一类生物演化模型的统计特性

在给出的生态系列演化模型中 ,首先 ,每次只让适应度最小的物种发生变异 ,直到其适应度比原来高为止 ,对此我们给出了每一次变异所需时间的数学期望 ,并证明了最小适应度序列是几乎必然收敛的 ;然后 ,逐渐增加相互作用的强度 ,通过数值模拟表明 ,相互作用是生态系统多样性的根源.

Studies on Evolutionary Behaviors of Some Biological Systems

Several models of biological systems are presented. Our purpose is to examine their evolutionary behaviors. In the first model, the species which has the lowest fitness will continuously mutate until its fitness becomes larger, the time takes to mutate is recorded and we call it life of system. Continue this process, we'll get a series of lives and a series of lowest fitness. It is found that the series of expectation of lowest fitness is convergent and furthermore the series of lowest fitness is almost surely convergent. Then, the interactions between species are gradually strengthened, with computer simulation, it is found that interactions are the reasons of diversities of complex systems.