Mathematical and computational study of dispersal in mixed landscapes

我的研究项目旨在了解种群如何在混合景观中分散和持续存在，特别是那些受到人为活动（包括农业、林业和气候变化）干扰的景观。在这个提议中，我专注于发展在周期性受到农业或林业干扰的景观中运行的智能分散器的数学理论。特别是，我感兴趣的是了解持久性是如何受到生物体动力学（世代时间，多年人口周期），人为活动（农业，林业）和再殖民化（种群分散回栖息地后，例如收获或种植）这三个相互作用的时间尺度的影响。大黄蜂和树松鼠都是沿着循环搜索资源的，这表明它们具有高度的认知能力：这些生物记得它们早些时候发现资源的位置，并且可以通过与其他生物的有针对性的交流来了解新的资源斑块。在农业景观中，大部分景观的开花时间同步，在资源分配中产生了强大的外部强迫，这对大黄蜂来说是一个挑战，事实上，全球野生蜜蜂数量正在下降。在管理的森林中，分散的生物被要求重新定居越来越多的景观：采伐计划在什么时候使重新定居过程不再可能完成？为了让我们了解智能分散者是如何定位新资源的，以及这是否能在受干扰的景观上足够快地完成，以确保种群的持久性，我们需要数学模型来描述它们的运动模式。目前的连续体模型没有将记忆考虑在内，同种生物之间的交流仅限于环境中储存的嗅觉线索或化学信号。我的研究项目将为智能扩散开发新的数学模型，然后对它们进行数值分析，以确定物种在空间和时间上周期性的人为干扰存在下的持久性。其结果将是开发新的PDE模型，这些模型以前从未被研究过，它们的分析将扩展我们对动力系统的理解，无论是在可以观察到的行为方面，还是在使用的分析和数值技术方面。最后，这些模型对人为活动在受管理的生态系统中的影响提供了重要的见解，特别是关于经济和/或美学关注的物种的物种持久性。

My research program aims to understand how populations disperse and persist in mixed landscapes, particularly those disturbed by anthropogenic activity including agriculture, forestry, and climate change. For this proposal, I am focussing on developing the mathematical theory for intelligent dispersers operating in landscapes periodically disturbed by agriculture or forestry. In particular, I am interested in understanding how persistence is affected by the three interacting timescales of organism dynamics (generation time, multi-annual population cycles), anthropogenic activity (agriculture, forestry), and recolonisation (populations dispersing back into habitat that has become habitable after, e.g., harvest or planting). Bumblebees and tree squirrels both search for resources along circular forays that demonstrate a high degree of cognition: The organisms remember locations where they found resources earlier, and can learn about new resource patches from targeted communication with others. In agricultural landscapes, the synchronisation of bloom time over large portions of the landscape creates a strong external forcing in the distribution of resources that is a challenge for bumblebees, indeed, wild bee populations are in decline globally. In managed forests, dispersing organisms are being asked to recolonise an increasing proportion of the landscape: at what point do harvesting schedules make it no longer possible for the recolonisation process to be completed? In order for us to understand how intelligent dispersers locate new resources, and whether or not this can be done quickly enough on disturbed landscapes to ensure population persistence, we need mathematical models for their movement patterns. Current continuum models do not take memory into account, and communication between conspecifics is limited to olfactory cues deposited in the environment or carried by chemical signals. My research program will develop new mathematical models for intelligent dispersal, and then analyse them numerically to determine species persistence in the presence of anthropogenic disturbance that is periodic in space and time. The result will be the development of novel PDE models that have never before been studied, and their analysis will expand our understanding of dynamical systems, both in terms of the behaviours that can be observed, and in the analytic and numerical techniques used. Finally, these models lend important insights into the effect of anthropogenic activity in managed ecosystems, particularly with regard to species persistence for species of economic and/or esthetic concern.