This is a tough question to answer......depends on the strain, stocked or wild fish and what stream they spawn in and what part of the great lakes.
This could turn out to be a novel.
I have caught spawning fish in Lake O tribs in late September and early October and as late as mid May just jacking around for bass and stuff. I find that most of the spawning takes place in January and another wave in late February and early March after the melt but that can vary from season to season and from the body of water they return to. I find that the fish in Lake E are early spawners compared to fish from Huron and G-Bay tribs that are mainly spring spawners in the March to May area.
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"God Put me on Earth to Fish"