The inquiry about the impact of alpha trees reminded me of a cute little diagram truncation by Briffa, Jones et al.
The most technical presentation of RCS at Tornetrask is in Briffa et al. [NATO 1996] (reference below). The theory of RCS standardization is that "low-frequency signals" are better preserved by fitting one negative exponential to all the ring width data, rather than trying to fit it to each individual tree. This is not per se a crazy idea, as fitting each individual tree (as is done in Jacoby and Graybill "conservative" standardization) may over-adjust periods in which the majority of trees are low-growth. This is more of an issue with short-lived trees than with bristlecones, since the juvenile growth spurt, if any, takes up a greater proportion of the tree’s life. (Merely framing the question in this way poses all kinds of obvious questions not squarely addressed in dendrochronological statistics.)
Anyway here is an emulation of the fit diagram as presented by Briffa et al. They calculated average ring widths in 5-year intervals, made a step diagram and fitted a negative exponential plus a constant. My emulation uses the 65-core subset, rather than the 435-core dataset used by Briffa (since the 435-core set is unarchived) and there are some differences in detail between the NATO 1996 diagram and the emulation: for example, the NATO 1996 diagram has values above the curve fit between ages 400 and 500, presumably reflecting contributions from other cores. Anyway the fit doesn’t look too bad and it seems to support the negative exponential model.
Figure 1. Emulation of Briffa et al  Figure 3 second panel, using 65-core swed019w dataset.
I didn’t mention that Briffa only showed the first 600 years. Here’s what you get if you plot all the data.
Figure 2. Emulation of Briffa et al  Figure 3 second panel, using 65-core swed019w dataset, with all information plotted.
The impact of alpha trees is pretty clear in the second diagram. The average ring width for trees over 600 years in age is pretty much equal to that of juvenile trees – this information is suppressed in the diagram. This poses a few questions:
1. as Larry asked, what is the impact of "alpha" trees on the specific chronology calculation?
2. what do "alpha trees" mean for the enterprise of negative exponential modeling? what is the actual process here viewed statistically? To get a curve looking like the observed curve, it sems to me that you have to consider a possible population where "weaker" trees die younger and alpha trees stay vigorous. The modeling gets quite hard quite fast.
3. if trees tend to germinate in warm periods (as seems likely), is the adjustment for juvenile growth taking out a contribution from prior warmth?
4. these rule-of-thumb adjustments may be fine if your age distribution remains unchanged, but what happens if the age distribution changes? This is far from an academic question, as illustrated by the average age at Tornetrask, in which the modern average age is unprecedented. The age distribution is obviously changing, so rule-of-thumb age adjustments may not be valid.
REFERENCE: Briffa, K.R., P.D. Jones, F.H. Schweingruber, S. Karlen and S.G. Shiyatov, 1996, Tree-ring variables as proxy-climate indicators: Problems with low-frequency signals, in P.D. Jones, R.S. Bradley and J. Jouzel, Climatic Variations and Forcing Mechanisms of the Last 2000 Years. Proceedings of the NATO Advanced Research Workshop. Springer 1996..