Rucker Iterations/Rucker Mania   Robert Leverett   Nov 10, 2004 06:14 PST  John and John:    Last night I updated the MTSF Rucker index through 13 iterations. I guess curiosity got the better of me. The iteration values follow.     134.45     132.27     130.34     127.76     127.59     126.93     126.09     125.33     124.13     122.97     121.97     121.91     120.99     120.32     The 14th iteration drops below 120, so I stopped.    It would be super sweet if we could get the 4th order index up to 130, but I seriously doubt we can. I do think we can extend the 120s out to maybe 16 or 17, but probably not much beyond.    The bread and butter species for us will continue to be white pine, white ash, sugar maple, red oak, black cherry, red maple, and maybe basswood. Beech would be, but too much of it has died and the distribution of bigtooth aspen, a solid performer through 10 iterations, is on the low side. Most of the performers come from a single small stand.     Even allowing for the death of some of the current champions, it is unlikley that Mohawk's 1st order index will drop below 133 over the next few years. But are there opportunities for it to rise above its present level? Well, with continued growth from the pines, ashes, maples, and oaks, it might conceivably climb back to 134.7 or 134.8, but I just can't see 135, now or in the future.     What are the opportunites? It is conceivable we could eventually get a 130-foot black cherry. That would replace the aging beech champ, but the beech will be gone, so gaining the cherry would only be a holding action. A few hemlocks could climb up into the low 130s. We might gain one or two tenths of a point.     Overall, I believe we are at the pinnacle of height development for the Mohawk forests and we get to experience them at their height zenith. Rather exciting when you think about it. Dale:     How far out the iteration path do you feel comfortable going with the Cook Forest? I don't even want to ask Will how far out he can hold up the low 150s. It's not fair, darn it. It's just not fair. Bob Robert T. Leverett Cofounder, Eastern Native Tree Society RE: Rucker Iterations/Rucker Mania   Will Blozan   Nov 10, 2004 15:58 PST  Bob, I will update a new Smokies RI soon, but an RI of 150 will likely hold for many hundreds, if not thousands of reiterations. All told, Mike Davie, Jess Riddle and I have only looked at a mere 5% or less of the Park, and much of the new stuff will be in the VAST acreages of second-growth that is now maturing (at a young age) into super forests that defy description. Sorry BVP, but HARDWOODS RULE, TOO!!! Will RE: Rucker Mania   Dale J. Luthringer   Nov 10, 2004 17:10 PST  Bob, You MUST have a lot of time on your hands... 14 iterations?!?! I'd be willing to wager a case of BVP's favorite beer that Cook should be able get 130 on the 5th order RI. Top species would most likely be ranked in the following order (high to low): White pine, hemlock, black cherry, tuliptree, white ash, cucumbertree, red maple, white oak, N. red oak, Am. beech Dale RE: Rucker Mania   Gary A. Beluzo   Nov 11, 2004 14:29 PST  Bob: Most impressive computing! I am wondering if there is a way to standardize the field work used to collect numbers for the Rucker Index calculations to compare different sites more fairly. My concern is that those sites that get far more effort (like MTSF by you or Zoar by Tom) will obviously do much better in RI reiterations than sites poorly visited/measured. I also wonder if there may be other "superlative" sites in the East that just haven't been identified yet. Is a different kind of sampling warranted? Perhaps the shear pride of individual dendromorphometrists at their home turf will ensure adequate "search models" for all of the maxima. The discussions about size distribution and statistical deviation have been interesting! Gary Gary A. Beluzo Professor of Environmental Science Holyoke Community College 303 Homestead Avenue Holyoke, MA 01040 RE: Rucker Mania   Edward Frank   Nov 11, 2004 19:20 PST  Bob (and John and anyone else with 2 cents to contribute), I have some questions concerning the Rucker Index Iterations. I am not trying to denigrate the usefulness of the process, just trying to understand. I have re-read everything published on the discussion list concerning the iterations. I understand how they work mathematically, my questions concern interpreting what they mean. Bob Leverett wrote, (March 09, 2004): "The Rucker index process when applied iteratively reveals the role of each species in the index. Fast growth pioneer species that form stands tend to play a significant role for many iterations. Therefore, fairly mature second growth forests can have the highest indices, especially in areas where a severe climate tends pare back the canopy. Colby has often mentioned the monotony of relatively young, tall, skinny second growth forests." So if there is a relatively even aged fast growing stand of pioneer species, they will show up for several iterations. I understand that. Why does doing an iteration, or multiple iterations of the Rucker index show this better than a simple plot of height range versus number for each individual species? I can see advantages for a series of height versus number plots, but really can't see an advantage for the multiple iterations. Bob also wrote, (March 09, 2004): "The iterative process also allows anomalies to be distinguished from the norms. There may be a statistical outlier that unduly impacts the index and promotes misleading images of a place. Successive iterations reveal the role of outliers." This harkens back to a comment I made a few days ago when I pointed out that by measuring only the tallest trees (for the first iteration of the Rucker Index) you are not really measuring the expected growth of a typical or average tree on the site, and may be getting statistical outliers from the general distribution plot. I would expect if all of the trees in a certain age range were measured they would form a generally bell shaped curve, but one that may not be symmetrical, may be skewed to a higher or lower median value, and be of varying broadness in shape depending on the species. The measurement of the tallest trees doesn't show what this distribution may be, how broad the curve would be, the median growth value, nor the skewness of the distribution. Bob's statement that multiple iterations will allow anomalies to be distinguished from the norm is what bothers me. When you do the second or successive iterations, you are eliminating the highest values from the previous iterations. If there was an anomalous high value, i.e. outside the normal distribution curve, it is true it would be eliminated. But at the same time you are eliminating the high values of less common, or less measured species from the equation, even though they may well be part of the normal height/frequency distribution for the species. You are as the old saying goes "throwing the baby out with the bath water." In these successive iterations, if you have managed to eliminate some anomalous heights, you are then comparing a mixture of the top end of some species, with the second tier of another species, and perhaps lower or anomalous values not yet filtered by the process. Do you want to filter out the contributions of the less common species at the site, and if so why? What I see the multiple iterations doing is demonstrating you have a lot of big trees and have done a lot of measuring to get a lot of height values. Bob Leverett said, (March 09, 2004): "In the big picture, we utilize the multiple iteration process to sharpen our awareness of the role that each species plays in a site. Stand-oriented species like white pine that form dense clusters often provide many trees of roughly the same height, so the role of those species is fairly uniform through many iterations. A disturbance species like bigtooth aspen is much more thinly represented in MTSF, but widely distributed. It has an impact over a large percentage of the Mohawk forest." Certainly stand oriented species will be consistent over a number of iterations and those that have grown from widely dispersed disturbances of varying ages will pop in and out of the iterations. Isn't that pretty self evident? In what way do the multiple iterations clarify this process? I am not a forest ecologist so perhaps I am missing something here, I don't know. John Eichholz wrote, (March 8, 2004): "It is a running question how the Rucker index values  would sort out if you actually used all the trees on your site to make up sets of ten. It would be some kind of bell curve I imagine." I would think if the forest was a mixed forest of both young and old stands the distribution not forma bell curve but you would get a downward trending concave line asymptotic to 0 as the number of trees in each size category increased as the heights decreased. If it were an open floor of a mature forest with little regrowth, you would have the same pattern but it would have a sharp break at the height of any secondary canopy. As I said before I am not a statistician, but have had some statistics courses, and I really want to understand what you are thinking. Ed Frank RE: Rucker Mania   John Eichholz   Nov 12, 2004 06:46 PST  Ed, et.al.: Let's see if we can make some more progress on this thorny issue. First, I would like to clarify my understanding of some of these issues.     If there was an anomalous high value, i.e. outside the normal distribution curve, it is true it would be eliminated. But at the same time you are eliminating the high values of less common, or less measured species from the equation, even though they may well be part of the normal height/frequency distribution for the species. When interpreting multiple iterations, you are right, successive iterations will devalue the contributions of less common species, while weeding out the outliers of common species.     What I see the multiple iterations doing is demonstrating you have a lot  of big trees and have done a lot of measuring to get a lot of height values. I think that is a valid point, i.e. the sporting aspect of the work. Not a bad thing. Some of the more thorough stratification work, such as counting trees into height classes would be much harder than doing several iterations, though.     The measurement of the tallest trees doesn't show what  this distribution may be, how broad the curve would be,  the median growth value, nor the skewness of the distribution. To get here, a stratification approach is the only way to go. We have to get the data.     "It is a running question how the Rucker index values would sort out if you actually used all the trees on your site to make up sets of ten. It would be some kind of bell curve I imagine." I would think if the forest  was a mixed forest of both young and old stands the distribution not forma bell curve but you would get a downward trending concave line asymptotic to 0 as the number of trees in each size category increased as the heights decreased.   Yes, I misstated in that comment. Counting the rucker iterations into height classes would likely yield a bell-type curve, though. Now for some further analysis: I would not advocate "throwing out" any of the iterations. Some of what they all contribute is: 1) Species composition of the canopy. Types of trees present. Conifers or hardwoods? 2) The maximum and co-maximum heights by species. 3) The relative heights of species i.e. is oak taller than hickory or vice versa. 4) Diversity. Are more than ten species present in the set of iterations? 5) Are there lots a that height or only a few? Likely to find higher examples? (Dozens at 125+ but none over 130 suggests further searching may uncover one.) 6) There should be some correlation between size of the site and the spread of the iteration values. A small site may have a foot or two between iterations, but one would expect a very large site (Smokies) to have a very small difference between successive iterations. If this does not happen, it says something about the uniqueness of the taller trees. I'm not sure what, though. 7) I still think an index made out of the modal height by species would show more about the overall site productivity, (but not about composition.) I'm sure this is just the surface of it. John RE: Rucker Mania   Edward Frank   Nov 12, 2004 07:31 PST  John, If the Rucker index and Iterations of the index are going to continue to be the mainstay of much of the discussion of ENTS it is manifest that we be able to clearly state the methodology of doing the calculations and their meaning. The methodology of the calculations has has been well described. I have been trying to plead, cajole, and brow-beat a concise listing of what these calculations show. This type of description has not been forthcoming. There are three parts of that question: What do the calculations show? What do they tend to imply? And what don't they show? The listing you have provided is the best answer yet. I think my discussions with Colby and others last fall provided a reasonably clear explanation of the basic Rucker Index. Thank you and I hope you and everyone else continues to try and refine the usage of these indices. Ed Frank   Home