Compatability relies on whether the Pokemon has the same or different original trainer and whether they are the same Pokemon or of a different species.
They will be more compatible with each other if they are the same species and if they are from different original trainers.
- If the Pokemon meet both of these requirements, They will get along very well, making the chance of getting an egg, 69.3%.
- If the Pokemon meet one of the requirements but not the other, They will get along, making the chance to recieve and egg to be 49.5%
- If they meet neither, the two will not get along very well, making the chance to recieve an egg 19.8%.
- If they are different egg groups, same gender, or one of them is from an undiscovered egg group, they will prefer to play with other Pokemon, and there will be no chance of recieving an egg.
So, the compatability is not affected by nature or characteristics, but instead from the Pokemons original trainer and if they are of the same species.