Arnold et al. (1) reported Mo isotope compositions of mid-Proterozoic black shale, which were different from those of euxinic sediments in the Black Sea. On the basis of a mass balance model calculation, they claimed that “the area of oxic sedimentation in the mid-Proterozoic oceans was nearly a factor of 10 smaller than the modern value, or the area of euxinic sedimentation approached a factor of 10 larger than the modern value, or, most likely, an intermediate situation occurred involving both substantial contraction of the extent of oxic deposition and expansion of the euxinic deep ocean.” Thus, they suggested that a widespread anoxia occurred in mid-Proterozoic oceans. However, this conclusion seems based on misinterpretation of their model calculation results.
According to the Arnold et al. calculation of total Mo removal, the fraction of Mo removal to Mn-oxide (fox) was ∼30% and of Mo removal to euxinic sediment (feux) was ∼70% in the mid-Proterozoic. Today, fox is ∼75% and feux is ∼25%. Thus, the ratio (fox/feux) changed from <0.4 in the mid-Proterozoic to 3 today. On the basis of this number, Arnold et al. (1) suggested widespread anoxia in mid-Proterozoic oceans. However, it is the ratio of the Mo fraction removed to oxic sediment to that removed to euxinic sediment (fox/feux) that changed 10-fold, rather than the Mo fractions themselves or the oxic deposition area. In fact, according to Arnold et al. (1), the fraction of Mo removal to Mn-oxide changed from 30% in the mid-Proterozoic to 75% today, a change less than 3-fold. Our calculation using their model and data shows that oxic area in mid-Proterozoic oceans was predominant relative to euxinic area.
If we let Fox and Feux account for fluxes (g m–2 year–1) of Mo to Mn-oxide and euxinic sediments, respectively, then the amount of Mo removal to Mn-oxide on an area of Aox in a unit of time is Aox·Fox, and the amount of Mo removal to euxinic sediment on an area of Aeux in a unit of time is Aeux·Feux. Assuming that the fractionation of Mo isotopes between seawater (δ97/95Mosw) and Mn-oxide is spatially and temporally constant (Δsw-eux = 2.1) (1–3) and that Mo fractionation between seawater and euxinic sediment is small (Δsw-eux = 0.3 to 0; 0.3 is used in the following calculation) as a result of quantitative Mo removal at euxinic conditions (1, 4)—the input of Mo to oceans having an average δ97/95Mo value of zero (1, 2, 4) and a steady-state balance of Mo input and output and isotope composition (1, 4)—then Eq. 1 of Arnold et al. (1) can be written as (1) If we let Fox/Feux = Kox/eux, which is a measure of relative Mo removal efficiency of oxic to euxinic sediments, similar to kox/keux of Arnold et al. [note 39 in (1)], then Eq. 1 becomes: (2)
Eq. 2 relates seawater δ97/95Mosw value to the ratio of oxic area to euxinic area (Aox/Aeux). In modern oceans, Kox/eux ≤ (75%/99.5%)/(25%/0.5%) ≈ 0.015, because Mo removal to the euxinic seafloor (which covers <0.5% of the total modern seafloor) accounts for ∼25% of annual Mo removal in the oceans, whereas Mo removal to oxic seafloor (which covers >99% of the total modern seafloor) accounts for ∼75% of annual Mo removal (1, 2, 5–7). The Kox/eux value is assumed to be constant [see note 39 in (1)]. Figure 1 shows the relation between δ97/95Mosw and the Aox/Aeux ratio expressed by Eq. 2 using these parameters. It shows that the present-day Aox/Aeux ratio is ∼200, corresponding to seawater δ97/95Mosw = 1.6‰, whereas the mid-Proterozoic δ97/95Mosw of 0.8‰ corresponded to Aox/Aeux = ∼27. This means that in the mid-Proterozoic, the euxinic deposition area was only about 3.7% of the oxic deposition area. This oceanic state is not consistent with the claim of widespread anoxia, although the effect of suboxic area on oceanic Mo isotopes needs more constraints. This may also imply that only a few percent euxinic area in the oceans (e.g., the existence of several semiclosed sea basins similar to the present-day Black Sea) could produce δ97/95Mo values similar to those of the mid-Proterozoic black shale analyzed by Arnold et al. (1).
According to this model, when Aox/Aeux < 10, the variation of δ97/95Mosw with Aox/Aeux would be within analytical error (∼0.24‰) (1), and thus Aox/Aeux change cannot be resolved by the Mo isotopic method (Fig. 1). If at some point in geological history there were a state of widespread anoxia with euxinic area exceeding, say, 30%, then concentration and residence time of dissolved Mo in the ocean would decrease greatly. The δ97/95Mo value of euxinic sedimentary Mo would be close to that of input, and the oceanic Mo isotope fractionation would not be controlled by oxic sedimentation processes as today. Transition from such an anoxic condition to the oxic condition of today cannot be described using a steady-state model, as proposed by Arnold et al. (1).