Transitivity of Species Definitions
I am pretty sure you cannot jump from an oak tree to an ape with whatever common definition of species you're using. But this is some kind of practical implication of your question.

The concept of species was already being used by Aristotle and was kept up to now although the grouping of living things into species might not be a clever thing to do. I don't think there is any non-arbitrary, logical way of making groups out of living organisms. Here is a podcast (It is in French, sorry!) that is interesting for those wanting to learn about how the concept of species evolved.

The case you describe is called Ring species. There has been lots of discussion in philosophy about the concept of species. The concept of species is unclear and if accurately defined, then in practice we don't really follow this definition to improve efficiency in how we name lineages. The term lineage has a much more rigorous meaning and is often of greater usefulness.

Ensatina eschscholtzii (a salamander; see DeVitt et al. 2011 and other articles from the same group) is a classic example of ring species.

You should definitely have a look at the post How could humans have interbred with Neanderthals if we're a different species? which discuss the concept of species. Some other sources of info include:


Species problem wikipedia
Reduction of species
The evolutionist view of the species concept: ESU
Stanford dictionary