Maximum R2 Research Articles

The importance of juveniles in modelling growth: butterflyfish at Lizard Island

I established and fitted von Bertalanffy growth functions to size-at-age data for four species of chaetodontids at Lizard Island. Special emphasis on juveniles provided detailed information of the early growth period. All four species demonstrated rapid initial growth achieving an average of 92% of maximum theoretical size in the first 2thinspyears. I used various constraints of the theoretical age at length zero (t0) in an analysis of both complete data sets and data sets using only adult fish. An unconstrained value of t0 resulted in the best-fit (maximum r2) curve when juveniles were included. When excluding juveniles, it was necessary to constrain t0 to an approximate settling size to most closely represent the growth of the species.

Higher Taxa as Surrogates of Plant Biodiversity in a Megadiverse Country

Abstract: An important question in conservation biology is the extent to which the number of taxonomic supraspecific categories can serve as surrogates of species richness. This issue has been little explored in highly diverse areas. We used 113 floristic inventories from throughout Mexico, a megadiverse country, to evaluate the potential of higher‐taxon richness for predicting local species richness of vascular plants. This large biodiversity data set includes the main vegetation types found across the country. In all, 247 families, 2,398 genera, and 11,890 species were used for the analysis, representing 99.6%, 90.2%, and 53.2% of the respective totals recorded in the country. We hypothesized that the number of genera and species would be accurately predicted by the richness of the higher taxon. To avoid getting spurious regressions resulting from the logical increase in lower‐taxon richness as a higher taxon becomes richer, we calculated new response variables by subtracting from the number of elements in the lower taxon group the number of those in the higher taxon; these variables were “excess species” (number of species minus number of genera or families) and “excess genera” (number of genera minus number of families). Our results indicate that genera provide very effective surrogates for estimation of local species richness (R2= 0.85), whereas families have a more limited potential for this purpose (R2= 0.64). The predictive capacity of the diversity of higher taxon increased when the analyses were constrained to particular vegetation types (maximum R2= 0.95 for genera). This surrogate method may be a valuable tool in locating and designing representative systems of protected areas for vascular plant diversity, especially in megadiverse countries, where conservation efforts are hindered by the lack of complete inventories and insufficient resources.

IMPROVING PHOSPHORUS SENSING BY ELIMINATING SOIL PARTICLE SIZE EFFECT IN SPECTRAL MEASUREMENT

This study investigated the effects of soil particle size on the reflectance spectra of sandy soils using ultraviolet,visible, and near-infrared spectroscopy in sensing phosphorus (P) concentration. Pure sandy soil was graded into threeparticle sizes. Sieve sizes were 125, 250, and 600 .m for fine, medium, and coarse, respectively. Phosphorus application ratesfor the soil samples were 0.0, 12.5, 62.5, 175.0, 375.0, 750.0, and 1000.0 mg kg-1. Concentrations of P in the soil sampleswere analyzed. The reflectance of the samples was measured between 225 and 2525 nm at 1 nm intervals. Overall, soils withcoarse particles absorbed light more than those with medium and fine particles. Detection analysis for soil particle sizes wasconducted using ratio and discriminant analysis methods. Prediction analyses for P concentration were performed usingmultiple linear regression (MLR; stepwise and maximum R2 methods) and linear partial least squares (PLS). Results showedthat detection of the particle size in a spectrum and then the prediction of P using individual calibration models for each soilparticle size produced lower prediction errors. For the maximum R2 MLR, stepwise MLR, and linear PLS analyses,respectively, the standard errors of prediction (SEPs) for determining P concentration without removing the particle size effectwere 105.8, 106.2, and 69.8 mg kg-1 and after removing the particle size effect were 52.8, 73.4, and 64.4 mg kg-1.

Sustainable Yield Index: An Approach to Evaluate the Sustainability of Long-Term Intensive Cropping Systems in India

ABSTRACT Several long-term fertilizer experiments conducted in different agro-ecological regions of India involving intensive cropping systems such as rice-wheat (Barrackpore), fingermillet-maize (Coimbatore and Bangalore) and soybean-wheat (Ranchi and Jabalpur) over the years (1972–2000) have demonstrated wide variations in crop productivity. Application of fertilizers over the years had showed significant impact on the status of soil organic carbon (SOC) and soil fertility, which in turn influence sustainability of cropping system. Sustainable Yield Index (SYI) was therefore, used as an approach to evaluate the minimum yield likely to be achieved in relation to changes in SOC and available N, P and K status of soil. Results showed that the SOC had significant effect on SYI in Inceptisols of Coimbatore (fingermillet-maize) and Jabalpur (soybean-wheat); and Alfisols of Ranchi (soybean-wheat) and Bangalore (fingermillet-maize). However, available soil N status did not much influence the SYI except in Inceptisols of Barrackpore under rice-wheat system. Phosphorus fertilization was important for all crops (finger-millet and maize at Coimbatore in particular) at all centers except in Alfisol of Bangalore. Soil available K status had, however, signified its role for maintaining SYI of different cropping system in Coimbatore, Jabalpur and Bangalore. The SYI was the lowest (0.17 and 0.14 for rice and wheat, respectively) when no manure and fertilizer was added in Inceptisols of BarracKpore. While Alfisols both at Ranchi and Bangalore aimlessly gave very low SYI ranging from 0 to 0.07 with N alone due to adverse effect of N fertilization alone compared to higher values (SYI 035 to 0.62) for NPK + FYM/lime treatment. The R2 values between SYI and SOC for soybean, wheat, fingermillet and maize at Ranchi, Jabalpur, Coimbatore and Bangalore, were approaching unity (ranging from 0.72** to 0.91**) indicating higher dependence of SYI on SOC. On the contrary, rice and wheat at BarracKpore showed relatively high R2 (0.93** and 0.94**) between SYI and only soil available N status. Similarly, the values of R2 between SYI and available soil P status were higher (08l**−0.99**) for all the crops except fingermillet and maize at Bangalore (0.51* and 0.52*) whereas finger millet and maize in Kandiustalfs of Bangalore showed maximum R2 value (0.97** and 0.98**) between SYI and available K followed by soybean (0.92**) and wheat (0.89**) in Chromustert of Jabalpur. Thus, the study highlighted that SOC followed by soil available P strongly influenced the SYI in majority of cropping systems/soil types. However, available N in rice-wheat in Inceptisols of Barrackpore is an important soil fertility parameter and that of available K in fingermillet-maize cropping system in Alfisols of Bangalore. The SYI with 100% N and NP were considerably lower (SYI 0.0–0.20) than SYI of 0.31–0.53 with 100% recommended NPK because of unbalanced and inadequate nutrition. Maximum SYI 037–0.62 achieved for 100% NPK + FYM treatment in almost all the locations indicating the beneficial effect of integrated use of nutrients on sustaining higher crop productivity by correcting marginal deficiencies of secondary and micronutrients.

Fusion of Small-Footprint Lidar and Multispectral Data to Estimate Plot- Level Volume and Biomass in Deciduous and Pine Forests in Virginia, USA

Abstract The principal study objective was to explore the feasibility of using small-footprint lidar data and multispectral imagery to estimate forest volume and biomass on small (0.017-ha) plots. In addition, the spatial dependency of residuals between ground-measured and lidar-estimated variables was investigated. The lidar data set was acquired over deciduous and pine stands in the southeastern United States. Individual trees were identified on the lidar-derived canopy height model by local maximum focal filtering with both square and circular windows of variable size. The size of the dynamically varying window was based on the height of the canopy and the taxonomic group as derived from coregistered multispectral optical data. Lidar-measured parameters at an individual tree level (height, crown diameter) were used with regression models and cross validation to estimate plot-level field inventory data, including volume, biomass, basal area, and diameter at breast height (dbh). Maximum R2 values for estimating biomass were 0.32 for deciduous trees (RMSE 44 Mg/ha) and 0.82 for pines (RMSE 29 Mg/ha). When estimating volume, maximum R2 values for deciduous trees were 0.39 (RMSE 52.84 m3/ha) and 0.83 for pines (RMSE 47.9 m3/ha). Calculation of Moran's I coefficient for each regression model revealed a lack of significant autocorellation of the residuals at 0.05 level. Both model fit and prediction for volume and biomass models for deciduous and pine plots indicated that the circular window shape is more appropriate to locate individual trees with lidar. Using the fused data set, lidar and optical imagery, as opposed to using lidar data alone, always improved biomass and volume estimates for pines and in some cases for deciduous plots as well. FOR. SCI. 50(4):551–565.

Dependency of Cotton Leaf Nitrogen, Chlorophyll, and Reflectance on Nitrogen and Potassium Availability

In‐season assessment of cotton (Gossypium hirsutum L.) leaf N and K concentration using remote sensing techniques is needed to address spatial and temporal variation of these two nutrients. The objective of this study was to evaluate the effects of varying N and K availability on cotton chlorophyll concentration and detection of leaf N utilizing reflectance properties. Fertilizer N rates of 0, 45, 90, 135, and 180 kg ha−1 in factorial combination with K rates of 0 and 112 kg ha−1 were applied to cotton under field conditions. Recently matured leaves on the main stem were collected at first bloom and peak bloom physiological stages of growth in 1999 and 2000 to determine leaf N and K concentrations, chlorophyll concentration, and spectral reflectance. Nutrient stress anomalies from spectral reflectance data were predicted using partial least‐squares regression. Partial least squares yielded a better predictability of leaf N concentration at first bloom and peak bloom when K was adequately supplied. The greatest predictability of leaf N was observed at peak bloom in 2000 with a maximum r2 of 0.77 and minimum standard error of prediction of 2.72. A red‐edge shift to longer wavelengths with increased N supply was observed when K was sufficient. Utilization of leaf N concentration sampled at a coarse resolution in combination with timely and appropriate imagery may enhance nutrient management capabilities in precision agriculture so long as other nutrients are not limiting.

Distribution of aboveground biomass in corn stover

Corn stover can be a principal feedstock for bioenergy and industrial applications because of its abundance and its current underutilization. Development of strategies/systems for the postharvest handling of corn stover involves quantifying what corn stover biomass is available over time after grain physiological maturity has been reached. It also involves understanding how the biomass is distributed in the different aboveground components of the corn plant. The objectives of this preliminary investigation were to measure the allocation of biomass to aboveground components of the corn plant over time and to develop relationships for estimating total aboveground corn plant biomass through simple corn plant dimensional measurements. Aboveground biomass distribution for two corn cultivars (Pioneer 32K61 and 32K64 Bt) was studied in standing plants from roughly 1 week before grain physiological maturity until 4 weeks after grain harvest from other plots in the field. Over the monitoring period, the amount of dry matter in stover averaged 50% of the total aboveground dry plant mass with stalks comprising 50% of the stover dry matter at the time grain was harvested. This study indicated that the more conservative 0.8:1 stover:grain fresh weight ratio, rather than the 1:1 widely used, may be more realistic at the grain harvest moisture range of 18–31% w.b. Such precondition has not been clearly emphasized in the literature. Regression equations involving stalk diameter and plant height for DeKalb 626 derived to estimate fresh green weight and dry matter of the corn plant above the ground had a maximum R2 of 0.75.

Soil Electrical Conductivity Map Variability in Limestone Soils Overlain by Loess

Sensors exist that allow rapid mapping of bulk soil electrical conductivity (EC); however, the utility of these sensors for Kentucky producers is unknown. The purpose of this study was to assess the nature and the causes of soil EC variability and to make a first assessment of its potential utility in Kentucky, particularly for fields containing soils derived from limestone residuum overlain by loess. Various geostatistical, correlation, and regression analyses were conducted at seven locations to examine EC map variability. Sensor drift and errors associated with changes in coulter depth were minimal. Bulk soil EC related fairly well with clay content across locations and sample dates (r2 = 0.40); however, many site‐ and time‐specific correlations were better. Clay (maximum r2 = 0.75), moisture content (maximum r2 = 0.76), Ca (maximum r2 = 0.67), and Mg (maximum r2 = 0.64) were positively correlated with EC, and depth to argillic or cambic horizon (maximum r2 = 0.62), depth to fragipan (maximum r2 = 0.81), and depth to bedrock (maximum r2 = 0.32) were negatively correlated with EC. A multiple‐regression model (R2 = 0.70) was developed to predict EC that included nine factors: clay, sand, soil moisture, buffer pH, base saturation, Ca, soil temperature, depth to cambic and argillic horizon, and slope. Soil EC variability was spatially structured, and spatial patterns were stable over time; however, the degree to which these patterns could be observed depended on the mapping procedures used. Our research suggested that EC mapping may have utility for Kentucky farmers.

Soil Electrical Conductivity Map Variability in Limestone Soils Overlain by Loess

Sensors exist that allow rapid mapping of bulk soil electrical conductivity (EC); however, the utility of these sensors for Kentucky producers is unknown. The purpose of this study was to assess the nature and the causes of soil EC variability and to make a first assessment of its potential utility in Kentucky, particularly for fields containing soils derived from limestone residuum overlain by loess. Various geostatistical, correlation, and regression analyses were conducted at seven locations to examine EC map variability. Sensor drift and errors associated with changes in coulter depth were minimal. Bulk soil EC related fairly well with clay content across locations and sample dates (r2 = 0.40); however, many site- and time-specific correlations were better. Clay (maximum r2 = 0.75), moisture content (maximum r2 = 0.76), Ca (maximum r2 = 0.67), and Mg (maximum r2 = 0.64) were positively correlated with EC, and depth to argillic or cambic horizon (maximum r2 = 0.62), depth to fragipan (maximum r2 = 0.81), and depth to bedrock (maximum r2 = 0.32) were negatively correlated with EC. A multiple-regression model (R2 = 0.70) was developed to predict EC that included nine factors: clay, sand, soil moisture, buffer pH, base saturation, Ca, soil temperature, depth to cambic and argillic horizon, and slope. Soil EC variability was spatially structured, and spatial patterns were stable over time; however, the degree to which these patterns could be observed depended on the mapping procedures used. Our research suggested that EC mapping may have utility for Kentucky farmers.

ESTIMATION OF CROP BIOPHYSICAL PARAMETERS THROUGH AIRBORNE AND FIELD HYPERSPECTRAL REMOTE SENSING

The potential of airborne hyperspectral remote sensing in crop monitoring and estimation of various biophysical parameters was examined in this study. A field experiment, consisting of four weed control strategies (no weed control, broadleaf control, grass control, and full weed control) as the main plot effect, factorially combined with three nitrogen (N) fertilization rates (60, 120, and 250 N kg ha–1), and replicated four times, was conducted. Hyperspectral data in 72 narrow wavebands (409 to 947 nm) from a Compact Airborne Spectrographic Imager (CASI) sensor were acquired 30 days after planting, at tasseling, and at the fully mature stage. In addition, measurements were made concurrently on various crop physiological parameters: leaf greenness (SPAD readings), leaf area index (LAI), plant height, leaf nitrogen content, leaf chlorophyll content, and associated factors such as soil moisture. Regression models were generated to estimate crop biophysical parameters and yield, in terms of reflectance at one or more wavebands, using the maximum r2 improvement criterion. The models that best represented the data had five wavebands as independent variables. Coefficients of determination (r2) were generally greater than 0.9, when based on the spectral data taken at the tasseling stage. Results were improved when normalized difference vegetation indices (NDVI) were used rather than the five–waveband reflectance values. The wavebands at 701 nm and 839 nm were the most prevalent in the NDVI–based models.

Predicting Average Feed Intake of Lactating Holstein Cows Fed Totally Mixed Rations

A dry matter intake (DMI) prediction equation was estimated by using a data file that contained 124 treatment means collected from published studies. Animal factors considered for inclusion in the prediction model were body weight (BW) and its natural logarithm, BW0.75, milk yield (MY) and its natural logarithm, milk fat and protein yields, month of lactation and its square, as well as its natural logarithm. The dietary factors considered were the percentages of neutral detergent fiber, acid detergent fiber, crude protein and hemicellulose in the ration dry matter together with the square of all these predictors. The multiple regression model selected by using the maximum R2 method include both animal and dietary factors as independent variables. The accuracy of this DMI prediction equation was evaluated and compared with that of five other equations previously published by using three independent datasets also containing treatment means collected from literature. Even though the latest NRC equation was slightly more accurate than the equation proposed in this study with the three evaluation datasets, the latter can be used for some applications for which the NRC equation is not appropriate.

Calculated follicle deviation using segmented regression for modeling diameter differences in cattle

Segmented linear regression alone or in combination with simple linear regression was evaluated as an objective method to calculate the beginning of follicle deviation by modeling the sequential (Experiment 1) and non-sequential or single-point (Experiment 2) differences in diameter between the future dominant (F1) and largest subordinate (F2) follicles of Wave 1 in cattle. The segmented regression consisted of Segment 1 representing the common growth phase, Segment 2 representing the period of dominance, and a Join Point connecting the two segments and representing the end of the common growth phase and the beginning of deviation. The model was fit to the diameter differences for each heifer in Experiment 1 (n=15) and the group of heifers in Experiment 2 (n=40). The optimal Join Point value that corresponded to the maximum R2 was designated the calculated hour (Experiment 1) or diameter of F1 (Experiment 2) at the beginning of deviation. In Experiment 1, simple linear regression was used to calculate the corresponding diameter of F1 at the beginning of deviation. Observed deviation was determined by inspection of the diameter profiles of F1 and F2 for comparison to calculated deviation. In Experiment 1, the observed method determined the beginning of deviation in 80% of the heifers, whereas, the regression method calculated deviation in 93% of the heifers including two of the three heifers in which observed deviation was not discernable (no significant difference between methods). The mean hours of deviation after wave emergence (Hour 0) and diameters of F1 at the corresponding hours were not significantly different between the observed (62h and 8.4mm) and calculated (61h and 8.8mm) methods. In Experiment 2, the diameter of F1 at the beginning of calculated deviation was 8.2mm. The results indicated that the segmented regression model can provide an objective and more accurate alternative to estimate follicle deviation, especially when observed deviation is obscured by the complexity of follicle development in some waves.

A Probability of Growth Model for Escherichia coli O157:H7 as a Function of Temperature, pH, Acetic Acid, and Salt

Data accumulated on the growth of Escherichia coli O157:H7 in tryptic soy broth (TSB) were used to develop a logistic regression model describing the growth-no growth interface as a function of temperature, pH, salt, sucrose, and acetic acid. A fractional factorial design with five factors was used at the following levels: temperature (10 to 30°C), acetic acid (0 to 4%), salt (0.5 to 16.5%), sucrose (0 to 8%), and pH (3.5 to 6.0). A total of 1,820 treatment combinations were used to create the model, which correctly predicted 1,802 (99%) of the points, with 10 false positives and 8 false negatives. Concordance was 99.9%, discordance was 0.1%, and the maximum rescaled R2 value was 0.927. Acetic acid was the factor having the most influence on the growth-no growth interface; addition of as little as 0.5% resulted in an increase in the observed minimum pH for growth from 4.0 to 5.5. Increasing the salt concentration also had a significant effect on the interface; at all acetic acid concentrations, increasing salt increased the minimum temperature at which growth was observed. Using two literature data sets (26 conditions), the logistic model failed to predict growth in only one case. The results of this study suggest that the logistic regression model can be used to make conservative predictions of the growth-no growth interface of E. coli O157:H7.

Financial Applications of a Tabu Search Variable Selection Model

We illustrate how a comparatively new technique, a Tabu search variable selection model [Drezner, Marcoulides and Salhi (1999)], can be applied efficiently within finance when the researcher must select a subset of variables from among the whole set of explanatory variables under consideration. Several types of problems in finance, including corporate and personal bankruptcy prediction, mortgage and credit scoring, and the selection of variables for the Arbitrage Pricing Model, require the researcher to select a subset of variables from a larger set. In order to demonstrate the usefulness of the Tabu search variable selection model, we: (1) illustrate its efficiency in comparison to the main alternative search procedures, such as stepwise regression and the Maximum R2 procedure, and (2) show how a version of the Tabu search procedure may be implemented when attempting to predict corporate bankruptcy. We accomplish (2) by indicating that a Tabu Search procedure increases the predictability of corporate bankruptcy by up to 10 percentage points in comparison to Altman's (1968) Z-Score model.

Ionic Ratios and Crop Performance: II. Effects of Interactions amongst Vanadium, Phosphorus, Magnesium and Calcium on Soybean Yield

Because vanadium (V) is easily reduced to a cationic form within plant cells, data from resin‐extraction of soil were analysed for evidence of interactions between V and the resin‐extractable concentrations of magnesium (Mg) and calcium (Ca) on soybean seed yield. Three varieties, 9091, 9061 and 704, were grown over a 3‐year period in a corn–soybean–wheat rotation. Surface soil samples (0–15 cm) were extracted with ion‐exchange resins, extracts were analysed by inductively coupled plasma methods (ICP), and the results were regressed against seed yield using SAS PROC STEPWISE analysis using forward selection, backward elimination and maximum R2 routines. The seed yield of each variety showed a correlation with a unique set of resin‐extractable concentrations of V, phosphorus (P), Mg and Ca, and the V:(V + P), Mg:(Mg + Ca), Mg:(Mg + 1000 V) and Ca:(Ca + 1000 V) ratios. Variety 9091 was most sensitive to the Mg:(Mg + Ca) ratio. Variety 9061 was most sensitive to extractable V and to the V:(V + P) ratio. Variety 704 was sensitive to extractable P, V and Ca and the Mg:(Mg + 1000 V) ratio. For variety 9091, Mg fertilization (not currently practised) may be an economical practice, whereas P fertilization of 704 may not be economical. Each regression technique varied slightly in identification of important factors in seed yield. Concentrations and ratios of resin‐extractable elements in soil provide insights into optimal genotype selection and possible management alternatives for a given soil.

Leaf nitrogen and phosphorus levels in macadamias in response to canopy position and light exposure, their potential as leaf-based shading indicators, and implications for diagnostic leaf sampling protocols

The relationships between leaf nutrient content, leaf age, and within-canopy light exposure were studied in 10–11-year-old Macadamia integrifolia cvv. 660, 781, and 344 at Alstonville (28˚59′S, 149˚E), New South Wales, during autumn and spring 1996. Quantum point sensors were placed at 16 positions in the canopy to give mean 24-hourly photosynthetic photon flux density (PFD) readings, which ranged from 13 to 540 mol/m2.sec. At each of these positions, the youngest terminal leaf (YTL), the youngest fully expanded leaf (FEL) from a current flush, and a 6–7-month-old hardened off leaf (HOL) were sampled. In 1997, at 12 sites in the Alstonville district, leaves of cv. 344 were sampled (FEL and HOL) at 5 equidistant positions from the bottom, a height of 1.2 m (position 1), to the top (position 5), on the N–NE side of trees in late spring. The sites varied in canopy density from 50% to 95% ground cover, and PFD from the bottom shaded position to the top exposed position in the canopy across all sites increased by a factor of 1.3 to 17.9. At Alstonville, leaf parameters [N%, P%, specific leaf weight (SLW), N amount per unit leaf area (N area), and P area] increased (P < 0.001) with increasing PFD. Using regression analyses, the maximum R2 was 0.59. Age affected (P < 0.05) leaf parameters: for N%, N area, and SLW, HOL > FEL = YTL; and for P% and P area, YTL = FEL > HOL. Cultivar did not affect (P > 0.05) N%, N area or SLW; for P% and P area, cv. 660 > 781 > 344 (P < 0.05). At the Alstonville district sites, leaf parameters increased with PFD (P < 0.05). At each tree sampling position there was a weak negative correlation (P < 0.05) between the leaf parameters and percentage ground cover across all sites, which declined with height (and PFD). Nitrogen area and P area gave the highest R values (–0.60 and –0.40 at low canopy positions), and neither was a suitable replacement for percentage ground cover as a leaf-based shading indicator. The slope of the regression line (regression coefficient) between a leaf parameter and tree height for each macadamia site was determined. The regression coefficient for N area gave the best correlation with percentage ground cover (R2 = 0.55, P < 0.01) and may be useful as a leaf-based shading indicator. At position 1, HOL N concentration ranged from 1.3% to 1.8% and P concentration from 0.06% to 0.11% across all sites. At each of the 5 tree positions, the N parameters were very poorly correlated with kernel yield, and for the HOL P parameters, there was a weak negative correlation (R = –0.521 to –0.673, P < 0.05) at tree positions 1 and 2 with kernel yield. Current recommendations to reduce macadamia leaf N concentrations because of detrimental effects of high leaf N on yield were not supported by the current study. Modification of the current diagnostic leaf sampling protocol is recommended to avoid the reduction in leaf N and P concentrations through shading and the cultivar effects on P concentration. We conclude that the current diagnostic leaf N and P standards cannot reliably diagnose the nutritional status of macadamia orchards.

Financial applications of a Tabu search variable selection model

We illustrate how a comparatively new technique, a Tabu search variable selection model [Drezner, Marcoulides and Salhi (1999)], can be applied efficiently within finance when the researcher must select a subset of variables from among the whole set of explanatory variables under consideration. Several types of problems in finance, including corporate and personal bankruptcy prediction, mortgage and credit scoring, and the selection of variables for the Arbitrage Pricing Model, require the researcher to select a subset of variables from a larger set. In order to demonstrate the usefulness of the Tabu search variable selection model, we: (1) illustrate its efficiency in comparison to the main alternative search procedures, such as stepwise regression and the Maximum R2 procedure, and (2) show how a version of the Tabu search procedure may be implemented when attempting to predict corporate bankruptcy. We accomplish (2) by indicating that a Tabu Search procedure increases the predictability of corporate bankruptcy by up to 10 percentage points in comparison to Altman's (1968) Z-Score model.

Application of new experimental and garnet Margules data to the garnet-biotite geothermometer

Garnet-biotite experiments now exist from Ferry and Spear (1978, FS), Perchuk and Lavrent’eva (1983, PL), and Gessmann et al. (1997, GE). Recent garnet Margules parameters exist from Berman and Aranovich (1996, BA), Ganguly et al. (1996, GA), and Mukhopadhyay et al. (1997, MU). A comparison of ΔGmix plots for garnet binaries shows similarity among models with some significant differences. In all, 20 garnet-biotite geothermometers were retrieved from the various data using a modified form of the approach of Holdaway et al. (1997, HO) such that experimental vs. calculated values of T , in °C, were regressed stepwise to a line with intercept of zero and slope of one, maximizing r2. All tests assumed the GA model for garnet MnMg and the HO Fe3+ correction and Δ W BioTi . The experimental combinations (sets) were: (1) GE + FS with GE values of VIAlBio in FS; (2) PL + FS with GE VIAlBio in FS; (3) PL + FS with GE VIAlBio in FS, increasing W GrMnMg by 5 kJ; (4) PL + FS with no VIAlBio in FS, increasing W GrMnMg by 5 kJ; (5) PL + FS with 0.10 VIAlBio in FS, increasing W GrMnMg by 5 kJ; (6) PL + FS + GE with 0.10 VIAlBio in FS, increasing W GrMnMg by 5 kJ. Models are designated by a number for the experimental set and letters to designate the above garnet model, e.g., 5BA. Experimental sets vary in maximum r2 as follows: (1) 0.892–0.896; (2) 0.943–0.956; (3) 0.943–0.955; (4) 0.980–0.982; (5) 0.980–0.983; and (6) 0.939–0.944. Application to the HO Maine biotite-garnet data gives the following sequence of increasing quality from experimental sets: 1 < 2 < 3 < 6 < 4 ≅ 5. The various garnet models show only small differences in r2 and in quality with the Maine data base. For all 20 models, average T (°C) for the Maine M3 staurolite zone varies between 554(15) and 588(13). The best models appear to be 5BA, 5GA, and 5MU, which allow for 0.10 VIAl in FS biotite. A model based on an average of the three garnet Margules models, 5AV, has some justification and provides a slight improvement. Model 5AV gives (in J) Δ G ex = 40198 – 7.80 T; W BioFeMg = 22998 – 17.40 T ; Δ W Al Bio = 245559 – 280.31 T , and Maine M3 average staurolite zone T = 571(12) °C. The high quality of sets based mainly on PL experiments (2–5 above) results in part from their experimental P of 6 kbar. The results suggest that FS biotite contained only minor VIAl. The wide ranges of derived exchange and biotite Margules parameters, which provide reasonable calibrations, indicate that while accuracy in parameters is important, consistency is even more important. These geothermometers (5BA, 5GA, 5MU, 5AV) are available on PC disk. I recommend geothermometer 5AV.

A mass balance model that uses low‐altitude meteorological observations and the area–altitude distribution of a glacier

A glacier mass balance model that requires only low‐altitude precipitation and temperature observations and the glacier's areaaltitude distribution is presented as an alternative to direct field measurements. Input to the model for South Cascade Glacier are daily weather observations at stations 30–60 km from the glacier and at altitudes 1300 to 1500 m lower than the glacier. The model relies on the internal consistency of mass balance variables that are generated by simulation using the low‐altitude weather data. The daily values of such balance variables as snowline altitude, zero balance altitude, glacier balance, balance flux and the accumulation area ratio are correlated throughout the ablation season using two‐degree polynomial regressions to obtain the lowest fitting error. When the minimum average error (or maximum R2) is attained, the generated balances and other variables are considered to be real. A simplex optimization technique is used to determine the optimal coefficient values that are used in algorithms to convert meteorological observations to snow accumulation and snow and ice ablation. The independently produced simulation results for the 1959–1996 period are compared with balances measured at the glacier. The agreement between annual balances for individual years is fair and between long‐term volume changes measured by the geodetic method is excellent.

Improving neural network prediction of amino acid levels in feed ingredients

Artificial neural networks (ANN) were trained to predict the amino acid (AA) profile of feed ingredients. The ANN more effectively identified the complex relationship between nutrients and feed ingredients than linear regression (LR). Three types of ANN (NeuroShell 2): three-layer backpropagation (BP3), Ward Backpropagation (WBP), a general regression neural network (GRNN); and LR (SAS Proc GLM) were used to predict the AA level in corn, soybean meal, meat and bone meal, fish meal, and wheat based on proximate analysis. In contrast to a past study, a variety of alternative ANN training parameters were examined to improve ANN performance. Predictive performance was judged on the basis of the maximum R2 value resulting from all defaults tested. Advanced selection of ANN training parameters led to further improvement in performance, especially within the GRNN architecture. In 34 of 35 ANN developed, the maximum R2 value for each individual AA in each feed ingredient was higher for GRNN than for LR, BP3, or WBP prediction methods. For example, the highest R2 value for Met in corn was 0.32 for LR, 0.40 for 3LBP, 0.51 for WBP, and 0.95 for GRNN analysis. Predictive performance was also improved overall as compared to results of a previous study. For example, corn maximum R2 values (GRNN) for Met, TSAA, and Trp were: 0.78, 0.81 and 0.44, previously, and 0.95, 0.96 and 0.88, in the current study. Current soybean meal maximum R values (GRNN) were: Met, 0.92; TSAA, 0.94; and Lys, 0.90. Current meat and bone mean maximum R2 values (GRNN) were: Met, 0.97; TSAA, 0.97; and Lys, 0.97. The ANN computation is a successful alternative to statistical regression analysis for predicting AA levels in feed ingredients.