Allometric constraints on Sr/Ca and Ba/Ca partitioning in terrestrial mammalian trophic chains

In biological systems, strontium (Sr) and barium (Ba) are two non-essential elements, in comparison to calcium (Ca) which is essential. The Sr/Ca and Ba/Ca ratios tend to decrease in biochemical pathways which include Ca as an essential element, and these processes are termed biopurification of Ca. The quantitative pathway of the biopurification of Ca in relation to Sr and Ba between two biological reservoirs (R _n and R_{n -1}) is measured with an observed ratio (OR) expressed by the (Sr/Ca) _Rn /(Sr/Ca) _Rn-1 and (Ba/Ca) _Rn /(Ba/Ca) _Rn-1 ratios. For a mammalian organism, during the whole biopurification of Ca starting with the diet to the ultimate reservoir of Ca which is the bone, the mean values for OR_Sr and OR_Ba are 0.25 and 0.2, respectively. In this study, published Sr/Ca and Ba/Ca ratios are used for three sets of soils, plants, and bones of herbivorous and carnivorous mammals, each comprising a trophic chain, to illustrate the biopurification of Ca at the level of trophic chains. Calculated OR_Sr and OR_Ba of herbivore bones in relation to plants and of bones of carnivores in relation to bones of herbivores give OR_Sr=0.30±0.08 and OR_Ba=0.16±0.08, thus suggesting that trophic chains reflect the Sr/Ca and Ba/Ca fluxes that are prevalent at the level of a mammalian organism. The slopes of the three regression equations of log(Sr/Ca) vs. log(Ba/Ca) are similar, indicating that the process of biopurification of Ca with respect to Sr and Ba is due to biological processes and is independent of the geological settings. Modifications of the logarithmic expression of the Sr/Ca and Ba/Ca relationship allow a new formula of the biopurification process to be deduced, leading to the general equation OR_Ba=OR_Sr^1.79±0.33,where the allometric coefficient is the mean of the slopes of the three regression equations. Some recent examples are used to illustrate this new analysis of predator-prey relations between mammals. This opens up new possibilities for the utilization of Ba/Ca and Sr/Ca in addition to stable isotope ratios (¹³C and ¹⁵N) for the determination of the relative contribution of different food sources to an animals diet.