道路干扰下的生态系统空间特性研究
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摘要
我国公路建设及公路交通的迅速发展,为人类社会的发展提供了巨大的推动力,同时,也给生态环境带来了许多问题。例如,环境污染、生物数量的减少等。因此,正确理解和全面分析道路对生态环境的影响,尤其是对生态系统的影响,从而最大限度地减少其对生态所产生的负面作用,对于保护生物多样性、维护生态系统的稳定具有重要的理论意义。本文将生态系统抽象为具有空间扩散性质的动力系统,从全局出发,运用系统动力学方法,从理论上研究了道路干扰下的生态系统的空间特性。本文的主要工作如下：
1.本文建立了二物种(predator-prey)空间动力系统,并对道路干扰下的二物种生态系统空间特性进行了稳定性分析和数值模拟。模拟结果表明：在相同的道路密度情况下,车流量越大,系统达到稳态的时间越长；在道路上车流量相同的情况下,道路密度越大,系统达到稳态的时间越长。
2.在考虑距离与车流量影响的情况下,改进原有模型,并从两方面对其进行了数值模拟分析,分别是：(1)分析了距离与车流量对二物种生态系统种群分布的影响；(2)在生态系统遭到破坏后(比如发生火灾),比较了有道路和无道路情况下生态系统的恢复能力。模拟结果显示：生态系统达到稳态时,距离道路越近,对种群分布的影响越大；道路上车流量的增加会扩大道路系统对生态系统影响的范围；道路系统的存在使得生态系统的鲁棒性下降,即生态系统的自我恢复能力下降。
3.在三物种动力系统中,引入石头—剪子—布(Rock-Paper-Scissors)博弈理论,通过石头—剪子—布(Rock-Paper-Scissors)模型的动力学演化机制来模拟道路干扰下的生态系统空间特性。通过模拟和统计发现：道路的干扰使生态系统中最大连通群落的数量减少；随着道路数量的增加,最大连通群落的数量逐渐减少。因此,道路系统的存在影响了生态系统的种群分布,使生态系统中动物的群居能力下降,甚至导致种群灭绝。
With the rapid development of the highway, it has brought a lot of environmental problems at the same time. Road and road traffic have brought enormous benefits to human society, but the impacts of their on ecosystem are increasing. So, it is very important to understand correctly and analyze the ecological impacts. In this paper the ecosystem is abstracted as a dynamical system. We study the spatial characteristics of ecosystem under the influence of the road in theory. The main contents of this paper are as follows:
1. Based the dual dynamical systems theory, we apply the dynamical system with spatial diffusion to describe the two species ecosystem, which can research the ecosystem under the influence of the road from the global level. By analysis of the stability and numerical simulation, the two species spatial characteristics of ecosystem are studied under the influence of the road. Simulation results show that:road density and traffic flow (roads diffusion coefficient) affect the system time of being stable. Under the same density of the road, the larger is traffic flow (diffusion coefficient of the road), the less is the system time of being stable; in the same traffic flow (roads diffusion coefficient), the greater is the road density, the longer is the time to achieve stability of the system.
2. Considering the impact of distance and traffic flow, we improve the dynamical system of two species, we do the numerical simulation from two aspects of the ecosystem, namely:(1) analyzing the influence of their population distribution under the influence of the road in the two species ecosystems; (2) After the destruction of the ecosystem (eg fire), compareing resilience under road and no road situations in ecosystem. The simulation results show that:when the ecosystem achieves the steady condition, the smaller is the distance from the road, the greater impact on population distribution; as the distance increases, the effect become smaller; at a certain range the increasing of traffic flow will expand the effect range of ecosystem; the existence of road system makes robustness of ecosystem decline, in other words self-recovery of the ecosystem goes down.
3. In the dynamical system of three species, we introduce the rock-paper-scissors game theory and simulate spatial characteristics of ecosystem under the road influence by rock-paper-scissors dynamics evolution. By the simulation and statistical discovery:the influence of the road makes the number of connected communities of the largest species reduce in the system; as the increasing number of roads, the number of connected of the largest species is gradually reduced. Therefore, the existence of the road system influences the population distribution of ecosystems, and makes the ability living in groups of animals decreased in the ecosystem.
1.本文建立了二物种(predator-prey)空间动力系统,并对道路干扰下的二物种生态系统空间特性进行了稳定性分析和数值模拟。模拟结果表明：在相同的道路密度情况下,车流量越大,系统达到稳态的时间越长；在道路上车流量相同的情况下,道路密度越大,系统达到稳态的时间越长。
2.在考虑距离与车流量影响的情况下,改进原有模型,并从两方面对其进行了数值模拟分析,分别是：(1)分析了距离与车流量对二物种生态系统种群分布的影响；(2)在生态系统遭到破坏后(比如发生火灾),比较了有道路和无道路情况下生态系统的恢复能力。模拟结果显示：生态系统达到稳态时,距离道路越近,对种群分布的影响越大；道路上车流量的增加会扩大道路系统对生态系统影响的范围；道路系统的存在使得生态系统的鲁棒性下降,即生态系统的自我恢复能力下降。
3.在三物种动力系统中,引入石头—剪子—布(Rock-Paper-Scissors)博弈理论,通过石头—剪子—布(Rock-Paper-Scissors)模型的动力学演化机制来模拟道路干扰下的生态系统空间特性。通过模拟和统计发现：道路的干扰使生态系统中最大连通群落的数量减少；随着道路数量的增加,最大连通群落的数量逐渐减少。因此,道路系统的存在影响了生态系统的种群分布,使生态系统中动物的群居能力下降,甚至导致种群灭绝。
With the rapid development of the highway, it has brought a lot of environmental problems at the same time. Road and road traffic have brought enormous benefits to human society, but the impacts of their on ecosystem are increasing. So, it is very important to understand correctly and analyze the ecological impacts. In this paper the ecosystem is abstracted as a dynamical system. We study the spatial characteristics of ecosystem under the influence of the road in theory. The main contents of this paper are as follows:
1. Based the dual dynamical systems theory, we apply the dynamical system with spatial diffusion to describe the two species ecosystem, which can research the ecosystem under the influence of the road from the global level. By analysis of the stability and numerical simulation, the two species spatial characteristics of ecosystem are studied under the influence of the road. Simulation results show that:road density and traffic flow (roads diffusion coefficient) affect the system time of being stable. Under the same density of the road, the larger is traffic flow (diffusion coefficient of the road), the less is the system time of being stable; in the same traffic flow (roads diffusion coefficient), the greater is the road density, the longer is the time to achieve stability of the system.
2. Considering the impact of distance and traffic flow, we improve the dynamical system of two species, we do the numerical simulation from two aspects of the ecosystem, namely:(1) analyzing the influence of their population distribution under the influence of the road in the two species ecosystems; (2) After the destruction of the ecosystem (eg fire), compareing resilience under road and no road situations in ecosystem. The simulation results show that:when the ecosystem achieves the steady condition, the smaller is the distance from the road, the greater impact on population distribution; as the distance increases, the effect become smaller; at a certain range the increasing of traffic flow will expand the effect range of ecosystem; the existence of road system makes robustness of ecosystem decline, in other words self-recovery of the ecosystem goes down.
3. In the dynamical system of three species, we introduce the rock-paper-scissors game theory and simulate spatial characteristics of ecosystem under the road influence by rock-paper-scissors dynamics evolution. By the simulation and statistical discovery:the influence of the road makes the number of connected communities of the largest species reduce in the system; as the increasing number of roads, the number of connected of the largest species is gradually reduced. Therefore, the existence of the road system influences the population distribution of ecosystems, and makes the ability living in groups of animals decreased in the ecosystem.
引文
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[29]Faria T, Magalhaes L T. Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation. Journal of Differential Equations. 1995.122(2).181-200.
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[31]W.Hirsch, M., S. Smale, and R.L. Devaney, eds. Differential Equations, Dynamical Systems, and an Introduction to Chaos,.2004, Elsevier.
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delayed competition system. Nonlinear Analysis:Theory, Methods & Applications.2009. 70(2).658-670.
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[34]Li, Wangtong, Yan Xiangping,Zhang Cunhua. Stability and Hopf bifurcation for a delayed cooperation diffusion system with Dirichlet boundary conditions. Chaos, Solitons & Fractals.2008.38(1).227-237.
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[37]Sinervo B, lively C M. The rock-paper-scissors game and the evolution of alternative male strategies, nature.1996.380.240-243
[38]Erwin Frey, Evolutionary Game Theory:non-equilibrium and non-linear dynamics of interacting particle systems. Nature.2002.418.171.
[39]Tobias Reichenbach, Mauro Mobilia, Erwin Frey. Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games nature.2007.448.1046-1049.
[40]Medinsky A. B, Petrovskii S V, Tikhonova I A, Malchow H, Li B L. Spatiotemporal Complexity of Plankton and Fish Dynamics SIAM Review.2002.44.311-370.
[41]Murray J. Mathematical biology.Ⅱ. Spatial models and biomedical applications,3rd edn. Interdisciplinary Applied Mathematics 18.2003, New York:Springer.
[42]Cantrell R, Cosner C. Spatial Ecology via Reaction-Diffusion Equations.2003, John Wiley and Sons,Ltd,Chichester:England.
[43]Segel L A,Jackson J L. Dissipative structure:An explanation and an ecological example. J.Theo.Biol.1972.37.545-559.
[44]Gierer A, Meinhardt H. A theory of biological pattern formation. Kybernetik,1972.12. 30-39.
[45]Levin S A, Segel L. Hypothesis for origin of planktonic patchiness. Nature,1976.259. 659.
[46]Schepers H E, Markus M. Two types of performance of an isotropic cellular automaton stationary(Turing)patterns and spiral waves. Physica A.1992.188.337.
[47]Klausmeier C A. Regular and Irregular Patterns in Semiarid Vegetation. Science.1999.
284.1826-1828.
[48]Baurmann M, Gross T, Feudel U. Instabilities in spatially extended predator-prey systems:Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. J.Theo.Biol.2007.245.220-229.
[49]Cushing J. Periodic time-dependent predator-prey system. SIAM J.Appl.Math.1977.32. 82-95.
[50]Kendall B, Cycles, chaos and noise in predator-prey dynamics. Chaos Soli.and Frac. 2001.12.321-332.
[51]马克明,祖元刚.羊草种群地上部分生物量与株高的分形关系,应用生态学报.1997.4.417-420.
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[56]Panping Liu, Zhen Jin. Pattern formation of a prey-prey model. Nonlinear Analysis:Hybrid System.2009.3.177-183.
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[2]Miller J R, Joyce L A, Knight R L, et al. Forest roads and landscape structure in the southern Rocky Mountains. landscape Ecology.1996.11.115-127.
[3]Lenz H Pruller S, Gruden D. Means of transportation and their effect on the environment J]. The Handbook of Environmental Chemistry.2003.3.107-173.
[4]Foman R T T, Sperling D, Blssonette J A. Road Ecology:Science and Solutions[M].2002: Washington DC. Island Press.
[5]Bohemen H D V, De Laakk W H J V. The influence of road infrastructureand traffic on soil, water, and air quality [J]. Environmental Management.2003.31.50-68.
[6]Andrews A, Fragmentation of habitat by roads and utility corridors:a review[J]. Australian Zoologist.1990.26.130-141.
[7]宗跃光,周尚德,彭萍等.道路生态学研究进展[J].生态学报.2003.23(11).2396-2405.
[8]Forman R T T. Road ecology:a solution for the giant embracing us[J]. Landscape Ecology. 1998.13.3-5.
[9]汪自书,增辉,魏建兵.道路生态学中的景观生态问题.生态学杂志.2007.26(10).1665-1670.
[10]Mc Clellan B N, Shackleton D M. Grizzly bears and resource extraction industries:Effects of roads on behavior,habitat use and demography journal of Applied Ecology.1988.25. 451-460.
[11]Lyon L J. Road density models describing habitat effectiveness for elk. Journal of Forestry. 1983.81.592-595.
[12]Forman R T T, Alexander L E. Roads and their major ecological effects Aunual Review of Ecology and Systematics.1998.29.207-231.
[13]李月辉,胡远满.道路生态研究进展.应用生态学报.2003.14(3).447-452.
[14]Reed R A, Johnson Bamard J, Baker W L. The contribution of roads to forest fragmentation in the Rocky Mountains. Conservation Biology.1996.10.1098-1106.
[15]Dale V H O, Neill R. V, Southworth F,et al. Causes and effects of land-use change in central Rondonia,Brazil. Photogrammtic Engineering and Remote Sensing,1993.59.
997-1005.
[16]李秀珍.从第15届美国景观生态学年会看当前景观生态学发展的热点和前沿[J].生态学报.2000.20(6).1113-1115.
[17]张鹏飞,姚成.高速公路与城市道路沿线交通噪音对环境的污染分析[J].城市环境与城市生态.1999.12(3).29-31.
[18]索有瑞,黄雅丽.西宁地区公路两侧土壤和植物中铅含量及其评价[J].环境科学.1996.17(2).74-76.
[19]宗跃光.城市景观生态规划中的廊道效应研究-以北京市区为例[J].生态学报.1999.19(2).145-150.
[20]高峻,宋永昌.上海西南城市干道两侧地带景观动态研究[J].应用生态学报.2001.12(4)605-609.
[21]伍玉容,杨成永.铁路建设对动物生态行为的影响与控制策略[J].交通环保.2001.22(1).42-44.
[22]包薇红,范兢.浅谈公路建设对生态环境的影响[J].交通环保.2000.21(3).42-44.
[23]陈华新,支喜兰.公路与环境[J].西安公路交通大学学报.1998.18(3).295-298.
[24]梅晓丹.浅谈GIS在道路生态学中的应用.哈尔滨师范大学自然科学学报.2004.20(4).105-108.
[25]Wang Mingxin. Stability and Hopf bifurcation for a prey-predator model with prey-stage structure and diffusion. Mathematical Biosciences.2008.212(2).149-160.
[26]Sun G.uiquan, Jin Zhen, Liu Quangxing. Dynamical complexity of a spatial predator-prey model with migration. Ecological Modelling,2008.219(1-2).248-255.
[27]Kiss, Krisztina. N-Dimensional ratio-dependent predator-prey systems with diffusion. Applied Mathematics and Computation.2008.205(1).325-335.
[28]Hu Guangping, Li Wantong. Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects. Nonlinear Analysis:Real World Applications. In Press, Corrected Proof.
[29]Faria T, Magalhaes L T. Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation. Journal of Differential Equations. 1995.122(2).181-200.
[30]Faria Teresa. Stability and Bifurcation for a Delayed Predator-Prey Model and the Effect of Diffusion. Journal of Mathematical Analysis and Applications.2001.254(2).433-463.
[31]W.Hirsch, M., S. Smale, and R.L. Devaney, eds. Differential Equations, Dynamical Systems, and an Introduction to Chaos,.2004, Elsevier.
[32]Zhang Jinzhu, Jin Zhen, Yan Jurang, Sun Guiquan. Stability and Hopf bifurcation in a
delayed competition system. Nonlinear Analysis:Theory, Methods & Applications.2009. 70(2).658-670.
[33]Yan Xiangping, Li Wantong. Bifurcation and global periodic solutions in a delayed facultative mutualism system. Physica D:Nonlinear Phenomena.2007.227(1).51-69.
[34]Li, Wangtong, Yan Xiangping,Zhang Cunhua. Stability and Hopf bifurcation for a delayed cooperation diffusion system with Dirichlet boundary conditions. Chaos, Solitons & Fractals.2008.38(1).227-237.
[35]Fan Yonghong, Li Wantong. Permanence in delayed ratio-dependent predator-prey models with monotonic functional responses. Nonlinear Analysis:Real World Applications,2007. 8(2).424-434.
[36]Dai Bingxiang, Su Huang, Hu Dianwang. Periodic solution of a delayed ratio-dependent predator-prey model with monotonic functional response and impulse. Nonlinear Analysis: Theory, Methods & Applications,2009.70(1).126-134.
[37]Sinervo B, lively C M. The rock-paper-scissors game and the evolution of alternative male strategies, nature.1996.380.240-243
[38]Erwin Frey, Evolutionary Game Theory:non-equilibrium and non-linear dynamics of interacting particle systems. Nature.2002.418.171.
[39]Tobias Reichenbach, Mauro Mobilia, Erwin Frey. Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games nature.2007.448.1046-1049.
[40]Medinsky A. B, Petrovskii S V, Tikhonova I A, Malchow H, Li B L. Spatiotemporal Complexity of Plankton and Fish Dynamics SIAM Review.2002.44.311-370.
[41]Murray J. Mathematical biology.Ⅱ. Spatial models and biomedical applications,3rd edn. Interdisciplinary Applied Mathematics 18.2003, New York:Springer.
[42]Cantrell R, Cosner C. Spatial Ecology via Reaction-Diffusion Equations.2003, John Wiley and Sons,Ltd,Chichester:England.
[43]Segel L A,Jackson J L. Dissipative structure:An explanation and an ecological example. J.Theo.Biol.1972.37.545-559.
[44]Gierer A, Meinhardt H. A theory of biological pattern formation. Kybernetik,1972.12. 30-39.
[45]Levin S A, Segel L. Hypothesis for origin of planktonic patchiness. Nature,1976.259. 659.
[46]Schepers H E, Markus M. Two types of performance of an isotropic cellular automaton stationary(Turing)patterns and spiral waves. Physica A.1992.188.337.
[47]Klausmeier C A. Regular and Irregular Patterns in Semiarid Vegetation. Science.1999.
284.1826-1828.
[48]Baurmann M, Gross T, Feudel U. Instabilities in spatially extended predator-prey systems:Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. J.Theo.Biol.2007.245.220-229.
[49]Cushing J. Periodic time-dependent predator-prey system. SIAM J.Appl.Math.1977.32. 82-95.
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