We propose a variation of the Guiol–Machado–Schinazi (GMS) model of evolution of species. In our version, as in the GMS model, at each birth, the new species in the system is labeled with a random fitness, but in our variation, to each extinction event is associated a random threshold and all species with fitness below the threshold are removed from the system. We present necessary and suficient criteria for the recurrence and transience of the empty configuration of species; we show the existence of a long time limit distribution of species in the system, and present necessary and suficient criteria for the finiteness of the number of species in that distribution. There is a remarkable symmetry between both sets of criteria. We also highlight fundamental differences between ours and the GMS model, putting them in different universality classes .

中文翻译：

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具有基于事件的灭绝的演化模型

我们提出了物种进化的Guiol-Machado-Schinazi（GMS）模型的变体。在我们的版本中，就像在GMS模型中一样，在每个出生时，系统中的新物种都带有随机适应度标记，但是在我们的变体中，每个灭绝事件都与一个随机阈值相关，并且所有适应度低于该阈值的物种都从系统中删除。我们提出了物种空配置的复发和短暂性的必要和充分的标准；我们显示了系统中存在一个长时限分布的物种，并提出了该分布中物种数量有限性的必要和充分标准。两组标准之间存在明显的对称性。我们还强调了我们与GMS模型之间的根本差异，将它们置于不同的通用性类别中。