It would obviously be a great advantage if a biological entity (e.g. an organism) could purposively evolve to exploit and environmental niche that already existed ready to receive it.
This overcomes the 'chicken or the egg?' difficulty that a new type of biological entity may not be viable until a suitable environment is provided; and a suitable environmental opportunity has no function if there is not an organism ready to exploit it.
An example is the scenario for positive-feedback, 'runaway' sexual selection imagined for the peacock's tail - which requires both the evolution of peacocks with large ornate tails, and also the evolution of a peahen preference for large ornate tails.
Conventionally, this is supposed to be a coincidence of (at least) two undirected genetic mutations - but clearly it would be a great advantage if such things were linked - if the large peacock tail evolved into an environment where peahens already had a preference for large tails.
This is merely one of innumerable situations in which natural selection becomes an extremely improbable explanation for adaptations; due to the extreme rarity of beneficial mutations and the multiplying improbabilities when multiple sequential mutations must be posited -- especially given that at any point in the proceedings the complex, cumulative process of adaptation could be destroyed by the occurrence of a much-more-highly-probable damaging mutation.
However, from the perspective of mainstream, materialistic biology; there are serious problems about any such complementarity of evolution, for example:
1. It requires teleology, or purposiveness - planning for the future (raising the question of what - or who - does the planning).
2. Teleology requires foresight - planning for the future requires valid prediction of the future -- not perfect prediction, but at least to a reasonable estimate. (raising the implication of some kind of cognitive activity; i.e. some kind of ... intelligence at word. You begin to see where this is pointing and why biologists don't want to go there?).
3. Complementarity needs some kind of mechanism of implementation - which would work on both the individual organism and the environment (something with such properties is hard to imagine, no such thing is currently known).
4. To be anything of interest to biologists, the idea of complementarity needs to be 'operationalised' so the biologists could detect it - and preferably make some use of it to enhance understanding and prediction - maybe intervention.
Complementarity in evolution would also need to solve something perceived to be a problem, for which current solutions are acknowledged to be unsatisfactory. Are there such problems?
I have argued that there are indeed several major unsolved problems in biology - of a kind for which complementarity (if it was real) would provide a solution: these problems include explaining the origins of biological life, the major transitions of evolutionary history and the origins of sexual reproduction.
In sum, complementarity implies that it originates in some kind of external and cognitive cause; and this cause would not necessarily be detectable or measurable - indeed presumably it would not be at least by current technological possibilities, or else it would probably already be known.
On the face of it, this sounds like a fatal objection - but that is not the case if the effect of the external cause can be hypothesised with sufficient specificity to make and test predictions. For example, gravity ('gravity waves') is not detectable (or, perhaps, not until the past few years), but its effects were early on hypothesised with enough precision to test.
So we could hypothesise that if there was some kind of organising principle that caused complementary evolution; then detecting certain changes in either one of the organism or the environment should be predictive of certain changes in the other. This would require observations extended over time to examine that the presumed cause precedes its presumed effect.
For example, if we could detect a novel differentiation of an organism - e.g an imaginary peacock that developed a square orange tail; then this should be preceded a peahen preference for square orange tails: the tail trait following the preference.
Or, if we can detect the emergence of a new preference among peahens for males with square orange tails - then this should be predictive of the emergence of a new kind of peacocks with such tails: the preference preceding the trait.
And in general - for complementary evolution to be happening, it should be possible to show that the environment was pre-adapted for the organism; that the organism adapted in response to an already-existing niche.
Such studies would be difficult (but then all useful new science is difficult in some way, or else it would already have been done) - but not impossible.