Logan J David, Joern Anthony, Wolesensky William
Department of Mathematics, University of Nebraska, P.O. Box 880323, Lincoln NE 68588-0323, USA.
Bull Math Biol. 2004 Jul;66(4):707-25. doi: 10.1016/j.bulm.2003.10.008.
Stoichiometric analysis recognizes that a herbivore is a mixture of multiple chemical elements, especially C, N, and P, that are fixed in various proportions. In the face of a variable quality food supply, herbivores must regulate ingested nutrients to maintain a homeostatic state. We develop a dynamic mathematical model, based on differential assimilation, that controls the C:N and C:P ratios in a herbivore within given tolerance ranges; the actual mathematical mechanism is to define the absorption coefficients to be dependent on these elemental ratios. The model inputs variable, time-dependent food and grazing rates and calculates the net dynamic consumer production (growth) of C, N, and P. It shows that total growth is equally sensitive to variations in both food quality and in assimilation rates, and it shows quantitatively how C-, N-, or P-limited growth could occur at different periods during the development period. The analysis generalizes earlier work limited to just two elements.
化学计量分析认识到，食草动物是多种化学元素的混合物，尤其是碳（C）、氮（N）和磷（P），它们以各种比例固定。面对质量可变的食物供应，食草动物必须调节摄入的营养物质以维持内稳态。我们基于差异同化开发了一个动态数学模型，该模型在给定的耐受范围内控制食草动物体内的碳氮比和碳磷比；实际的数学机制是定义吸收系数取决于这些元素比例。该模型输入随时间变化的可变食物和放牧率，并计算碳、氮和磷的净动态消费者产量（生长量）。结果表明，总生长量对食物质量和同化率的变化同样敏感，并且定量地显示了在发育阶段的不同时期如何出现碳、氮或磷限制的生长。该分析概括了早期仅局限于两种元素的研究工作。
