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

Gross0110920 研究人员开发方法来进行spatiallyexplicit控制连接自然和人为的力量，影响生物资源的需求与这些资源的动态。 虽然已经有许多替代方法被用来在人口模型中添加空间成分，但很少有人试图处理空间控制。 调查人员评估扩展动力系统的最优控制方法的空间问题，重点是一般的数学和计算问题的空间控制与非生物强迫的人口。 这一努力的动机是两个具体的例子。 第一个是关于阿巴拉契亚山脉南部的黑熊，这一种群具有与橡子产量相关的明确的环境强迫，在时间和空间上变化很大。 这与狩猎相互作用，狩猎在空间上受到限制。 第二个例子涉及到一种外来入侵植物，即佛罗里达南部大沼泽地的海金沙。 该物种可以完全覆盖该地区的原生树岛，水文的空间控制可能会限制其生长。 当前区域管理中的许多问题涉及空间控制问题--做什么、在哪里做以及在什么时间段做。 例子包括土地使用、森林采伐、水坝位置和水控制的替代计划。 美国各种各样的主要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，可以帮助管理人员和公众比较土地和区域资源的替代管理计划。 其目的也是允许forcomparison的替代标准，产生于不同的利益相关者，以判断不同的spatialmanagement计划的公共事业。 该项目得到了数学、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.