Dozens of preliminary data reevaluations were conducted to verify the ratio-related mathematical theory. Differences in total elements among treatments, times and/or conditions frequently confound interpretation because total element values affect isotopic ratios. Eventually, twelve (six 87Sr:86Sr, three 15N:14N, two 13C:12C and one 34S:32S) well-performed studies were selected as examples. Sr studies: Source evaluations better describe migration patterns for ancient humans and animals, better align speleothem isotopic data with known climate changes, better define the dynamics of isotopic data within a watershed, and better describe sources of soil Sr. N studies: Source evaluations change interpretations for isotopic fractionation in sediments; N tracer treatments on potted plants; and trophic level assignments for different species in a marsh. C studies: Total C confounds 13C:12C data for isotopic fractionation experiments in forest soils and complicates an evaluation of whether past life existed in Martian sediments collected by the Curiosity rover. S studies: Total S also confounds 34S:32S evaluations of the same Martian sediments. We intend to emphasize that source analyses provide better isotopic interpretations than observed ratios in agricultural, biological and environmental studies. Observed isotopic ratio changes do not necessarily reflect source changes. Source analyses improved the Sr, N, C and S isotope evaluations.

Stable mass isotopic ratios (such as 13C:12C, 15N:14N, 18O:16O 87Sr:86Sr and 34S:32S) are used to interpret archaeological, climate change, ecological, geological, and physiological studies. Most isotopic reports evaluate changes in observed isotopic ratios or ratio-based expressions over time or among treatments. To address concerns that ratios or ratio-based expressions may not produce conclusions that support known physiological or ecological principles, source (isotopic ratio of the material being added or lost) analyses are proposed as an alternative to statistically analysing observed isotopic ratios. Mathematically defined relationships between observed ratios, backgrounds (isotopic ratio of a system before any loses or gains), sources and total element concentrations as well as denominator vs. numerator relationships are presented. These mathematical relationships suggest that source-based approaches often produce conclusions that differ from ratio-based evaluations. Total element concentrations, necessary for source analyses, are presented in less than half of isotopic publications. Without evaluating total element, relative background and source ratios cannot be determined. Even, when total element data is available, researchers rarely conduct source analyses. This is unfortunate because determining sources solves most interpretive issues. Our goal is to advocate better methods when analyzing isotopic ratios in the thousands of mass isotope publications annually produced.

The environmental implications of unconventional oil and gas extraction are only recently starting to be systematically recorded. Our research shows the utility of microbial communities paired with geochemical markers to build strong predictive random forest models of unconventional oil and gas activity and the identification of key biomarkers. ABSTRACT Unconventional oil and gas (UOG) extraction is increasing exponentially around the world, as new technological advances have provided cost-effective methods to extract hard-to-reach hydrocarbons. While UOG has increased the energy output of some countries, past research indicates potential impacts in nearby stream ecosystems as measured by geochemical and microbial markers. Here, we utilized a robust data set that combines 16S rRNA gene amplicon sequencing (DNA), metatranscriptomics (RNA), geochemistry, and trace element analyses to establish the impact of UOG activity in 21 sites in northern Pennsylvania. These data were also used to design predictive machine learning models to determine the UOG impact on streams. We identified multiple biomarkers of UOG activity and contributors of antimicrobial resistance within the order Burkholderiales. Furthermore, we identified expressed antimicrobial resistance genes, land coverage, geochemistry, and specific microbes as strong predictors of UOG status. Of the predictive models constructed (n = 30), 15 had accuracies higher than expected by chance and area under the curve values above 0.70. The supervised random forest models with the highest accuracy were constructed with 16S rRNA gene profiles, metatranscriptomics active microbial composition, metatranscriptomics active antimicrobial resistance genes, land coverage, and geochemistry (n = 23). The models identified the most important features within those data sets for classifying UOG status. These findings identified specific shifts in gene presence and expression, as well as geochemical measures, that can be used to build robust models to identify impacts of UOG development. IMPORTANCE The environmental implications of unconventional oil and gas extraction are only recently starting to be systematically recorded. Our research shows the utility of microbial communities paired with geochemical markers to build strong predictive random forest models of unconventional oil and gas activity and the identification of key biomarkers. Microbial communities, their transcribed genes, and key biomarkers can be used as sentinels of environmental changes. Slight changes in microbial function and composition can be detected before chemical markers of contamination. Potential contamination, specifically from biocides, is especially concerning due to its potential to promote antibiotic resistance in the environment. Additionally, as microbial communities facilitate the bulk of nutrient cycling in the environment, small changes may have long-term repercussions. Supervised random forest models can be used to identify changes in those communities, greatly enhance our understanding of what such impacts entail, and inform environmental management decisions.

Plant analysis is best viewed as a useful tool rather than as a means of making a rigid diagnosis. Using leaf analysis enables growers to better manage their orchards. Although much is known about factors that affect nutritional composition and leaf analysis interpretation, it is difficult to evaluate the interacting set of circumstances that occur in an orchard setting. Calcium, potassium, and magnesium interactions also complicate simple interpretations. Furthermore, modifying one factor will likely alter another. Evaluating nutritional interactions before implementing management decisions is important. In some fruit-growing areas, mineral fruit analyses are used to aid in postharvest management decisions. The best analysis, critical values, and interpretation are of little value without standard sampling procedures and methods of sample preparation. Leaves, petioles, stems, spurs, and fruit samples collected at different times from different locations within the tree have all been used. A leaf sample should represent a relatively homogeneous management unit.

Talakhaya watershed in Rota is identified as a Coral Reef Management Priority site for CNMI (Commonwealth of Northern Mariana Islands). In 2010 federal and jurisdictional partners developed a Conservation Action Plan (CAP) for the Talakhaya Watershed. The goal of this initial Watershed Soil Loss Assessment therefore, was to assist in evaluating the re-vegetation objectives of ‘Mitigating Sediment Load’ in the Talakhaya watershed by making a thorough characterization of its main river systems. The objectives of this project were to reach those goals by measuring the hydrological parameters following the installation and the use of water meters, barometric level loggers, turbidity meters and rain gauges. The water flow as well as the turbidity level of each stream leading to the ocean from the Talakhaya Watershed was measured and sedimentation level was assessed accordingly. The results from the monitoring of the watershed conducted during the project timeline reported here show that all four rivers under study have statistically different stage-discharge curves. The river's relationship between time and turbidity also vary especially in the summer months of the first-year observations. Linear and convex polynomial relationships were sometimes observed in the different rainfall groupings for the four river systems, however relationships were often not significant. This-being-said, Quantile Regressions suggest that when data from all four river systems are combined for cases where there is some detectable rainfall, a maximum possible turbidity level can be defined.

Most sugar mills would like to make preharvest predictions of either cane weight or sugar yield for individual fields. Sugarcane growth, maturity and yield were measured at Mitr Phol Sugarcane Research Center farmers’ fields from September 2008 to March 2009. The major sugarcane cultivars (K84-200, K88-92 and LK92-11) planted in the Mitr Phukhieo Sugar Mill area were selected for this study. The soil textures of these fields were grouped into coarse (sand) and fine (loam and light clay) categories. Both high-resolution (20 meter) SPOT and moderate-resolution (250 meter) MODIS satellite images were evaluated to find out whether or not a combination of ground-based measurements and remote sensing data can predict growth and sugar content. Earlyseason yield and stalks per hectare were strongly correlated to final cane yield (r= 0.89 and 0.87, respectively). Remote assessments and simple cane measurements (degree brix, height, diameter, number of nodes, weight) in themselves were not strongly associated with final yield or sugar content. Neither the SPOT nor MODIS NDVI could detect yield differences associated with different soil textures or sugarcane cultivars. The simple use of early-season cane number per 10 m of row and row spacing to estimate canes per hectare provides a usable approach to predict final yield. The tedious and expensive measurement of early-season yield provides a little more prediction strength than simply counting canes. Combining early-season canes per hectare with an evaluation of early-season brix at the base of the canes provides a usable approach to predicting final sugar yield (r = 0.82). Adding other ground-based measurements and SPOT or MODIS image-derived values to predictive equations did not improve cane yield or sugar yield prediction.

The effects of nitrogen (N) fertilizer application on plant growth, N uptake, and biomass and N allocation in highbush blueberry ( Vaccinium corymbosum L. ‘Bluecrop’) were determined during the first 2 years of field establishment. Plants were either grown without N fertilizer after planting (0N) or were fertilized with 50, 100, or 150 kg·ha −1 of N (50N, 100N, 150N, respectively) per year using 15 N-depleted ammonium sulfate the first year (2002) and non-labeled ammonium sulfate the second year (2003) and were destructively harvested on 11 dates from Mar. 2002 to Jan. 2004. Application of 50N produced the most growth and yield among the N fertilizer treatments, whereas application of 100N and 150N reduced total plant dry weight (DW) and relative uptake of N fertilizer and resulted in 17% to 55% plant mortality. By the end of the first growing season in Oct. 2002, plants fertilized with 50N, 100N, and 150N recovered 17%, 10%, and 3% of the total N applied, respectively. The top-to-root DW ratio was 1.2, 1.6, 2.1, and 1.5 for the 0N, 50N, 100N, and 150N treatments, respectively. By Feb. 2003, 0N plants gained 1.6 g/plant of N from soil and pre-plant N sources, whereas fertilized plants accumulated only 0.9 g/plant of N from these sources and took up an average of 1.4 g/plant of N from the fertilizer. In Year 2, total N and dry matter increased from harvest to dormancy in 0N plants but decreased in N-fertilized plants. Plants grown with 0N also allocated less biomass to leaves and fruit than fertilized plants and therefore lost less DW and N during leaf abscission, pruning, and fruit harvest. Consequently, by Jan. 2004, there was little difference in DW between 0N and 50N treatments; however, as a result of lower N concentrations, 0N plants accumulated only 3.6 g/plant (9.6 kg·ha −1 ) of N, whereas plants fertilized with 50N accumulated 6.4 g/plant (17.8 kg·ha −1 ), 20% of which came from 15 N fertilizer applied in 2002. Although fertilizer N applied in 2002 was diluted by non-labeled N applications the next year, total N derived from the fertilizer (NDFF) almost doubled during the second season, before post-harvest losses brought it back to the starting point.

We demonstrate that delta values (delta) 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 (Delta) or delta values (delta), 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.

A study was done to determine the macro- and micronutrient requirements of young northern highbush blueberry plants ( Vaccinium corymbosum L. ‘Bluecrop’) during the first 2 years of establishment and to examine how these requirements were affected by the amount of nitrogen (N) fertilizer applied. The plants were spaced 1.2 × 3.0 m apart and fertilized with 0, 50, or 100 kg·ha −1 of N, 35 kg·ha −1 of phosphorus (P), and 66 kg·ha −1 of potassium (K) each spring. A light fruit crop was harvested during the second year after planting. Plants were excavated and parts sampled for complete nutrient analysis at six key stages of development, from leaf budbreak after planting to fruit harvest the next year. The concentration of several nutrients in the leaves, including N, P, calcium (Ca), sulfur (S), and manganese (Mn), increased with N fertilizer application, whereas leaf boron (B) concentration decreased. In most cases, the concentration of nutrients was within or above the range considered normal for mature blueberry plants, although leaf N was below normal in plants grown without fertilizer in Year 1, and leaf B was below normal in plants fertilized with 50 or 100 kg·ha −1 N in Year 2. Plants fertilized with 50 kg·ha −1 N were largest, producing 22% to 32% more dry weight (DW) the first season and 78% to 90% more DW the second season than unfertilized plants or plants fertilized with 100 kg·ha −1 N. Most DW accumulated in new shoots, leaves, and roots in both years as well as in fruit the second year. New shoot and leaf DW was much greater each year when plants were fertilized with 50 or 100 kg·ha −1 N, whereas root DW was only greater at fruit harvest and only when 50 kg·ha −1 N was applied. Application of 50 kg·ha −1 N also increased DW of woody stems by fruit harvest, but neither 50 nor 100 kg·ha −1 N had a significant effect on crown, flower, or fruit DW. Depending on treatment, plants lost 16% to 29% of total biomass at leaf abscission, 3% to 16% when pruned in winter, and 13% to 32% at fruit harvest. The content of most nutrients in the plant followed the same patterns of accumulation and loss as plant DW. However, unlike DW, magnesium (Mg), iron (Fe), and zinc (Zn) content in new shoots and leaves was similar among N treatments the first year, and N fertilizer increased N and S content in woody stems much earlier than it increased biomass of the stems. Likewise, N, P, S, and Zn content in the crown were greater at times when N fertilizer was applied, whereas K and Ca content were sometimes lower. Overall, plants fertilized with 50 kg·ha −1 N produced the most growth and, from planting to first fruit harvest, required 34.8 kg·ha −1 N, 2.3 kg·ha −1 P, 12.5 kg·ha −1 K, 8.4 kg·ha −1 Ca, 3.8 kg·ha −1 Mg, 5.9 kg·ha −1 S, 295 g·ha −1 Fe, 40 g·ha −1 B, 23 g·ha −1 copper (Cu), 1273 g·ha −1 Mn, and 65 g·ha −1 Zn. Thus, of the total amount of fertilizer applied over 2 years, only 21% of the N, 3% of the P, and 9% of the K were used by plants during establishment.

Cane growth in rain-fed sugarcane production, with an abrupt end to rainfall months before harvest, could differ from what is known in better-studied systems. Therefore, we evaluated the relationship between the normalized difference vegetation index (NDVI) from the Moderate Resolution Imaging Spectrometer (MODIS) obtained for 2,854 sugarcane farmers’ fields and rainfall patterns in northeastern Thailand. Temporal changes of NDVI were related to rainfall patterns. The regional monthly average NDVI and the regional monthly average rainfall, calculated by averaging weather station data representing four individual provinces in the region were linearly related (r 2 = 0.867, p<0.001) during the rainy season. Similarly, the average monthly MODIS NDVI for farmers’ fields situated within a five km radius of the weather stations representing sugarcane management zones, was significantly related to monthly rainfall for both individual weather stations and average weather station data. Neither average rainfall nor average MODIS NDVI was related to the average sugarcane yield of the farmers’ fields situated within the five km radius of the nine weather stations. On a larger scale, MODIS NDVI had a positive correlation (r = 0.565) with yield when averaged across all nine management zones, but only for the rainy-season planting. Commercial pre-harvest yield prediction would likely need to be made between the end of the rainy season (mid-October) and mid-January. Our results showed that NDVI is a confounded measurement during this evaluation period which is associated with the differences in both plant biomass and cane maturity. Once the rainy season ends, NDVI declines while stalk weight increases. Therefore, NDVI-based yield predictions may be difficult even with higher quality imagery.

It is not appropriate to compare ratio-based expressions for different cultivars or treatments if a plot of the denominator versus the numerator of a ratio-based expression has a nonzero y -intercept and the values for either the denominators or numerators differ with cultivars or treatments. Whenever nonzero y -intercepts are encountered, the value for a ratio-based expression will be dependent on both the denominator and numerator. The “ratio problem” is demonstrated with shoot N concentration in blueberries ( Vaccinium corymbosum L.) and amino acid accumulation in almonds [ Prunis dulcis (Mill.) D.A. Webb]. Data were collected from the first and second growth flush of blueberry shoots on plants that were at two in-row spacings and two rates of N fertilizer. Free amino acid:total amino acid ratios were measured in dormant almond trees fertilized at different rates with and without foliar N supplements. Functions describing the relationship between dry weight and total N content in blueberry tissues have positive y -intercepts for both N fertilizer application rates. Functions describing the relationship between total amino acids and free amino acids in almond trees have a negative y -intercept. Differences attributable to fertilization rate in blueberries probably were the result of differences in N uptake and N utilization, but the effects of spacing and growth flush are indirect and can be accounted for by differences in dry weight. Likewise, effects of fertilization rate and foliar N supplement in almonds are indirect and can be accounted for by differences in the total amino acids in dormant trees. With regression one can determine if the relationship between the denominator and numerator differs for the groups or treatments being studied. When an analysis of covariance is used to account for differences in the denominators of ratio-based expressions, results are consistent with the regression analysis. When a conclusion is based on statistical differences of a ratio-based expression, it is the researcher's responsibility to determine whether these effects are direct or indirect.

The relationships between grapevine (Vitis vinifera) vigor variation and resulting wine anthocyanin concentration and composition and pigmented polymer formation were investigated. The study was conducted in a commercial vineyard consisting of the same clone, rootstock, age, and vineyard management practices. Vine vigor parameters were used to designate vigor zones within two vineyard sites (A and B) to produce research wines (2003 and 2004) and conduct a model extraction experiment (2004 only) to investigate the vine-fruit-wine continuum. Wines and model extracts were analyzed by HPLC and UV-vis spectrophotometry. For the model extractions, there were no differences between sites for pomace weight, whereas juice volume was higher for site A. This was not related to a larger berry size. Site A had a higher anthocyanin concentration (milligrams per liter) in the model extracts than site B specifically for the medium- and low-vigor zones. For anthocyanin composition in the model extraction, site B had a greater proportion of malvidin-3-O-glucoside and less of the remaining anthocyanin glucosides (delphinidin, cyanidin, petunidin, and peonidin) compared to site A. In the wines, there was a vintage effect, with the 2003 wines having a higher anthocyanin concentration (milligrams per liter) than the 2004 wines. This appears to have been primarily due to a greater accumulation of anthocyanins in the fruit. In general, the medium-vigor zone wines had higher anthocyanin concentrations than either the high- or low-vigor zone wines. There was also vintage variation related to anthocyanin composition, with the 2003 wines having a higher proportion of delphinidin and petunidin glucosides and lower malvidin-3-O-glucoside compared to 2004. In both years, there were higher proportions of delphinidin and petunidin glucosides in wines made from low-vigor-zone fruit. Wines made from low-vigor zones showed a greater propensity to form vitisin A as well as pigmented polymers. Low-vigor-zone wines had a approximately 2-fold increase in pigmented polymer concentration (milligrams per liter) over high-vigor-zones wines. There was a strong positive relationship between pigmented polymer concentration, bisulfite bleaching resistant pigments, proanthocyanidin concentration, and color density in wines. Overall, differences found in the wines magnified variation in the fruit.

Sedona & Montezuma Castle National Monument TourTravel back in time to Montezuma Castle National Monument.The short path to this prehistoric Sinagua Indian cliff dwelling along the banks of beautiful Beaver Creek.The next stop on the tour takes you to the amazing red rocks of Sedona, where you can find yourself surrounded by such famous rock formations as Bell Rock

Net photosynthetic rates often are dependent on leaf size when expressed on a leaf-area basis (CO 2 assimilation as μmol·m −2 ·s −1 ). Therefore, distinguishing between leaf-size-related and other causes of differences in net photosynthetic rate cannot be determined when data are presented on a leaf-area basis. From a theoretical perspective, CO 2 assimilation expressed on a leaf-area basis (μmol·m −2 ·s −1 ) will be independent of leaf area only when total net CO 2 assimilation (leaf CO 2 assimilation as μmol·s −1 ) is linearly related to leaf area and the function describing this relationship has a nonzero y intercept. This situation was not encountered in the data sets we evaluated; therefore, ratio-based estimates of CO 2 assimilation were often misleading. When CO 2 assimilation data are expressed on a per-leaf-area basis (the standard procedure in the photosynthesis literature), it is difficult to determine how photosynthetic efficiency changes as leaves or plants mature and difficult to compare the efficiency of treatments or cultivars when leaf size or total plant leaf area varies.

The relationships between grapevine (Vitis vinifera) vigor variation and resulting fruit anthocyanin accumulation and composition were investigated. The study was conducted in a commercial vineyard consisting of the same clone, rootstock, age, and vineyard management practices. The experimental design involved assigning vigor zones in two vineyard sites based upon differences in vine growth. Fruits and wines were analyzed by HPLC from designated vigor zones in 2003 and 2004. Average berry weight (grams), average dry skin weight (milligrams), degrees Brix, and pH were higher and titratable acidity (grams per liter) was lower in 2003 compared to 2004. In 2003, only the highest and lowest vigor zones had differences in berry weight, whereas there were no differences in 2004. In both years, high vigor zones had lower degrees Brix and higher titratable acidity (milligrams per liter). Accumulation of anthocyanins (milligrams per berry) was greater in 2003 compared to 2004. There was a trend for lower anthocyanin concentration (milligrams per berry) in high vigor zones in both years. In 2004 compared to 2003, there was a higher proportion of malvidin-3-O-glucoside and lower proportions of the other four anthocyanins (delphinidin-, cyanidin-, petunidin-, and peonidin-3-O-glucosides) found in Pinot Noir. In both years, site A had proportionally higher peonidin-3-O-glucoside and lower malvidin-3-O-glucoside than site B. Some of these differences may be related to the higher exposure and temperatures found in site B compared to site A and also in the low vigor zones.

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. Log(10) fertiliser N vs. log(10) 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 x 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.

Two approaches for estimating the amount of nitrogen (N) in plant tissues derived from labeled fertilizer were evaluated for two tissue types (root and shoot) in three different genera. In the first, atom percentage values obtained by mass spectrometry were converted to the portion of N derived from the fertilizer (NDFF). In the second, the slope of the regression line for the relationship between total N and labeled fertilizer N was used to represent the incremental increase in fertilizer N for each unit increase in total N. These two approaches were applied to data collected during container experiments. Unless a plot of total N versus labeled fertilizer N passes through the origin, conventional ratio-based estimates of the amount of NDFF for plants or tissues are often misleading. When nonzero intercepts occur, NDFF is dependent on the size (total N content) of the tissue or plant. Nonzero intercepts were frequently encountered. An analysis of regression lines describing the relationship between total N gain and fertilizer N produces a different interpretation than evaluations of the NDFF for treatment means. When an analysis of covariance was used to account for differences in total N between tissues and genera, results were generally consistent with the graphical observations and regression analysis. If only ratio-based approaches are used, it is difficult to determine if there are real physiological differences among treatments, genera, and tissues or if differences in NDFF are size-related. Because the data easily can be analyzed several ways, simultaneously evaluating data with ratio-based NDFF, covariates, and regression is appropriate.