具有空间结构的种群模型及分布格局研究
|
摘要
数学生态学研究的主要内容包括两个问题:种群的数量变化和空间分布。种群数量的时间动态的研究,一般以动力学方程等数学模型为基础,相关的研究在过去几十年中取得了许多重要的成果。然而相对于种群的时间动态的研究,种群的空间动态研究的发展则相对滞后。本文重点关注种群的空间动态,即种群的空间模型和空间分布格局分析,其研究内容共包含四章。第一章主要从数学生态学的角度,回顾了种群动态研究的历史,介绍数学生态学研究从非空间模型到空间模型的发展过程。同时比较了几种常用的空间建模方法,并从动力学的角度进行了分类研究。第二章主要研究了两个具有空间结构的种间竞争系统模型。首先,我们将非空间的竞争系统扩展到具有空间结构的竞争系统,其次我们的研究重点从一般的竞争关系转移到一种新的具有循环结构的竞争系统之上。本章使用的第一个模型是积分微分方程模型,第二个模型为具有空间网格结构的元胞自动机模型。通过对模型的分析,我们验证了空间结构和非层次的竞争关系有利于物种共存的理论。相关结果对生物多样性的理论发展提供了依据和支持。第三章介绍了一种基于个体的模型,并利用矩动力学方程,研究了个体在空间中的分布格局的变化。本章使用的基于个体的模型(individual-based model),引入了矩动力学的分析方法,研究了一个具有追逐和逃逸的竞争系统。通过与非空间的模型比较,我们发现,个体之间的相互运动可以延缓竞争排斥的过程,因而有利于物种的共存。第四章主要介绍了空间点过程以及点格局分析在研究种群空间分布中的应用。本章首先给出了两种计算点格局聚集指数的方法,K-function以及邻体距离抽样方法。然后我们给出了一个估计点格局密度的方法,并利用实验数据进行了验证。结果表明,本章给出的极大似然估计,在估计个体密度,计算点格局聚集指数等方面,有很高的准确性和稳定性。本研究给出的方法,在实际野外调查研究中有很强的可操作性,对从事相关领域的研究者有很大帮助。
The size and spatial distribution of populations are the two major subjects in mathematical ecology. Classical methods from mathematics have played an important role in studying the problems about population size. Generally, the temporal dynamics of the populations are modeled by the dynamical equations, where many well-known achievements also have been obtained On the contray, few studies have contributed to the subject of spatial distributions of populations and related research is not thrived at all. This PhD thesis, in which four chapters are included, will mainly focus on the spatial dynamics of populations—spatial models and spatial distributions. In chapter one, we briefly reviewed the history of the development of population models from the view point of mathematical ecology. The transition from non-spatial models to spatial models is also included. Moreover, some newly developed methods which are used in modeling spatial dynamics of populations are introduced. All these methods are compared and categorized from the perspective of dynamics theory. In chapter two, two spatially-structured competitive systems are studied: The first one is an integro-differential model while the second one is cellular automata model: After a comprehensive analysis, the theory that spatial structure and non-transitive competition favor coexistence of species is verified. The importance of this research is providing some theoretical evidence and support to biodiversity. In chapter three, a individual-based model (IBM) is introduced and its spatial dynamics and patterns are approximated by a group of moment equations. Actually, the IBM is an interactive particle system, where two competitive species are placed on a plane. Some new results are obtained and a comparison with previous studies about non-spatial system is also conducted. It proves that the dispersal of individuals favor the coexistence of interspecific competitive species. In chapter four, we first introduced the application of spatial point process and spatial analysis in population pattern analysis. The first concern in this chapter is to compute aggregation parameter which reflects the aggregation level of the spatial point pattern. Two new methods, K-function and distance sampling, are proposed. The other concern in this chapter is to give an ideal-estimator of the density. Based on distance sampling (distance from individual to individual), we propose a maximum likelihood estimator of the density. All above methods are assessed by simulated point patterns and mapped point patterns from real forests. The meaning of this research is helping field workers to complete inventory and survey efficiently.
The size and spatial distribution of populations are the two major subjects in mathematical ecology. Classical methods from mathematics have played an important role in studying the problems about population size. Generally, the temporal dynamics of the populations are modeled by the dynamical equations, where many well-known achievements also have been obtained On the contray, few studies have contributed to the subject of spatial distributions of populations and related research is not thrived at all. This PhD thesis, in which four chapters are included, will mainly focus on the spatial dynamics of populations—spatial models and spatial distributions. In chapter one, we briefly reviewed the history of the development of population models from the view point of mathematical ecology. The transition from non-spatial models to spatial models is also included. Moreover, some newly developed methods which are used in modeling spatial dynamics of populations are introduced. All these methods are compared and categorized from the perspective of dynamics theory. In chapter two, two spatially-structured competitive systems are studied: The first one is an integro-differential model while the second one is cellular automata model: After a comprehensive analysis, the theory that spatial structure and non-transitive competition favor coexistence of species is verified. The importance of this research is providing some theoretical evidence and support to biodiversity. In chapter three, a individual-based model (IBM) is introduced and its spatial dynamics and patterns are approximated by a group of moment equations. Actually, the IBM is an interactive particle system, where two competitive species are placed on a plane. Some new results are obtained and a comparison with previous studies about non-spatial system is also conducted. It proves that the dispersal of individuals favor the coexistence of interspecific competitive species. In chapter four, we first introduced the application of spatial point process and spatial analysis in population pattern analysis. The first concern in this chapter is to compute aggregation parameter which reflects the aggregation level of the spatial point pattern. Two new methods, K-function and distance sampling, are proposed. The other concern in this chapter is to give an ideal-estimator of the density. Based on distance sampling (distance from individual to individual), we propose a maximum likelihood estimator of the density. All above methods are assessed by simulated point patterns and mapped point patterns from real forests. The meaning of this research is helping field workers to complete inventory and survey efficiently.
引文
[1]姜启源,数学模型(第二版)[M].北京:高等教育出版社,1993.
[2]陈兰荪,数学生态学模型与研究方法[M].北京:科学出版社,1991.
[3]E.C.Pielo,数学生态学(卢泽愚译)[M].北京:科学出版社,1988.
[4]马知恩,种群生态学的数学建模与研究[M].合肥:安徽教育出版社,1996.
[5]HofbauerJ.M.Sigmund K进化对策与种群动力学(陆征一,罗勇译)[M].成都:四川科学技术出版社,2002.
[6]张炳根,数学生态学模型[M].青岛:青岛海洋大学出版社,1990.
[7]孙儒泳,动物生态学原理[M].北京:北京师范大学出版社,2001.
[8]张锦炎,冯贝叶,微分方程几何理论与分支问题[M].北京:北京大学出版社,2000.
[9]叶彦谦,极限环论[M].上海:上海科技出版社,1984.
[10]郝柏林,从抛物线谈起-混沌动力学引论[M].上海:上海科技教育出版社,1993.
[11]张锋,生物博弈的空间效应:生境破坏、破碎以及空间尺度对进化动态的影响(博士论文).兰州大学,2005.
[12]杨维明,时空混沌与耦合映像格子[M].上海:上海科技教育出版社,1994.
[13]漆安慎,杜婵英,免疫的非线性模型[M].上海:上海科技教育出版社,1998.
[14]张大勇,理论生态学研究[M].北京:高等教育出版社,2000.
[15]权硕,三维竞争型生态系统的共存与灭绝(硕士论文).兰州大学,2001.
[16]欧阳颀,反应扩散方程的斑图动力学[M].上海:上海科技教育出版社,2000.
[17]刘嘉琨,应用随机过程[M].北京:科技出版社,2000.
[18]Tilman D.,Kareiva P.,Spatial Ecology:the role of space in population dynamics and interspecific interactions.Princeton University Press,1997.
[19]Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000.
[20]McGlade J.M.,Advanced Ecological Theory:Principle and applications. Oxford Blackwell Science,1999.
[21]Keeling M.,Spatial models of interacting populations(in McGlade J.M.,Advanced Ecological Theory:Principle and applications.Oxford Blackwell Science,1999,pp:100-142).
[22]McGlade J.M.,Individual based models(in McGlade J.M.,Advanced Ecological Theory:Principle and applications.Oxford Blackwell Science,1999,pp:1-22).
[23]Kot M.,Elements of Mathematical Ecology.Cambridge University Press,2001.
[24]Murry J.D.,Mathematical Biology(2nd edition),Springer Verlag,1993.
[25]Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997.
[26]Holling C.S.,The characteristics of simple types of population and parasitism.Canadian Entomologist,(1959a)91:385-398.
[27]Holling C.S.,The compontents of predation as relealed by a study of small predation of European pine sawly.Canadian Entomologist,(1959b)91:293-320.
[28]Kuang Y.Delay differential equations with applications in Population dynamics,Academic Press,1993.
[29]May R.M.,Stablity and complexity in model ecosystems.Princeton University Press,1975.
[30]May R.M.,Periodical cicadas,Nature,(1979),277:347-349.
[31]May R.M.,Oster G.F.,Bifurcation and dynamic complexity in simple ecological models.Am.Nat.(1976),110:573-599.
[32]Beddington J.R.,Free G.A.,Lawton J.H.Dynamic complexity in predatorprey models framed in difference equations,Nature,(1975)255:58-60.
[33]Kaitala,V.Ylikarjula J.,Heino M.,Complex non-unique dynamics in simple ecological interactions",J.Theor.Biol,(1999)197:331-341.
[34]Tang S.Y.,Chen L.S.,Chaos in functional response host- parasitoid ecosystem models”,Chaos,Solitons and Fracral,(2002),13 :875-884.
[35]Xu C,Boyce M.S.,Dynamic complexities in a mutual interference hostparasitoid model”,Chaos,Solitons and Fracral,(2005)24:175-182 .
[36]Lesile P.H.,On the use of matrices in certain population mathematics Bio- metrika,(1945),33:183-212.
[37]Fisher R.A.,The wave of advance of advantageous genes.Annals of Eugenics,(1937),7:355-369.
[38]Holmes,E.E.,Lewis,M.A.,Banks,J.E.,Veit,R.R.,1994.Partial differential equations in ecology:spatial interactions and population dynamics.Ecology 75,17-29.
[39]Okubo,A.,Levin,S.A.,2001.Diffusion and ecological problems:Modern Perspectives.Springer,New York.
[40]Gurney,W.S.C,Veith,A.R.,Cruickshank,I.,McGeachin,G.,.Circles and spirals:population persistence in a spatially explicit predator-prey model.Ecology(1998)79,2516-2530.
[41]Hutson V.,Vicker G.T.,Methods for Reaction-diffusion models(in Dieckmann et al.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:456-481).
[42]Biktaskev,V.N.,Brindley,J.,Holden,A.V.,Tsyganov,M.A.,Pursuitevasion predator prey waves in two spatial dimensions.Chaos(2004)14,988-994.
[43]Tsyganov,M.A.,Brindeley,J.,Holden,A.V.,Biktashev,V.N.,Quasi-soliton interaction of pursuit-evasion waves in a predator-prey system.Phys.Rev.Lett.,(2003)91,218102.
[44]Tsyganov,M.A.,Brindeley,J.,Holden,A.V.,Biktashev,V.N.,Soliton-like phenomena in one-dimensional cross-diffusion systems:a predator-prey pursuit and evasion example.Physica.D(2004)197,18-33.
[45]Hanski,I.,Metapopulation dynamics.Nature(1998)396,42-49.
[46]Jansen,V.A.A.,Phase locking:another cause of synchronicity in predatorprey systems.Trends Ecol.Evol(1999)14,278-279.
[47]Jansen,V.A.A.,Lloyd,A.L.,Local stability analysis of spatially homogeneous solutions of multi-patch systems.J.Math.Biol.(2000)41,232-252.
[48]Jansen,V.A.A.,De Roos,A.M.,(2000)The role of space in reducing population cycles.(In:Dieckmann,U.,Law,R.,Metz,J.A.J.(Eds.),The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,Cambridge).
[49]Jansen,V.A.A.,The dynamics of two diffusively coupled predator-prey populations.Theoret.Popul.Biol.(2001)59,119-131.
[50]Kaneko K.,Period-doublings of Kink-antikink patterns,qquasiperiodicity in antiferro-like structure and spatial intermittency in coupled logistic lattice:towards a prelude of a “field theory of chaos” Prog.Theor.Phys,(1984),72:480.
[51]Kaparal R.,Pattern formation in two dimensional arrays of coupled discrete time oscillations,Phys.Rev.A,(1985),31:3868.
[52]Waller I.,Kapral R.,Spatial and temporal structure in system of coupled nonlinear oscillators Phys.Rev.A.(1984)30:2047.
[53]Hasell M.P.,Comins H.N.,May R.M.,Species coexistence of self-organizing spatial dynamics,Nature,(1994),370:290-292.
[54]Wolfram S.,Computation theory of cellular automata Coram.Math.Phys.(1984),96:15.
[55]Wolfram S.,Theory and application of cellualar automata.Singapore,World Scientific Publishing,1984.
[56]Nowak M.A.,May R.M.,Evolutionary games and spatial chaos.Nature,(1992)359:826-829.
[57]Nowak M.A.,May R.M.,The spatial dilemmas of evolution.Int.J.Bifurcation and chaos.(1993),3(l)35-78.
[58]Eubank S.,Farmer J.D.,Introduction to dynamical system(in Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997,pp:55-105).
[59]Moen J.,Diffuse competition:a diffuse concept.Oikos,(1989),54:260-263.
[60]Frean M.,Abraham E.R.,Rock-scissors-paper and the survival of the weakest,Proc.R.Soc.Lond.B 268(2001)1323-1327.
[61]Kerr B.,Riely M.A.,Feldman M.W.,Bohannan B.J.M.,Local dispersal promotes biodiversity in a real-life game of roc-paper-scissors,Nature 418(2002)171-174.
[62]Sinervo B.,Lively C.M.,The rock-scissors-paper game and the evolution of alternative male strategies,Nature,(1996),340:240-243.
[63]Paguin C.E.,Adaams J.,Relative fitness can decrease in evolving a sexual populations of S.cerevisiae,Nature,(1983),306:368-371.
[64]Nakamaru M.,Iwasa Y.,Competition between allelopathy proceeds in travelling waves: Colocin-immune strain aids colicin-sensitive strain.Theor.Popul.Biol.(2000),12-41.
[65]Cazaran T.L.,Hoekstra R.F.,Pagie L.Chemical warfare between microbes promotes biodiversity.Proc.NAt.Acd.Sci.USA.(2002),99:786-790.
[66]May R.M.,Leonard W.J.,Nonlinear aspect of competition between three species SIAM J.Appl.Math.(1975),29:243-253.
[67]Gilpin M.E.,Limits cycles in competition communities.Am.Nat.(1975),109:51-60.
[68]Schuster P.,Sigmund K.Wolff R.,On w-limits for competition between three species.SIAM J.Appl.Math.(1979)49-54.
[69]Zhang F.,Li Z.,Hui C,Spatiptemporal dynamics and distribution patterns of cyclic competition in metapopulation.Ecol.Model.,(2006),193:721-735.
[70]Durrett R.,Levin S.,Alllopathy in spatially distributed populations,J.Theor.Biol.(1997),185:165-171.
[71]Durrett R.,Levin S.,Spatial aspects of interspecific competition.Theor.Popul.Biol.(1998),53:30-43.
[72]Durrett R.,Levin S.,The importance of being discrete(and spatial).Theor.Popul.Biol.(1994),46:363-394.
[73]Durrett R.,Levin S.,Stochastic spatial models :a user's guide to ecological applications.Phil.TRans.Roy.Soc.Lond.B,(1994),343:329-350.
[74]Durrett R.,Nehauser C,Particle systems and reaction-diffusion equations.Ann.Appl.Probab.(1994),22(l):289-333.
[75]Anderson K.,Neuhauser C.,Patterns in spatial simulations- are they real? Ecol.Model.155(2002)19-30.
[76]Gao M.,Li Z.,Asymptotical stability and spatial patterns of a spatial cyclic competitive system,Applied Mathematics and Computation,(2006),183:1165-1169.
[77]Matsuda H.,Ogita N.,Sasaki A.,Sato K.,Satistical mechanics of population:the lattice Lotka-Volterra model.Proc.Theor.Phys.(1992),88:1035-1049.
[78]Sato K.,Iwasa Y.,Pair approximation fo lattice-based ecological models(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:341-358.)
[79]Iwasa Y.,Lattice models and pair approximation in ecology,(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:227-251)
[80]Harada Y.,Iwasa Y.,Lattice population dynamics for plants with dispersing seeds and vegetative population.Res.Popul.Ecol.(1994),36:237-249.
[81]Tainaka K.,Paradoxical effect in a three-candidate voter model.Phys.Lett.A.,(1993),176:303-306.
[82]Tainaka K.,Indirect effect in cyclic voter models Phys.Lett.A.,(1995),207:53-57.
[83]Van Baalen M.,Pair approximation for different spatial geometries(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:359-387)
[84]Rand D.A.,Correlation equations and pair approximations for spatial ecologies (in McGlade J.M.,Advanced Ecological Theory:Principle and applications.Oxford Blackwell Science,1999,pp:100-142)
[85]Morris A.J.,Representing spatial interactions in simple ecological models.PhD thesis,Warwick University,1997.
[86]Hardin G.,The competitive exclusion principle.Science,(1960),131:1292-1297.
[87]Zhang D.Y.,Lin K.,The effect of competitive displacement:how robust is Hubbell's community drift model? J.Theor.Biol.(1997),188:361-367.
[88]Tilman D.,Competitive and biodiversity in spatially structured habita.Ecology (1994),75:2-16.
[89]Hutchinson G.E.,The paradox of the plankton.Am.Nat.(1961),75:137-145.
[90]Chesson P.L.,Warner R.R.,Environmental variability systems.Am.Nat.,(1981),117:923-943.
[91]Frachebourg L.,Krapivsky P.L.,Ben-Naim E.,Spatial organization in cyclic Lotka-Volterra.systems.Physical Review E.,(1996),54:6186-6200.
[92]Szabo G.,Santos M.A.,Mendes J.F.F.,Votex dynamics in a three-states model under cyclic dominace.Physical Review E.,(1999),60:3776-3780.
[93]Szab(?)G.,Szolnoki A.,Three-state cyclic voter model extended with Potts energy.Physical Review E.,(2002),65:036115.
[94]Ravasz M.,Szab(?)G.,Szolnoki A.,Spreadings of famihes in cyclic predatorprey models.Physical Review E.,(2004),70:012901.
[95]Hierro J.L.,Callaway R.M.,Allelopathy and exotic plant invasion.Plant and Soil.(2003),256:29-39.
[96]Nowak M.A.,Sigmund K.,Bacterial game dynamics,Nature,(2002),418:139-139.
[97]Hiebeler D.,Tatar R.,Cellular automata and discrete Physics(in Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997,pp:275-295)
[98]Abraham R.A.,Visualization Techniques for cellular automata(in Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997.pp:296-307)
[99]Law R.,Dieckmann U.,Moment approximation of individual-based model (in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:252-270)
[100]Bolker B.M.,Pacala S.W.,Levin S.A.,Moment methods for ecological processes in continuous space(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:388-411.)
[101]Dieckmann U.,Law R.,Relaxation projections and the method of moment (in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:412-455.)
[102]McCann,K.,Hastings,A.,Harrison,S.,Wilson,W.,Population outbreaks in a discrete world.Theoret.Popul.Biol.(2000)57,97-108.
[103]Bolker B.,Pacala S.W.,Using moment equation to understand stochasticity driven spatial pattern formation in ecological systems.Theor.Popul.Biol.(1997),52:179-197.
[104]Law.R.,Dieckmann U.,A dynamical system from neighborhoods in plant communities.Ecology,(2000),81:2137-2148.
[105]Law R.,Murrell D.J.,Dieckmann U.,Population growth in space and time:spatial logistic equations.Ecology,(2003),84:252-262.
[106]Murrell D.J.,Dieckmann U.,Law.R.,On the moments closures for population dynamics in continuous space.J.Thepr.Biol.(2004),229:421-432.
[107]Van Kampen N.G.,Stochastic processes in Physics and Chemistry.Amsterdam Netherlands,1992.
[108]Pielou,E.C.A single mechanism to account for regular,random and aggregated populations.J.Ecol.(1960)48:575-584.
[109]Pielou,E.C.Segregation and symmetry in two-species population as studied by nearest-neighbor relationships.J.Ecol.(1961)49:255-269.
[110]Stoyan,D.and Penttinen.A.,Recent Applications of Point Process Methods in Forestry Statistics.Statistical Science(2000),15:61-78
[111]Legendre,P.and M.J.Fortin.Spatial pattern and ecological analysis.Vegetatio (1989)80:107-138.
[112]Baddeley A.,Gill R.D.,Kaplan-meier estimators of distance distributions for spatial point processes.Annl.Statistics.,(1997)25:263-292.
[113]Wiegand T.,Moloney K.A.,Rings,circles,and null-models for point pattern analysis in ecology.Oikos,(2004)104:209-229.
[114]Barbini P.,Cevenini G.E.,and Massai M.R.Nearest-neighbor analysis of spatial point patterns:application to biomedical image interpretation,Computers and Biomedical Research(1996)29:482-493.
[115]Bliss,C.I.Fisher,R.A..Fitting the Negative Binomial Distribution to Biological Data.Biometrics(1953)9:176-200.
[116]He,F.and K.J.Gaston.Occupancy-abundance relationships and sampling scales.Ecography(2000)23:503-511.
[117]Dacey F.M.,1964.Modified Poission probability law for point pattern in more regular than random.Annals of Assoc,of Ameri.Geogrs.(1964)54:559-565.
[118]He,F.and K.J.Gaston.Estimating species abundance from occurrence.American Naturalist.(2000)156:553-559.
[119]Archibald E.E.A.Plant populations I.A new application of Neyman's contagious distribution.Annals of Botony.(1948)12:221-235.
[120]Thomas M.,A generalization of Poission's binomial limit for use in ecology.Biometrika,(1949)36:18-25.
[121]Boswell,M.T.,and Patil G.P.(1970)Chance mechanisms generating the negative binomial distributions.Pages 3-22 in G.P.Patil,ed.Random counts in models and structures.Pennsylvania State University Press,University Park.
[122]Quenouille M.H.,A relation between the logarithmic,Poission,and Negative Binomial series.Biometrics,(1949)5:162-164.
[123]Clark,P.J.and Evans F.C.Distance to nearest neighbor as a measure of spatial relationships in populations in populations.Ecology(1954)35:445-453.
[124]Green R.H.Measurement of non-randomness in spatial distributions.Research in Population Ecology.(1966)8:l-7.
[125]Thompson,H.R.Distribution of distance to n-th nearest neighbor in a population of randomly distributed individuals.Ecology(1956)37:391-394
[126]Eberhardt,L.L.Some developments in 'distance sampling'.Biometrics(1967)23:207-216.
[127]Ripley,B.D.The second-order analysis of stationary point processes,Journal of Applied Probability(1976)13,255-266.
[128]Ripley,B.D.Modelling spatial patterns,Journal of the Royal Statistical Society,Series B(1977)39,172-192.
[129]Ripley,B.D.Tests of 'randomness' for spatial point patterns,Journal of the Royal Statistical Society,Series B(1979)41,368-374.
[130]Ripley,B.D.(1981).Spatial Statistics,Wiley,New York.
[131]Engeman,R.M.,Sugihara R.T.,Pank L.F.,Dusenberry W.E.A comparison of plotless density estimators using Monte CArlo simulation.Ecology(1994)75,1769-1779.
[132]Picard N,Kouyate,A.M,Dessard,H.Tree density estimations using a distance method in Mali Savanna.For.Sci.(2005)31:7-18
[133]Diggle,P.J.Robust density estimation using distance methods.Biometrika (1975)62:39-48.
[134]Persson,O.Distance methods:The use of distance measurements in the estimation of seedling density and open space frequency.Skogshogskolan(1964)15:68 pp
[135]Byth, K.On robust distance-based intensity estimators.Biometrics(1982)38:127-135
[136]Kleinn,C,Vilcko F.Design-unbiased estimation for point-totree distance sampling.Can J For Res(2006)36:1407-1414
[137]Morisita,M.A new method for the estimation of density by the spacing method applicable to non-randomly distributed populations.Physiol Ecol(1957)7:134-144.
[138]Magnussen,S.,Kleinn,C.Picard N.Two new density estimators for distance sampling.Eur J Forest Res(2008)127:213-224.
[2]陈兰荪,数学生态学模型与研究方法[M].北京:科学出版社,1991.
[3]E.C.Pielo,数学生态学(卢泽愚译)[M].北京:科学出版社,1988.
[4]马知恩,种群生态学的数学建模与研究[M].合肥:安徽教育出版社,1996.
[5]HofbauerJ.M.Sigmund K进化对策与种群动力学(陆征一,罗勇译)[M].成都:四川科学技术出版社,2002.
[6]张炳根,数学生态学模型[M].青岛:青岛海洋大学出版社,1990.
[7]孙儒泳,动物生态学原理[M].北京:北京师范大学出版社,2001.
[8]张锦炎,冯贝叶,微分方程几何理论与分支问题[M].北京:北京大学出版社,2000.
[9]叶彦谦,极限环论[M].上海:上海科技出版社,1984.
[10]郝柏林,从抛物线谈起-混沌动力学引论[M].上海:上海科技教育出版社,1993.
[11]张锋,生物博弈的空间效应:生境破坏、破碎以及空间尺度对进化动态的影响(博士论文).兰州大学,2005.
[12]杨维明,时空混沌与耦合映像格子[M].上海:上海科技教育出版社,1994.
[13]漆安慎,杜婵英,免疫的非线性模型[M].上海:上海科技教育出版社,1998.
[14]张大勇,理论生态学研究[M].北京:高等教育出版社,2000.
[15]权硕,三维竞争型生态系统的共存与灭绝(硕士论文).兰州大学,2001.
[16]欧阳颀,反应扩散方程的斑图动力学[M].上海:上海科技教育出版社,2000.
[17]刘嘉琨,应用随机过程[M].北京:科技出版社,2000.
[18]Tilman D.,Kareiva P.,Spatial Ecology:the role of space in population dynamics and interspecific interactions.Princeton University Press,1997.
[19]Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000.
[20]McGlade J.M.,Advanced Ecological Theory:Principle and applications. Oxford Blackwell Science,1999.
[21]Keeling M.,Spatial models of interacting populations(in McGlade J.M.,Advanced Ecological Theory:Principle and applications.Oxford Blackwell Science,1999,pp:100-142).
[22]McGlade J.M.,Individual based models(in McGlade J.M.,Advanced Ecological Theory:Principle and applications.Oxford Blackwell Science,1999,pp:1-22).
[23]Kot M.,Elements of Mathematical Ecology.Cambridge University Press,2001.
[24]Murry J.D.,Mathematical Biology(2nd edition),Springer Verlag,1993.
[25]Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997.
[26]Holling C.S.,The characteristics of simple types of population and parasitism.Canadian Entomologist,(1959a)91:385-398.
[27]Holling C.S.,The compontents of predation as relealed by a study of small predation of European pine sawly.Canadian Entomologist,(1959b)91:293-320.
[28]Kuang Y.Delay differential equations with applications in Population dynamics,Academic Press,1993.
[29]May R.M.,Stablity and complexity in model ecosystems.Princeton University Press,1975.
[30]May R.M.,Periodical cicadas,Nature,(1979),277:347-349.
[31]May R.M.,Oster G.F.,Bifurcation and dynamic complexity in simple ecological models.Am.Nat.(1976),110:573-599.
[32]Beddington J.R.,Free G.A.,Lawton J.H.Dynamic complexity in predatorprey models framed in difference equations,Nature,(1975)255:58-60.
[33]Kaitala,V.Ylikarjula J.,Heino M.,Complex non-unique dynamics in simple ecological interactions",J.Theor.Biol,(1999)197:331-341.
[34]Tang S.Y.,Chen L.S.,Chaos in functional response host- parasitoid ecosystem models”,Chaos,Solitons and Fracral,(2002),13 :875-884.
[35]Xu C,Boyce M.S.,Dynamic complexities in a mutual interference hostparasitoid model”,Chaos,Solitons and Fracral,(2005)24:175-182 .
[36]Lesile P.H.,On the use of matrices in certain population mathematics Bio- metrika,(1945),33:183-212.
[37]Fisher R.A.,The wave of advance of advantageous genes.Annals of Eugenics,(1937),7:355-369.
[38]Holmes,E.E.,Lewis,M.A.,Banks,J.E.,Veit,R.R.,1994.Partial differential equations in ecology:spatial interactions and population dynamics.Ecology 75,17-29.
[39]Okubo,A.,Levin,S.A.,2001.Diffusion and ecological problems:Modern Perspectives.Springer,New York.
[40]Gurney,W.S.C,Veith,A.R.,Cruickshank,I.,McGeachin,G.,.Circles and spirals:population persistence in a spatially explicit predator-prey model.Ecology(1998)79,2516-2530.
[41]Hutson V.,Vicker G.T.,Methods for Reaction-diffusion models(in Dieckmann et al.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:456-481).
[42]Biktaskev,V.N.,Brindley,J.,Holden,A.V.,Tsyganov,M.A.,Pursuitevasion predator prey waves in two spatial dimensions.Chaos(2004)14,988-994.
[43]Tsyganov,M.A.,Brindeley,J.,Holden,A.V.,Biktashev,V.N.,Quasi-soliton interaction of pursuit-evasion waves in a predator-prey system.Phys.Rev.Lett.,(2003)91,218102.
[44]Tsyganov,M.A.,Brindeley,J.,Holden,A.V.,Biktashev,V.N.,Soliton-like phenomena in one-dimensional cross-diffusion systems:a predator-prey pursuit and evasion example.Physica.D(2004)197,18-33.
[45]Hanski,I.,Metapopulation dynamics.Nature(1998)396,42-49.
[46]Jansen,V.A.A.,Phase locking:another cause of synchronicity in predatorprey systems.Trends Ecol.Evol(1999)14,278-279.
[47]Jansen,V.A.A.,Lloyd,A.L.,Local stability analysis of spatially homogeneous solutions of multi-patch systems.J.Math.Biol.(2000)41,232-252.
[48]Jansen,V.A.A.,De Roos,A.M.,(2000)The role of space in reducing population cycles.(In:Dieckmann,U.,Law,R.,Metz,J.A.J.(Eds.),The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,Cambridge).
[49]Jansen,V.A.A.,The dynamics of two diffusively coupled predator-prey populations.Theoret.Popul.Biol.(2001)59,119-131.
[50]Kaneko K.,Period-doublings of Kink-antikink patterns,qquasiperiodicity in antiferro-like structure and spatial intermittency in coupled logistic lattice:towards a prelude of a “field theory of chaos” Prog.Theor.Phys,(1984),72:480.
[51]Kaparal R.,Pattern formation in two dimensional arrays of coupled discrete time oscillations,Phys.Rev.A,(1985),31:3868.
[52]Waller I.,Kapral R.,Spatial and temporal structure in system of coupled nonlinear oscillators Phys.Rev.A.(1984)30:2047.
[53]Hasell M.P.,Comins H.N.,May R.M.,Species coexistence of self-organizing spatial dynamics,Nature,(1994),370:290-292.
[54]Wolfram S.,Computation theory of cellular automata Coram.Math.Phys.(1984),96:15.
[55]Wolfram S.,Theory and application of cellualar automata.Singapore,World Scientific Publishing,1984.
[56]Nowak M.A.,May R.M.,Evolutionary games and spatial chaos.Nature,(1992)359:826-829.
[57]Nowak M.A.,May R.M.,The spatial dilemmas of evolution.Int.J.Bifurcation and chaos.(1993),3(l)35-78.
[58]Eubank S.,Farmer J.D.,Introduction to dynamical system(in Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997,pp:55-105).
[59]Moen J.,Diffuse competition:a diffuse concept.Oikos,(1989),54:260-263.
[60]Frean M.,Abraham E.R.,Rock-scissors-paper and the survival of the weakest,Proc.R.Soc.Lond.B 268(2001)1323-1327.
[61]Kerr B.,Riely M.A.,Feldman M.W.,Bohannan B.J.M.,Local dispersal promotes biodiversity in a real-life game of roc-paper-scissors,Nature 418(2002)171-174.
[62]Sinervo B.,Lively C.M.,The rock-scissors-paper game and the evolution of alternative male strategies,Nature,(1996),340:240-243.
[63]Paguin C.E.,Adaams J.,Relative fitness can decrease in evolving a sexual populations of S.cerevisiae,Nature,(1983),306:368-371.
[64]Nakamaru M.,Iwasa Y.,Competition between allelopathy proceeds in travelling waves: Colocin-immune strain aids colicin-sensitive strain.Theor.Popul.Biol.(2000),12-41.
[65]Cazaran T.L.,Hoekstra R.F.,Pagie L.Chemical warfare between microbes promotes biodiversity.Proc.NAt.Acd.Sci.USA.(2002),99:786-790.
[66]May R.M.,Leonard W.J.,Nonlinear aspect of competition between three species SIAM J.Appl.Math.(1975),29:243-253.
[67]Gilpin M.E.,Limits cycles in competition communities.Am.Nat.(1975),109:51-60.
[68]Schuster P.,Sigmund K.Wolff R.,On w-limits for competition between three species.SIAM J.Appl.Math.(1979)49-54.
[69]Zhang F.,Li Z.,Hui C,Spatiptemporal dynamics and distribution patterns of cyclic competition in metapopulation.Ecol.Model.,(2006),193:721-735.
[70]Durrett R.,Levin S.,Alllopathy in spatially distributed populations,J.Theor.Biol.(1997),185:165-171.
[71]Durrett R.,Levin S.,Spatial aspects of interspecific competition.Theor.Popul.Biol.(1998),53:30-43.
[72]Durrett R.,Levin S.,The importance of being discrete(and spatial).Theor.Popul.Biol.(1994),46:363-394.
[73]Durrett R.,Levin S.,Stochastic spatial models :a user's guide to ecological applications.Phil.TRans.Roy.Soc.Lond.B,(1994),343:329-350.
[74]Durrett R.,Nehauser C,Particle systems and reaction-diffusion equations.Ann.Appl.Probab.(1994),22(l):289-333.
[75]Anderson K.,Neuhauser C.,Patterns in spatial simulations- are they real? Ecol.Model.155(2002)19-30.
[76]Gao M.,Li Z.,Asymptotical stability and spatial patterns of a spatial cyclic competitive system,Applied Mathematics and Computation,(2006),183:1165-1169.
[77]Matsuda H.,Ogita N.,Sasaki A.,Sato K.,Satistical mechanics of population:the lattice Lotka-Volterra model.Proc.Theor.Phys.(1992),88:1035-1049.
[78]Sato K.,Iwasa Y.,Pair approximation fo lattice-based ecological models(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:341-358.)
[79]Iwasa Y.,Lattice models and pair approximation in ecology,(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:227-251)
[80]Harada Y.,Iwasa Y.,Lattice population dynamics for plants with dispersing seeds and vegetative population.Res.Popul.Ecol.(1994),36:237-249.
[81]Tainaka K.,Paradoxical effect in a three-candidate voter model.Phys.Lett.A.,(1993),176:303-306.
[82]Tainaka K.,Indirect effect in cyclic voter models Phys.Lett.A.,(1995),207:53-57.
[83]Van Baalen M.,Pair approximation for different spatial geometries(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:359-387)
[84]Rand D.A.,Correlation equations and pair approximations for spatial ecologies (in McGlade J.M.,Advanced Ecological Theory:Principle and applications.Oxford Blackwell Science,1999,pp:100-142)
[85]Morris A.J.,Representing spatial interactions in simple ecological models.PhD thesis,Warwick University,1997.
[86]Hardin G.,The competitive exclusion principle.Science,(1960),131:1292-1297.
[87]Zhang D.Y.,Lin K.,The effect of competitive displacement:how robust is Hubbell's community drift model? J.Theor.Biol.(1997),188:361-367.
[88]Tilman D.,Competitive and biodiversity in spatially structured habita.Ecology (1994),75:2-16.
[89]Hutchinson G.E.,The paradox of the plankton.Am.Nat.(1961),75:137-145.
[90]Chesson P.L.,Warner R.R.,Environmental variability systems.Am.Nat.,(1981),117:923-943.
[91]Frachebourg L.,Krapivsky P.L.,Ben-Naim E.,Spatial organization in cyclic Lotka-Volterra.systems.Physical Review E.,(1996),54:6186-6200.
[92]Szabo G.,Santos M.A.,Mendes J.F.F.,Votex dynamics in a three-states model under cyclic dominace.Physical Review E.,(1999),60:3776-3780.
[93]Szab(?)G.,Szolnoki A.,Three-state cyclic voter model extended with Potts energy.Physical Review E.,(2002),65:036115.
[94]Ravasz M.,Szab(?)G.,Szolnoki A.,Spreadings of famihes in cyclic predatorprey models.Physical Review E.,(2004),70:012901.
[95]Hierro J.L.,Callaway R.M.,Allelopathy and exotic plant invasion.Plant and Soil.(2003),256:29-39.
[96]Nowak M.A.,Sigmund K.,Bacterial game dynamics,Nature,(2002),418:139-139.
[97]Hiebeler D.,Tatar R.,Cellular automata and discrete Physics(in Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997,pp:275-295)
[98]Abraham R.A.,Visualization Techniques for cellular automata(in Lui Lam,Introduction to Nonlinear Physics,Springer Verlag,1997.pp:296-307)
[99]Law R.,Dieckmann U.,Moment approximation of individual-based model (in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:252-270)
[100]Bolker B.M.,Pacala S.W.,Levin S.A.,Moment methods for ecological processes in continuous space(in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:388-411.)
[101]Dieckmann U.,Law R.,Relaxation projections and the method of moment (in Dieckmann U.,Law R.,Metz J.A.J.The Geometry of Ecological Interactions:Simplifying Spatial Complexity.Cambridge University Press,2000,pp:412-455.)
[102]McCann,K.,Hastings,A.,Harrison,S.,Wilson,W.,Population outbreaks in a discrete world.Theoret.Popul.Biol.(2000)57,97-108.
[103]Bolker B.,Pacala S.W.,Using moment equation to understand stochasticity driven spatial pattern formation in ecological systems.Theor.Popul.Biol.(1997),52:179-197.
[104]Law.R.,Dieckmann U.,A dynamical system from neighborhoods in plant communities.Ecology,(2000),81:2137-2148.
[105]Law R.,Murrell D.J.,Dieckmann U.,Population growth in space and time:spatial logistic equations.Ecology,(2003),84:252-262.
[106]Murrell D.J.,Dieckmann U.,Law.R.,On the moments closures for population dynamics in continuous space.J.Thepr.Biol.(2004),229:421-432.
[107]Van Kampen N.G.,Stochastic processes in Physics and Chemistry.Amsterdam Netherlands,1992.
[108]Pielou,E.C.A single mechanism to account for regular,random and aggregated populations.J.Ecol.(1960)48:575-584.
[109]Pielou,E.C.Segregation and symmetry in two-species population as studied by nearest-neighbor relationships.J.Ecol.(1961)49:255-269.
[110]Stoyan,D.and Penttinen.A.,Recent Applications of Point Process Methods in Forestry Statistics.Statistical Science(2000),15:61-78
[111]Legendre,P.and M.J.Fortin.Spatial pattern and ecological analysis.Vegetatio (1989)80:107-138.
[112]Baddeley A.,Gill R.D.,Kaplan-meier estimators of distance distributions for spatial point processes.Annl.Statistics.,(1997)25:263-292.
[113]Wiegand T.,Moloney K.A.,Rings,circles,and null-models for point pattern analysis in ecology.Oikos,(2004)104:209-229.
[114]Barbini P.,Cevenini G.E.,and Massai M.R.Nearest-neighbor analysis of spatial point patterns:application to biomedical image interpretation,Computers and Biomedical Research(1996)29:482-493.
[115]Bliss,C.I.Fisher,R.A..Fitting the Negative Binomial Distribution to Biological Data.Biometrics(1953)9:176-200.
[116]He,F.and K.J.Gaston.Occupancy-abundance relationships and sampling scales.Ecography(2000)23:503-511.
[117]Dacey F.M.,1964.Modified Poission probability law for point pattern in more regular than random.Annals of Assoc,of Ameri.Geogrs.(1964)54:559-565.
[118]He,F.and K.J.Gaston.Estimating species abundance from occurrence.American Naturalist.(2000)156:553-559.
[119]Archibald E.E.A.Plant populations I.A new application of Neyman's contagious distribution.Annals of Botony.(1948)12:221-235.
[120]Thomas M.,A generalization of Poission's binomial limit for use in ecology.Biometrika,(1949)36:18-25.
[121]Boswell,M.T.,and Patil G.P.(1970)Chance mechanisms generating the negative binomial distributions.Pages 3-22 in G.P.Patil,ed.Random counts in models and structures.Pennsylvania State University Press,University Park.
[122]Quenouille M.H.,A relation between the logarithmic,Poission,and Negative Binomial series.Biometrics,(1949)5:162-164.
[123]Clark,P.J.and Evans F.C.Distance to nearest neighbor as a measure of spatial relationships in populations in populations.Ecology(1954)35:445-453.
[124]Green R.H.Measurement of non-randomness in spatial distributions.Research in Population Ecology.(1966)8:l-7.
[125]Thompson,H.R.Distribution of distance to n-th nearest neighbor in a population of randomly distributed individuals.Ecology(1956)37:391-394
[126]Eberhardt,L.L.Some developments in 'distance sampling'.Biometrics(1967)23:207-216.
[127]Ripley,B.D.The second-order analysis of stationary point processes,Journal of Applied Probability(1976)13,255-266.
[128]Ripley,B.D.Modelling spatial patterns,Journal of the Royal Statistical Society,Series B(1977)39,172-192.
[129]Ripley,B.D.Tests of 'randomness' for spatial point patterns,Journal of the Royal Statistical Society,Series B(1979)41,368-374.
[130]Ripley,B.D.(1981).Spatial Statistics,Wiley,New York.
[131]Engeman,R.M.,Sugihara R.T.,Pank L.F.,Dusenberry W.E.A comparison of plotless density estimators using Monte CArlo simulation.Ecology(1994)75,1769-1779.
[132]Picard N,Kouyate,A.M,Dessard,H.Tree density estimations using a distance method in Mali Savanna.For.Sci.(2005)31:7-18
[133]Diggle,P.J.Robust density estimation using distance methods.Biometrika (1975)62:39-48.
[134]Persson,O.Distance methods:The use of distance measurements in the estimation of seedling density and open space frequency.Skogshogskolan(1964)15:68 pp
[135]Byth, K.On robust distance-based intensity estimators.Biometrics(1982)38:127-135
[136]Kleinn,C,Vilcko F.Design-unbiased estimation for point-totree distance sampling.Can J For Res(2006)36:1407-1414
[137]Morisita,M.A new method for the estimation of density by the spacing method applicable to non-randomly distributed populations.Physiol Ecol(1957)7:134-144.
[138]Magnussen,S.,Kleinn,C.Picard N.Two new density estimators for distance sampling.Eur J Forest Res(2008)127:213-224.