Q:

Authorship allocation - is it common to grant equal credit to two last authors?

I am working on a project in which I have a direct supervisor in addition to the head professor of the lab. The direct supervisor only agrees to being written first or last on the article we are writing. Needless to say, my professor won't agree to be anywhere but last. He also feels that I deserve to be written in the first place. Is it possible to write both of them in the last place as co-last authors?

A:

Is it possible to write both of them in the last place as co-last authors?

No.
As expected, an author list is not a tree or a weighted graph, but a simple flat (one-dimensional) list.
There is exactly one last author. Possible solutions or mitigation of the issue include:

Alphabetical author list. This happens in some field, and is totally unheard of in some others (including chemistry and biology, which is your field, so this might not be a possibility).
Having two contact authors, or have the professor who is not last author to be the contact author. In the past I have used this as a way to “pacify” a co-author who wasn't happy with his spot on the author list. (Needless to say, it's a perversion of the system, and should only be done if the author can actually act as contact author.)
Have a statement indicating the contributions of each author (“X and Y contributed to this work equally”). Some journals require such statements, some will refuse to include them, so your mileage may vary. I doubt this will pacify your reluctant supervisor, though: people who are worried about their rank in the author list are most probably thinking about how it looks like on a publication list or CV.
Have the head professor take responsibility for the final decision (as senior professor and project instigator). That's the most sound solution, but it does not mean it's an easy one.

Good luck with your negotiation! And remember that they're not yours to handle (see my last point)!

A:

This happens in biology quite frequently.  Take a look at this example:

§ Both authors contributed equally to this work.

In this case it can be any two authors on the list.  If the notes are on the first two or last two authors, then this is often viewed as the two primary and equal collaborators. 

