in plants in modern greenhouses with high pCO 2 would necessarily be the same if the species was allowed millions of years to evolve and adapt to suit its conditions.
ii Carbon isotopes in alkenones
When organisms photosynthesize they strongly fractionate( discriminate between) the two stable isotopes of carbon( 12 C and 13 C) and it so happens that the degree of fractionation is itself related to the CO 2 content of the environment that the organism lives is. So if we can measure the carbon isotope ratio( � 13 C) of organic compounds and we know the carbon isotope ratio of the inorganic carbon in their environment, we can in principle calculate the pCO 2. Early work was done on bulk organic matter but the degree of fractionation varies quite widely between compounds and organisms so a more sophisticated approach is to use a particular class of compounds. The molecule of choice in many palaeo-studies is called an alkenone, a long chain ketone formed by a particular group of marine algae. But like the other proxies, there are complicating factors. We need to assume that the dissolved CO 2 at the study site is in equilibrium with the atmosphere( which means no significant upwelling or downwelling). Temperature has a predictable effect on the carbon isotope fractionation, so this has to be measured( using a temperature proxy) and factored in to the calculation. Physiological effects such as cell size and growth rate also seem to have a large effect on the carbon isotope ratio independent of CO 2 but they can be difficult to estimate for the past and might well have changed through time or with local conditions. Some workers have tried to develop corrections for these. The assumption that ancient extinct species of algae that lived in waters enriched or depleted in CO 2 relative to today fractionated carbon isotopes like the modern ones also has to be made.
iii Boron isotopes in biogenic calcite
Carbon dioxide is an acidic gas that mixes into the ocean where it reacts to yield carbonic acid, bicarbonate and carbonate ions. This changes the acidity of the water( ocean acidification is sometimes known as‘ the other CO 2 problem’). If we can estimate the pH of ancient seawater at a place that was close to equilibrium with the atmosphere, and simultaneously make an assumption of how much carbon was dissolved in it, we can calculate the pCO 2 of the ocean and hence atmosphere. It so happens we can estimate the pH of seawater by exploiting the isotopic composition of the element boron incorporated into fossil calcite( such as the shells of planktonic foraminifera, algae or corals). This is because dissolved boron speciates in seawater( like carbon), in response to pH( forming boric acid and the borate ion). There is a known isotopic exchange between these species and only borate gets incorporated into calcite. So, provided these assumptions hold, to get pH all we need to do is measure the boron isotope ratio( � 11 B) of fossil shells and we can calculate the rest. An advantage of this method is that it is based on known physical chemistry that ought to hold good across time, and is not just some modern empirical calibration. Unfortunately it does involve a variety of tricky assumptions, including knowing the seawater temperature and salinity which can also affect the boron isotope equilibrium. If we want to go back millions of years( which we do), we have to estimate the boron isotopic composition of seawater which might well have changed through time. This latter problem becomes the biggest uncertainty for periods greater than a few million years old and it is currently not very well constrained. We also need to assume that whatever organism we study secretes its calcite shell as if it was an inorganic crystal with respect to � 11 B or, if it does not, perhaps develop species-specific calibrations.
iv Others