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