Simple Biological Aging On A Lattice Based On Noisy Penna Model

In the domain of biological mathematics, there are many means to study biological aging. P.Biecek and S.Cebrat proposed the noisy Penna model in January 2006. Compared with the Penna model, there is no declared threshold T by introducing the noise, and there are both inside and outside pressure for different individuals to survive at different time.There are four chapters in this paper. In chapter one, the current situation of models of biological mathematics and bio-simulation is introduced briefly, such as the generation, development and problems. We also gave the conceptions of the neighbor and boundary conditions on a lattice which used by the core part of this paper.In chapter two, we gave the introduction of the Penna model with the age structure. Besides we gave the concrete application of the rules and some results in asexual reproduction, sexual reproduction and on a lattice.The details of the main prototype model were told in chapter three, including the noisy Penna model and its development and application.The noisy Penna model on a lattice was built in chapter four which describes the biological aging and references to mathematical models of biological. Through the simulation, we come to the conclusion that the simulations and empirical results of the number and the distribution of fitness are in good agreement in an equilibrium state. The proportion of individuals of all ages increased with age exponentially. When the basic environment is smaller on a lattice it mainly depends on the diffusion whether the individual will die, whereas it's up to the noise. The mortality of all ages except for the maximum age is affected by the age weakly from the simulations given. At the same time if there is multi-block but small proportion of terrain whose basic environment can lead the population to extinct, the fate of population extinction can be delayed on the sites that are adjacent to the good sites, but the population still goes towards the extinction finally. If the local terrain changes violently, the population changes significantly, whereas the population doesn't change significantly. And we also discussed the influence of the diffusion and the minimum age at reproduction on the spatial distribution of biological evolution, and got the corresponding conclusions.