Survival of the Fittest

Darwin's theory was based on the concept of the survival of the fittest. There are many species that mate for life. In this case does each male or female look for the fittest or the most appropriate? When there is a battle for mating among some species the male exhausts himself during the rutting season and often dies during the next winter. Does this mean that he is the fittest? He may be the fittest physically but is he the fittest in terms of survival instincts?