The setting is as follow. In a planet like earth, one day, 10% of the population suddenly becomes immortal. The "immortals" are not physiologically different from the "mortals" and initially it is hard to differentiate the mortals from Immortals. The only way to differentiate in the early stage is to kill a person. If he revives, he's an "immortal".
Now, this power of immortality is transferable. Through copulation. The rules are as follows:
If an "immortal" copulates with a "mortal", the "mortal" becomes "immortal" and vice-versa.
If both parties are "mortal"/"immortal" the status effect does not change.
In a scenario where more than two parties are involved (in the act of copulation) status effect does not change.
If a "mortal" and an "immortal" has a child, the child has 50% probability to be "immortal". If the child turns out to be "immortal", the parent with immortality loses his status effect. The status effect loss happens AFTER the baby is born (i.e. one of the parent is still "immortal" during pregnancy).
If two "immortal" have a child, the child will also be "immortal". Parents would retain their status effect.
"Immortals" age normally upto age 25. After that they only age once the status effect is removed.
A "mortal" above the age 25 stops ageing whenever they recieve the status effect.
Am "immortal" loses his/her immortality, if he/she does not copulate with another "immortal" in 50 years.
At the beginning, no one is aware of their status effect. They may come to know later (once they revive after death or once they realise they are not getting old). Also, the rules about the transfer of immortality is not known to the population a priori (though someone down the line might figure it out).
Given the rules, constrains and the transferable nature of immortality, how would the population of the "immortals" evolve over the years?
The "immortals" could start selective "breeding" to increase the population of "immortals" once ALL the immortality transfer rules have been discovered. What is the timeframe for this to happen?
Assume humanity (i.e. most people won't be willing to burn their babies to check if they are "immortal").
Edit: added rule 8 (was previously missed).