I don't think the evolutionary theory of Khaldun is relevant to sociology. Its mainly a biological concept. Ibni-Khaldun's most lasting contribution to the field of sociology was the concept of social solidarity. He termed it as Assabiyah and later Emile Durkheim also built on the same concept to explain what pushed people to comit suicide though durkhiem called a lack of this "social solidarity" as Anomie.

Here are a few more points on Asabiyah as explained by Khaldun. It is the emotions of similarity (bonds) which keeps the people of a group united to have common actions. Gives rise to tribes and clans. Asabiyah causes fall and rise of civilizations. All civilizations have a certain sense of Asabiyah from nomads to big empires. Asabiyah is the sense of unity, group consciousness, cohesion and shared purpose.

RURAL & URBAN SOLIDARITY:
RURAL (Bedouins): Strong Asabiyah, Blood relations and purity of lineage important, Brave and generous, live in deserts or mountains (in wild), have very basic needs, hard worker, rely on nature for livelihoods.
URBAN (Haziri): Less Asabiyah, Luxurious lives, more culturally inclined, always busy in race for money and power, less time for families, live in towns and cities.

Another lasting contribution of Ibn-i-khaldun was actually a practical application of the concept of assabiyah and it was his theories on social change. He believed that the rise and fall of civilizations are natural and cyclical and are directly linked to levels of Assabiyah. Other factors like religious, economical, political are responsible as well. Societies move from simple to complex. Corruption and hunger for wealth and power weaken asabiyah while religion and good leadership improve asabiyah.

Social change stages/cycle: evolution(40 years), development(40 years), decline(40 years). He believed that a total life cycle of a civilzation is 120 years but the time span is flexible.

A simple explanation of the stages: first there are smaller tribes with very strong assabiyah (the bedouins). They win some clan wars and start to integrate and soon cities form with central administration. City-dwellers (the haziris) have considerably less assabiyah and hence corruption and greed grow. They become disorganised. Slowly this civilization(A) that has risen to this point starts to crumble and a new group of tribes or a younger civilzation (B) comes (with stronger assabiyah) and defeats the original civilzation (A). In time the civilization (B) will also become lazy and weak and will fall as well. Hence the cycle continues.

Countless examples from history have backed up this theory like the mughals, the ottomons, even the romans.