Modeling growth of total height using early data from forest inventories in fast growing Eucalyptus spp plantations

This work evaluated the growth trend represented by three biological models used for modeling forest growth and production (Schumacher; Chapman-Richards; Logistic). These curves were chosen because they are widely used by forest science professionals. The functions were adjusted under the hypothesis that there is influence of the initial, 6 and 12 month measurements on the shape of the production curves and, consequently, in the estimate of their parameters. The data that formed the adjustment basis were generated by the continuous monitoring performed at 6, 12, and 24 months and later at each 12 months in order to yield the growth patterns for the evaluated plantations. The results herein presented allow us to conclude that independently of the type of adjustment, the Chapman-Richards function was the one that exhibited the best statistics, with the BIAS values reduced in up to 30% when compared to the others. The Schumacher function presented the worst performance among the proposed criteria in this study. So, given the results obtained, we suggest a broader reflection about the growth and production issue, especially for the use of biometric models applied to forest production forecast, in which stability and adherence of the curves to the data are expected

Evaluation of the mixed effects model and quantile regression approaches for predicting tree height in larch (Larix olgensis) plantations in northeastern China

Tree height (<i>H</i>) is one of the most important tree variables and is widely used in growth and yield models, and its measurement is often time-consuming and costly. Hence, height-diameter (H-D) models have become a great alternative, providing easy-to-use and accurate tools for <i>H</i> prediction. In this study, H-D models were developed for <i>Larix olgensis</i> in Northeast China. The Chapman-Richards function with three predictors (diameter at breast height, dominant tree height, and relative size of individual trees) performed best. Nonlinear mixed effects (NLME) models and nonlinear quantile regressions (NQR9, 9 quantiles; NQR5, 5 quantiles; and NQR3, 3 quantiles) were further used and improved the generalized H-D model, successfully providing accurate <i>H</i> predictions. In addition, the <i>H</i> predictions were calibrated using several measurements from subsamples, which were obtained from different sampling designs and sizes. The results indicated that the predictive accuracy was higher when calibrated by using any number of height measurements for the NLME model and more than 3 height measurements for the NQR3, NQR5 and NQR9 models. The best sampling strategy for the NLME and NQR models involved sampling the medium-sized trees. Overall, the newly developed H-D models can provide highly accurate height predictions for <i>L. olgensis</i>.

Growth Functions as a tool to model SARS-CoV-2 pandemic trajectory and related-deaths worldwide

The international scientific community from different areas of knowledge has made efforts to provide information and methods that contribute to the adoption of the most appropriate measures to curb the spread of the COVID-19 disease. In particular, the data analysis community has been very active in publishing a large number of papers. A good part of them is related to the prediction of epidemic variables (number of cases and deaths) in different time horizons. To solve the problem of the prediction of COVID-19, an important place is occupied by the sigmoidal growth functions, as they have often been used successfully in previous epidemic outbreaks. The objective of this work was to investigate, on a statistical basis, the ability of classical growth functions to model the data from the COVID-19 pandemic. But for that, it was necessary to establish a clear classification of the 5 types of problems that can be faced with data analysis techniques in this specific context and to define a methodology based on quantitative metrics to measure the performance in solving these different types of problems. The basic concept used was that of an epidemic wave consisting of an initial-increasing and a final-decreasing phase. A classification of the COVID-19 waves in 4 types was done based on mining data from all available countries. Thus, it was possible to determine the resolvability of each type of problem depending on the stage of the epidemic wave. The biggest conclusion was the impossibility of solving the long-term forecasting problems (problem 5 – to estimate the total value of an epidemic wave) with data from the first phase only. Using this theoretical-methodological framework, we evaluated, using metrics specifically designed for these types of problems, the performance of 3 classic growth functions: Logistics, Gompertz and Richards (a generalization of the previous two) in 2 types of problems: (1) Description of the trajectory of the epidemic and (2) Prediction of the total numbers of cases and deaths. We used data from 10 countries, 7 of them with more than 100 daily deaths on the peak day. The results show a generalized underperformance of the logistic function in all aspects and place the Gompertz function as the best cost-benefit alternative, as it has performance comparable to the Richards function, but it has one less parameter to be adjusted, in the process of regression of the model to the observed data.

Forecasting COVID-19 cases and deaths in epidemic-mitigating European countries by Richards function-based regression analyses

The COVID-19 pandemic has hit many countries, and in some European countries it has been mitigated since April. Here we applied Richards function to simulate and forecast the course of COVID-19 epidemics in Italy, Spain, France, Germany, Turkey, Belgium, Ireland, Netherlands, Portugal and Switzerland. Potential total COVID-19 confirmed cases in these countries were estimated to be 240400±1300, 294100±4000, 178500±800, 176900±700, 155400±1000, 57900±400, 24000±200, 46200±300, 30000±300 and 30700±100 respectively. Most of these countries are predicted to approach ending stage between late May and early June such that daily new cases will become minimal, which may guide societal and economic restorations. In addition, total COVID-19 deaths were estimated to be 33500±300, 28200±200, 27800±200, 8740±80, 4500±30, 9250±70, 1530±20, 6240±50, 1380±10 and 1960±8, respectively. To our best knowledge, this is the first study forecasting the COVID-19 epidemic by applying the Richard function-based regression analysis.

Modelling of Beetroot Seedlings with Modified Generalized Logistic Functions

Modified generalized logistic functions (also known as Koya-Goshu functions) were used for mathematical description of germination. These functions constitute natural modification of traditionally used Richards' function for description of plants germination that introduces a non-linear time increase in exponent and an element related to time shift. Curves were adjusted to experimental data based on minimization of the square sum of difference between experimental data and a mathematical model (the smallest squares method). Results of simulation research show that the determined parameters of curves (e.g., values of the growth parameter, time shift or upper limit of population) describing the number of seedlings as a time function stay compliant to interpretation with regard to biology of the investigated processes. Based on the research, it was stated that for control and application of plant extracts to soil, Koyu-Gosha model has better adjustment to experimental data in comparison to the generalized logistic model.

Modeling genetic effects on growth of diverse provenances and families of loblolly pine across optimum and deficient nutrient regimes

Optimal deployment of improved loblolly pine (Pinus taeda L.) planting stock in the southeastern United States requires knowing how diverse seed sources and families perform over time across the wide range of sites used for plantations. This study tests if the relative growth performance of provenances and families is the same at the individual-tree and stand levels for family block plantings and determines what type of adjustment may be required to account for genetic differences when modeling growth and yield. Ten open-pollinated families from two very different provenances, Atlantic Coastal Plain and “Lost Pines” Texas, were grown in single-family block plots to test for growth differences between provenances and among families under severely deficient and optimal nutrition regimes on a nutrient-deficient, dry site. The three-parameter Chapman–Richards function was fit to plot means over time by provenance, family, and nutrition treatments. Models with provenance- or family-specific parameters of the Chapman–Richards function were tested for significant improvement over global parameters. At age 14 years, family, provenance, and nutrition treatments all significantly affected individual-tree growth traits of height, diameter, and volume. Significant nutrition by provenance interactions were found for stand-level traits of basal area per hectare and volume per hectare. Family differences were also significant for these traits. Provenance- or family-specific asymptotic parameters accounted for differences in growth over time. Several traits required the use of local asymptotic and rate parameters in the fertilized treatment only. For modeling growth, a multiplier would be sufficient to account for genetic effects on the majority of traits.