QEIB: Spatially-distributed Population Models with External Forcing and Spatial Control

研究人员开发了在空间上进行显式控制的方法，以将影响生物资源需求的自然和人为力量与这些资源的动态联系起来。虽然已经采取了许多替代办法来在人口模型中增加空间部分，但很少有人尝试处理空间控制问题。研究人员评估了动力系统的最优控制方法对空间问题的扩展，重点放在与非生物强迫种群有关的空间控制的一般数学和计算问题上。这一努力是由两个具体的例子推动的。第一个是关于阿巴拉契亚山脉南部的黑熊，这个种群具有明显的环境压力，与橡子杆的生产有关，这在时间和空间上有很大的差异。这与狩猎相互作用，而狩猎在空间上是受限的。第二个例子涉及南佛罗里达州大沼泽地的非侵入性外来植物物种小叶石蒜(旧世界气候蕨类)。该物种可完全覆盖该地区的原生树岛，并可应用水文空间控制来限制其生长。目前区域管理中的许多问题都涉及空间控制问题--做什么、在哪里做以及在什么时间段进行。例子包括土地利用、森林采伐、水坝选址和水控制的替代计划。在美国，各种各样的重大环境公共政策问题需要对替代管理的影响进行科学评估。研究人员开发了新的数学和计算方法，可以帮助管理者和公众比较土地和区域资源的替代管理计划。目的还在于能够比较不同利益攸关方提出的替代标准，以判断不同空间管理计划的公用事业。该项目得到了应用数学、计算数学和人口生物学项目以及MPS多学科活动办公室的支持。

Gross0110920 The investigators develop methods to carry out spatiallyexplicit control to link natural and anthropogenic forces thatinfluence the demand for biological resources with the dynamicsof those resources. While there have been numerous alternativeapproaches taken to add spatial components to population models,few of these have attempted to deal with spatial control. Theinvestigators evaluate extensions of optimal control methods fordynamical systems to spatial problems, with a focus on generalmathematical and computational issues for spatial control linkedwith abiotic forcing of populations. The effort is motivated bytwo specific examples. The first concerns black bears in thesouthern Appalachians, a population with explicit environmentalforcing associated with acorn mast production, which variesconsiderably in time and space. This interacts with hunting,which is spatially restricted. The second example involves aninvasive exotic plant species, Lygodium microphyllum (Old WorldClimbing Fern), in the Everglades of South Florida. This speciescan completely cover the native tree islands of the region andspatial control of hydrology may be applied to limit its growth. Many of the current problems in regional management involveissues of spatial control -- what to do, where to do it and forwhat time periods. Examples include alternative plans for landuse, forest harvesting, location of dams, and water control. Awide variety of the major environmental public policy issues inthe US require scientific assessments of the impacts ofalternative management. The investigators develop newmathematical and computational approaches that can aid managersand the public to compare alternative management plans of landand regional resources. The objective also is to allow forcomparisons of alternative criteria, arising from differentstakeholders, to judge the public utility of different spatialmanagement plans. The project is supported by the AppliedMathematics, Computational Mathematics, and Population Biologyprograms and by the MPS Office of Multidisciplinary Activities.