Centre model. This climate model also uses the PALEOMAP Atlas⁶⁷ but at a lower resolution (3.75° × 2.5°). The reconstructed palaeo-precipitation regimes are obtained for each individual palaeo-elevation map after running the climate model for at least 5,000 model years to reach a dynamic equilibrium of the deep ocean¹⁵. In addition to palaeo-elevation grids, there are two additional time-dependent boundary conditions that were set in the climate model: the solar constant; and the atmospheric CO₂ concentrations. Regarding the last condition, two alternative CO₂ estimates are proposed¹⁵ and we chose the palaeo-precipitation and evapotranspiration maps generated from the set of HadCM3 climate simulations using the CO₂ local weighted regression curve from ref. ⁶⁸.
为了模拟河流过程，所使用的古降水数据集是使用大气-海洋-植被耦合哈德利中心模型的变体 HadCM3BL-M2.1aD（参考文献¹⁵ ）生成的。该气候模型也使用 PALEOMAP Atlas ⁶⁷ ，但分辨率较低（3.75° × 2.5°）。在运行气候模型至少 5,000 个模型年以达到深海动态平衡¹⁵后，为每个单独的古海拔图获得了重建的古降水状况。除了古海拔网格之外，气候模型中还设置了两个额外的与时间相关的边界条件：太阳常数；和大气CO ₂浓度。关于最后一个条件，提出了两种替代的 CO ₂估计值¹⁵ ，我们选择了使用参考文献中的 CO ₂局部加权回归曲线从 HadCM3 气候模拟集生成的古降水量和蒸散图。 ⁶⁸ .

From the palaeo-elevation and palaeo-runoff maps, we generate the input files for goSPL by resampling the global temporal grids on an icosahedral mesh composed of more than 10 million nodes and 21 million cells (corresponding to an averaged resolution of about 5 km globally—about 0.05° resolution at the Equator). Inspired by techniques used in palaeoclimate modelling^15,67, we designed an approach to achieve a dynamic equilibrium (erosion rates balance tectonics; equation (1) and Extended Data Fig. 2) under steady boundary conditions (rainfall, tectonic uplift and erodibility). For each individual time slice, we run two sets of simulations over 168 CPUs to estimate their corresponding physiographic characteristics and associated water and sediment dynamics (Extended Data Fig. 1). A first simulation is carried out over an interval of 2 Myr under prescribed elevation and runoff conditions and simulates landscape evolution and associated water discharge and sediment flux assuming no other forcing. Under this setting, the role of surface processes is not counterbalanced by tectonics, and they excessively erode the reconstructed elevation, trimming part of the major long-lived orogenic belts and upland areas, and causing extensive floodplains. The resulting elevations are then corrected by assimilating the palaeo-elevation information¹³. Model predictions account for landscape evolution, and at this stage already contain a more detailed representation of terrestrial landforms (for example, canyons, valleys, incised channels and basins to cite a few) than the initial palaeo-elevation (Extended Data Fig. 2a). To preserve these morphological features during the correction step, high-amplitude and high-frequency structures are removed using a combination of moving average windows (ranging from 0.5° to 2°) that conserves the global distribution of the initial palaeo-elevation with minimal change of its hypsometry (≤0.5%; Extended Data Fig. 2c). We then derive a tectonic map (uplift and subsidence rates) by computing the local differences between the palaeo-elevation values and the adjusted ones.
根据古高程和古径流图，我们通过在由超过 1000 万个节点和 2100 万个单元组成的二十面体网格上重新采样全局时间网格来生成 goSPL 的输入文件（对应于全球约 5 公里的平均分辨率） —赤道分辨率约为 0.05°）。受到古气候建模技术的启发^{15 , 67} ，我们设计了一种在稳定边界条件（降雨、构造隆起和侵蚀性）下实现动态平衡（侵蚀率平衡构造；方程（ 1 ）和扩展数据图2 ）的方法。对于每个单独的时间片，我们在 168 个 CPU 上运行两组模拟，以估计其相应的地形特征以及相关的水和沉积物动态（扩展数据图1 ）。第一次模拟是在规定的海拔和径流条件下以 2 Myr 的间隔进行的，并在假设没有其他强迫的情况下模拟景观演变以及相关的水流量和沉积物通量。在这种背景下，地表过程的作用没有被构造作用所抵消，它们过度侵蚀了重建的高程，修剪了部分主要的长寿造山带和高地地区，并造成了大面积的洪泛区。然后通过同化古海拔信息来校正所得到的海拔¹³ 。模型预测考虑了地貌演化，并且在这个阶段已经包含了比初始古海拔更详细的陆地地貌表征（例如峡谷、山谷、下切河道和盆地等）（扩展数据图2a ） 。 为了在校正步骤中保留这些形态特征，使用移动平均窗口（范围从 0.5° 到 2°）的组合来去除高振幅和高频结构，从而以最小的变化保留初始古海拔的全局分布其高度测量（≤0.5%；扩展数据图2c ）。然后，我们通过计算古海拔值与调整后的海拔值之间的局部差异来得出构造图（隆升率和沉降率）。

A second simulation starts with previous palaeo-elevation and runoff conditions and additionally accounts for tectonic forcing. This simulation runs until dynamic equilibrium is reached (that is, erosion rates compensate tectonic uplift rates) within the first million years of landscape evolution (Extended Data Fig. 2c). The outputs of this second simulation are then used to evaluate water and sediment flux for the considered time slice, as well as the major catchment characteristics (river networks, drainage areas, and erosion and deposition rates).
第二次模拟从之前的古海拔和径流条件开始，并另外考虑了构造强迫。该模拟一直运行，直到在景观演化的前一百万年内达到动态平衡（即侵蚀率补偿构造抬升率）（扩展数据图2c ）。然后，第二次模拟的输出用于评估所考虑时间片的水和沉积物通量，以及主要流域特征（河网、流域面积以及侵蚀和沉积率）。

The parametrization of equation (1) is obtained by calibrating its variables with modern estimates of average global erosion rates¹⁸ (mean value of 63 m Myr⁻¹ with a standard deviation of 15 m Myr⁻¹; Extended Data Fig. 6c) and of suspended sediment flux from the BQART model^19,20 (corresponding to 12.8 Gt yr⁻¹). Following calibration, we predict an average present-day global erosion rate of 71 m Myr⁻¹, and a sediment flux of 12.15 Gt yr⁻¹ (assuming an average density of 2.7 g cm⁻³). On the basis of the multiple-flow IDA approach used to integrate runoff over upstream catchments⁵⁹ (IDA algorithm), we also extract the spatial distribution of the largest water discharges and sediment flux (Extended Data Fig. 3a) and their respective basin characteristics.
方程（ 1 ）的参数化是通过用现代估计的全球平均侵蚀率¹⁸ （平均值为63 m Myr ^-1 ，标准差为15 m Myr ^-1 ；扩展数据图6c ）和来自 BQART 模型^{19 、 20 的}悬浮沉积物通量（对应于 12.8 Gt yr ^-1 ）。校准后，我们​​预测当今全球平均侵蚀率为 71 m Myr ^-1 ，沉积物通量为 12.15 Gt yr ^-1 （假设平均密度为 2.7 g cm ^-3 ）。在用于整合上游流域径流的多流IDA方法⁵⁹ （IDA算法）的基础上，我们还提取了最大水流量和泥沙通量的空间分布（扩展数据图3a ）及其各自的流域特征。

Sr isotopic variations from mantle origin
地幔起源的锶同位素变化

We use the geochemical archive of oceanic sediments to test the validity of the model predictions. The ⁸⁷Sr/⁸⁶Sr isotopic ratio of seawater (Extended Data Fig. 4) reflects the balance between continental weathering and mantle dynamics (hydrothermalism at mid-ocean ridges and weathering of island arcs and oceanic islands)^69,70, making it a classic proxy to diagnose the relative importance of geodynamic and climatic forcings through time^71,72.
我们使用海洋沉积物的地球化学档案来测试模型预测的有效性。海水⁸⁷ Sr/ ⁸⁶ Sr 同位素比（扩展数据图4 ）反映了大陆风化与地幔动力学（洋中脊的热液作用以及岛弧和大洋岛屿的风化）之间的平衡^{69 , 70} ，使其成为经典诊断整个时间段内地球动力学和气候强迫的相对重要性的代理^{71 , 72} 。

From the measured isotopic budget of the ocean (O), present-day low ⁸⁷Sr/⁸⁶Sr ratios (about 0.703) are produced from mantle sources (M), whereas high ratios (about 0.713) come from continental runoff (CR, measured from main rivers worldwide)⁶⁹. As a result, the strontium isotope oceanic mass balance has the following form:
根据测量的海洋同位素收支 (O)，目前较低的⁸⁷ Sr/ ⁸⁶ Sr 比率（约 0.703）来自地幔来源（M），而高比率（约 0.713）来自大陆径流（CR，测得）来自世界各地的主要河流） ⁶⁹ .因此，锶同位素海洋质量平衡具有以下形式：

in which ξ represents the mass fraction of the Sr coming from the mantle (Q_M/(Q_M + Q_S) with Q_S being the predicted net sediment flux to the ocean derived from our simulation) and the flux of mantle origin (Q_M). At the present day, Q⁰_M is given by the percentages defined above:
其中xi代表来自地幔的 Sr 的质量分数（ Q _M /（ Q _M + Q _S ），其中Q _S是根据我们的模拟得出的预测的进入海洋的净沉积物通量）和地幔来源的通量（ Q_米）。目前， Q ⁰ _M由上面定义的百分比给出：

Assuming that weathering scales with erosion rates, our reconstructed global net sediment flux to the ocean (Q_S) offers an independent alternative to existing approaches evaluating Sr flux from tectonic origin and could be used to infer past tectonic activity^73,74,75,76. Under this assumption, differences (∆(⁸⁷Sr/⁸⁶Sr)) between our predicted Sr ratio and the one from the geological record³⁹ would reflect the dynamics of the Earth’s exogenic system, with positive ∆(⁸⁷Sr/⁸⁶Sr) values corresponding to periods of higher tectonic activities relative to the present day and negative ones coinciding with more quiescent periods. We then use the isotope oceanic mass balance to independently derive the mantle contribution to the ⁸⁷Sr/⁸⁶Sr ratio, relying on our estimates of terrigenous flux and on the observed ⁸⁷Sr/⁸⁶Sr ratio of seawater. We crudely use the Sr isotope oceanic mass balance to estimate the Sr flux of mantellic origin (Q_M; Extended Data Fig. 4) in the mass fraction ξ:
假设风化作用随侵蚀率变化，我们重建的全球海洋净沉积物通量（ Q _S ）为评估构造起源的 Sr 通量的现有方法提供了独立的替代方案，并可用于推断过去的构造活动^{73 , 74 , 75 , 76} 。在此假设下，我们预测的 Sr 比率与地质记录³⁹中的比率之间的差异 (Δ( ⁸⁷ Sr/ ⁸⁶ Sr)) 将反映地球外生系统的动态，正值 Δ( ⁸⁷ Sr/ ⁸⁶ Sr) 对应相对于当今的较高构造活动时期和与较静止时期同时发生的负构造活动时期。然后，我们根据对陆源通量的估计和观测到的海水⁸⁷ Sr/ ⁸⁶ Sr 比率，使用同位素海洋质量平衡独立推导地幔对⁸⁷ Sr/ ⁸⁶ Sr 比率的贡献。我们粗略地使用 Sr 同位素海洋质量平衡来估计质量分数xi中的地幔来源的 Sr 通量（ Q _M ；扩展数据图4 ）：

Note that we assume that the isotopic ratios ${\left[\frac{{}^{87}\mathrm{S}\mathrm{r}}{{}^{86}\mathrm{S}\mathrm{r}}\right]}_{\mathrm{C}\mathrm{R}}$ and ${\left[\frac{{}^{87}\mathrm{S}\mathrm{r}}{{}^{86}\mathrm{S}\mathrm{r}}\right]}_{\mathrm{M}}$ remained equivalent to those of the present day. Whereas the Sr ratio from the mantle budget might change marginally (⁸⁷Sr/⁸⁶Sr about 0.703 for mid-ocean ridge hydrothermal and about 0.7035 for island arcs and oceanic islands⁶⁹), the contribution of the continental crust to the Sr ratio is highly dependent on the type of weathered materials⁷⁰ (⁸⁷Sr/⁸⁶Sr about 0.708 for limestones, compared to about 0.721 for silicates⁶⁹).
请注意，我们假设同位素比率 ${\left[\frac{{}^{87}\mathrm{S}\mathrm{r}}{{}^{86}\mathrm{S}\mathrm{r}}\right]}_{\mathrm{C}\mathrm{R}}$ 和 ${\left[\frac{{}^{87}\mathrm{S}\mathrm{r}}{{}^{86}\mathrm{S}\mathrm{r}}\right]}_{\mathrm{M}}$ 仍然与当今相同。虽然地幔预算中的 Sr 比率可能略有变化（洋中脊热液的 Sr/Sr 约为 0.703，岛弧和大洋岛屿的 Sr/Sr 约为 0.7035），但大陆地壳对 Sr 比率的贡献很大程度上取决于类型风化材料（石灰石的 Sr/Sr 约为 0.708，而硅酸盐的 Sr/Sr 约为 0.721）。

We find that the contributions of mantle and terrigenous sources relative to those of the present day covary at long wavelengths, with two periods of reinforced influx from both sources separated by a quieter period during Pangaea. This trend mirrors the Wilson cycle. It indicates that the periods of high erosion, coinciding with periods of continental aggregation and contraction, increased elevation and wetter climates, also match periods of reinforced tectonic activity. Seafloor expansion is faster during periods of continental dispersal, and the total length of ridges increases during breakup⁷⁷. As the mantle input to the ⁸⁷Sr/⁸⁶Sr ratio of seawater is partially driven by seafloor kinematics, we find several similarities between the predicted mantle Sr flux and subduction rates^72,74,76 that can be taken as a proxy for oceanic spreading rates; Extended Data Fig. 4). Notably, over the past 250 Ma, we deduce that mantle fluxes were low during Pangaea, and subsequently increased during Pangaea breakup; flux decreased during the late Palaeogene, mirroring the decrease in crustal production rates in the Atlantic and Pacific oceans⁷⁸ and the consumption of the East Pacific ridge.
我们发现，在长波长下，地幔和陆源源的贡献相对于当今的共变，在盘古大陆期间，两个源头的增强流入期被一个较安静的时期隔开。这一趋势反映了威尔逊周期。它表明，高侵蚀时期与大陆聚集和收缩、海拔升高和气候湿润的时期同时发生，也与构造活动加强的时期相匹配。在大陆扩散期间，海底扩张速度更快，并且海脊的总长度在分裂期间增加⁷⁷ 。由于地幔对海水⁸⁷ Sr/ ⁸⁶ Sr 比率的输入部分是由海底运动学驱动的，我们发现预测的地幔 Sr 通量和俯冲速率之间存在一些相似之处^{72 , 74 , 76} ，可以作为海洋扩张速率的代表;扩展数据图4 )。值得注意的是，在过去的 250 Ma 中，我们推断盘古大陆期间地幔通量较低，随后在盘古大陆分裂期间增加；古近纪晚期通量减少，反映了大西洋和太平洋⁷⁸地壳生产率的下降以及东太平洋海脊的消耗。

Our model predictions of sediment flux compare at first order to the observed increase in the ⁸⁷Sr/⁸⁶Sr ratio of seawater over the past 150 Myr (Extended Data Fig. 4). Assuming that weathering scales with erosion rates, it corroborates the first-order impact of Cenozoic orogenesis⁷⁹ on the Sr ratio. Likewise, over the entire Phanerozoic, short-lived (20–40 Myr) increases in predicted erosion flux can explain the increase in the ⁸⁷Sr/⁸⁶Sr record during major orogenic phases⁸⁰, whereas the long-term variations of the record can be at first order explained by the coevolution of the terrigenous and mantle sources during the Wilson cycle. These results indirectly substantiate our model predictions of sediment flux to the oceans.
我们的沉积物通量模型预测与过去 150 Myr 期间观察到的海水⁸⁷ Sr/ ⁸⁶ Sr 比率的增加进行了比较（扩展数据图4 ）。假设风化作用与侵蚀率成正比，它证实了新生代造山运动⁷⁹对 Sr 比率的一级影响。同样，在整个显生宙，预测侵蚀通量的短暂（20-40 Myr）增加可以解释主要造山阶段⁸⁰期间⁸⁷ Sr/ ⁸⁶ Sr 记录的增加，而记录的长期变化可以解释为威尔逊旋回期间陆源和地幔源的共同演化可以解释第一阶。这些结果间接证实了我们对海洋沉积物通量的模型预测。

Limitations and sensitivity
局限性和敏感性

In goSPL¹², erosion is defined using a first-order parametrization of the physics at play (equation (1)), which captures the long-term, large-scale landscape evolution^22,57,81. More sophisticated treatments directly linked to sediment transport theory and incorporating different erosional behaviours have been proposed (for example, by accounting for mobile sediment and bed resistance to erosion, or using different formulations of sediment transport based on transport-limited equations)^82,83,84.
在 goSPL ¹²中，侵蚀是使用物理场的一阶参数化（方程（ 1 ））来定义的，它捕获了长期、大规模的景观演化^{22 , 57 , 81} 。已经提出了与沉积物输运理论直接相关并结合不同侵蚀行为的更复杂的处理方法（例如，通过考虑移动沉积物和河床对侵蚀的抵抗力，或使用基于输运限制方程的不同沉积物输运公式） ^{82、83 、 84} .

In addition, the erodibility parameter does not consider spatiotemporal variations that could be induced by environmental (for example, temperature gradients and seasonal precipitation), geological (for example, soil composition and fault-induced bedrock weakening) or biological (for example, plant root growth and soil microbial activity) mechanisms^{6,85,86,87,88,89}. Instead, we assume uniform erodibility across all continents. Accounting for variable lithologies in model space could be achieved by assigning an erodibility prefactor depending on the surface rock composition in the stream power law term of equation (1) by an erodibility prefactor depending on the type of surficial lithology classes (typically with values ranging between 1.0 and 3.2; ref. ⁹⁰). However, this approach would require global palaeo-lithological surficial cover data that are difficult to obtain when looking into deep geological times. Although we do not account for seasonality variations, the weathering impact of precipitation and its role on river incision enhancement is incorporated by scaling the erodibility coefficient with the local mean net annual precipitation rate⁵⁸. One could also incorporate the effect of temperature on weathering of rocks according to rock composition by scaling the erodibility coefficient using the palaeoclimate temperature distribution. Such refinement possibilities are many, and although in principle desirable to better reproduce observations, adding those would necessarily add poorly controlled degrees of freedom in the parameterization, and lead to illusory enhanced predictive capabilities.
此外，可蚀性参数不考虑可能由环境（例如，温度梯度和季节性降水）、地质（例如，土壤成分和断层引起的基岩弱化）或生物（例如，植物根系）引起的时空变化。生长和土壤微生物活性）机制^{6 , 85 , 86 , 87 , 88 , 89} 。相反，我们假设各大洲的侵蚀性是一致的。考虑模型空间中的可变岩性，可以通过根据流幂律项（ 1 ）中的表面岩石成分分配侵蚀性前因子来实现，通过根据地表岩性类别的类型（通常值范围为1.0 和^3.2 ；然而，这种方法需要全球古岩性地表覆盖数据，而这些数据在研究深层地质时代时很难获得。尽管我们没有考虑季节性变化，但通过将侵蚀系数与当地平均年净降水率进行缩放，可以纳入降水的风化影响及其对河流切入增强的作用⁵⁸ 。人们还可以根据岩石成分，通过使用古气候温度分布缩放侵蚀系数来纳入温度对岩石风化的影响。这种细化的可能性有很多，虽然原则上希望更好地再现观察结果，但添加这些可能必然会增加参数化中控制不良的自由度，并导致虚幻的增强预测能力。

By design, our simulation is sensitive to both the climatic and palaeo-elevation reconstructions. Although other palaeogeography reconstructions exist^62,64,65,66, many are restricted to specific geological intervals and, to our knowledge, are not tied to a series of palaeo-precipitation maps for the entire Phanerozoic. Consequently, we chose to evaluate model sensitivity on palaeo-elevation using a single time slice (Aptian period about 120 Ma) by comparing our predicted sediment flux with a different set of palaeogeography and palaeoclimate reconstructions⁹¹. The results highlight several differences at the regional scale (Extended Data Fig. 5). For instance, a more humid equatorial climatic zone in the second reconstruction⁹² induces higher erosion rates on the northern and central part of Gondwana. The palaeo-elevation differences also redefine the drainage network and the volumes of sediment transported to the oceans or stored in continental basins. This is the case in Antarctica and on the eastern part of Eurasia where we note higher erosion rates or an increase in terrestrial sediment accumulation depending on the considered palaeogeography. Despite these local variations, those disparities become more tenuous when evaluating the global response. As an example, the percentage of endorheic basins varies from 24 to 26.5% between the two simulations and the net sediment flux to the ocean changes from 2.72 to 2.26 km³ yr⁻¹ (Extended Data Fig. 5). This suggests that although regional differences exist and if the imposed forcing conditions are not too dissimilar (both in terms of palaeoclimates and palaeogeographies), the reported global evolution and global trends that are presented in the study should remain relatively unchanged between reconstructions.
根据设计，我们的模拟对气候和古海拔重建都很敏感。尽管存在其他古地理重建^{62 , 64 , 65 , 66} ，但许多都仅限于特定的地质区间，并且据我们所知，与整个显生宙的一系列古降水图无关。因此，我们选择通过将我们预测的沉积物通量与一组不同的古地理和古气候重建进行比较，使用单个时间片（Aptian 周期约 120 Ma）来评估模型对古海拔的敏感性⁹¹ 。结果突出了区域尺度上的几个差异（扩展数据图5 ）。例如，第二次重建中更潮湿的赤道气候带⁹²导致冈瓦纳北部和中部地区的侵蚀率更高。古海拔差异还重新定义了排水网络以及输送到海洋或储存在大陆盆地中的沉积物量。南极洲和欧亚大陆东部就是这种情况，我们注意到，根据所考虑的古地理，侵蚀率较高或陆地沉积物积累增加。尽管存在这些地方差异，但在评估全球反应时，这些差异变得更加微弱。例如，两次模拟之间内流盆地的百分比从 24% 变化到 26.5%，流入海洋的净沉积物通量从 2.72 km 3 yr -1 变化到 2.26 km ³ yr ^-1 （扩展数据图5 ）。 这表明，尽管存在区域差异，并且如果施加的强迫条件不太相似（在古气候和古地理方面），则研究中报告的全球演化和全球趋势在重建之间应该保持相对不变。

To evaluate the model sensitivity to palaeo-runoff, we ran a full series of simulations throughout the Phanerozoic. The palaeoclimate reconstructions from ref. ¹⁵ have been carried out with two different CO₂ conditions (the atmospheric concentrations from ref. ⁶⁸ and a smoothed curve), but the mean global continental runoff remains very similar in both cases; Extended Data Fig. 6a) and should only very marginally change our results. Instead, we opted for the recent Phanerozoic palaeo-precipitation reconstruction from ref. ⁹³ that was run at 10-Myr intervals using the PALEOMAP palaeogeographic atlas¹⁴ with a much higher resolution (1°) than those of ref. ¹⁵. The release from ref. ⁹³ does not contain the evapotranspiration time slices, and we could therefore use the total palaeo-precipitation only as a proxy for runoff. Global mean continental runoff from ref. ⁹³ exhibits a similar temporal trend to the ones from ref. ¹⁵ but, because evapotranspiration could not be accounted for, with higher values (about 0.3 m yr⁻¹ on average over the Phanerozoic; Extended Data Fig. 6a). As erosion scales with runoff (equation (1)), this inflated runoff directly affects the global net sediment flux to the ocean (about 0.84 km³ yr⁻¹ on average) and to a lesser extent the continental deposition flux (<0.1 km³ yr⁻¹ on average; Extended Data Fig. 6b). The spatial distributions of these two runoff scenarios and their relative impact on denudation rates show substantial spatial differences over time (Extended Data Fig. 7). At the continental scale, the higher resolution in ref. ⁹³ should better account for the control of topography on the spatial variability in precipitation. For example, we note at 40 Ma (Extended Data Fig. 7) the orographic control of the Himalayas on the regional rainfall regime with its implications on erosion and deposition.
为了评估模型对古径流的敏感性，我们在整个显生宙进行了一系列的模拟。参考文献的古气候重建。 ¹⁵是在两种不同的 CO ₂条件下进行的（参考文献⁶⁸中的大气浓度和平滑曲线），但两种情况下的平均全球大陆径流仍然非常相似；扩展数据（图6a ））并且应该只会非常轻微地改变我们的结果。相反，我们选择了参考文献中最近的显生宙古降水重建。 ⁹³是使用 PALEOMAP 古地理图集¹⁴以 10 Myr 间隔运行的，其分辨率 (1°) 比 ref. 93 的分辨率高得多。 ¹⁵ .参考文献的发布。 ⁹³不包含蒸散时间切片，因此我们只能使用总古降水量作为径流的代理。来自参考的全球平均大陆径流。 ⁹³表现出与参考文献相似的时间趋势。 ¹⁵但是，由于无法解释蒸散量，因此具有较高的值（显生宙平均约 0.3 m yr ^-1 ；扩展数据图6a ）。由于侵蚀随着径流而扩大（方程（ 1 ）），这种膨胀的径流直接影响到海洋的全球净沉积物通量（平均约0.84 km ³ yr ^-1 ），并在较小程度上影响大陆沉积通量（ < 0.1 km）平均³年^-1 ；扩展数据图6b )。 这两种径流情景的空间分布及其对剥蚀率的相对影响随着时间的推移显示出巨大的空间差异（扩展数据图7 ）。在大陆尺度上，参考文献中的分辨率更高。 ⁹³应更好地考虑地形对降水空间变化的控制。例如，我们注意到在 40 Ma（扩展数据图7 ），喜马拉雅山的地形对区域降雨状况的控制及其对侵蚀和沉积的影响。

The sensitivity analysis provides two important pieces of information. First, both simulations show similar responses in terms of global sediment flux and denudation rates (Pearson correlations of 0.94 and 0.92, respectively). This suggests that irrespectively of the chosen palaeoclimatic reconstruction, our interpretation of the relationships between predicted sedimentary flux and biodiversity still holds. Second, the runoff has a stronger effect on the amplitudes in net sediment flux to the ocean and denudation rates when considering similar palaeo-elevation reconstruction (Extended Data Fig. 6b). Instead, differences in palaeo-elevations affect continental sediment cover and sediment accumulation in endorheic basins (Extended Data Fig. 5).
敏感性分析提供了两条重要信息。首先，两个模拟在全球沉积物通量和剥蚀率方面显示出相似的响应（皮尔逊相关系数分别为 0.94 和 0.92）。这表明，无论选择何种古气候重建，我们对预测的沉积通量与生物多样性之间关系的解释仍然成立。其次，当考虑类似的古高程重建时，径流对海洋净沉积物通量的幅度和剥蚀率有更强的影响（扩展数据图6b ）。相反，古海拔的差异会影响大陆沉积物覆盖和内流盆地的沉积物积累（扩展数据图5 ）。

Another limitation of our approach is to propose a hypothesis by comparing time series of mean model outputs with independent variables, but similar trends could possibly be expected for any model that accounts for plate tectonics—with essentially two cycles of continental aggregation and dispersal over the Phanerozoic eon—and subsequent climate reconstructions. The highly relevant correlations that we found can be however advocated to hierarchize these studies. As plate tectonics—and the breakup of Pangaea in particular—form the cornerstone of such studies^11,40,41, we thus compared continental fragmentation⁴¹ with Phanerozoic marine diversity, which yields only moderate correlations (Pearson coefficients of 0.46 with number of marine families²; 0.54 to 0.58 with the number of genera^2,5; Extended Data Fig. 8).
我们方法的另一个局限性是通过将平均模型输出的时间序列与自变量进行比较来提出假设，但是对于任何解释板块构造的模型都可能预期类似的趋势 - 基本上有两个大陆聚集和分散周期在显生宙亿万年——以及随后的气候重建。然而，我们发现的高度相关的相关性可以提倡对这些研究进行分层。由于板块构造，特别是盘古大陆的分裂，构成了此类研究的基石^{11 , 40 , 41} ，因此我们将大陆破碎⁴¹与显生宙海洋多样性进行了比较，这仅产生中等相关性（皮尔逊系数为 0.46 与海洋科的数量） ² ; 0.54 至 0.58 与属数^{2 、 5} ； 8 ).

Physiographic diversity and variety
地貌多样性和多样性

To evaluate the relationships between physiography and the Phanerozoic climate and tectonics, we define a unique continuous variable (named the physiographic diversity index) that encapsulates several of the reconstructed morphometric attributes. Simulation outputs are first interpolated from the icosahedral mesh on a regular 0.05° grid (open-access online release, HydroShare¹⁶).
为了评估地貌与显生宙气候和构造之间的关系，我们定义了一个独特的连续变量（称为地貌多样性指数），它包含了几个重建的形态测量属性。模拟输出首先从规则 0.05° 网格上的二十面体网格插值（开放获取在线版本，HydroShare ¹⁶ ）。

First, we quantify palaeo-landforms by calculating the topographic position index on each cell i (TPI_i) that measures the relative relief⁹⁴:
首先，我们通过计算测量相对地形的每个单元i上的地形位置指数 (TPI) 来量化古地貌⁹⁴ ：

in which z_i is the considered elevation at cell i and z_k is the mean of its surrounding cells (z_k), with n being the number of cells contained inside an annulus neighbourhood. Topographic position is an inherently scale-dependent calculation⁹⁵. To circumvent this problem, TPI is computed considering two scales of observation, a fine one ranging between 0.05° and 0.15° and a coarser one from 0.25° to 0.5°. As elevation is generally spatially autocorrelated, TPI values increases with scale, making it difficult to compare both scales of observation directly. To overcome this issue, we calculate a standardized TPI_S (equation (5)), in which $\overline{\mathrm{T}\mathrm{P}\mathrm{I}}$ is the mean over the entire grid and σ_TPI is its standard deviation⁹⁶ (top map in Extended Data Fig. 9a).
其中 是单元的考虑高程，是其周围单元 () 的平均值，是环形邻域内包含的单元数。地形位置本质上是依赖于比例的计算。为了解决这个问题，TPI 的计算考虑了两种观测尺度，一种是 0.05° 到 0.15° 之间的细尺度，另一种是 0.25° 到 0.5° 之间的粗尺度。由于海拔通常在空间上自相关，TPI 值随着尺度的增加而增加，因此很难直接比较两个观测尺度。为了克服这个问题，我们计算了一个标准化的TPI（方程（）），其中 $\overline{\mathrm{T}\mathrm{P}\mathrm{I}}$ 是整个网格的平均值，是其标准差（扩展数据图中的顶部图）。

We also extract the slope and water discharge for each time slice (bottom maps in Extended Data Fig. 9a). Note that we selected these three variables—TPI, slope and discharge—as morphometric indicators of the physiographic diversity but other ones such as aspect (that is, the direction of maximum gradient), and erosion and deposition rates could equally be added⁹⁷. From these continuous variables, we then derive categorical variables by defining seven categories from the slope, five from the water flux and ten from the TPI_S (Extended Data Fig. 9a,b and Supplementary Table 1; ref. ⁹⁸).
我们还提取每个时间片的坡度和排水量（扩展数据图9a中的底部图）。请注意，我们选择这三个变量——TPI、坡度和流量——作为地貌多样性的形态指标，但其他变量，如坡向（即最大梯度的方向）、侵蚀和沉积速率也可以同样添加⁹⁷ 。然后，我们通过从坡度定义七个类别、从水通量定义五个类别、从 TPI _S定义十个类别，从这些连续变量中导出分类变量（扩展数据图9a、b和补充表1 ；参考文献⁹⁸ ）。

From the categorical variables, we quantify the physiographic diversity index P_DIV (Supplementary Fig. 1a,b) using Shannon’s equitability (continuous variable [0,1]), which is calculated by normalizing the Shannon–Weaver diversity index (d_SW):
根据分类变量，我们使用香农公平性（连续变量[0,1]）量化地理学多样性指数P _DIV （补充图1a,b ），该指数是通过标准化香农-韦弗多样性指数（ d _SW ）计算得出的：

with p_k being the proportion of observations of type k in each neighbourhood and $\mathcal{C}$ being the number of categorical variables (here $\mathcal{C}$ = 3). The physiographic diversity index is calculated at each location for the 108 reconstructed time slices spanning the Phanerozoic (Supplementary Fig. 1c). The variations of P_DIV can be described either spatially for a given period (Supplementary Fig. 1c) or across time (Supplementary Fig. 2). As it characterizes how landscape complexity evolves over the geological timescale⁹⁹, this index can be used to infer the role physiography, and changes thereof, might have played on species migration, dispersal or isolation at both global and continental scales. Biodiversity richness emerges from many abiotic and biotic interactions; however, the role physiography might have played has often been overlooked¹⁰⁰. The high-resolution global maps generated from our simulation could be used as an additional palaeoenvironmental layer in mechanistic eco-evolutionary models^101,102.
是每个邻域中该类型的观测值的比例， $\mathcal{C}$ 是分类变量的数量（这里 $\mathcal{C}$ = 3）。计算了跨越显生宙的 108 个重建时间切片的每个位置的地貌多样性指数（补充图）。的变化可以在给定时期的空间上（补充图）或跨时间（补充图）来描述。由于它描述了景观复杂性在地质时间尺度上如何演变，因此该指数可用于推断地理学及其变化可能对全球和大陆尺度的物种迁移、扩散或隔离所发挥的作用。生物多样性的丰富性源于许多非生物和生物的相互作用；然而，地理学可能发挥的作用常常被忽视。我们的模拟生成的高分辨率全球地图可以用作机械生态进化模型中的附加古环境层。

To compare the temporal evolution of physiographic diversity with biotic^2,5 or abiotic geochemical and geophysical proxies, the mean value of P_DIV is insufficient, as it ignores the variety of landforms, which is better accounted for by the probability density function: the probability density function can be usefully reduced to a unique scalar—physiographic variety—given by the interquartile range P_VAR = Q₃ − Q₁ (that is, the range between the first quartile (Q₁; 25%) and the third quartile (Q₃;75%); Supplementary Fig. 2c).
为了将地貌多样性的时间演化与生物^{2 、 5}或非生物地球化学和地球物理指标进行比较， P _DIV的平均值是不够的，因为它忽略了地貌的多样性，这可以通过概率密度函数更好地解释：密度函数可以有效地简化为由四分位距P _VAR = Q ₃ − Q ₁ （即，第一个四分位 (Q ₁ ; 25%) 和第三个四分位数 (Q ₃ ;75%); 补充图2c )。

As an example, we observe an increase in physiographic diversity of South America from the Upper Cretaceous to the Palaeocene related to the Andean mountain building period (Supplementary Fig. 2b,c) and concomitant with microflora diversity patterns in northern South America¹⁰³ and plant diversification in Patagonia¹⁰⁴. We also note periods of low P_VAR values around 50 Ma and 28 Ma related to the intermittent development of internal seas or lakes in the central part of the Amazon basin. Periods of increasing P_VAR follow each of these episodes, suggesting that the Pebas basin could have acted as a permeable biogeographical system favouring biotic exchange and adaptation in the region¹⁰⁵.
例如，我们观察到南美洲从上白垩纪到古新世的地貌多样性增加，与安第斯造山时期有关（补充图2b，c ），并伴随着南美洲北部的微生物区系多样性模式¹⁰³和植物多样化在巴塔哥尼亚¹⁰⁴ 。我们还注意到 50 Ma 和 28 Ma 左右的低P _VAR值时期与亚马逊盆地中部内海或湖泊的间歇性发育有关。 P _VAR增加的时期伴随着每一个事件，这表明佩巴斯盆地可能充当了一个有利于该地区生物交换和适应的渗透性生物地理系统¹⁰⁵ 。

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