David R. Sandrock

Scaling confounds the interpretation of isotopic data

We demonstrate that delta values (δ) and other relative ratio-based isotopic expressions can vary with the total amount of isotopes present in the system or subject being evaluated. Although these scaling effects are routinely overlooked, interpretive errors such as noting of spurious treatment effects or not detecting significant effects may occur. Algebraic conversions of linear or log-log equations (rare isotope predicted by common or total isotope) that suggest apparently miniscule scaling will fit the observed relationship between isotopic ratios and total or common isotopes. When the ranges of scaling induced differences in isotopic ratios are converted to the equivalent discrimination expressions (Δ) or delta values (δ), differences are within the range that is generally reported in the isotopic literature. Therefore, interpreting observed differences in isotopic ratios may require an evaluation to determine whether treatments directly affect how a rare isotope is accumulated or are associated with differences in denominator size. If effects are direct, points for different treatments fall on different linear and log-log (total isotope vs. rare isotope or common isotope vs. rare isotope) regression lines. Slope differences or derivatives may be more revealing than changes in isotopic ratios and better represent system change in a scaling system. By simply recording total common isotope or total elemental content, standard statistical procedures that evaluate changes in slopes or derivatives can be combined with an ANCOVA to better evaluate isotopic data. In many cases, scaling issues will not interfere with interpretations. In other situations it may be difficult to untangle a combination of ubiquitous scaling, treatment induced scaling and direct treatment effects.

Slope-based and ratio-based approaches to determine fertiliser-derived N in plant tissues for established perennial plants

Summary Two approaches for estimating the amount of N in plant tissues derived from labelled fertiliser were evaluated. In the first, atom percentage values obtained by mass spectrometry were converted to the percentage of total N derived from the fertiliser (%NDFF). In the second, the slope of the regression line for the relationship between labelled fertiliser N and total N was used to represent the incremental increase in fertiliser N for each unit increase in total N. These two approaches were applied to data collected for a blueberry (Vaccinium corymbosum L.) field trial, where the effects of N rate and plant spacing on fertiliser accumulation were evaluated. Since varying degrees of biological scaling can occur, and many perennial plant tissues have an initial biomass, regression equations for different tissues produced both positive and negative y-intercepts. Log10 fertiliser N vs. log10 total N plots produced slopes that did not equal 1.0 (from 0.40 to 1.65, depending on tissue). When either non-zero y-intercepts for linear regression lines, or slopes not equal to 1.0 for log-log plots occur, %NDFF is dependent on the size (total N) of the tissue or plant. Depending on the tissue evaluated, the %NDFF can be unrelated, or negatively or positively related to plant or tissue size. Furthermore, increased nitrogen application alters the relationship between %NDFF and plant size. For tissues in which %NDFF declines with increasing total N, the relationship weakens as more N is applied. For tissues in which %NDFF increases with increasing total N, the relationship strengthens as more N is applied. An analysis of the slopes and y-intercepts of labelled fertiliser N vs. total N relationships produces a different interpretation than evaluations of the %NDFF for treatment means. Significant %NDFF differences for spacing treatments, and significant spacing tissue interactions were size-related rather than having other physiological causes. Increases in %NDFF associated with increasing N rate were directly related to differences in N accumulation. Difficulties associated with evaluating the ratio-based %NDFF in established perennial plants are even more problematic than the difficulties previously reported for plant systems with little initial N content. Similar scaling issues could be important when any exogenous substance is introduced into organisms or ecosystems.