How sequence of information polymer and reproduction (growth and division) of vesicles were linked is a fundamental question about the emergence of the living systems. To address the origin of this linkage, we have investigated the relationship between amino acid sequence and vesicle growth using short peptides and fatty acid vesicles. The growth of fatty acid vesicles was measured by a dynamic light scattering technique when fatty acid molecules and peptides were fed into a fatty acid vesicle suspension. The obtained relationship between amino acid sequences of peptides and vesicle growth rate (fitness) was visualized as the fitness landscape. The growth rate of fatty acid vesicles depends on the amino acid sequence, and specific amino acid sequences significantly promote vesicle growth. Furthermore, when amino acids in a peptide are replaced by other amino acids, the change in fitness depends on the remaining amino acid sequence, so-called epistasis, which guarantees the diversity of peptide-fatty acid vesicle systems (protocell). The observed linkage between amino acid sequence and vesicle growth indicates that the peptide-fatty acid vesicle systems can lead to primitive evolution. Finally, we demonstrate that the promotion of vesicle growth by peptides is driven by the modulation of the chemical potential of fatty acid molecules. Thus, the vesicle growth promoted by peptides is a spontaneous process that is thermodynamically driven.