Iterations:  numbers, numbers, numbers
  Mar 06, 2004 11:24 PST 


   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.

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 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 


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.

RE: numbers, numbers, numbers   Robert Leverett
  Mar 08, 2004 07:46 PST 


   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.

RE: numbers, numbers, numbers   Dale J. Luthringer
  Mar 08, 2004 10:29 PST 


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.

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.


RE: Iterations   John Eichholz
  Mar 08, 2004 20:16 PST 

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.

RE: Iterations   Robert Leverett
  Mar 09, 2004 07:06 PST 


   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

   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.

RE: Iterations   Robert Leverett
  Mar 09, 2004 08:20 PST 


   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.

RE: Iterations    Gary Beluzo
   Mar 09, 2004 09:38 PST 


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 A. Beluzo
Professor of Environmental Science
Holyoke Community College
303 Homestead Avenue
Holyoke, MA 01040