This is a nice technical question involving some organic chemistry I do not comprehend. I'll begin with what I do know about bittering contributions from alpha acid and beta acids.
These acids are components of the hop cone and contribute to bitterness in slightly different ways. The more familiar one is probably alpha acid since most hop bags are labeled with the percent of AA. This number represents the percentage of the hop, by weight, that is composed of alpha acids.
Alpha acids do not actually contribute to bitterness until boiled in wort (or water even). At this time the acids change form, lining up to become isomerized alpha acid. The process takes time, which is why bittering hops are boiled for at least 60 minutes. iso-alpha acid is the main component of the bitter flavor in beer.
Beta acid, like alpha, almost immediately dissolves into solution when added to boiling wort. However, unlike alpha acid, it does not isomerize and passes into the finished product unchanged. In this form they do not contribute to beer's bitterness, but do lend aroma.
During storage and aging (and in fermentation) the beer is exposed, to some degree, to oxygen. Under these circumstances iso-alpha acid degrades and loses bitterness. When beta acid oxidizes it transforms into a bitter-tasting compound. On-balance the beer looses bitterness.
There is little research into how this transformation affects the flavor stability of beer. What I have read is that hop varieties with at least twice as much alpha as beta acids generally keep their bitterness over time. I know of no software or formula that takes the ratio and stability into account when calculating IBUs.
Further listening and reading: