Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach
Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach
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DOI：
10.1073/pnas.2103779118
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Li Xu;Denis D. Patterson;A. Staver;S. Levin;Jin Wang
中科院分区：
文献类型：
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作者：
Li Xu;Denis D. Patterson;A. Staver;S. Levin;Jin Wang
描述波动下生态系统的稳定性和动态性是生态学长期面临的挑战。基于非平衡统计物理的景观通量理论框架，研究了波动下森林-稀树草原模型的生态动力学，发现生态动力学是由种群景观梯度和稳态概率通量共同决定的。稀树草原和森林状态在一定条件下共存，而在波动情况下，在确定性情况下看不到的草原状态出现了。内在景观被确定为量化生态系统全局稳定性的李雅普诺夫函数。我们量化了势垒高度、动力学路径和稳定状态之间的转换速率。平均通量、熵产率、时间不可逆性、时间轨迹的方差和波动作为量化分岔开始/偏移的标记。频率分布可以表征与生态状态稳定性相关的人口潜力景观。我们通过分析森林-稀树草原模型来说明这种方法的实际效用。稀树草原和森林状态在某些条件下共存，这与过去的理论工作和经验观察相一致。然而，在相应的确定性模型中看不到的草原状态，在波动下作为一种替代的准稳定状态出现，为一些实证分析中广泛草原的出现提供了理论基础。生态动态是由种群-潜在景观梯度和稳态概率通量共同决定的。通量量化了生态系统的净投入/产出，因此也量化了非平衡程度。景观和通量共同决定了以主导路径和转换速率为特征的稳定状态之间的转换。内在势能景观允许李雅普诺夫函数，它提供了全球稳定性的定量度量。我们发现在有限波动和零波动下，平均通量、熵产率和自由能在分岔附近都有显著的变化。这些可以提供分岔的动力学和热力学起源。我们确定了观察到的频率、时间轨迹、波动和时间不可逆性的差异作为分岔的运动学度量。这一框架开辟了描述全球生态系统的方式，揭示了它们如何在状态之间变化，并量化了随机波动下准稳定状态的出现。
Significance Characterizing stability and dynamics of ecological systems under fluctuations is a longstanding challenge in ecology. We study the ecodynamics of a forest–savanna model under fluctuations via a landscape-flux theoretical framework from nonequilibrium statistical physics and show that ecological dynamics are determined by both population landscape gradients and steady-state probability fluxes. Savanna and forest states coexist under certain conditions, and a grassland state unseen in deterministic cases emerges under fluctuations. The intrinsic landscape is identified with a Lyapunov function for quantifying global stability of ecological systems. We quantify barrier heights, kinetic paths, and switching rates between stable states. Average flux, entropy production rate, time irreversibility, variances in time traces, and fluctuations serve as markers to quantify onset/offset of bifurcations. The frequency distributions can characterize the population-potential landscape related to the stability of ecological states. We illustrate the practical utility of this approach by analyzing a forest–savanna model. Savanna and forest states coexist under certain conditions, consistent with past theoretical work and empirical observations. However, a grassland state, unseen in the corresponding deterministic model, emerges as an alternative quasi-stable state under fluctuations, providing a theoretical basis for the appearance of widespread grasslands in some empirical analyses. The ecological dynamics are determined by both the population-potential landscape gradient and the steady-state probability flux. The flux quantifies the net input/output to the ecological system and therefore the degree of nonequilibriumness. Landscape and flux together determine the transitions between stable states characterized by dominant paths and switching rates. The intrinsic potential landscape admits a Lyapunov function, which provides a quantitative measure of global stability. We find that the average flux, entropy production rate, and free energy have significant changes near bifurcations under both finite and zero fluctuation. These may provide both dynamical and thermodynamic origins of the bifurcations. We identified the variances in observed frequency time traces, fluctuations, and time irreversibility as kinematic measures for bifurcations. This framework opens the way to characterize ecological systems globally, to uncover how they change among states, and to quantify the emergence of quasi-stable states under stochastic fluctuations.