Natural selection. IV. The Price equation

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation's greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen.     

Modelling the contribution of arbuscular mycorrhizal fungi to plant phosphate uptake

In this paper, we investigate the role of arbuscular mycorrhizal fungi in plant phosphorus nutrition. We develop a mathematical model which quantitatively assesses the contribution of external fungal hyphae to plant phosphate uptake.We derive an equation for solute uptake by a growing fungal mycelium which we couple with a model for root uptake. We analyse the model using nondimensionalization and numerical simulations.Simulations predict that removal of phosphate from soil is dominated by hyphal uptake as opposed to root uptake. Model analysis shows that the depletion zones around hyphae overlap within 8 h and that the transfer between fungus and root is a critical step for the behaviour of phosphorus within the mycelial phase. We also show that the volume fraction of mycelium is negligibly small in comparison to other soil phases.This is the first model to quantify the contribution of mycorrhizal fungi to plant phosphate uptake. A full data set for model parametrization and validation is not currently available. Therefore, more complete sets of experimental measurements are necessary to make this model more applicable.     

Hydration of 3-cyanopyridine to nicotinamide by crude extract nitrile hydratase

Summary The kinetic and stability characteristics of crude extract nitrile hydratase fromBrevibacterium R-312 were studied for the hydration of 3-cyanopyridine to nicotinamide. The enzyme was substrate and product inhibited and had the following kinetic constants:K _m =28 mM;K _p =36 mM;K _s =155 mM;V _m =5.8 mol/min/mg protein (25°C). Itsmaximum temperature and pH (phosphate buffer) were 35°C and 8.0, respectively and it had half-lives of 50 days, 10 days and 1 day at 4°C, 10°C and 25°C, respectively. The crude extract also exhibited amidase activity on nicotinamide, but it became significant only at nicotinamide concentrations greater than 300 mM. Mathematical models for batch and fed-batch hydrations were developed to account for substrate and product inhibitions and for enzyme decay. They predicted to within 10% experimental results for initial substrate and final product concentrations up to 300 mM; the accuracies decreased at higher concentrations primarily because of the relatively rapid hydrolysis of nicotinamide.     

Predicting responses of photosynthesis and root fraction to elevated [CO2]a: interactions among carbon,nitrogen, and growth*

At elevated atmospheric CO₂ concentrations ([CO₂]_a), photosynthetic capacity (A_max) and root fraction (η_R, the ratio of root to plant dry mass) increased in some studies and decreased in others. Here, we have explored possible causes of this, focusing on the relative magnitudes of the effects of elevated [CO₂]_a on specific leaf (n_m) and plant (n_p) nitrogen concentrations, leaf mass per unit area (h), and plant nitrogen productivity (α). In our survey of 39 studies with 35 species, we found that elevated [CO₂]_a led to decreased n_m and n_p in all the studies and to increased h and α in most of the studies. The magnitudes of these changes varied with species and with experimental conditions. Based on a model that integrated [CO₂]_a-induced changes in leaf nitrogen into a biochemically based model of leaf photosynthesis, we predicted that, to a first approximation, photosynthesis will be upregulated (A_max will increase) when growth at increased [CO₂]_a leads to increases in h that are larger than decreases in n_m. Photosynthesis will be downregulated (A_max will decrease) when increases in h are smaller than decreases in n_m. The model suggests that photosynthetic capacity increases at elevated [CO₂]_a only when additional leaf mesophyll more than compensates the effects of nitrogen dilution. We considered two kinds of regulatory paradigms that could lead to varying responses of η_R to elevated [CO₂]_a, and compared the predictions of each with the data. A simple static model based on the functional balance concept predicts that η_R should increase when neither n_p nor h is very responsive to elevated [CO₂]_a. The quantitative and qualitative agreement of the predictions with data from the literature, however, is poor. A model that predicts η_R from the relative sensitivities of photosynthesis and relative growth rate to elevated [CO₂]_a corresponds much more closely to the observations. In general, root fraction increases if the response of photosynthesis to [CO₂]_a is greater than that of relative growth rate.     

激光与生物组织相互作用：光子迁移与生物传热理论

激光热疗中,激光与生物组织相互作用研究主要包含两方面：光子在生物组织中的迁移规律,以及光生扫热在生物组织在的传导。对前者的描述主要为,基于传输理论的解析法和Ｍｏｎｔｅ￣Ｃａｒｌｏ模拟,生物组织中光子迁移规律的研究能定量描述组织中的光分布,并进一步获得生物组织中的热分布;考虑到了生物组织特性,所建立了生物组织中温度场分布及变化规律。光子迁移与生物传热理论是研究激光热序不可分割的传热模型,全面描述了生     

A functionally based model for hydrolysis of cellulose by fungal cellulase

A new functionally based kinetic model for enzymatic hydrolysis of pure cellulose by the Trichoderma cellulase system is presented. The model represents the actions of cellobiohydrolases I, cellobiohydrolase II, and endoglucanase I; and incorporates two measurable and physically interpretable substrate parameters: the degree of polymerization (DP) and the fraction of beta-glucosidic bonds accessible to cellulase, F(a) (Zhang and Lynd, 2004). Initial enzyme-limited reaction rates simulated by the model are consistent with several important behaviors reported in the literature, including the effects of substrate characteristics on exoglucanase and endoglucanase activities; the degree of endo/exoglucanase synergy; the endoglucanase partition coefficient on hydrolysis rates; and enzyme loading on relative reaction rates for different substrates. This is the first cellulase kinetic model involving a single set of kinetic parameters that is successfully applied to a variety of cellulosic substrates, and the first that describes more than one behavior associated with enzymatic hydrolysis. The model has potential utility for data accommodation and design of industrial processes, structuring, testing, and extending understanding of cellulase enzyme systems when experimental date are available, and providing guidance for functional design of cellulase systems at a molecular scale. Opportunities to further refine cellulase kinetic models are discussed, including parameters that would benefit from further study.     

Mathematical modeling of an aqueous film coating process in a Bohle Lab-Coater: Part 2: Application of the model

For the prediction of the air and product temperatures, the product moisture, and the air humidity during a coating process in a Bohle Lab-Coater, a model was developed. The purpose of this work was to determine the limit moisture, the critical moisture, and the constant for the exchange rate between both zones and to use these values for other sets of experiments to test the model. The adaptation of the 3 parameters (limit moisture, critical moisture, and exchange rate constant), was done by calculation of the product temperature in both zones for several sets of parameters in order to minimize the sum of square deviation between the calculated and the measured product temperatures. This set of parameters was used to test the validity of the model. By applying the model, the product temperature could be predicted based on the product, process, and equipment-related parameters. Hence, the model can be used to theoretically investigate the influence of different process paramaters. The mean difference between the predicted, and measured product temperatures in the steady state is ≈2 up to 3 K using the determined parameter set for the limit moisture, the critical moisture, and the exchange rate constant. The model is useful for the prediction of the air and product temperatures, the product moisture, and air humidity during a coating process in the Bohle Lab-Coater using round, biconvex tablets.     

嵌套式回归建立树木生物量模型

 该文介绍了一种建立树木生物量模型的简单快速方法——嵌套式回归。基本原理是以枝轴为基本单位, 逐级拟合。过程是把枝条分解成枝轴, 从枝轴到枝条, 再到单株, 拟合不同层次或尺度的生物量模型。建立枝轴生物量方程, 估计各级枝轴生物量, 将枝轴生物量(实测值或模拟值)总和起来便得到枝条生物量。由于样本单元之间有包含关系, 实际测定的样本很小, 具有快速实用的特点。检验结果显示, 模型预测值和实测值具有较高的一致性。