Re: abiotic oil: As a high school math (sub) teacher it occurs to me that "adding" a constant function to a logistics function would yield a peak not all that far off from the peak of  the logistics function alone.  From that I imagine that a constant abiotic "seep" would not affect the fact of a peak, nor its timing.  This would be even more true for a peak function that looks like an upside-down "v".  Thus the abiotic argument is reduced, isn't it, to the notion that there may be oil somewhere else, anywhere else, and we ought to drill everywhere... ?
I'm not sure the analogy to various mathematical functions is entirely valid when it comes to grappling with the abiotic oil belief, which it is important to realize encompasses several different notions, depending on who the particular abiotic proponent happens to be and how technically sophisticated he/she is.  

To play pro-abiotic devil's advocate for a moment: to believe that abiotic oil is replenishing existing oil fields does not automatically require a belief that the abiotic oil is oozing to the surface everywhere on the face of the earth or doing so at the same rate. The fact that the surface of the earth is not swimming in abiotic oil is not necessarily proof that the abiotic theory is wrong. Some parts of the global may have no abiotic movement whatsoever, while other parts may have substantial amounts.

To use another analogy: let us say that we have a soda vending machine. There is a reserve of perhaps a hundred cans of soda stacked up inside the machine. However, we don't have cans of soda continuously falling out of the machine onto the floor. A can of soda only becomes available after the can of soda ahead of it has been withdrawn by a person using the machine. In the same vein, I suppose  it could be argued (not necessarily correctly) that the abiotic oil 'way down there' and the shallow oil in a known reserve are in a kind of static equilibrium, and that only when oil is withdrawn from the reserve is that equilibrium disturbed, thus causing the abiotic oil to migrate into the reserve. Fanciful? Perhaps, but from a purely logical point of view, it is a valid argument.

The other aspect of abiotic belief is that due to the orthodoxy of conventional petroleum geology it is presumed that oil can only be found in certain geologic formations and not others. Thus, they claim,  oil discovery is a self-fulfilling prophecy: you find oil where you do because that's where you were looking for it in the first place. The abiotic people are always saying that if we only looked in the right places, we'd find abiotic oil. While that sounds reasonable on the face of it, the counter argument (and I'm reaching here, as I'm an engineer and not a geologist) is that regardless of the origin of the oil, you only find oil where it is likely to be trapped. Oil, be it of fossil or abiotic origin, will tend to very slowly migrate to the surface, a process that can take eons. The trouble is that there are a variety of microorganisms that are capable of feeding on the various components of petroleum, so if the oil did make it to the surface, it wouldn't last long, at least on a geologic time frame.

That is how I see this whole argument shaping up. The important thing to remember is that not everybody advancing the abiotic theory has a technical backround  and that many of the arguments are of a more ideologic nature.

I think the abiotic oil advocates have not proved their case. Sorry I don't have a link but I read a paper a few months back that tried to put the abiotic oil theories to rest.

The points I remember:

At large depths the pressure and temperature would not lead to the formation of oil.

Isotopic analysis of oil indicates biological origin.

Holes drilled in atypical rock formations have not produced oil.

In a few cases where oil appeared in unusual cases it could be explained as leaking sideways from known fields.