Analyzing mixing systems using a new generation of Bayesian tracer mixing models.

The ongoing evolution of tracer mixing models has resulted in a confusing array of software tools that differ in terms of data inputs, model assumptions, and associated analytic products. Here we introduce MixSIAR, an inclusive, rich, and flexible Bayesian tracer (e.g., stable isotope) mixing model framework implemented as an open-source R package. Using MixSIAR as a foundation, we provide guidance for the implementation of mixing model analyses. We begin by outlining the practical differences between mixture data error structure formulations and relate these error structures to common mixing model study designs in ecology. Because Bayesian mixing models afford the option to specify informative priors on source proportion contributions, we outline methods for establishing prior distributions and discuss the influence of prior specification on model outputs. We also discuss the options available for source data inputs (raw data versus summary statistics) and provide guidance for combining sources. We then describe a key advantage of MixSIAR over previous mixing model software-the ability to include fixed and random effects as covariates explaining variability in mixture proportions and calculate relative support for multiple models via information criteria. We present a case study of Alligator mississippiensis diet partitioning to demonstrate the power of this approach. Finally, we conclude with a discussion of limitations to mixing model applications. Through MixSIAR, we have consolidated the disparate array of mixing model tools into a single platform, diversified the set of available parameterizations, and provided developers a platform upon which to continue improving mixing model analyses in the future.

Quantitative assessment of Pb sources in isotopic mixtures using a Bayesian mixing model.

Lead (Pb) isotopes provide valuable insights into the origin of Pb within a sample, typically allowing for reliable fingerprinting of their source. This is useful for a variety of applications, from tracing sources of pollution-related Pb, to the origins of Pb in archaeological artefacts. However, current approaches investigate source proportions via graphical means, or simple mixing models. As such, an approach, which quantitatively assesses source proportions and fingerprints the signature of analysed Pb, especially for larger numbers of sources, would be valuable. Here we use an advanced Bayesian isotope mixing model for three such applications: tracing dust sources in pre-anthropogenic environmental samples, tracking changing ore exploitation during the Roman period, and identifying the source of Pb in a Roman-age mining artefact. These examples indicate this approach can understand changing Pb sources deposited during both pre-anthropogenic times, when natural cycling of Pb dominated, and the Roman period, one marked by significant anthropogenic pollution. Our archaeometric investigation indicates clear input of Pb from Romanian ores previously speculated, but not proven, to have been the Pb source. Our approach can be applied to a range of disciplines, providing a new method for robustly tracing sources of Pb observed within a variety of environments.

Seasonal and long-term effects of CO2 and O3 on water loss in ponderosa pine and their interaction with climate and soil moisture.

Evapotranspiration (ET) is driven by evaporative demand, available solar energy and soil moisture (SM) as well as by plant physiological activity which may be substantially affected by elevated CO2 and O3. A multi-year study was conducted in outdoor sunlit-controlled environment mesocosm containing ponderosa pine seedlings growing in a reconstructed soil-litter system. The study used a 2 x 2 factorial design with two concentrations of CO2 (ambient and elevated), two levels of O3 (low and high) and three replicates of each treatment. The objective of this study was to assess the effects of chronic exposure to elevated CO2 and O3, alone and in combination, on daily ET. This study evaluated three hypotheses: (i) because elevated CO2 stimulates stomatal closure, O3 effects on ET will be less under elevated CO2 than under ambient CO2; (ii) elevated CO2 will ameliorate the long-term effects of O3 on ET; and (iii) because conductance (g) decreases with decreasing SM, the impacts of elevated CO2 and O3, alone and in combination, on water loss via g will be greater in early summer when SM is not limiting than to other times of the year. A mixed-model covariance analysis was used to adjust the daily ET for seasonality and the effects of SM and photosynthetically active radiation when testing for the effects of CO2 and O3 on ET via the vapor pressure deficit gradient. The empirical results indicated that the interactive stresses of elevated CO2 and O3 resulted in a lesser reduction in ET via reduced canopy conductance than the sum of the individual effects of each gas. CO2-induced reductions in ET were more pronounced when trees were physiologically most active. O3-induced reductions in ET under ambient CO2 were likely transpirational changes via reduced conductance because needle area and root biomass were not affected by exposures to elevated O3 in this study.

Elevated CO2 and O3 effects on fine-root survivorship in ponderosa pine mesocosms.

Atmospheric carbon dioxide (CO(2)) and ozone (O(3)) concentrations are rising, which may have opposing effects on tree C balance and allocation to fine roots. More information is needed on interactive CO(2) and O(3) effects on roots, particularly fine-root life span, a critical demographic parameter and determinant of soil C and N pools and cycling rates. We conducted a study in which ponderosa pine (Pinus ponderosa) seedlings were exposed to two levels of CO(2) and O(3) in sun-lit controlled-environment mesocosms for 3 years. Minirhizotrons were used to monitor individual fine roots in three soil horizons every 28 days. Proportional hazards regression was used to analyze effects of CO(2), O(3), diameter, depth, and season of root initiation on fine-root survivorship. More fine roots were produced in the elevated CO(2) treatment than in ambient CO(2). Elevated CO(2), increasing root diameter, and increasing root depth all significantly increased fine-root survivorship and median life span. Life span was slightly, but not significantly, lower in elevated O(3), and increased O(3) did not reduce the effect of elevated CO(2). Median life spans varied from 140 to 448 days depending on the season of root initiation. These results indicate the potential for elevated CO(2) to increase the number of fine roots and their residence time in the soil, which is also affected by root diameter, root depth, and phenology.

Elevated CO(2) and temperature alter net ecosystem C exchange in a young Douglas fir mesocosm experiment.

We investigated the effects of elevated CO(2) (EC) [ambient CO(2) (AC) + 190 ppm] and elevated temperature (ET) [ambient temperature (AT) + 3.6 degrees C] on net ecosystem exchange (NEE) of seedling Douglas fir (Pseudotsuga menziesii) mesocosms. As the study utilized seedlings in reconstructed soil-litter-plant systems, we anticipated greater C losses through ecosystem respiration (R(e)) than gains through gross photosynthesis (GPP), i.e. negative NEE. We hypothesized that: (1) EC would increase GPP more than R(e), resulting in NEE being less negative; and (2) ET would increase R(e) more than GPP, resulting in NEE being more negative. We also evaluated effects of CO(2) and temperature on light inhibition of dark respiration. Consistent with our hypothesis, NEE was a smaller C source in EC, not because EC increased photosynthesis but rather because of decreased respiration resulting in less C loss. Consistent with our hypothesis, NEE was more negative in ET because R(e) increased more than GPP. The light level that inhibited respiration varied seasonally with little difference among CO(2) and temperature treatments. In contrast, the degree of light inhibition of respiration was greater in AC than EC. In our system, respiration was the primary control on NEE, as EC and ET caused greater changes in respiration than photosynthesis.

The shifting baseline of northern fur seal ecology in the northeast Pacific Ocean.

Historical data provide a baseline against which to judge the significance of recent ecological shifts and guide conservation strategies, especially for species decimated by pre-20th century harvesting. Northern fur seals (NFS; Callorhinus ursinus) are a common pinniped species in archaeological sites from southern California to the Aleutian Islands, yet today they breed almost exclusively on offshore islands at high latitudes. Harvest profiles from archaeological sites contain many unweaned pups, confirming the presence of temperate-latitude breeding colonies in California, the Pacific Northwest, and the eastern Aleutian Islands. Isotopic results suggest that prehistoric NFS fed offshore across their entire range, that California populations were distinct from populations to the north, and that populations breeding at temperate latitudes in the past used a different reproductive strategy than modern populations. The extinction of temperate-latitude breeding populations was asynchronous geographically. In southern California, the Pacific Northwest, and the eastern Aleutians, NFS remained abundant in the archaeological record up to the historical period approximately 200 years B.P.; thus their regional collapse is plausibly attributed to historical hunting or some other anthropogenic ecosystem disturbance. In contrast, NFS populations in central and northern California collapsed at approximately 800 years B.P., long before European contact. The relative roles of human hunting versus climatic factors in explaining this ecological shift are unclear, as more paleoclimate information is needed from the coastal zone.

Bole water content shows little seasonal variation in century-old Douglas-fir trees.

Purportedly, large Douglas-fir trees in the American Pacific Northwest use water stored in bole tissues to ameliorate the effects of seasonal summer drought, the water content of bole tissues being drawn down over the summer months and replenished during the winter. Continuous monitoring of bole relative water content (RWC) in two 110-120-year-old Douglas-fir trees with ThetaProbe impedance devices provided an integrated measure of phloem-sapwood water content over 4 years. Seasonal changes in RWC closely tracked cambial activity and wood formation, but lagged changes in soil water content by 2-3 months. The RWC in the combined phloem and sapwood markedly increased during earlywood production in the late spring and early summer to maximum values of 64-77% as plant available soil water (ASW) decreased by approximately 60%. With transition and latewood formation, RWC decreased to minimum values of 59-72%, even as ASW increased in the fall. The difference between minimum RWC in the fall and maximum RWC in midsummer was only approximately 5%. Seasonal changes in bole RWC corresponded to cambial phenology, although decreasing AWS appeared to trigger the shift from earlywood to latewood formation.

CO2 and N-fertilization effects on fine-root length, production, and mortality: a 4-year ponderosa pine study.

We conducted a 4-year study of juvenile Pinus ponderosa fine root (< or =2 mm) responses to atmospheric CO2 and N-fertilization. Seedlings were grown in open-top chambers at three CO2 levels (ambient, ambient+175 mumol/mol, ambient+350 mumol/mol) and three N-fertilization levels (0, 10, 20 g m(-2) year(-1)). Length and width of individual roots were measured from minirhizotron video images bimonthly over 4 years starting when the seedlings were 1.5 years old. Neither CO2 nor N-fertilization treatments affected the seasonal patterns of root production or mortality. Yearly values of fine-root length standing crop (m m(-2)), production (m m(-2) year(-1)), and mortality (m m(-2) year(-1)) were consistently higher in elevated CO2 treatments throughout the study, except for mortality in the first year; however, the only statistically significant CO2 effects were in the fine-root length standing crop (m m(-2)) in the second and third years, and production and mortality (m m(-2) year(-1)) in the third year. Higher mortality (m m(-2) year(-1)) in elevated CO2 was due to greater standing crop rather than shorter life span, as fine roots lived longer in elevated CO2. No significant N effects were noted for annual cumulative production, cumulative mortality, or mean standing crop. N availability did not significantly affect responses of fine-root standing crop, production, or mortality to elevated CO2. Multi-year studies at all life stages of trees are important to characterize belowground responses to factors such as atmospheric CO2 and N-fertilization. This study showed the potential for juvenile ponderosa pine to increase fine-root C pools and C fluxes through root mortality in response to elevated CO2.

Estimating the timing of diet shifts using stable isotopes.

Stable isotope analysis has become an important tool in studies of trophic food webs and animal feeding patterns. When animals undergo rapid dietary shifts due to migration, metamorphosis, or other reasons, the isotopic composition of their tissues begins changing to reflect that of their diet. This can occur both as a result of growth and metabolic turnover of existing tissue. Tissues vary in their rate of isotopic change, with high turnover tissues such as liver changing rapidly, while relatively low turnover tissues such as bone change more slowly. A model is outlined that uses the varying isotopic changes in multiple tissues as a chemical clock to estimate the time elapsed since a diet shift, and the magnitude of the isotopic shift in the tissues at the new equilibrium. This model was tested using published results from controlled feeding experiments on a bird and a mammal. For the model to be effective, the tissues utilized must be sufficiently different in their turnover rates. The model did a reasonable job of estimating elapsed time and equilibrial isotopic changes, except when the time since the diet shift was less than a small fraction of the half-life of the slowest turnover tissue or greater than 5-10 half-lives of the slowest turnover tissue. Sensitivity analyses independently corroborated that model estimates became unstable at extremely short and long sample times due to the effect of random measurement error. Subject to some limitations, the model may be useful for studying the movement and behavior of animals changing isotopic environments, such as anadromous fish, migratory birds, animals undergoing metamorphosis, or animals changing diets because of shifts in food abundance or competitive interactions.

Combining sources in stable isotope mixing models: alternative methods.

Stable isotope mixing models are often used to quantify source contributions to a mixture. Examples include pollution source identification; trophic web studies; analysis of water sources for soils, plants; or water bodies, and many others. A common problem is having too many sources to allow a unique solution. We discuss two alternative procedures for addressing this problem. One option is a priori to combine sources with similar signatures so the number of sources is small enough to provide a unique solution. Aggregation should be considered only when isotopic signatures of clustered sources are not significantly different, and sources are related so the combined source group has some functional significance. For example, in a food web analysis, lumping several species within a trophic guild allows more interpretable results than lumping disparate food sources, even if they have similar isotopic signatures. One result of combining mixing model sources is increased uncertainty of the combined end-member isotopic signatures and consequently the source contribution estimates; this effect can be quantified using the IsoError model (http://www.epa.gov/wed/pages/models/isotopes/isoerror1_04.htm). As an alternative to lumping sources before a mixing analysis, the IsoSource mixing model (http://www.epa.gov/wed/pages/models/isosource/isosource.htm) can be used to find all feasible solutions of source contributions consistent with isotopic mass balance. While ranges of feasible contributions for each individual source can often be quite broad, contributions from functionally related groups of sources can be summed a posteriori, producing a range of solutions for the aggregate source that may be considerably narrower. A paleo-human dietary analysis example illustrates this method, which involves a terrestrial meat food source, a combination of three terrestrial plant foods, and a combination of three marine foods. In this case, a posteriori aggregation of sources allowed strong conclusions about temporal shifts in marine versus terrestrial diets that would not have otherwise been discerned.

Source partitioning using stable isotopes: coping with too many sources.

Stable isotopes are increasingly being used as tracers in environmental studies. One application is to use isotopic ratios to quantitatively determine the proportional contribution of several sources to a mixture, such as the proportion of various pollution sources in a waste stream. In general, the proportional contributions of n+1 different sources can be uniquely determined by the use of n different isotope system tracers (e.g., delta13C, delta15N, delta18O) with linear mixing models based on mass balance equations. Often, however, the number of potential sources exceeds n+1, which prevents finding a unique solution of source proportions. What can be done in these situations? While no definitive solution exists, we propose a method that is informative in determining bounds for the contributions of each source. In this method, all possible combinations of each source contribution (0-100%) are examined in small increments (e.g., 1%). Combinations that sum to the observed mixture isotopic signatures within a small tolerance (e.g., +/-0.1 per thousand ) are considered to be feasible solutions, from which the frequency and range of potential source contributions can be determined. To avoid misrepresenting the results, users of this procedure should report the distribution of feasible solutions rather than focusing on a single value such as the mean. We applied this method to a variety of environmental studies in which stable isotope tracers were used to quantify the relative magnitude of multiple sources, including (1) plant water use, (2) geochemistry, (3) air pollution, and (4) dietary analysis. This method gives the range of isotopically determined source contributions; additional non-isotopic constraints specific to each study may be used to further restrict this range. The breadth of the isotopically determined ranges depends on the geometry of the mixing space and the similarity of source and mixture isotopic signatures. A sensitivity analysis indicated that the estimated ranges vary only modestly with different choices of source increment and mass balance tolerance parameter values. A computer program (IsoSource) to perform these calculations for user-specified data is available at http://www.epa.gov/wed/pages/models.htm.

Optimizing minirhizotron sample frequency for an evergreen and deciduous tree species.

• When using minirhizotrons to study fine dynamics in natural ecosystems, it is important to determine how sample collection frequency influences estimates of fine root production and mortality. Minirhizotron images were collected twice per week from mature Pseudotsuga menziesii and Tilia cordata trees and analyzed to estimate fine root production and mortality. These data were used to create data sets reflecting sample frequencies of 1, 2, 4 or 8 wk. • When the sampling interval is long, fine roots can appear and disappear between samplings, leading to underestimates of production and mortality. For example, with an 8-wk sample frequency, 24 and 35% of the fine root production in P. menziesii and T. cordata , respectively, is not measured. Fine root mortality displays the same sensitivity to sample frequency. • Our experimental observations supported the previously published simulation analysis, which provides an estimate of the proportion of fine roots missed at different sample frequencies and is a tool that can be used to select a sample frequency to balance production and mortality accuracy with sampling and analytical effort.

Incorporating concentration dependence in stable isotope mixing models.

Stable isotopes are often used as natural labels to quantify the contributions of multiple sources to a mixture. For example, C and N isotopic signatures can be used to determine the fraction of three food sources in a consumer's diet. The standard dual isotope, three source linear mixing model assumes that the proportional contribution of a source to a mixture is the same for both elements (e.g., C, N). This may be a reasonable assumption if the concentrations are similar among all sources. However, one source is often particularly rich or poor in one element (e.g., N), which logically leads to a proportionate increase or decrease in the contribution of that source to the mixture for that element relative to the other element (e.g., C). We have developed a concentration-weighted linear mixing model, which assumes that for each element, a source's contribution is proportional to the contributed mass times the elemental concentration in that source. The model is outlined for two elements and three sources, but can be generalized to n elements and n+1 sources. Sensitivity analyses for C and N in three sources indicated that varying the N concentration of just one source had large and differing effects on the estimated source contributions of mass, C, and N. The same was true for a case study of bears feeding on salmon, moose, and N-poor plants. In this example, the estimated biomass contribution of salmon from the concentration-weighted model was markedly less than the standard model estimate. Application of the model to a captive feeding study of captive mink fed on salmon, lean beef, and C-rich, N-poor beef fat reproduced very closely the known dietary proportions, whereas the standard model failed to yield a set of positive source proportions. Use of this concentration-weighted model is recommended whenever the elemental concentrations vary substantially among the sources, which may occur in a variety of ecological and geochemical applications of stable isotope analysis. Possible examples besides dietary and food web studies include stable isotope analysis of water sources in soils, plants, or water bodies; geological sources for soils or marine systems; decomposition and soil organic matter dynamics, and tracing animal migration patterns. A spreadsheet for performing the calculations for this model is available at http://www.epa.gov/wed/pages/models.htm.

Uncertainty in source partitioning using stable isotopes.

Stable isotope analyses are often used to quantify the contribution of multiple sources to a mixture, such as proportions of food sources in an animal's diet, or C3 and C4 plant inputs to soil organic carbon. Linear mixing models can be used to partition two sources with a single isotopic signature (e.g., δ(13)C) or three sources with a second isotopic signature (e.g., δ(15)N). Although variability of source and mixture signatures is often reported, confidence interval calculations for source proportions typically use only the mixture variability. We provide examples showing that omission of source variability can lead to underestimation of the variability of source proportion estimates. For both two- and three-source mixing models, we present formulas for calculating variances, standard errors (SE), and confidence intervals for source proportion estimates that account for the observed variability in the isotopic signatures for the sources as well as the mixture. We then performed sensitivity analyses to assess the relative importance of: (1) the isotopic signature difference between the sources, (2) isotopic signature standard deviations (SD) in the source and mixture populations, (3) sample size, (4) analytical SD, and (5) the evenness of the source proportions, for determining the variability (SE) of source proportion estimates. The proportion SEs varied inversely with the signature difference between sources, so doubling the source difference from 2‰ to 4‰ reduced the SEs by half. Source and mixture signature SDs had a substantial linear effect on source proportion SEs. However, the population variability of the sources and the mixture are fixed and the sampling error component can be changed only by increasing sample size. Source proportion SEs varied inversely with the square root of sample size, so an increase from 1 to 4 samples per population cut the SE in half. Analytical SD had little effect over the range examined since it was generally substantially smaller than the population SDs. Proportion SEs were minimized when sources were evenly divided, but increased only slightly as the proportions varied. The variance formulas provided will enable quantification of the precision of source proportion estimates. Graphs are provided to allow rapid assessment of possible combinations of source differences and source and mixture population SDs that will allow source proportion estimates with desired precision. In addition, an Excel spreadsheet to perform the calculations for the source proportions and their variances, SEs, and 95% confidence intervals for the two-source and three-source mixing models can be accessed at http://www.epa.gov/wed/pages/models.htm.

Effects of elevated CO(2) and nitrogen on the synchrony of shoot and root growth in ponderosa pine.

We monitored effects of elevated CO(2) and N fertilization on shoot and fine root growth of Pinus ponderosa Dougl. ex P. Laws. and C. Laws. grown in native soil in open-top field-exposure chambers at Placerville, CA, over a 2-year period. The experimental design was a replicated 3 x 3 factorial with the center treatment missing; plants were exposed to ambient (~365 micro mol mol(-1)) air or ambient air plus either 175 or 350 micro mol mol(-1) CO(2) in combination with one of three rates of N addition (0, 100 or 200 kg ha(-1) year(-1)). All CO(2) by N interactions were nonsignificant. Both the CO(2) and N treatments increased plant height, stem diameter and leaf area index (LAI). Elevated CO(2) increased fine root area density and the occurrence of mycorrhizae, whereas N fertilization increased coarse root area density but had no effect on fine root area density. Spring flushes of shoot height and diameter growth were initiated concurrently with the increase in new root area density but height and diameter growth reached their maxima before that of fine roots. The temporal patterns of root and shoot growth were not altered by providing additional CO(2) or N. Greatest root loss occurred in the summer, immediately following the period of greatest new fine root growth. Elevated N initially reduced the fine root area density/LAI ratio independently of CO(2) treatment, indicating that the relationship between fine roots and needles was not changed by CO(2) exposure.