The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate.
The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate.
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DOI：
10.1371/journal.pcbi.1005988
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发表时间：
2018-03
影响因子：
4.3
通讯作者：
Mazza C
中科院分区：
文献类型：
--
作者：
Dougoud M;Vinckenbosch L;Rohr RP;Bersier LF;Mazza C
复杂性带来生态系统稳定性的共识在七十年代受到了挑战，这一结果最近扩展到了生态启发的网络。这些方法假设存在一个可行的均衡，即具有正丰度。然而，这一关键假设尚未得到验证。我们提供的分析结果补充模拟表明，平衡的可行性消失在物种丰富的系统。这一结果使我们处于一种不舒服的境地，在这种境地中，局部稳定性准则中所假设的可行平衡的存在远非理所当然。我们通过改变相互作用的结构和强度来扩展我们的分析，并发现无论物种丰富度如何，弱相互作用的可行性和稳定性都是必要的。有趣的是，我们发现，生态启发架构的动态行为是非常不同的，比非结构化系统更丰富。我们的研究结果表明，生态系统动力学的一般理解需要关注的相互作用强度和网络结构之间的相互作用。找到导致稳定平衡的条件，即平衡对小扰动的鲁棒性，是理解生态系统持久性的关键特征。在历史上，生态系统中涉及的物种数量以及它们之间的关系数量被认为是决定稳定性的主要因素。然而，后者总是为特定的平衡计算的，它需要并且通常被假设为只包含正丰度。到目前为止，这个假设几乎没有在系统规模方面进行过测试。我们在这里提供的分析结果补充的数值模拟表明，它几乎是不可能找到的平衡只包含正的丰度在物种丰富的系统，或者，如果是这样的话，参数受到约束，导致生态无意义的丰度在非结构化系统。有趣的是，只有生态启发的架构允许一个获得可行的平衡与丰富和明智的动态行为。
The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture. Finding conditions leading to stable equilibria, i.e. equilibria robust to small perturbations, is a key feature in understanding how persistent are ecological systems. The number of species involved in the ecosystem as well as the number of relations between them has historically been pointed out to be the prominent ingredients determining stability. The latter is however always computed for a particular equilibrium, which needs and is usually assumed to contain only positive abundances. This assumption has until now only barely been tested in relation to system size. We provide here analytical results complemented by numerical simulations which show that it is almost impossible to find equilibria containing only positive abundances in species rich systems or, if so, the parameters are constrained to lead to ecologically-nonsensical abundances in unstructured systems. Interestingly, only ecologically-inspired architectures permit one to obtain feasible equilibria with a rich and sensible dynamical behavior.