Improving provenance studies in migratory birds when using feather hydrogen stable isotopes

Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X-axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry-asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate.

Stable hydrogen-isotope ratios (deltaD) of keratin provide a novel means for tracking geographical movements of birds and other species. Here we describe a rapid, low cost, analytical approach to facilitate online continuous-flow isotope-ratio mass spectrometry (CF-IRMS) deltaD analyses of keratins (120-160 samples per day) through the use of calibrated keratin working standards and "comparative equilibration" to correct for the effects of moisture on exchangeable hydrogen. It is anticipated that this analytical approach and CF-IRMS will greatly aid in providing cost effective and directly comparable deltaD results on keratins and feathers among various laboratories and researchers involved in animal migration studies.