STATISTICAL-MECHANICS OF POPULATION - THE LATTICE LOTKA-VOLTERRA MODEL
STATISTICAL-MECHANICS OF POPULATION - THE LATTICE LOTKA-VOLTERRA MODEL
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DOI：
10.1143/ptp.88.1035
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发表时间：
1992-12-01
影响因子：
--
通讯作者：
SATO, K
中科院分区：
文献类型：
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作者：
MATSUDA, H;OGITA, N;SATO, K
为了研究生物个体的遗传特性对种群特征的影响，研究了格点Lotka-Volterra模型，该模型定义为格点空间状态的马尔可夫过程。晶格位置要么是空的，要么被某种类型或物种的个体占据。该过程的转移率给出的参数表示的个人的特质，如固有的出生和死亡和迁移率的每一种类型。密度是一个变量，定义为某一地点被某种类型占据的概率。在给定的场地状态下，其最近邻场地被某种类型占用的条件概率称为该场地的环境密度。格模型的基本假设已经考虑到了个体的相互排斥。通过假设实际的出生率、死亡率和迁移率取决于环境密度，可以考虑个体之间的其他相互作用。扩展普通马尔萨斯参数的概念，我们定义马尔萨斯的动态变量指定的时间发展的密度。正的平稳密度和进化稳定性（ES）的条件，对突变类型的入侵给出的马尔萨斯。使用对近似（PA），一个最简单的解耦近似考虑到空间相关性，我们得到的固定密度的分析结果，和ES在两种类型的情况下的临界参数。假设死亡率依赖于环境密度，我们推导出利他主义进化的条件。通过与计算机仿真结果的比较，讨论了功率放大器的有效性及其改进。
To derive the consequence of heritable traits of individual organisms upon the feature of their populations, the lattice Lotka-Volterra model is studied which is defined as a Markov process of the state of the lattice space. A lattice site is either vacant or occupied by an individual of a certain type or species. Transition rates of the process are given in terms of parameters representing the trait of an individual such as intrinsic birth and death and migration rate of each type. Density is a variable defined as a probability that a site is occupied by a certain type. Under a given state of a site the conditional probability of its nearest neighbor site being occupied by a certain type is termed environs density of the site. Mutual exclusion of individuals is already taken into account by the basic assumption of the lattice model. Other interaction between individuals can be taken into account by assuming that the actual birth and death and migration rates are dependent on the environs densities. Extending the notion of ordinary Malthusian parameters, we define Malthusians as dynamical variables specifying the time development of the densities. Conditions for the positive stationary densities and for the evolutional stability (ES) against the invasion of mutant types is given in terms of Malthusians. Using the pair approximation (PA), a simplest decoupling approximation to take account of spatial correlation, we obtain analytical results for stationary densities, and critical parameters for ES in the case of two types. Assuming that the death rate is dependent on the environs density, we derive conditions for the evolution of altruism. Comparing with computer simulation, we discuss the validity of PA and its improvement.