Statistical Mechanics of Population : The Lattice Lotka-Volterra Model : Invited Papers
スポンサーリンク
概要
- 論文の詳細を見る
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.
- 理論物理学刊行会の論文
- 1992-12-25
著者
-
Matsuda Hirotsugu
Department Of Biology Faculty Of Science Kyushu University
-
Sasaki Akira
Department Of Applied Physics Tokyo Institute Of Technology
-
SATO Kazunori
Department of Biology, Faculty of Science, Kyushu University
-
OGITA Naofumi
Fujitsu Limited
関連論文
- Collagen type Iα1 gene polymorphism may be associated with the rate of bone mineral density decrease in female hemodialyzed patients
- Standardization of basic skills for laparoscopic liver surgery towards laparoscopic donor hepatectomy
- Use of automated image registration to generate mean brain SPECT image of Alzheimer's patients
- A comparison of Tc-99m HMPAO brain SPECT images of young and aged normal individuals
- A method for the quantification of benzodiazepine receptors by using ^I-iomazenil and SPECT with one scan and one blood sampling
- Geometrical Analysis of Crystallization of the Soft-Core Model in an FCC Crystal Formation
- Geometrical Analysis of Crystallization of the Soft-Core Model
- Computer Simulation for the Melting Curve Maximum Phenomenon : Two-Species Soft-Core Model
- Molecular Dynamics Studies on the Soft-Core Model
- Theoretical Prediction of Curie Temperature in (Zn, Cr)S, (Zn, Cr)Se and (Zn, Cr)Te by First Principles Calculations