Types of mutations in coevolution
(1) A mutation in just one species produces a benefit for that species and maybe also for other species -- there is no need for a corresponding mutation in another species (and in parasitism and predation a corresponding mutation in other species might actually counteract the first mutation's benefit). This type of mutation is common in parasite/host and predator/prey relationships. Because a benefit is produced, such a mutation is likely to spread rapidly, and such a rapid spread will increase the chances that this mutation will meet a corresponding mutation in another kind of organism. Sometimes this single mutation may never meet a corresponding mutation in another kind of organism -- that situation is sometimes not considered to be coevolution because the prefix "co" means "mutual," "together," or "reciprocal," implying that there are corresponding adaptations in other kinds of organisms. However, if the prefix "co" is interpreted as meaning "together" with other living things, then even a one-sided adaptation to other living things can be considered to be coevolution. Whether or not a mutation is coevolutionary should not depend on whether or not there is ever a corresponding mutation in another type of organism, hence IMO all mutations that are adaptations to other organisms should be considered to be coevolutionary. A one-sided adaptation could be difficult if the adaptation is very specific and complex, e.g., some kinds of parasitisms and orchids' mimicry of female wasps' sex pheromones. I propose calling these one-sided adaptations "unilateral" coevolutionary adaptations or mutations.
(2) Corresponding mutations are required in both kinds of organisms to produce a benefit. Isolated mutations of this type (i.e., mutations not accompanied by the corresponding mutation in the other organism at the same time and place) will not tend to spread rapidly because there is no benefit and hence will have a low tendency to meet a needed corresponding mutation, and this is obviously a big problem for coevolution. This type of mutation can be further subdivided into mutations that are neutral when isolated and mutations that are fatal or harmful when isolated -- the latter type of mutation is obviously even less likely to survive and spread. This need for corresponding mutations can exist even where coevolution can be gradual. An additional problem with this kind of mutation is that the two kinds of organisms might only be able to interact in large numbers, requiring large numbers of both kinds of organisms to suddenly appear at the same time and place. I propose calling these two-sided adaptations "bilateral" coevolutionary adaptations or mutations.