Mormon 4:13

And it came to pass that the Lamanites did take possession of the city Desolation, and this because their number did exceed the number of the Nephites.

The Lamanites took over the city Desolation. This happened because there were more Lamanites than Nephites.

The Lamanites took the city of Desolation because they simply outnumbered the Nephites.