Protein sites with more coevolutionary connections tend to evolve slower, while more variable protein families acquire higher coevolutionary connections.

: Amino acid exchanges within proteins sometimes compensate for one another and could therefore be co-evolved. It is essential to investigate the intricate relationship between the extent of coevolution and the evolutionary variability exerted at individual protein sites, as well as the whole protein. : In this study, we have used a reliable set of coevolutionary connections (sites within 10Å spatial distance) and investigated their correlation with the evolutionary diversity within the respective protein sites. : Based on our observations, we propose an interesting hypothesis that higher numbers of coevolutionary connections are associated with lesser evolutionary variable protein sites, while higher numbers of the coevolutionary connections can be observed for a protein family that has higher evolutionary variability. Our findings also indicate that highly coevolved sites located in a solvent accessible state tend to be less evolutionary variable. This relationship reverts at the whole protein level where cytoplasmic and extracellular proteins show moderately higher anti-correlation between the number of coevolutionary connections and the average evolutionary conservation of the whole protein. : Observations and hypothesis presented in this study provide intriguing insights towards understanding the critical relationship between coevolutionary and evolutionary changes observed within proteins. Our observations encourage further investigation to find out the reasons behind subtle variations in the relationship between coevolutionary connectivity and evolutionary diversity for proteins located at various cellular localizations and/or involved in different molecular-biological functions.