This has been (and continues to be) a heavy snow year in Alaska, so some of my comments may be a bit delayed - things will take a lot longer to melt out this Spring. Normally in/around Anchorage we get the first big mosquito hatches in June. Once they die off as things dry out, the big black horse flies make their appearance, usually around late July through August. Both respond well to high deet repellents but be sure to wash the palms of your hands after using it. As a fly fisher I can confirm high levels of deet will damage the plastic coating on fly lines. I've heard it's bad on the rubber armor on binoculars, but so far my older armored bins haven't been affected.
But bottom line: Expect hungry mosquitoes after the initial melt-off as the temps get warm (50s to 60s), then flies as the summer progresses. It's not that the mosquitoes disappear, the flies are more noticeable.