Banks H T, Kareiva P M, Murphy K A
Center for Control Sciences, Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA.
Department of Zoology, University of Washington, 98195, Seattle, WA, USA.
Oecologia. 1987 Dec;74(3):356-362. doi: 10.1007/BF00378930.
The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.
通过一个捕食者 - 猎物模型展示了偏微分方程参数估计技术的应用。虽然生态学家经常在模型中估计参数，但他们以前无法对描述异质环境中相互作用的模型进行参数估计。我们描述的用于偏微分方程的技术通常将对空间复杂环境中相互作用物种的模型以及包括生物体运动的模型有用。我们使用来自瓢虫（七星瓢虫）和蚜虫（桃蚜）相互作用的实地数据来演示我们的方法。我们的参数估计算法可用于识别能解释超过80%观察到的蚜虫和瓢虫密度变化的模型。这种参数估计技术可以弥合丰富细节的实验研究与抽象数学模型之间的差距。通过将从我们的实验数据中确定的特定最佳拟合模型与关于瓢虫行为的其他信息相关联，我们得出结论，模型中需要一个描述瓢虫向猎物（在这种情况下是蚜虫）局部趋性的项。
