The Great Oxygenation Event as a consequence of ecological dynamics modulated by planetary change

The study addresses why and how atmospheric oxygen rose permanently during the Great Oxygenation Event (~2.4 Ga). While geological evidence clearly records the transition from an anoxic to an oxygenated surface environment, there remains debate over whether the GOE was driven primarily by increased oxygen production (e.g., proliferation of cyanobacterial oxygenic photosynthesis) or decreased oxygen consumption (e.g., diminished reductant fluxes), or by atmospheric-planetary processes (e.g., changes in volcanic gases, methane oxidation, or hydrogen escape). The authors posit that ecological competition between anoxygenic photosynthetic bacteria (APB) and cyanobacteria, modulated by evolving geochemical fluxes of reductants and nutrients, can explain the timing and nature (gradual vs sudden) of the GOE. They aim to develop and analyze a mathematical eco-geochemical model that captures these interactions and identifies critical thresholds for the transition.

Multiple lines of evidence constrain Archean-to-Proterozoic redox evolution: decline in banded iron formation deposition, loss of detrital redox-sensitive minerals, appearance of red beds and sulfates, and disappearance of mass-independent fractionation of sulfur isotopes indicate a rise in pO2 from <10^-5 PAL to ~1–10% PAL. Prior hypotheses emphasize: (1) atmospheric-planetary drivers (hydrogen escape; shifts to more oxidized volcanic gases; reduced hydrothermal Fe fluxes; P limitation of productivity); (2) atmospheric chemistry leading to bistability and hysteresis in O2 (Goldblatt et al.); (3) biogeochemical constraints such as nickel limitation of methanogens (Konhauser et al.) and trends in carbon isotopes suggesting biological innovations. Some models implicitly assume abundant pre-GOE cyanobacteria. However, modern ecology shows APB dominate sunlit anoxic niches; sulfide and possibly Fe2+ can inhibit oxygenic photosynthesis; geochemical records imply localized Archean "oxygen oases" long before the GOE. Jones et al. and Ozaki et al. argued that the ratio of alternative electron donors (e.g., Fe2+, H2, H2S) to phosphorus controls competition, and that APB could suppress cyanobacteria by thriving at low light and limiting nutrient upwelling. Knoll and Nowak previously modeled APB–cyanobacteria competition with Fe and O2; here that framework is expanded and solved analytically with explicit phosphate and oxygen source/sink terms.

The authors formulate a coupled eco-geochemical model tracking two functional groups and three chemical species: APB (x1), cyanobacteria (x2), Fe2+ (y1), phosphate PO4^3− (y2), and O2 (z). The ODE system (after nondimensionalization and setting certain rate constants to 1) is: ẋ1 = x1*y1*y2 − x1 + μ1; ẋ2 = c*x2 − x2 + μ2; ẏ1 = f1 − x1*y1*y2 − b*y1*z; ẏ2 = f2 − a*x2*y2 − b*y2*z − x2*y2; ż = a*x2*y2 − b*y1*z − b*y2*z. Parameters: c (cyanobacterial reproductive rate/competitive advantage), f1 (influx of reductants, represented by Fe2+ but generalizable to H2 or H2S), f2 (influx of phosphate), a (biogenic O2 production rate), b (proportional geochemical O2 consumption rate). Small migration rates u1 and u2 allow inoculation from privileged refugia; primary analysis assumes they are negligible for steady-state calculations. The system conserves redox by construction and includes geochemical sinks for Fe2+ and PO4 and O2 consumption via reactions with Fe2+ and PO4 terms. Analytical approach: On the assumption that planetary parameters change slowly relative to microbial population dynamics, the system is analyzed at quasi–steady state. Fixed points are derived for: (E1) APB-only dominance with z=0, (E2) cyanobacteria-only dominance with oxygen present, and an interior coexistence equilibrium (Ê). Linear stability analysis yields threshold conditions: (2) Stability of E1 against cyanobacteria invasion requires f1 − f2 > (c+1)(c−1). (3) Stability of E2 against APB invasion requires a(cf2 − 1)(b + c) ≥ (f1 − c). (4) Coexistence equilibrium Ê is stable if b > c(a − 1) and unstable otherwise. These define parameter regions where APB dominate, cyanobacteria dominate, stable coexistence occurs, or bistability arises. Bifurcation structures are mapped in the (f1, f2) plane for different b. Scenarios examined: (i) Decreasing f1 (declining reductant flux) or (ii) increasing f2 (rising phosphate flux) to trigger the GOE; (iii) changes in c due to biological innovation or environmental factors; (iv) increases in a or decreases in b (sources/sinks of O2). The nature of the transition depends on b relative to c(a−1): gradual via stable coexistence when b > c(a−1); sudden with bistability and hysteresis when b < c(a−1). Migration u2 strongly influences whether changes in a or b alone can trigger the GOE and affects the magnitudes of APB decline and cyanobacteria/O2 rise, but has negligible effect on equilibrium abundances within the dominant regimes. Numerical integration (fourth-order Runge–Kutta) validates analytical predictions and illustrates phase portraits and bifurcations. Model robustness is checked with extensions including bounded growth rates and explicit organic carbon cycling (Supplementary Notes).

- A simple eco-geochemical competition model can reproduce a GOE-like transition from APB dominance (no O2) to cyanobacterial dominance (oxygenated) as Earth’s reductant and nutrient fluxes evolve. - Critical trigger: The GOE initiates when the difference between reductant and phosphate influxes drops below a threshold that increases with cyanobacterial reproductive advantage, i.e., when f1 − f2 ≤ (c+1)(c−1). Thus, timing depends on the difference f1 − f2 rather than their absolute values. - Stability conditions: APB-dominated equilibrium E1 is stable if f1 − f2 > (c+1)(c−1). Cyanobacterial, oxygen-rich equilibrium E2 resists APB invasion if a(cf2 − 1)(b + c) ≥ (f1 − c). A mixed coexistence equilibrium Ê is stable when b > c(a − 1). - Nature of transition: If b > c(a − 1), the GOE is gradual and reversible through a stable coexistence phase as f1 decreases or f2 increases. If b < c(a − 1), the transition is sudden (discontinuous), with bistability and hysteresis over a parameter range; once oxygenated, moderate rebounds in f1 will not readily return the system to APB dominance. - Robust drivers: Decreasing reductant influx (f1) and/or increasing phosphate influx (f2) reliably trigger oxygenation; these changes are consistent with secular mantle cooling, continental emergence, and evolving hydrothermal/oxidant fluxes. - Sources/sinks of oxygen: Increasing a (O2 production) or decreasing b (O2 consumption) can also trigger oxygenation, but only if cyanobacteria are sufficiently present (requiring sufficiently large migration u2). Such transitions are necessarily sudden via a saddle-node bifurcation; if a is too small, reducing b alone cannot trigger oxygenation regardless of how small b becomes. - Migration effects: u1 and u2 minimally affect dominant-regime abundances but control the amplitude of APB decline and cyanobacteria/O2 rise across the transition, and determine feasibility of a/b-driven triggers. - Model robustness: Key thresholds and the possibility of both gradual and sudden GOE transitions persist when including bounded growth rates and explicit organic carbon dynamics (shown in Supplementary Notes).

The findings directly address the longstanding question of what caused the GOE by showing that ecological competition, modulated by planetary geochemical evolution, can by itself generate the observed transition. Declining reductant inputs (e.g., Fe2+, H2, H2S) and/or increasing phosphorus supply, both expected from Earth’s secular cooling and continental growth, naturally shift competitive advantage from APB to cyanobacteria. The timing depends on the difference f1 − f2 rather than their absolute magnitudes. The model also clarifies when oxygenation should be gradual versus abrupt: the balance of O2 sources and sinks (parameter b relative to c(a − 1)) governs whether coexistence is stable or whether the system exhibits bistability and hysteresis, potentially explaining geological evidence for transient O2 and stepwise oxygenation. Importantly, modifying O2 sources or sinks alone cannot trigger oxygenation if cyanobacteria are rare (small u2); hence, previous emphasis on atmospheric sinks/sources as primary triggers may be insufficient without considering the ecological state of cyanobacteria. Overall, the work integrates biological ecology with planetary change, providing mechanistic thresholds linking environmental fluxes to biospheric state shifts.

This study provides an analytically tractable eco-geochemical framework that links the GOE to competition between APB and cyanobacteria under evolving fluxes of reductants and phosphorus. It identifies a simple controlling quantity (f1 − f2) and explicit stability criteria that determine whether the transition is gradual or sudden, and clarifies when changes in O2 sources/sinks can be effective. The results argue that the GOE emerged from the interplay of ecological dynamics and planetary evolution rather than from purely physical or purely biological drivers. Future research could: (1) quantitatively constrain time histories of f1, f2, a, b, and c from geological proxies and laboratory measurements; (2) extend the model to include spatial heterogeneity (e.g., stratified water columns, nutrient upwelling) and explicit niche structure; (3) incorporate additional nutrient and redox cycles (N, S, trace metals) and feedbacks; (4) test model predictions against high-resolution stratigraphic datasets documenting transient oxygenation and iron formation resurgence; and (5) explore genomic/physiological innovations in cyanobacteria affecting c and a over time.

The model simplifies complex Earth system processes: it aggregates diverse reductants into a single variable (y1) and represents phosphorus with a single pool (y2), assumes quasi–steady-state on ecological timescales while planetary parameters vary slowly, and largely neglects spatial structure and transport except through small, constant migration terms (u1, u2). Biological interactions are reduced to two functional groups with mass-action-like kinetics, and some rate constants are normalized to 1. Oxygen consumption is parameterized with a single proportional rate b without resolving specific sinks. Trigger scenarios involving changes in a and b depend sensitively on cyanobacterial presence (u2), and the model is not calibrated to absolute concentrations or directly fitted to data. While extensions including bounded growth and organic carbon show robustness, additional processes (e.g., sediment diagenesis, variable light regimes, micronutrient limitations) are treated only implicitly or not at all.