Modeling of crossbred cattle growth, comparison between cubic and piecewise random regression models

Two analyses, cubic and piecewise random regression, were conducted to model growth of crossbred cattle from birth to about two years of age, investigating the ability of a piecewise procedure to fit growth traits without the complications of the cubic model. During a four-year period (1994-1997) of the Australian "Southern Crossbreeding Project", mature Hereford cows (N = 581) were mated to 97 sires of Angus, Belgian Blue, Hereford, Jersey, Limousin, South Devon, and Wagyu breeds, resulting in 1141 steers and heifers born over four years. Data included 13 (for steers) and eight (for heifers) live body weight measurements, made approximately every 50 days from birth until slaughter. The mixed model included fixed effects of sex, sire breed, age (linear, quadratic and cubic), and their interactions between sex and sire breed with age. Random effects were sire, dam, management (birth location, year, post-weaning groups), and permanent environmental effects and for each of these when possible, their interactions with linear, quadratic and cubic growth. In both models, body weights of all breeds increased over pre-weaning period, held fairly steady (slightly flattening) over the dry season then increased again towards the end of the feedlot period. The number of estimated parameters for the cubic model was 22 while for the piecewise model it was 32. It was concluded that the piecewise model was very similar to the cubic model in the fit to the data; with the piecewise model being marginally better. The piecewise model seems to fit the data better at the end of the growth period.     

Study of the fatigue curve in quadriceps and hamstrings of soccer players during isokinetic endurance testing

Many studies have presented regression models of quadriceps (Q) muscle strength loss with fatigue development. Paradoxically, the hamstrings (H), which are the principal site of muscle injury in soccer players, have received little attention, and no regression model has been established. This study investigated strength loss in the Q and H to establish a regression model using the lowest number of flexions-extensions during isokinetic endurance testing. Twenty-four semiprofessional soccer players performed 50 flexion-extension movements at 180 degrees x s(-1) on an isokinetic dynamometer. The theoretical equations were calculated from the first 10, first 15, first 20, and first 25 contractions for each muscle group by several regression models (linear, quadratic, cubic). The linear model was the best fit to this exercise protocol to describe the strength loss in both muscle groups. The quadratic model was the best fit to predict the changes in the H/Q ratio. This study showed that a regression model can be established for both muscle groups. A minimum of 20 extensions and 15 flexions was needed to establish a linear model that represented strength loss in, respectively, Q and H. A minimum of 25 flexions-extensions was needed with the quadratic model to accurately determine the decrease in the H/Q ratio. Isokinetic endurance testing can be carried out with only 25 flexions-extensions. This reduction should facilitate the implementation of this protocol. Regular evaluation would contribute to the efforts to prevent muscle injury during competitive sports activity.     

稻纵卷叶螟卷叶有虫率与化蛹率关系的研究

探索利用稻纵卷叶螟 Cnaphalocrocis medinalis（Guenée）卷叶有虫率估测化蛹率的方法和途径。本文基于稻纵卷叶螟化蛹进度的田间调查数据,用化蛹率（y）和卷叶有虫率（x）分别拟合直线函数、一元二次函数、一元三次函数、对数函数、指数函数和幂函数6种不同模型。结果表明,以一元三次函数方法估计精度最高,误差最小,应用效果最好,并根据最优数学模型建立化蛹率（y）与卷叶有虫率（x）的关系速查表。生产中可以应用拟合的 最优数学模型对田间稻纵卷叶螟化蛹进度进行监测。     

Regression analysis for general adaptation in pearl millet using different environmental indices

Summary Regression analyses on grain yield of 20 hybrid and 13 composite varieties of pearl millet (Pennisetum typhoides (Burm. S. & H.)) evaluated at 19 sites in India were performed to assess their relative stability and to compare different measures of environmental values. A large portion of the significant genotype X environment interactions was attributed to the non-linear component and deviations mean squares (S_di ²) were a very important parameter for selection of stable varieties. The mean grain yield was positively associated with regression coefficients and deviations mean squares. The hybrids MH 31, MH 35, MH 36 and MH 62 and composite populations MP 16, MP 31 and MP 36 possessed general adaptability. The use of dependent, independent and near-independent measures of environmental values has been found to have little influence on the general interpretation of regression analysis in pearl millet.     

QUANTIFICATION OF THE SINUSOIDAL TRAJECTORY IN TISSUE MASS AND CONDITION INDICES OF A BIVALVE (EGERIA RADIATA) IN THE CROSS RIVER, NIGERIA

Variation in monthly values of dry tissue mass (DTM) and twodifferent types of condition indices of the bivalve Egeria radiata(Lamarck, 1804) was studied for 32 consecutive months. To quantifythe seasonal trajectory of variation these data were fittedto one- and two-compartment sinusoidal models; and also to aquadratic, cubic and quartic models. The cyclic events in thevariation of the DTM and both indices of condition were adequatelydescribed by the one-compartment sinusoidal model whose parametersare biologically interpretable. The fit of the data is progressivelyimproved as one moves from the quadratic through the cubic tothe quartic model whose fit was best. Although biological meaningcould be found for the one-compartment sinusoidal model, thebiological meaning of the coefficients of the parabolic-basedmodels are obscure. Multiple regression analysis shows thatof all the four environmental parameters (temperature, salinity,pH and phytoplankton) tested, temperature has the greatest effecton DTM and one of the condition indices, while pH has the greatestimpact on the other condition index. This implies that the twoindices are not only intrinsically different, but that theyrespond to different sets of factors. Inter- and intra-specificcomparison of the many recommended ‘standard’ indicesof condition found in the literature, especially with regardto their innate sensitivity to seasonal variation in internal(e.g. state of gravidity) and external (physicochemical parametersof water) factors is necessary. (Received 1 May 1996; accepted 30 August 1996)     

Mammary growth patterns in guinea pigs during puberty, pregnancy and lactation

Mammary gland growth patterns were studied in 110 guinea pigs during the growth phase, pregnancy and lactation. Body weight changes were studied and, in addition, mammary indices were wet weight, dry fat-free tissue (DFFT), deoxyribonucleic acid (DNA) and ribonucleic acid (RNA). Statistical analyses were mathematical regression models to best fit the actual data. These included linear, quadratic, cubic, and several forms of exponential regression models. Data were separated into growth phase (60 guinea pigs in 10 age groups), pregnancy (20 guinea pigs in 4 groups), and lactation (30 guinea pigs in 6 groups). Data during pregnancy and the first 5 days of lactation were pooled and analyzed also because mammary growth continued beyond pregnancy to Day 5 of lactation. Mammary wet weight increased according to a cubic expression in the growth phase, while mammary DFFT, DNA and RNA were rectilinear through 200 days of age. During pregnancy and the first 5 days of lactation, mammary growth parameters followed the pattern of an exponential equation. Daily rates of increase for mammary DFFT and DNA were twice the rate for mammary wet weight. During lactation, mammary gland indices increased to Day 5 and then decreased gradually from Day 10 to Day 20. The best mathematical models for these change were those which are used to describe lactation curves, but all mammary gland indices decreased later and more gradually than milk production. Comparisons in growth rates of guinea pig mammary glands were made with those published for dairy goats and dairy cows. Rates of mammary DNA changed inversely to lengths of gestation in these 3 species.     

The regulation of human exposure to mutagens amidst scientific controversy

Human peripherial lymphocytes were irradiated with different doses of 15.0-MeV neutrons. The frequency of different aberration types was determined and the dose-response relation was calculated. The data were fitted by least-squared regression analysis to different models. The dicetric, dicentric+centric ring, and different acentric data gave the best fit to the linear quadratic model. The RBE of 15.0-MeV neutrons versus 220 kV X-rays decreased significantly with increasing dose.     

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.     

A simple method to fit geometric series and broken stick models in community ecology and island biogeography

Species abundance distributions are widely used in explaining natural communities, their natural evolution and the impacts of environmental disturbance. A commonly used approach is that of rank-abundance distributions. Favored, biologically founded models are the geometric series (GS) and the broken stick (BS) model. Comparing observed abundance distributions with those predicted by models is an extremely time-consuming task. Also, using goodness-of-fit tests for frequency distributions (like Chi-square or Kolmogorov–Smirnov tests) to compare observed with expected frequencies is problematic because the best way to calculate expected frequencies may be controversial. More important, the Chi-square test may prove if an observed distribution statistically differs from a model, but does not allow the investigator to choose among competing models from which the observed distribution does not differ. Both models can be easily tested by regression analysis. In GS, if a log scale is used for abundance, the species exactly fall along a straight line. The BS distribution shows up as nearly linear when a log scale is used for the rank axis. Regression analysis is proposed here as a simpler and more efficient method to fit the GS and BS models. Also, regression analysis (1) does not suffer from assumptions related to Chi-square tests; (2) obviates the need to establish expected frequencies, and (3) offers the possibility to choose the best fit among competing models. A possible extension of abundance-rank analysis to species richness on islands is also proposed as a method to discriminate between relict and equilibrial models. Examples of application to field data are also presented.     

基于分位数回归的长白落叶松人工林最大密度线

基于东北地区378块固定样地和415块临时样地的调查数据和Reineke方程,利用线性分位数回归技术建立了不同分位点(τ=0.90、0.95、0.99)下的长白落叶松人工林最大林分密度与林木平均胸径的关系模型,选出拟合长白落叶松人工林最大密度线的最优模型. 利用人为选取最大的拟合数据,采用最小二乘(OLS)和最大似然(ML)回归同时建立最大密度线模型. 采用极值统计理论的广义Pareto模型推算现实林分特定径阶的极限最大株数,进一步建立极限密度线模型. 将线性分位数回归模型与其他方法进行对比.结果表明: 在全部径阶范围内选取5个最大数据点拟合的方法能够得到现实林分的最大密度线,选取的样点过多会使模拟结果偏离最大密度线,且ML法要优于OLS法. 分位点为0.99的线性分位数回归模型能够取得与ML接近的拟合结果,但分位数回归模型参数的估计结果更稳定. 人为选取拟合数据具有一定的人为性,最终选取分位点为0.99的分位数回归模型为拟合最大密度线的最优模型,参数估计结果为k=11.790、β=-1.586,极限密度线模型的参数估计结果为k=11.820、β=-1.594. 所确定的极限密度线位置略高于最大密度线,但二者差异不明显. 由固定样地数据的验证结果可知,所建立的最大林分密度线及极限密度线能够对现实林分的最大密度及极限密度进行预测,为长白落叶松人工林的合理经营提供依据.     

Relationship between plant species richness and biomass in a coastal Maine Quercus-Pinus forest

Abstract. Several researchers have hypothesized that plant species richness has a unimodal relationship with biomass, while others have argued for a linear relationship. Data from various types of herbaceous communities show some support for the unimodal hypothesis, but this has not been tested extensively for forests and questions remain concerning its generality. We used linear and quadratic regression models to examine the relationship between overstory biomass and richness in a coastal Maine Quercus-Pinus forest across and within cover types using data from two plot sizes (2500-m² quadrats and 625-m² sub-quadrats). Understory data from 1-m² plots were also analysed. Richness was quadratically related to biomass at both plot sizes for all cover types combined, but the amount of variation explained by the models was very low (R²s < 0.09). Richness and biomass were not significantly related at either plot size for the mixed mesic cover type, the most common type in the forest. The best fit (R²= 0.43) was obtained with a quadratic model for the conifer cover type at the sub-quadrat level, with the quadratic model for the 1-m² data having the second highest R² (0.24). Across all six data sets, the quadratic model was the only one with a significant fit in two cases, and had considerably higher R²s (1.3–1.9 ×) in two others. The remaining two data sets could not be fit with a significant model of either type. For this forest, these results suggest little support for a linear relationship between plant species richness and biomass and variable, often weak, support for a unimodal relationship. Density, a potentially confounding variable in this type of analysis, was only weakly correlated with richness and was not found to alter the relationship between biomass and richness.     

A simple method to fit geometric series and broken stick models in community ecology and island biogeography

Species abundance distributions are widely used in explaining natural communities, their natural evolution and the impacts of environmental disturbance. A commonly used approach is that of rank-abundance distributions. Favored, biologically founded models are the geometric series (GS) and the broken stick (BS) model. Comparing observed abundance distributions with those predicted by models is an extremely time-consuming task. Also, using goodness-of-fit tests for frequency distributions (like Chi-square or Kolmogorov–Smirnov tests) to compare observed with expected frequencies is problematic because the best way to calculate expected frequencies may be controversial. More important, the Chi-square test may prove if an observed distribution statistically differs from a model, but does not allow the investigator to choose among competing models from which the observed distribution does not differ. Both models can be easily tested by regression analysis. In GS, if a log scale is used for abundance, the species exactly fall along a straight line. The BS distribution shows up as nearly linear when a log scale is used for the rank axis. Regression analysis is proposed here as a simpler and more efficient method to fit the GS and BS models. Also, regression analysis (1) does not suffer from assumptions related to Chi-square tests; (2) obviates the need to establish expected frequencies, and (3) offers the possibility to choose the best fit among competing models. A possible extension of abundance-rank analysis to species richness on islands is also proposed as a method to discriminate between relict and equilibrial models. Examples of application to field data are also presented.     

Polynomials to model the growth of young bulls in performance tests

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.     

Modeling the impact of plant structure on host-finding behavior of parasitoids

For many parasitoid species, the final step of host location occurs on plants whose structure varies in time and space, altering the capacity of parasitoids to exploit hosts. Plant structure can be defined by its size, heterogeneity and connectivity. We tested the hypothesis that these three components and all possible interactions affect the level of parasitism of Trichogramma evanescens and that parasitism can be predicted if the structure of a plant is measured. We quantified and varied the structure of three-dimensional artificial plants to determine which component(s) of plant structure explain variability of parasitism and to develop a model that predicts parasitism by Trichogramma females. This model was validated with three natural tritrophic systems. The experiment with artificial plants revealed that plant structure affected host-finding success, which was higher on plants with a simple structure and low on plants with a complex structure. A response surface regression showed that the linear and quadratic terms of connectivity were highly significant, indicating that connectivity best explained the variability in the rate of parasitism obtained. The interaction between connectivity and heterogeneity was also significant. Observed values of parasitism from experiments with three natural tritrophic systems fit predicted values of parasitism generated by the model, indicating that parasitism can be predicted if heterogeneity and connectivity of a plant are known. Consequences of these results in regard to population dynamics, evolution and biological control are discussed.     

A reappraisal of the evidence for regulation of wolf populations

The dogma that gray wolf (Canis lupus) population densities in naturally occurring systems are limited almost solely by available ungulate biomass is based upon studies that fit straight line linear regressions (Type 1 numerical response) to data collected at 32 sites across North America. We fit Type 1, 2, and 3 response functions to the data using linear and nonlinear regression as appropriate and found that the evidence supported wolf population regulation by density-dependence as much as limitation by prey availability. When we excluded 4 of 32 points from the original data set because those points represented exploited or expanding wolf populations the data suggested that wolf populations are self regulated rather than limited by prey biomass by at least a 3:1 margin. In establishing goals for sustainable wolf population levels, managers of wolf reintroductions and species recovery efforts should account for the possibility that some regulatory mechanism plays an important role in wolf population dynamics. © 2011 The Wildlife Society.     

Organogenetic capacity of mutant lines and their hybrids ofArabidopsis thaliana (L.) Heynh

An experiment was performed to reveal the organogenetic capacity of some mutant lines ofArabidopsis thaliana (L.) Heynh. and their hybrids. The mutant lines have lower shoot- and root-forming capacity than the normal line, but their hybrids recovered the capacity to the level of the normal parent line, and in some cases they showed hybrid vigor. Leaf segments showed both the shoot- and root-forming capacity in the normal line and in hybrids. Stem segments showed high shoot-forming and low root-forming capacity in all the lines and hybrids. Calluses showed root-forming capacity but scarcely formed shoots in both the parent lines and hybrids.     

Effect of temperature on toxicity of three pyrethroids to horn flies

Predictive models describing best-fit regression equations for per cent mortality of horn flies as a function of temperature were determined for each of three pyrethroid insecticides (fenvalerate, flucythrinate and permethrin) over the temperature range 20-35 degrees C. Susceptible horn flies, Haematobia irritans (L.), were exposed to c. an LC70 dose of each pyrethroid using a residue-on-glass method. This technique used confined exposure in chambers with temperatures of 20, 25, 30 and 35 degrees C. Within this range, mortality was greatest at 25 degrees C with all three insecticides. Estimated temperature-mortality equations for each pyrethroid revealed different responses of horn flies to each of these insecticides. Horn flies exposed to flucythrinate demonstrated a linear mortality response that varied inversely with temperature. The response to permethrin was described by a quadratic equation, while the response to fenvalerate was best fitted by a cubic equation.     

Enhanced butanol production by optimization of medium parameters using Clostridium acetobutylicum YM1

A new isolate of the solvent-producing Clostridium acetobutylicum YM1 was used to produce butanol in batch culture fermentation. The effects of glucose concentration, butyric acid addition and C/N ratio were studied conventionally (one-factor-at-a-time). Moreover, the interactions between glucose concentration, butyric acid addition and C/N ratio were further investigated to optimize butanol production using response surface methodology (RSM). A central composite design was applied, and a polynomial regression model with a quadratic term was used to analyze the experimental data using analysis of variance (ANOVA). ANOVA revealed that the model was highly significant (p < 0.0001) and the effects of the glucose and butyric acid concentrations on butanol production were significant. The model validation experiment showed 13.82 g/L butanol was produced under optimum conditions. Scale up fermentation in optimized medium resulted in 17 g/L of butanol and 21.71 g/L of ABE. The experimental data of scale up in 5 L bioreactor and flask scale were fitted to kinetic mathematical models published in the literature to estimate the kinetic parameters of the fermentation. The models used gave the best fit for butanol production, biomass and glucose consumption for both flask scale and bioreactor scale up.     

A statistical model of laboratory death rate measurements for airborne bacteria

Summary From 270 published laboratory airborne death rate measurements, two regression models relating the death rate constant for 15 bacterial species to aerosol age in the dark, Gram reaction, temperature, and an evaporation factor which is a function of RH and temperature were obtained. The independent variables accounted for 94% of the variation in the data for each of the two models. In both models the regression shows an increased survival rate with aerosol age accounting for approximately 90% of the total variation in the data. The remainder of the total variation was explained by temperature and RH (in interaction with the Gram reaction) in one model and by the evaporation function (in interaction with the Gram reaction) in the order model. Death rate data for gaseous atmospheric contamination, and light experiments were too few for building a regression model. In addition, these points were not well fit by the model indicating further research is needed to prepare realistic prediction models for airborne bacterial survival.     

Identification of an index tissue to predict zinc status of wheat

The critical concentration of Zn in wheat tissues for the prediction of Zn response and diagnosis of Zn deficiency was examined in a glasshouse experiment with wheat (Triticum aestivum, line QT 4118) grown to anthesis in two Vertisols at Zn application rates of 0, 1.25, 2.5, 5, 10, 15 and 30 kg ha^-1 equivalent as ZnSO₄ 7H₂O. The wheat tissues examined were the youngest mature leaf blade (YMB), the leaf immediately below the youngest mature leaf blade (YMB-1), the older leaves, the ear, the stem and the whole tops. The minimum Zn concentration required in a tissue at 0.90 relative yield, referred to as the critical Zn concentration, was determined using the Cate-Nelson graphical and statistical models, the Mitscherlich equation and a two-intersecting straight lines model. The Zn status of wheat was best defined by the Zn concentration in the YMB. Although the critical Zn concentration of the YMB did not vary much with the method of estimation, the Cate-Nelson statistical procedure explained a higher percentage of the variation in Zn concentration in the YMB and relative yield than the Mitscherlich and the two intersecting straight lines models. The critical concentration of Zn in the YMB was 16.0 mg kg^-1 dry matter. It is concluded that determination of Zn concentration in the YMB is the best procedure for evaluating the Zn status of wheat plants.