Mathematical and computational study of dispersal in mixed landscapes

我的研究计划旨在了解人口如何分散，并坚持在混合景观，特别是那些受人为活动，包括农业，林业和气候变化的干扰。对于这个建议，我专注于开发智能分散器在农业或林业周期性干扰的景观中运行的数学理论。特别是，我有兴趣了解持久性是如何受到生物动态（世代时间，多年人口周期），人类活动（农业，林业）和繁殖（人口分散回到栖息地后，已成为可居住的三个相互作用的时间尺度影响，例如，收获或种植）。大黄蜂和树松鼠都是沿着沿着环形路径寻找资源的，这表明它们具有高度的认知能力：这些生物体记得它们早先发现资源的位置，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压力，这对大黄蜂来说是一个挑战，事实上，野生蜜蜂种群在全球范围内正在下降。在管理的森林中，分散的生物被要求使景观的比例越来越大：在什么时候采伐计划使景观化过程不再可能完成？为了让我们了解智能扩散器如何找到新的资源，以及是否可以在受干扰的景观中快速完成以确保种群的持久性，我们需要它们的运动模式的数学模型。目前的连续体模型没有考虑到记忆，同种之间的交流仅限于环境中储存的或由化学信号携带的嗅觉线索。我的研究计划将开发新的智能扩散数学模型，然后对其进行数值分析，以确定在空间和时间上周期性的人为干扰存在下的物种持久性。其结果将是开发新的PDE模型，以前从未被研究过，他们的分析将扩大我们的理解动力系统，无论是在可以观察到的行为，并在使用的分析和数值技术。最后，这些模型提供了重要的见解，在管理的生态系统中的人类活动的影响，特别是关于物种的持久性的经济和/或美学的关注。

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.