Similar to land plants, marine algae are also more likely to assimilate the lighter carbon isotope ¹²C over the heavier ¹³C, and the carbon isotopic composition of their biomolecules, δ¹³C_phyto, is therefore ~10-25‰ lower than the δ¹³C of dissolved CO₂ in surface seawater. Assuming most of the CO₂ arrives at the site of photosynthesis by diffusion through the algal cell membranes, the degree to which algae discriminate against ¹³C, commonly expressed as εp, depends on the concentration of their aqueous carbon source; the more carbon is available, the more selective the algae can be and this will lower the δ¹³C_phyto (see Figure). This basic theory has been confirmed in laboratory and field experiments, but the same experiments have also identified a number of additional factors that can affect δ¹³C_phyto, including growth rate, cell size, irradiance, and the actual carbon source, i.e. carbon dioxide (CO₂) or bicarbonate ion (HCO₃^-). For instance, the faster algae grow, the less selective they are in their carbon isotope uptake, so that δ¹³C_phyto increases. There have been several attempts to approximate the degree to which growth rate and other physiological processes modify the original [CO₂] signal. In their simplest form, physiological influences have been summarized by an empirical ‘b’ factor, which relates to the carbon-specific and enzymatic carbon isotope fractionation as follows:
εp = εf - b/[CO₂]
where εp is the carbon isotope fractionation between aqueous CO₂ and δ¹³C_phyto (εp ≈ δ¹³C_CO2– δ¹³C_phyto), and εf is the carbon isotope fractionation associated with enzymatic carbon fixation, which is typically assumed to be constant at 25‰. Using this framework, paleo-CO₂ can be estimated when δ¹³C_phyto data can be paired with independent estimates of temperature, cell size, growth rate and δ¹³CCO₂. It should also be noted that one of the major advantages of the proxy is that the ¹³C/¹²C ratio of biomarkers tends to be preserved well in ocean sediments and thereby alleviates one of the concerns associated with many paleoproxies, i.e. the potential modification of the original proxy signal through diagenetic processes. For additional information, see also General background and some commonalities of paleo-CO₂ proxies.
The first paleoreconstructions using the εp proxy analyzed bulk organic matter (i.e. all organic carbon in a sample). However, the mixture of different kinds of algae in bulk organic matter quickly led researchers to focus on long-chain alkenones (Jasper and Hayes, 1990) which are biomolecules that are produced by a specific group of marine algae, the haptophytes. Although alkenones are found throughout the Cenozoic and even the Cretaceous (cf. Brassell, 2014) the current alkenone-based CO₂ reconstructions are restricted to the past ~40 million years, when alkenones were more abundant in deep-sea sediments (Pagani et al., 2005b; Zhang et al., 2013).

While paleo-CO₂ estimates from alkenones provide significant evidence for the marked CO₂ decline from the “greenhouse” climate of the Paleogene, to the “ice house” climate of the Neogene (Pagani et al., 2011; Pagani et al., 2005a), data younger than 20 million years show much reduced CO₂ levels and only modest CO₂ change. However, some of the earlier studies had relied on planktic foraminiferal δ18O-derived sea surface temperature (SST) estimates, that were subsequently recognized to be largely compromised by carbonate diagenesis (Pagani et al., 2010; Super et al., 2018). The incorrect, cooler SSTs led to erroneously low CO₂ estimates in such studies because SSTs are used to determine the temperature-dependent isotopic fractionation, as well as in Henry’s Law, which relates the aqueous CO₂ reconstructed from algal ¹³C fractionation to atmospheric CO₂. Recent studies using temperature estimates unaffected by diagenesis place average middle Miocene alkenone-CO₂ levels higher (Super et al., 2018; Zhang et al., 2013), and more in line with other proxy estimates.
Despite generally convincing CO₂ estimates during geologic periods of globally warmer climates, comparisons between ice-core and alkenone-derived CO₂ estimates over the past 800,000 years suggest that the latter perform poorly, and have led to questions about the accuracy and validity of the diffusive uptake of carbon by algae. The presence of active carbon concentrating mechanisms has been invoked by some investigators (Badger et al., 2019; Stoll et al., 2019) to explain the low sensitivity of alkenone-δ¹³C to the low CO₂ levels of the past ~20 million years. Others (Zhang et al., 2019), however, have suggested that study sites with low modern b values are inherently biased by lower sensitivity of εp_37:2 to changing CO₂, and that with proper site selection and constraints on the physiological b parameter, it will be possible to reconstruct relatively small atmospheric CO₂ changes of the late Pleistocene from alkenones.
The systematics of the alkenone δ¹³C proxy response to past CO₂ levels are an area of active research today and ongoing validation efforts center on evaluating the relative significance of vital effects associated with haptophyte species assemblages, cell size, growth rate, carbon concentrating mechanisms (Badger et al., 2019; Bolton et al., 2016; Bolton and Stoll, 2013; Stoll et al., 2019; Zhang et al., 2019), and the fundamental systematics of carbon isotope fractionation in algae (Boller et al., 2011; Wilkes and Pearson, 2019). Although less research has been done to identify and evaluate controls other than aqueous CO₂ on other algae biomarkers, paleo-CO₂ has been estimated from such biomarkers across the entire Phanerozoic (Freeman and Hayes, 1992; Naafs et al., 2016; Pancost et al., 2013; Sinnighe Damsté et al., 2008; Witkowski et al., 2018). Based on the information currently available for the alkenone proxy, other biomarker reconstructions will have to undergo a similar level of scrutiny to be evaluated in detail. Depending on the outcome of ongoing studies, re-calculation of paleo-CO₂ from previously published data may change absolute CO₂ values from this proxy. However, the major trend in Cenozoic CO₂ estimates from this proxy, i.e. higher CO₂ prior to 20 million years ago and lower CO₂ levels thereafter, is unlikely to change and agrees well with other proxy estimates for CO₂ over this time interval.

The figure above shows a simple flow chart of the different parameters required to calculate CO₂ from this proxy. A template for entering new paleo-CO₂ estimates from marine phytoplankton δ¹³C can be found here. For adding new data, please fill out the template and submit it to the paleo-CO₂ database at the NOAA National Centers for Environmental Information (formerly known as the National Climatic Data Center, NCDC), using email address paleo@noaa.gov.

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