Abstract

During this work, the viability of encapsulated replicators systems as a function of the vesicle size is revisited. Now, instead of considering in detail the diffusion process, the existence of a well-mixed solution inside the vesicle was assumed. Our results corroborated previous numerical estimations about the existence of a minimal size for vesicles immersed in an extremely hostile environment. In this particular case, we found analytical expressions for the critical radius as a function of the kinetics parameters for the two different families of replicators considered during the study. Furthermore, we also reported the existence of an optimal radius of the vesicle where the replicator population reaches a maximum, a value that may change slightly according to the replicator type. On the other hand, we also found that there is not a critical radius if the conditions of the external environment are not so extreme. However, even in this case, there is an optimal radius where the replicator population within the vesicle is noticeably larger than its value in the external medium. According to our results, the size of the vesicle may determine how efficiently the process of encapsulation took place on early Earth, probably one of the key steps during the process of abiogenesis.