GLOBAL STABILITY IN TIME-DELAYED 3-DIMENSIONAL RICHARDS MODEL

We obtain the global attractivity and global asymptotical stability of positive equilibria to a 3-dimensional Richards model with delays. Our results do not depend on the size-asymmetry parameter which measures the degree of the curvature of size-growth among individuals over the entire growth curve, and the shape parameter which affects the shape of model curve. Lastly, we gave a numerical simulation to verify the feasibility of our main results.

Mixed-effects modeling for tree height prediction models of Oriental beech in the Hyrcanian forests

Height–diameter relationships are essential elements of forest assessment and modeling efforts.In this work,two linear and eighteen nonlinear height–diameter equations were evaluated to find a local model for Oriental beech（Fagus orientalis Lipsky） in the Hyrcanian Forest in Iran.The predictive performance of these models was first assessed by different evaluation criteria： adjusted R^2（R^2_（adj））,root mean square error（RMSE）,relative RMSE（%RMSE）,bias,and relative bias（%bias） criteria.The best model was selected for use as the base mixed-effects model.Random parameters for test plots were estimated with different tree selection options.Results show that the Chapman–Richards model had better predictive ability in terms of adj R^2（0.81）,RMSE（3.7 m）,%RMSE（12.9）,bias（0.8）,%Bias（2.79） than the other models.Furthermore,the calibration response,based on a selection of four trees from the sample plots,resulted in a reduction percentage for bias and RMSE of about 1.6–2.7%.Our results indicate that the calibrated model produced the most accurate results.

Modeling the growth of individuals in crowded plant populations

Aims We present an improved model for the growth of individuals in plant populations experiencing competition.Methods Individuals grow sigmoidally according to the Birch model,which is similar to the more commonly used Richards model,but has the advantage that initial plant growth is always exponential.The individual plant growth models are coupled so that there is a maximum total biomass for the population.The effects of size-asymmetric competition are modeled with a parameter that reflects the size advantage that larger individual have over smaller individuals.We fit the model to data on individual growth in crowded populations of Chenopodium album.Important Findings When individual plant growth curves were not coupled,there was a negative or no correlation between initial growth rate and final size,suggesting that competitive interactions were more important in determining final plant size than were plants’initial growth rates.The coupled growth equations fit the data better than individual,uncoupled growth models,even though the number of estimated parameters in the coupled competitive growth model was far fewer,indicating the importance of modeling competition and the degree of size-asymmetric growth explicitly.A quantitative understanding of stand development in terms of the growth of individuals,as altered by competition,is within reach.

A primer on stable parameter estimation and forecasting in epidemiology by a problem-oriented regularized least squares algorithm

Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks.For instance,simple epidemic models relying on a small number of parameters can play an important role in characterizing epidemic growth and generating short-term epidemic forecasts.In the absence of reliable information about transmission mechanisms of emerging infectious diseases,phenomenological models are useful to characterize epidemic growth patterns without the need to explicitly model transmission mechanisms and the natural history of the disease.In this article,our goal is to discuss and illustrate the role of regularization methods for estimating parameters and generating disease forecasts using the generalized Richards model in the context of the 2014e15 Ebola epidemic in West Africa.