1988 Fiscal Year Final Research Report Summary
Statistical physics of lattice models applied for biological populations.
| Project/Area Number |
62540282
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | Kyushu University |
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Principal Investigator |
MATSUDA Hirotsugu Department of Biology, Faculty of Science, Kyushu University, Fukuoka 812, Japan, 理学部, 教授 (10027336)
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| Co-Investigator(Kenkyū-buntansha) |
OGITA Naofumi System Laboratory, Fujitsu Co., 1-17-25, Shin-Kamata, Oota-ku, Tokyo 144, Japan, システムラボラトリー, 顧問 (30087366)
IWASA Yoh Department of Biology, Faculty of Science, Kyushu University, Fukuoka 812, Japan, 理学部, 助手 (70176535)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Lattice model / biological population / altruism / evolution / cyclic succession / dynamic epidemiology / pair-approximation / 血縁淘汰 |
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| Research Abstract |
Lattice models describe the population processes in which the population size is locally regulated and in which the dispersal and interaction of individuals has the spatical scale much smaller than that for the distribution range of the whole population. In the models. the habitat has a lattice-structure. In which each point may be occupied by an individual. The time development of the system is assumed Markovian.
1. The condition for the evolution of altruism is analyzed when individual cannot discriminate its kins from nonkins. The reproduction occurs by invasion of offspring to an empty size. and the neighboring individual interact to modify the survivorship. The altruism can evolve only in low density if the invasion occurs only between neighbors. But not possible if the invasion occurs to any empty site.
2. As an example of asymmetric interaction. the evolution of the tree height for light competition is analyzed. In addition to the evolutionarily stable tree height, we discovered t
… More
he possibility of cyclic succession, in which dominant short trees are replaced by successively taller ones and then again invaded by very short ones.
3. Pair bond approximation is developed to analyze the lattice models. For example. the differen-tial equations are derived for the conditional probabilities of a randomly chosen neighboring site t be occupied for an occupied site(p)and that for an empty site(q). The approximation can predict the computer simulation fairly well if q is not very small.
4. The spread of infectious disease to the host population which lives on lattice-structured habit-at. The importance of the dimensionality of the lattice is discovered -- 1-dimensional lattice. In which transmission occurs only between neighbors, the disease is difficult to propagate. On the other hand, the population on a 2-dimensional lattice or the population without structure. in which each host individual has possibility to contact with all the others, the coexistence of infected and susceptives is possible. Less
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