Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored. Unlike the existing work in detecting early warning signals, this paper presents the most probable transition paths to characterize the regime shifts. The most probable transition paths are obtained by minimizing the Freidlin-Wentzell (FW) action functional and Onsager-Machlup (OM) action functional, respectively. The most probable path shows the movement trend of the lake eutrophication system under noise excitation, and describes the global transition behavior of the system. Under the excitation of Gaussian noise, the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths. Under the excitation of Gaussian white noise and periodic force, we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.     

两种群随机动力系统的信息熵和动力学研究

随机种群动力学模型是研究种群间以及种群与不确定性环境间相互作用的动力学行为的数学模型. 本文从概率密度以及信息熵流、熵产生的演化角度探讨了两种群生态系统的Itô (或Statonovich)意义下随机模型的动力学行为.利用Fokker-Planck方程及其边界条件 和信息熵定义导出信息熵流(平均散度)和熵产生的关系式,并通过数值路径积分法捕 捉到熵流的非线性变化趋势以及信息熵的极值点位置与概率密度的快速迁移和分岔的联系. 应用数值路径积分法计算结果表明Itô (或Statonovich)意义下两种随机模型的概率密度 和信息熵的极值点位置不同但演化趋势一致.     

对绿洲生态学范式的哲学思考

拟结合绿洲生态学研究在哲学理论方面的最新进展,对干旱区绿洲生态学范式进行分析,并对涉及到的绿洲生态系统平衡与非平衡,同质性与异质性,等级缀块等生态范式等问题加以探讨。     

具有时滞的高维生态系统的稳定性

本文引用了混合单调流的概念,利用其性质,我们得到了一类时滞生态系统的稳定性判别准则,推广了文[2][3]的结果。     

两斑块环境中一般形式的捕食-食饵扩散生态系统的周期解

考虑周期系数的两斑块环境中一般形式的捕食-食饵扩散生态系统，系统是由3种群组成的，其中一个为捕食者，另两个为食饵种群，食饵种群间存在扩散．本文利用拓扑度连续性定理，得到了该系统正周期解存在性的充分条件．     

VIABILITY MODEL OF TROPHIC INTERACTIONS IN MARINE ECOSYSTEMS

ABSTRACT. An attempt to use viability models for studying marine ecosystems is proposed as a possible alternative to classical ecosystem modeling. Viability models do not consider optimal solutions but instead define all possible evolutions of a dynamical system under given constraints. Applied to marine ecosystems, a viability model is formulated based on the trophic coefficients of a mass‐balanced model. This requires relatively few assumptions about the processes involved and can integrate uncertainty associated with the required estimates of input parameters. An iterative algorithm is proposed to calculate the viability kernel, i.e., the envelope of all viable trajectories of the ecosystem. An application to the Benguela ecosystem is presented, considering interactions between detritus, phytoplankton, zooplankton, pelagic fish, demersal fish and fisheries. Results show how a viability kernel could be used to better define the healthy states of a marine ecosystem, by defining what states should be avoided. The paper discusses how viability models of trophic interactions could help to define a new ecosystem‐based indicator for fisheries management. It then discusses how this approach can potentially contribute to a paradigm shift that is emerging in the management of renewable resources.     

1995—2015年关中平原城市群生态系统服务价值（ESV）及其时空差异

为探究关中平原城市群土地利用程度对生态系统服务价值（ecosystem service value，ESV）的影响及变化情况，基于1995—2015年研究区5期土地利用数据，利用当量因子评估法、热点分析法和敏感性指数法对关中平原城市群ESV进行了评估，并分析了其时空规律。结果表明，20 a来，关中平原城市群ESV总体下降49.59亿元；在生态系统服务类型中，调节服务作用突出，其中水文调节占主导地位；ESV 冷点和热点分布具有明显的区域特征，主城区主要为ESV 冷点集群区，而秦巴山地、山西省东部林地及黄河、渭河等主要河流周边是ESV 热点集群区； 林地、水域和耕地对区域内ESV变化影响较大。获得的研究区ESV宏观变化规律，可为今后关中平原城市群生态环境保护、补偿和城镇发展规划的编制提供理论支撑。     

AN AUTOMATED METHOD FOR EXTENDING SENSITIVITY ANALYSIS TO MODEL FUNCTIONS

Abstract Parameter sensitivity analysis is a relatively well‐developed field compared with function sensitivity analysis. How sensitive are model conclusions to the choice of functions used in the right‐hand side of difference or differential equation models? Most work in this area has been scenario based where alternative functions are tested. This requires knowledge of plausible alternatives and is usually restricted to well‐known functions. In this work, a method is proposed for function sensitivity analysis, which it is hoped will provide a starting point for discussion and stimulating further research on this important but neglected topic. The method provides information on the sensitivity of a model's results to changes in the shape of the functions. This is done in an automated way without the need to specify alternative functional forms. The proposed method is illustrated on a small ecosystem model.     

Co-Evolution of Predator-Prey Ecosystems by Reinforcement Learning Agents

The problem of finding adequate population models in ecology is important for understanding essential aspects of their dynamic nature. Since analyzing and accurately predicting the intelligent adaptation of multiple species is difficult due to their complex interactions, the study of population dynamics still remains a challenging task in computational biology. In this paper, we use a modern deep reinforcement learning (RL) approach to explore a new avenue for understanding predator-prey ecosystems. Recently, reinforcement learning methods have achieved impressive results in areas, such as games and robotics. RL agents generally focus on building strategies for taking actions in an environment in order to maximize their expected returns. Here we frame the co-evolution of predators and preys in an ecosystem as allowing agents to learn and evolve toward better ones in a manner appropriate for multi-agent reinforcement learning. Recent significant advancements in reinforcement learning allow for new perspectives on these types of ecological issues. Our simulation results show that throughout the scenarios with RL agents, predators can achieve a reasonable level of sustainability, along with their preys.     

Verticum-type systems applied to ecological monitoring

In the paper ecological interaction chains of the type resource - producer - primary user - secondary consumer are considered. The dynamic behaviour of these four-level chains is modelled by a system of differential equations, the linearization of which is a verticum-type system introduced for the study of industrial verticums. Applying the technique of such systems, for the monitoring of the considered ecological system, an observer system is constructed, which makes it possible to recover the whole state process from the partial observation of the ecological interaction chain.