Poisonous Weeds’ Invasion Process And Space Simulation Based On The Birth And Death Process

In this paper, we have mainly discussed the changing relationship of population quantity including migration effects, the model of poisonous weed invaded forage grass between two patches, and the model of poisonous weed invading forage grass among several patches and space simulation.Firstly, we get the condition of simple birth and death process population’s extinction through the birth and death process model of single population based on Markov process theory. And then we built the birth and death model with the migration effects, computed the transition probability of status, therefore we calculated the average number of two patches, and analyzed the changing trend of two populations with migration effects. Finally, we tested and verified the result of theoretical derivation by computer simulating in Matlab.Secondly, we built the model of poisonous weed invading forage grass between two patches based on the theory of birth and death process combining the ecological setting theory. We get the average number of poisonous weed by solving the transition probability indirectly, and then we get the variance by calculating the secondary moment, and get condition of poisonous weed successfully invading the ambient patches. According to the theoretical deviation results, we set the parameters, and then found that the result of simulation is same as the theoretical derivation when the parameters satisfied poisonous weed invading successfully.Finally, since the interactions of population among several patches in ecosystem, so we built the model of poisonous weed invading forage grass among several patches by applying the birth and death model to the space patches. Then we derived the relationship between the poisonous weed invading and ambient patches of the forage grass with limited number. Therefore, we get the condition of poisonous weed successfully invading the ambient patches. At last, we simulated the changing process of the poisonous weed invading the forage grass by computer. Through the hypothesis test, we derived conclusion that the invasion can accelerate the distribution pattern of population aggregation.