Iterations:  numbers, numbers, numbers   dbhg-@comcast.net   Mar 06, 2004 11:24 PST  ENTS:    I just finished recalculating the Rucker index through 15 iterations and correcting mistakes and omissions from quick updates that I did this past week. The numbers are: 1    134.45 2    131.75 3    128.61 4    127.82 5    126.49 6    125.47 7    124.12 8    123.11 9    122.11 10   120.99 11   119.61 12   118.72 13   118.14 14   117.10 15   116.57    Based on what I know, I believe the index would hold to 110 by the 100th iteration. Interestingly the big performers for Mohawk remain throughout the reiterations: white pine, white ash, sugar maple, northern red oak, hemlock, and red maple. At one time American beech would have remained a big performer indefinitely. Bob RE: numbers, numbers, numbers   Gary A. Beluzo   Mar 06, 2004 15:46 PST  Greetings ENTS, For the uninitiated, what is the significance of 25, 50, 75, or 103 iterations of the Rucker Index? I am wondering where the inflection points might be (if they are conspicuous) and would they be different for each site, or might there be some interesting convergences? I would like to see a discussion (speculation?) as to the real value of the Rucker Index beyond the tallest tree species? Are there reasons for using 10 species (other than the number of digits we have on our hands and feet) rather than say 15 or 20? Gary Gary A. Beluzo Professor of Environmental Science Holyoke Community College 303 Homestead Avenue Holyoke, MA 01040 Re: numbers, numbers, numbers   Colby Rucker   Mar 06, 2004 17:02 PST  Gary, Ed Frank and I have had some good discussions regarding the index. The first iteration is a measure of both maximum height potential and the diversity of the dominant species. Ten species is high enough to offset the high numbers associated with the emergent giants, and low enough so that few sites are pressed into averaging numbers from interface species that are much smaller than the shorter species on a site with greater dominant diversity.   Higher numbers in succeeding iterations are correlated to large acreage and second growth monotony. Yes, ten is better than eleven because we just move the decimal point, all due to those little fingers. Colby RE: numbers, numbers, numbers   Robert Leverett   Mar 08, 2004 07:46 PST  John:    I'll give some serious thought to your questions and answer in a few days. I still owe Colby some comments on the role of successive iterations. Regardless, we're making progress toward figuring out what use we want to put the Rucker index and successive iterations of it. I've sent you a spreadsheet off list that may further open avenues of investigation. BTW, did you see the e-mail about the new yellow birch champ that John Knuer and I found yesterday? We actually broke the old record twice. Bob RE: numbers, numbers, numbers   Dale J. Luthringer   Mar 08, 2004 10:29 PST  Bob, As per your 15 RI iterations, MTSF definitely has some nice depth for tall trees in the Northeast. 120 for the 1st 10 is very nice. It also shows the immense amount of work you and others have gone to, to be able to achieve these results. It looks like I'll have to update my Cook Forest RI iterations next. They're definitely due for an update/upgrade. Dale Iterations   Ed Frank   Mar 08, 2004 19:26 PST  Bob, others, I have been reading discussions for the past year, and longer from the archives, about iterations you are running to project the potential tree height for a specific locality. What I want to ask, for the edification of those on this list, myself, and people who might visit the website... What are you talking about? It is a fairly straight forward process calculating the Rucker index, the average height of the ten tallest tree species. What is an iteration and how do you calculate it? Where do the numbers come from? How do you do ten or twenty iterations? How is this result used to project tree height potential in an area? Keep in mind that we are all not Ted Kazinski's, so keep it simple. Ed RE: Iterations   John Eichholz   Mar 08, 2004 20:16 PST  Ed: A Rucker Index for a site, as it was described to me is the average height of the ten tallest specimens of the ten tallest species of trees on a site. That is one tree for each species. The site can be as large or small as you define it to be. An iteration, is a repetition of this process. I would simply say that you have to use different trees for each iteration. Your best ten trees are your first iteration, your second best ten trees is your second iteration, and so on. You have to actually find all those trees in order to have all those iterations. It gets hard to keep finding those 130 foot oaks or whatever to fill out your 32nd iteration so you have to settle for using the next best trees you have data for. That is why each successive iterations will have a "lower" number. 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. John RE: Iterations   Robert Leverett   Mar 09, 2004 07:06 PST  Ed:    John has explained the mechanics very well. In a limited sense, it is akin to sampling without replacement -except we are consciously looking for the tallest specimens of each species that haven't already been selected and each time taking the top ten with each species entering an iteration only once. We're not interested in maintaining the same distribution of species within each iteration. When that occurs, it occurs because those particular species are sufficiently tall and sufficiently abundant to maintain their place in the hierarchy.    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    The average age of a tree in the first iteration of MTSF's Rucker index is between 130 and 140 years. In highly protected areas the older trees can be the tallest, so terrain plays a crucial part in explaining the patterns that emerge from successive iterations.     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.     For MTSF, there are 5 species that drive the high numbers over many iterations: white pine, white ash, sugar maple, N. red oak, and eastern hemlock. There are a few species, bitternut hickory, American basswood, American beech, and bigtooth aspen that add significantly to the index for the first few iterations, but then their impacts diminish because of their lower abundance. Red maple is abundant throughout and tends to be near the long term average. There are about 18 or 19 species that serves to keep the index above 100 for many, many iterations.     One point needs to be emphasized. Identical indices, one computed on a diverse old growth forest and the other on a mix of forest age classes created by a possibly long history of human use represent very different places. Comparisons are for sport only. I would be the last person to equate forests because they have similar Rucker indices, at least through a few iterations.     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.     We'll eventually experiment with several measures of central tendency and dispersion in analyzing the patterns that are reflected in the indices and we'll always be looking at the impacts of human activities and lack there of. One lesson that has emerged from our extensive profiling of a half dozen public forests in Massachusetts is that I do not want to see an explosion of cutting in our state forests. I don't want to see us appease the short-sighted or greedy, nor do I want to bow to those who think that the only good forests are the intensively managed ones - regardless of how well intentioned they think they are.     The numbers coming out of Mohawk strongly suggest that in our state forests, a combination of preservation and long term rotations administered with a light touch is by far the best course. A heavier hand on the land does not lead to the result that is so often promoted by very active timber interests. Bob RE: Iterations   Robert Leverett   Mar 09, 2004 08:20 PST  Ed:    A few more thoughts about the implications accompanying the computing of the Rucker index and the whole iteration process.    First a caution. When Dale, Tom, and I compute the Rucker index for our respective forest icons and compare them to one another, the resulting numbers are broadcasted on the list largely for fun and sport. However, when we go through the iteration process and examine the role of each species, it is for science. there is a world of difference. So, the light-hearted banter about which site has the highest index could mislead a new list member into thinking that we see the disparate sites as similar if they have indices there are numerically close. Of course, nothing could be further from the truth. We may look for site to site similarities, but we also look for differences in the roles that the different species play at each site.    Now here is the crucial point. The iterative process allows each of us to form mental pictures of our sites as to species mix, species age, and canopy structure across the ranges of habitats and topography. Consequently, each of us becomes highly sensitized to the role played by each species and we develop the sensitization much more rapidly than we would by concentrating on fixed plots - although putting in some plots for micro-sampling will always be important.     The iteration process can be described as a top down approach to species mapping that prevents us from becoming drowned in the averages. We see the species and individual trees much better and form good mental images as to where each fits into the forest structure.     We do the same thing with diameter distributions. We've just been concentrating on height, but we clearly distinguish the tall, slender forests and groves of trees from stockier, shorter ones. The forest is never generic to us.     In the prior e-mail, I alluded to the management implications that are flowing from our indexing and the implications are clearly toward protecting diversity in our public forests. I'm not interested in making compromises so that a few people can benefit disproportionately in a financial sense from exploiting the modest public forest acreages we have. Nor do I see any need to locking all the public forests up. However, the more intensively we manage (or mismanage) private forests, the less intensively should we manage the public ones. Bob RE: Iterations    Gary Beluzo    Mar 09, 2004 09:38 PST  Bob, I am thinking about some things we could do with GIS and the Rucker Index iterations...for one thing we could map all of the trees, color code them or symbolize what iteration each individual takes part in and then do some spatial analyis with terrain shape index (TSI), soils, slope, aspect, etc to see what interesting patterns emerge.. Gary Gary A. Beluzo Professor of Environmental Science Holyoke Community College 303 Homestead Avenue Holyoke, MA 01040   Home