Mathematical model for predicting fungal growth and decomposition rates based on improved Logistic equations

As the function of the decomposition of fungi has been clearly researched in the global carbon cycle,it is obviously of value to explore the decomposition rate of fungal populations.This study analyzed the relationship between environmental factors and biodiversity step by step.In order to explore the interaction between the fungi and the relationship between the decomposition rate of fungi with time,the model based on the Logistic model was built and the Lotka-Volterra model was employed in the condition of two kinds of fungi existing in an environment with limited resources.The changing trend of population number and decomposition rate of several fungi under different environmental conditions can be predicted through the model.To illustrate the applicability of the model,Laetiporus conifericola and Hyphoderma setigerum were applied as examples.The results showed that the higher the degree of population diversity,the greater the decomposition rate,and the higher the decomposition efficiency of the ecosystem.Its rich species diversity is conducive to accelerating the decomposition of litter,lignocellulose,and the circulation of the entire ecosystem.Based on the above model and using the data from measuring the mycelial elongation rate of each isolate at 10℃,16℃,and 22℃ under standardized laboratory conditions,the growth patterns of the five fungi combinations were simulated.The results revealed a general increase in growth rate with increasing temperature,which verifies the accuracy of the model.Moreover,it also revealed that the total decomposition rate after fungal incorporation was negatively correlated with the decomposition rate of a fungal single action.Based on the above model,predictions can be made for fungal growth in different environments,and suitable environments for fungal growth can be determined.In the future,the model can be further optimized,and lignin and cellulose decomposition factors can be added to fit the decomposition of logs.The application scenarios of the model can be further broadened,which can contribute to the restoration and management of the ecological environment,as well as produce good effects in the fields of fungi assisting the global carbon cycle and soil problem restoration.

Growth Process of Eucalyptus urophylla × E.grandis Stand Based on Logistic Equation

Eucalyptus is the most valuable cultivated forest genus in the tropical and subtropical areas nowadays. It has been a challenge for foresters to model growth due to the genetic variations, management regimes, and multiple products generated from the plantations. In this paper, Logistic equation was used to study the stock growth process of E. urophylla × E. grandis plantation at age of 14 with 6 spacing treatments. And the biological interpretation of the parameters of Logistic equation was analyzed. The results show that it is flexible, precise and accurate to fit the growth process.

A Logistic-growth-equation-based Intensity Prediction Scheme for Western North Pacific Tropical Cyclones

Accurate prediction of tropical cyclone(TC)intensity remains a challenge due to the complex physical processes involved in TC intensity changes.A seven-day TC intensity prediction scheme based on the logistic growth equation(LGE)for the western North Pacific(WNP)has been developed using the observed and reanalysis data.In the LGE,TC intensity change is determined by a growth term and a decay term.These two terms are comprised of four free parameters which include a time-dependent growth rate,a maximum potential intensity(MPI),and two constants.Using 33 years of training samples,optimal predictors are selected first,and then the two constants are determined based on the least square method,forcing the regressed growth rate from the optimal predictors to be as close to the observed as possible.The estimation of the growth rate is further refined based on a step-wise regression(SWR)method and a machine learning(ML)method for the period 1982−2014.Using the LGE-based scheme,a total of 80 TCs during 2015−17 are used to make independent forecasts.Results show that the root mean square errors of the LGE-based scheme are much smaller than those of the official intensity forecasts from the China Meteorological Administration(CMA),especially for TCs in the coastal regions of East Asia.Moreover,the scheme based on ML demonstrates better forecast skill than that based on SWR.The new prediction scheme offers strong potential for both improving the forecasts for rapid intensification and weakening of TCs as well as for extending the 5-day forecasts currently issued by the CMA to 7-day forecasts.

Differential Calculus the Study of the Growth and Decay of an Entity’s Population

Population Growth and Decay study of the growth or the decrease of a population of a given entity, is carried out according to the environment. In an infinite environment, i.e. when the resources are unlimited, a population P believes according to the following differential equation P’ = KP, with the application of the differential calculus we obtasin an exponential function of the variable time (t). The function of which we can predict approximately a population according to the signs of k and time (t). If k > 0, we speak of the Malthusian croissant. On the other hand, in a finite environment i.e. when resources are limited, the population cannot exceed a certain value. and it satisfies the logistic equation proposed by the economist Francois Verhulst: P’ = P(1-P).

A numerical study of coupled maps representing energy exchange processes between two environmental interfaces regarded as biophysical complex systems

The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. Following the definition of environmental interface by Mihailovic and Bala? [1], such interface can be, for example, placed between: human or animal bodies and surrounding air, aquatic species and water and air around them, and natural or artificially built surfaces (vegetation, ice, snow, barren soil, water, urban communities) and the atmosphere, cells and surrounding environment, etc. Complex environmental interface systems are (i) open and hierarchically organised (ii) interactions between their constituent parts are nonlinear, and (iii) their interaction with the surrounding environment is noisy. These systems are therefore very sensitive to initial conditions, deterministic external perturbations and random fluctuations always present in nature. The study of noisy non-equilibrium processes is fundamental for modelling the dynamics of environmental interface regarded as biophysical complex system and for understanding the mechanisms of spatio-temporal pattern formation in contemporary environmental sciences. In this paper we will investigate an aspect of dynamics of energy flow based on the energy balance equation. The energy exchange between interacting environmen- tal interfaces regarded as biophysical complex systems can be represented by coupled maps. Therefore, we will numerically investigate coupled maps representing that exchange. In ana- lysis of behaviour of these maps we applied Lyapunov exponent and cross sample entropy.

From Pressure-Volume Relationship to Volume-Energy Relationship: A Thermo-Statistical Model for Alveolar Micromechanics

The connective tissue fiber system and the surfactant system are essential and interdependent components of lung elasticity. Despite considerable efforts over the last decades, we are still far from understanding the quantitative roles of either the connective tissue fiber or the surfactant systems. Through thermo-statistic considerations of alveolar micromechanics, the author introduced a thermo-statistic state function “entropy” to analyze the elastic property of pulmonary parenchyma based on the origami model of alveolar polyhedron. By use of the entropy for alveolar micromechanics, from the logistic equation for the static pressure (P)-volume (V) curves including parameters a, b, c, and k (V - a = b/[1+ exp{-k (P - c)}]), a set of equations was obtained to define the internal energy of lungs (UL) and its corresponding lung volume (VL). Then, by use of parameters a, b, c, and k, an individual volume-internal energy (VL - UL) diagram was constructed from reported data in patients on mechanical ventilation. Each VL - UL diagram constructed was discussed that its minimal value Uo = c (a + b/2) and its shape parameter b/k represent quantitatively the energy of tissue force and the energy of surface force. Furthermore, by use of the VL - UL relationship, the hysteresis of lungs estimated by entropy production was discussed as dependent on the difference in the number of contributing pulmonary lobules. That is, entropy production might be a novel quantitative indicator to estimate the dynamics of the bronchial tree. These values obtained by combinations of parameters of the logistic P-V curve seem useful indicators to optimize setting a mechanical ventilator. Thus, it is necessary to develop easy tools for fitting the individual sigmoid pressure-volume curve measured in the intensive care unit to the logistic equation.

Permanence and extinction of a single species model in polluted environment

Under the assurmption that the growth of the population satisfies the generalized logistic equation,a new single specics model in polluted environment is proposed in this work.Sufficient conditions for permanence and extinction of the species in the model are given respectively.It is shown that our model and the results are improvements of those in He and Wang.