Biological Invasion Model On A Lattice

Penna model proposed by Penna TJP in1995using bit-string is about biological evolution of a single species. This model considers age, disease, breed and mutation of individual. The model didn’t base on some region, but used a factor of Verhulst to show the effect of environment. Danuta Makowiee used the model of Monte Carlo in grid of L x L for the first time. In this model, confirm next status of a lattice by its Von Neumann neighbor, and the rule of death by local environment replaces Verhulst of Penna model. It solved the problems of survival and evolution of the whole of a species effectively. However, it is only a model of a single species and can’t solve problem of simultaneous update.Based on Penna model with local rule and simultaneous update mechanism of cellular automata was defined cellular automata model of two species on a grid. This paper introduced grass in above-mentioned model and considered grass as a limited resource. Use Moore neighbor to control distribution of offspring of grass, which forms a model of three species. Advanced animals had a priority over low-grade animals, with which we control predation, movement and breed of individuals. Then, corresponding descriptions are more close to reality.The paper used computer to imitate biologic evolution of wolf, sheep and grass. For a given N value (a given region), there were three different imitation results of the number of each species by selecting different initial individual quantity:three species coexist (wolf, sheep, grass); two species coexist (sheep, grass); a single species survive (grass). We select a group of parameters that can get the first result. In these conditions, we discussed biological invasion and invasive species was at the bottom of food-chain. We gave the invasive species the same breed mechanism as grass. In this system, we defined competitive mechanism because there are two kinds of plant to compete soil resource. Through changing the competitive power of invasive species, we got three different results:invade successfully; coexist with local species; invade unsuccessfully, then analyzed these results.