Mathematical models of neuronal growth

Biomechanics and Modeling in Mechanobiology - The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons...     

Mathematical models for calculating volume growth, represented by the yield tables for the principal wood-producing species of Czechoslovakia

Methods for the construction of volume increment tables for stands on the basis of the volume mean stem are described. The volume increment of the stand (iv) is expressed by the equation (Formula: see text). The stem number of stands (N) is determined directly by 100% or representative enumeration. The mean annual increment (iv) is calculated with the aid of the regression function (Formula: see text) (v) being volume of mean stem and (t) age of stand. The relations (2) were derived for 5 tree species (spruce, fir, pine, beach, oak) from the data of the new Czechoslovak yields tables (1975). The mathematical model for the tree species spruce and pine was tested on the basis of empirical material collected by the Tharandt department of forest management an forest yield science (within the framework of joint research activities) and good results were obtained. The results should be regarded as provisional ones. Further tests are envisaged.     

Mathematical foundations of the dendritic growth models

At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.     

Seed and seedling vigour in relation to crop growth and yield

In theory, seed germination, vigour and size (three aspects of seed quality) may influence crop yield through both indirect and direct effects. The indirect effects include those on percentage emergence and time from sowing to emergence. These influence yield by altering plant population density, spatial arrangement, and crop duration. Direct effects on subsequent plant performance are more difficult to discern. A number of different approaches to testing the hypothesis that seed quality affects subsequent plant performance (implicit in some definitions of vigour) are illustrated. The results show that it is possible to detect such effects in some circumstances.     

Mathematical and numerical comparisons of five single-population growth models

We investigate the properties of five mathematical models used to represent the growth of a single population. By imposing a common set of (normalizing) initial conditions, we are able to calculate and explicitly compare the time intervals required to reach specific values of population levels. Based on these results, we conclude that one must be careful when applying these models to interpret the dynamics of single-population growth. An additional implication is that they provide evidence that such caution should also be extended to the incorporation of these models into the formulation of interacting, multi-population models, which are used, for example, to study the spread of disease.     

Effects of ultraviolet-B radiation on the growth and yield of crop plants

This paper reviews growth chamber, greenhouse, and field studies on the effects of ultraviolet-B (UV-B. between 280 and 320 nm) radiation on agricultural crop plants. Our understanding of the physiological effects of UV-B radiation comes primarily from growth chamber studies, where UV-B is artificially supplied via filtered lamps. Both photosystems I and II, as well as carboxylating enzymes, are sensitive to UV-B radiation. Ultraviolet-B radiation also affects stomatal resistance, chlorophyll concentration, soluble leaf proteins, lipids, and carbohydrate pools. In general, the effects of UV-B radiation are accentuated by the low levels of visible radiation typically found inside growth chambers. Ultraviolet-B radiation has also been shown to affect anatomical and morphological plant characteristics. Commonly observed UV-B induced changes include plant stunting, reductions in leaf area and total biomass, and alterations in the pattern of biomass partitioning into various plant organs. In sensitive plants, evidence of cell and tissue damage often appears on the upper leaf epidermis as bronzing, glazing, and chlorosis. Epidermal transmission in the UV region decreases in irradiated leaves. This decrease is primarily associated with a stimulation in flavonoid biosynthesis and is thought to be a protective, screening response to the deleterious effects of UV-B. A considerable degree of variability exists in sensitivity to UV-B radiation between different species. Approximately 30% of the species tested were resistant, another 20% were extremely sensitive, and the remainder were of intermediate sensitivity, in terms of reductions in total dry weight. In addition to this sizable interspecific variability, there appears to be a similarly wide intraspecific variability in UV-B response. The effects of UV-B radiation on crop yield have only been examined in a limited number of field studies, with ambient levels of UV-B radiation being supplemented with fluorescent sun lamps. Due to various deficiencies, all these field experiments to date have only limited utility for assessing the potential impact of enhanced levels of UV-B on crop productivity.     

Mathematical models of bacterial growth,inhibition and death under combined stress conditions

Summary In this report we review the history of growth theories. We show how classical growth models may be derived as special cases of a generic growth rate equation. We show how growth models may be modified to represent survival data. We use linear combinations of growth and survival models to represent complex growth/survival curves and give practical examples utilizing nonlinear regression analysis. We show that traditional methods of estimating D values are inappropriate for complex, multiphasic growth/survival data. We show how such data may be modeled mathematically and illustrate methods for estimating true D values from such data.     

不同种植模式对作物根系生长、产量及根际土壤微生物数量的影响

采用多年大田试验研究了小麦-大豆(A1)、小麦-甘薯(A2)、玉米(A3)、小麦/玉米/大豆(A4)和小麦/玉米/甘薯(A5)5种种植模式的根际环境变化特征和根系生长特性.结果表明:与A1、A2、A3和A5相比,A4提高了小麦、玉米、大豆在开花期和成熟期的生物量、根系活力和根干质量,提高了各作物根际土壤细菌、真菌和放线菌数量.各种植模式之间,植株生物量和根际微生物数量的变化规律为套作＞单作、大豆茬口＞甘薯茬口、边行＞中行.小麦/玉米/大豆(A4)套作模式通过改善3种作物的根际环境,促进了作物地下部根系生长和地上部生物量的增加,从而实现作物增产.     

Responses of tree-ring growth and crop yield to drought indices in the Shanxi province,North China

In this paper, we analyze the relationships among the tree-ring chronology, meteorological drought (precipitation), agricultural drought (Palmer Drought Severity Index PDSI), hydrological drought (runoff), and agricultural data in the Shanxi province of North China. Correlation analyses indicate that the tree-ring chronology is significantly correlated with all of the drought indices during the main growing season from March to July. Sign test analyses further indicate that the tree-ring chronology shows variation similar to that of the drought indices in both high and low frequencies. Comparisons of the years with narrow tree rings to the severe droughts reflected in all three indices from 1957 to 2008 reveal that the radial growth of the trees in the study region can accurately record the severe drought for which all three indices were in agreement (1972, 1999, 2000, and 2001). Comparisons with the dryness/wetness index indicate that tree-ring growth can properly record the severe droughts in the history. Correlation analyses among agricultural data, tree-ring chronology, and drought indices indicate that the per-unit yield of summer crops is relatively well correlated with the agricultural drought, as indicated by the PDSI. The PDSI is the climatic factor that significantly influences both tree growth and per-unit yield of summer crops in the study region. These results indicate that the PDSI and tree-ring chronology have the potential to be used to monitor and predict the yield of summer crops. Tree-ring chronology is an important tool for drought research and for wider applications in agricultural and hydrological research.     

Importance of the description of light interception in crop growth models

Canopy light interception determines the amount of energy captured by a crop, and is thus critical to modeling crop growth and yield, and may substantially contribute to the prediction uncertainty of crop growth models (CGMs). We thus analyzed the canopy light interception models of the 26 wheat (Triticum aestivum) CGMs used by the Agricultural Model Intercomparison and Improvement Project (AgMIP). Twenty-one CGMs assume that the light extinction coefficient (K) is constant, varying from 0.37 to 0.80 depending on the model. The other models take into account the illumination conditions and assume either that all green surfaces in the canopy have the same inclination angle (θ) or that θ distribution follows a spherical distribution. These assumptions have not yet been evaluated due to a lack of experimental data. Therefore, we conducted a field experiment with five cultivars with contrasting leaf stature sown at normal and double row spacing, and analyzed θ distribution in the canopies from three-dimensional canopy reconstructions. In all the canopies, θ distribution was well represented by an ellipsoidal distribution. We thus carried out an intercomparison between the light interception models of the AgMIP–Wheat CGMs ensemble and a physically based K model with ellipsoidal leaf angle distribution and canopy clumping (KellC). Results showed that the KellC model outperformed current approaches under most illumination conditions and that the uncertainty in simulated wheat growth and final grain yield due to light models could be as high as 45%. Therefore, our results call for an overhaul of light interception models in CGMs.     

The relationship between crop yield and petiole nitrate concentration at various growth stages

Summary The critical concentration of a mineral element in plants is usually defined by reference to the curve relating yield to plant nutrient concentration. This curve alters shape depending on the stage of growth, species, and other factors such as light and temperature, so that the critical concentration also varies. It is shown that this effect could arise from two simple, but reasonable assumptions: first, that the percentage depression of growth rate due to nutrient deficiency is related by a simple diminishing-returns type function to plant nutrient concentration in a manner which is independent of growth stage: and second, that the absolute growth rate of non-limited plants declines as their weight increases beyond a certain value. If the critical concentration were to be defined in terms of percentage growth rate depression, it is possible that it would be found to be much less variable than it now seems. re]19760730