ELKHART, Iowa — Mike Wilson glared dejectedly through the mist on his silver-frame glasses at the soggy field of tall, dense brush, tilting the barrel of his 12-gauge shotgun toward the gray clouds.

“All I want to do,” he said, “is see a bird at this point.”

More than two hours into this pheasant hunt, the colorful rooster that one of Mr. Wilson’s hunting partners had shot that morning was now a distant memory. Only one other pheasant had graced the skies since, and it was too far off to even try a shot.