Stability of steady states of meta-food webs on discrete spatial networks
Stability of steady states of meta-food webs on discrete spatial networks
复制标题
离散空间网络上元食物网稳态的稳定性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
P. Gramlich
中科院分区：
文献类型：
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作者：
P. Gramlich
食物网的概念简单得令人难以置信。一张简单的物种间相互作用的地图。
空间离散的网络也不是一个特别令人生畏的结构。然而，即使经过近世纪的
关于食物网及其空间延伸，还有许多未解之谜，
食物网，也许最紧迫的一个是，用“现代生态学之父”的话来说（Slack，2010），
乔治伊芙琳哈钦森：
“怎么会有这么多动物？”（哈钦森，1959年）
复杂的食物网是如何保持相对稳定和强大的，这一点还有待令人满意的理解。
真实的物种关系的压倒性的复杂性和生物学家和生态学家的困难
在收集精确和广泛的现场数据，使它几乎不可能忠实地重现所有
食物网的细微差别这使得这个话题特别吸引那些喜欢
抽象问题以揭示基本原理。因此，本论文的中心重点是提供
关于元食物网稳定性主题的其他工具和见解。
广义建模方法特别适合于这项任务，因为它是围绕以下思想建立的：
标准化到稳定状态，可以分析它们的稳定性。
我们通过检查最简单的食物网来介绍这种方法，
单一的捕食者和单一的猎物这提供了一个基本的条款和可能性看看
的广义建模方法，并给出了一些基本趋势的稳定性的食物网，
令人惊讶的是，在他们的适用性，例如，概念，大指数的初级生产
生物质的破坏是不稳定的。
然后，我们添加了一个空间因素与第二个补丁，使我们正在处理一个元食物网。的
每个斑块上的食物网都是同质的，我们关注的是两者之间的迁移效应
补丁.扩散总体上是不稳定的，但对于适应性迁移来说，
某些参数范围。我们还提出了这样一个问题，即在从
从稳定到不稳定的系统，这将我们带到了属于
分叉这些简单的系统显示了包括简单模式构建在内的所有分叉。
从那里，我们通过将异质的食物网纳入每一个
补丁.这种不对称性允许在分叉点有更广泛的行为，
必须考虑斑块和物种之间同步的额外因素。的
在扰动的情况下，振荡行为的比率增加，并且振荡变得更加反
相比较均匀的食物网;更高的鲁棒性的指标。对线性的影响
稳定性不容易预测。
然后，我们将元食物网从两个斑块和两个物种扩展到空间上的多个物种
尽管只有同质的局部食物网。我们展示了
在连续空间和网络上的反应扩散系统之间，以及如何应用
到超食物网利用固有结构，我们可以制定一个主稳定性函数，
允许拓扑影响和源于食物网动态的影响分离。Meta-
对于较大的食物网，群落一般变得不太稳定，
在空间结构上。它们主要表现为振荡反应，而且很可能是局部反应
这些干扰是元社区稳健性的论据。
最后，我们总结了不同部分的结果。食物网的稳定状态
随着复杂性的增加，空间网络变得越来越不稳定，
增强鲁棒性。
The concept of a food web is deceivingly simple. A simple map of interaction links between species.
Nor is a spatially discrete network a particular daunting construct. Yet, even after almost a century of
research there are still many unanswered questions about food webs and their spatial extensions, meta-
food webs, and the perhaps most urgent one is, in the words of “father of modern ecology” (Slack, 2010),
George Evelyn Hutchinson:
“Why are there so many kinds of animals?” (Hutchinson, 1959)
It has yet to be satisfyingly understood how complex food webs remain relatively stable and robust.
The overwhelming complexity of real species relations and the difficulty for biologists and ecologists
in gathering both precise and extensive field data makes it nearly impossible to faithfully recreate all
nuances of actual food webs. This makes the topic particular appealing to the physicist who delights in
abstracting problems to reveal underlying principles. The central focus of this thesis is thus to provide
additional tools and insights to the topic of stability in meta-food webs.
The generalized modelling method is particularly suited to this task as it is built around the idea of
normalization to steady states which can be analysed concerning their stability.
We offer an introduction to this method by examining the most simple food web possible consisting of a
single predator and a single prey species. This provides a look at the fundamental terms and possibilities
of the generalized modelling approach and gives some basic trends for the stability of food webs that are
surprisingly sturdy in their applicability, e.g. the notion that large exponents for the primary production
of biomass are destabilizing.
We then add a spatial factor with a second patch so that we are dealing with a meta-food web. The
food webs on each patch are homogeneous and we focus on the effect of migration between the two
patches. Dispersal is overall destabilizing but can become less destabilizing for adaptive migration in
certain parameter ranges. We also ask the question what dynamics occur during the transition from
a stable to an unstable system which leads us to the phenomena that fall under the umbrella term of
bifurcation. These simple systems show the full range of bifurcations including simple pattern building.
From there we increase the complexity by incorporating heterogeneous food webs on each of the
patches. This asymmetry allows for a wider range of behaviour at the point of bifurcation and now
the additional element of synchrony between patches and species has to be taken into account. The
ratio of oscillatory behaviour in case of perturbation increases and the oscillations becomes more anti-
phasic compared to the homogeneous food webs; indicators of a higher robustness. The impact on linear
stability cannot be easily predicted.
We then extend the meta-food web from two patches and two species to many species on spatially
distributed networks of patches though only with homogeneous local food webs. We show the analogy
between reaction-diffusion systems on continuous space and on networks and how this can be applied
to meta-food webs. Exploiting the inherent structure we can formulate a master stability function that
allows for a separation of topological influences and those that stem from food web dynamics. Meta-
communities become in general less stable for larger food webs and can be stable or unstable depending
on the spatial configuration. They show primarily oscillatory and most likely rather localized responses
to disturbances which are arguments for the robustness of the meta-communities.
Finally, we summarize the results from the different sections. The steady states of food webs on
spatial networks become less and less stable for increasing complexity but at the same time show signs
of increasing robustness.