Ups and downs of the Phanerozoic biosphere: a mathematical approach

Palaeontologists became aware that the fossil record was marked by bursts of extinctions as data about fossil diversity through time steadily grew. That it did was a matter of dogged collection wherever field work was possible, identifying different species, classifying them, publishing the data and cataloguing them, each with a leavening of dispute. Only when those databases had become increasingly global and been collated in digital form did it become possible to chart the course of evolution in a comprehensive and comprehensible manner. First, that was simply as time series then in relation to other kinds of geological record, such as those of broad sea-level and climatic changes, environmental geochemistry, tectonics and relatively short-lived events such as large igneous provinces (LIPs) and asteroid impacts.

The fluctuation of life on Earth during Phanerozoic Eon: the last 542 Ma. Credit: Wikimedia Commons

‘Everyone knows’ the ‘Big Five’ mass extinctions: at the ends of the Ordovician (a loss of 85% of species at ~444 Ma); Devonian (70% of species at ~369 Ma); Permian (81% of species at 252 Ma); Triassic (70% of species at 201 Ma); and Cretaceous (75% of species at 66 Ma) Periods. The magnitudes relate to marine life, the terrestrial fossil record being more incomplete and less reliable. And there have been many lesser bursts of extinction and evolutionary radiations that followed to replenish and further diversify life.  Extinction peaks signify sudden environmental change for which several plausible ‘causes’ have been suggested: asteroid impact, LIPs, ocean anoxia and a few others involving astronomical factors.  Biodiversity during the Phanerozoic was always in a state of flux, but with progressive increases after each major crisis to modern times. There are many physical or abiotic processes that may have influenced biodiversity. So there is much uncertainty in the interplay of cause and effect, in much the same way as fluctuations in the world economy since the Industrial Revolution are difficult to fathom, even though financial data are much more precise and limited. Fossil and environmental data are plagued by heterogeneity, irregular sampling and the uncertainties in geochronology and the largely geochemical proxies deployed to monitor past environmental change. Another factor is the plain fact that, as well as abiotic processes, life itself affects environments; again economics – e.g. the interplay of supply, demand and price – offers stark lessons about the reductionism that still dominates much scientific discourse.

A multinational group led by mathematician Ivan Sudakow of the Open University have analysed carbon and oxygen data from the last 539 Ma – the Phanerozoic Eon – to model how the link between the carbon cycle and Earth’s climate relates to the fossil record. Rather than trying to grapple with a reductionist approach, i.e. ‘cause and effect’, they have attempted to show how the ‘backdrop’ to evolution varied through time: how the Earth System was organised during the half-billion years of ‘visible life’ (Sudakow, I. Et al. 2026. Transitions between persistent climate–carbon regimes coincide with elevated Phanerozoic biosphere vulnerability. Nature Communications v. 17, article 7559; DOI: 10.1038/s41467-026-75655-9). They omit the 100 Ma-long Ediacaran Period (635 to 539 Ma) when tangible life was abundant, if primitive.  A measure of biotic vulnerability derived from the fossil record is central to their comparative analysis. It conflates the turnover of genera with biotic diversity. The authors suggest that a high turnover at a time of low diversity indicates high vulnerability. The Ediacaran fauna is nowhere near as diverse as those following the Cambrian Explosion and simply vanished from the record at the end of the Neoproterozoic, hence its omission.

Biotic vulnerability through the five ‘mega-climate’ states of the Phanerozoic, and the ‘Big Five’ mass extinction events. Credit: Sudakow et al. 2026; Fig. 5

The methodology, data plots and language used by Sudakow et al. are pretty obscure for a general geological audience and thus for me! Be that as it may, their complex analysis leads them to suggest plausibly that climate and the carbon cycle remained in persistent states during five long periods: Cambrian–Upper Ordovician (539–447 Ma); Upper Ordovician–lowermost Carboniferous (447–358 Ma); Carboniferous–Middle Triassic (358–239 Ma). Middle Triassic–early Palaeogene (239–57 Ma); Post-Palaeogene (57–0 Ma). Biotic vulnerability fluctuated within them, the largest mass extinctions occurring when it rose to peaks towards the start and/or end of each persistent climate-carbon state. But their work grossly simplifies the vast complexity of interwoven biotic and abiotic processes. It leaves out global changes in sea-level, the varying supply of elements released to the oceans by continental weathering – nutrients (N, K, P and Fe), toxins (e.g. Hg and S) and skeleton-building elements (e.g. Si, Ca and Mg) – and fluctuations in dissolved oxygen that reflect varying redox conditions; to name but four. Each of them would impact on life in different ways, and each can be parameterised in detail by geochemical data from sedimentary rocks

So, a useful test for the authors’ hypothesis would be to perform the same kind of analysis using, for instance, well-documented sea-level changes since the Early Cambrian, which would have shifted the availability and location of ecological niches. Likewise, the course of super-continent accretion and break up. There are also Phanerozoic time series for the oxygenation of seawater, especially for deep-water sediments, which show irregular pulses of anoxia, some of which are implicated in extinctions such as the end-Permian. And there are more data that are relevant to the co-evolution of Earth and life. I would not be surprised if such studies produced different scenarios from those arising from investigations of just surface average temperature (SAT) and the carbon cycle. No doubt others will follow where Sudakow et al. have led. Perhaps that team has plans to diversify its approach.

A cautionary philosophical question, however, is, ‘How far can rationalisation, even using mathematically sophisticated methods, hope to unravel geological history and past fluctuations in the biosphere?’

The compendium of peer-reviewer comments and suggestions helped me to follow the logic of this somewhat arcane paper. Readers might also benefit from reading them.

See also: Shifts between stable climate-carbon states coincide with increased Phanerozoic biosphere vulnerability. Scienmag, 5 August 2026; Study of climate–carbon behaviour through the ages gives vital lessons on the earth’s capacity when under threat. Open University News, 30 July 2026

Ocean-floor sediments reveal the influence of Mars on long-term climate cycles

In 1976 three scientists from Columbia and Brown (USA) and Cambridge (UK) Universities published a paper that revolutionised the study of ancient climates (Hays J.D., Imbrie J. and Shackleton N.J. 1976. Variations in the Earth’s Orbit: Pacemaker of the Ice Ages. Science, v. 194, p. 1121-1132;  DOI: 10.1126/science.194.4270.1121). Using variations in oxygen isotopes from foraminifera through two cores of sediments beneath the floor of the southern Indian Ocean they verified Milutin Milankovich’s hypothesis of astronomical controls over Earth’s climate. This centred on changes in Earth’s orbital parameters induced by gravitational effects from the motions of other planets: its orbit’s eccentricity, and the tilt and precession of its rotational axis. Analysis of the frequency of isotopic variations in the resulting time series yielded Milankovich’s predictions of ~100, 41 and 21 ka periodicities respectively. The time spanned by the cores was that of the last 500 ka of the Pleistocene and thus the last 5 glacial-interglacial cycles. Subsequently, the same astronomical climate forcing  has been detected  for various climate-induced changes in the earlier sedimentary record, including the glacial cycles of the Carboniferous and Neoproterozoic, Jurassic climate changes due to oceanic methane emissions and many other types of cyclicity during the Phanerozoic.

One hemisphere of Mars captured by ESA’s Mars Express. Credit: ESA / DLR / FU Berlin /

As well as time series based on isotopic and other geochemical changes in marine cores, other variables such as thickness of turbidite beds or cyclical repetitions of short rock sequences such as the ‘cyclothems’ of Carboniferous age (repetitions of a  limestone, sandstone, soil, coal sequence) have also been subject to frequency analysis. Sedimentary features that have not been tried are gaps or hiatuses in stratigraphic sequences where strata are missing from a deep-sea sequence. These signify erosion of sediment due to vigorous bottom currents in sequences otherwise dominated by continuous deposition under low-energy conditions. Three geoscientists from the University of Sydney, Australia and the Sorbonne University, France, have subjected records of gaps in Cenozoic sedimentation from 293 deep-sea drill cores to time-series analysis to discover what such ‘big data’ might reveal as regards climate fluctuations on the order of millions of years (Dutkiewicz, A., Boulila, S. & Müller, R.D. 2024. Deep-sea hiatus record reveals orbital pacing by 2.4 Myr eccentricity grand cycles. Nature Communications, v. 15, article 1998; DOI: 10.1038/s41467-024-46171-5).

In theory gravitational interrelationships between all the orbiting planets should have an effect on the orbital parameters of each other, and thus the amount of received solar radiation and changes in global climate. As well as the Milankovich effect, longer astronomical ‘grand cycles’ may therefore have been reflected somehow in Earth’s climatic history (Laskar, J. et al. 2004. A long-term numerical solution for the insolation quantities of the Earth. Astronomy & Astrophysics, v. 428, p. 261-285; DOI: 10.1051/0004-6361:20041335). Based on Laskar et al.’s calculations Adriana Dutkiewicz and colleagues sought evidence for two predicted ‘grand cycles’ that result from orbital interactions between Earth and Mars. These are a 2.4 Ma period in the eccentricity of Earth’s orbit and one of 1.2 Ma in the tilt of its axis.

The authors were able to detect cyclicity in the hiatus time series that is close to the 2.4 Ma Mars-induced waxing and waning of solar heating. Warming would increase mixing of ocean water through cyclones and hurricanes. That would then induce more energetic deep ocean currents and more erosion on the deep ocean floor: more gaps in sedimentation. Cooler conditions would ‘calm’ deep ocean currents so that deposition would outweigh evidence of erosion. The 1.2 Ma axial tilt cyclicity is not apparent in the data. Interestingly, the ~2.4 Ma cyclicity underwent a significant deviation at the Palaeocene-Eocene Boundary’ (56Ma), seemingly predicted by Laskar et al’s  astronomical solutions as a chaotic orbital transition between 56 and 53 Ma. Dutkiewicz et al. also chart the relations between the sedimentary-hiatus time series and major tectonic, oceanographic, and climatic changes during the Cenozoic Era, and found that terrestrial processes did disrupt the Mars-related orbital eccentricity cycles.

The findings suggest that long-term astronomical climate forcing needs to be borne in mind for better understanding the future response of the ocean to global warming. Also, if Mars had such an influence so must have Venus, which is more massive and closer. That remains to be investigated, and also the effects of the giant planets. In the very distant past there behaviour may have resulted in unimaginable astronomical changes. According to the bizarrely named Nice Model a back and forth shuffling of the Giant Planets was probably responsible for the Late Heavy Bombardment 4.1 to 3.8 billion years (Ga) ago. Such errant behaviour may even have triggered the flinging of some of the Sun’s original planetary complement out of the solar system and changed the outward order of the existing eight. Fortunately, the present planetary set-up seems to be stable …

See also: Dutkiewicz, A., & Müller, R. D. 2022. Deep-sea hiatuses track the vigor of Cenozoic ocean bottom currents. Geology, v. 50, p. 710–715; DOI: 10.1130/G49810.1; Mars drives deep-ocean circulation in Earth’s oceans, study suggests. Sci News, 13 March 2024.