Rucker Index Multiple Iterations    Edward Frank
   May 16, 2005 21:45 PDT 
Bob Leverett, John Eichholz, others using Multiple Rucker Iterations

What I am trying to figure out, is what do multiple iterations tell you
beyond what you can learn from the basic Rucker Index, and a listing of the
tallest trees for each individual species? I have read your posts and
explanations many times, and I am still not seeing it. I can see the value
of the Rucker Index itself, but when it comes to the multiple iterations...

I have constructed a logic exercise on what running a multiple Rucker
Index iteration would show of a theoretical forest. Perhaps if you could
provide a more specific or more detailed explanation of the merits of
multiple iterations of the Rucker Index, and point out where my thinking is
flawed or diverges from real life forests, it would help me and others
understand what you people are doing. You say it helps you understand the
structure of the forest. How does it help you do that?


I have been thinking about the idea of multiple iterations of the Rucker
Index and the structure of forests we are measuring. The Rucker index is
the numerical average of the tallest individual of each of the ten tallest
species in a forest. Multiple iterations can be run by first doing a
standard first iteration Rucker Index for the site. For the next and each
successive iteration these individuals are excluded from the set, and a new
Rucker Index is created from the ten tallest individuals of each of the ten
tallest species remaining in the dataset. Clearly to do a large number of
meaningful iterations requires a large number of measurements.

In a forest a typical tree species will have individuals of a variety of
sizes. The tallest trees will be rare. The next tallest category includes
those trees shorter than the tallest trees, but still above commonly
reached height. These will be uncommon in occurrence, but will still be
present in greater numbers than are the tallest trees. The third tallest
group are those trees in the canopy of a "commonly reached height." The
number of trees reaching this height in a particular forest will be in
excess of the numbers of iterations used in most analysis. One example
from Cook Forest State Park indicates that there is only 1 tree in excess
of 180 feet, 4 in excess of 170 feet, 24 in excess of 160 feet, and 73 in
excess of 150 feet. (These numbers are subject to updates.) Trees of
shorter heights will be even more common. An open forest, like is found at
MTSF, will have trees ranging in size from seedlings, to saplings, to
canopy, and occasional super canopy trees.   A plot of population numbers
versus height would yield a generally concave curve with the numbers of
individuals getting progressive larger with decreasing size. In forests
dominated by a single aged trees, the same pattern will be found, but there
will be discontinuities in the graph where the population numbers "jump"
between different age groups.

How would the trees in a forest displaying these parameters be reflected in
a series of multiple Rucker Index iterations? The initial index would
include only those ten trees that represented the uppermost, tallest,
rarest, examples of those species populations.   The next successive
iteration would show the same pattern, and likely would include the same
species. This will be true until the tallest, rarest individual of another
species would break into the Index when it was greater in height than the
second, third, or fourth, etc. tallest individual of one of the original
species. This would be the rarest tallest individual of a new species
besting the second height tier - uncommonly reached height - for the
initial species. In the following iteration, this new species may hold its
place, or the first species may reappear, as it should have more
individuals of any particular height than a shorter species (the assumption
is that reasonably large numbers of each species are present.) Through
this process species will be replaced in the index, and may reappear, as
the tallest of other species poke their way into the list. Once the
"commonly reached height" of a given species appears in the index, that
species will not be replaced on the list by further iterations.
Eventually, given that the numbers of individuals increases as the height
decreases, the Rucker Index of the nth iteration will consist of the ten
tallest "commonly reached heights" for ten species.

What I am trying to figure out, is what do multiple iterations tell you
beyond what you can learn from the basic Rucker Index, and a listing of the
tallest trees for each individual species?

1) The first Rucker Index reports the average height of the tallest of the

2) From there the multiple iterations will include successive species that
at their maximum height are greater than the commonly reached height of the
ten tallest species in the forest.

3) At the nth iteration, it will consist solely of trees from the 10
tallest "commonly reached height" species.

4) It will tell you what species are taller than this iteration, and you
can tell what order they will appear, but the same can be said for a
listing of maximum height for each species.

5) It may indicate how great a range there exists between the maximum
height of a species and that species "commonly reached height."

6) Differences in the species composition in the initial index from those
in the nth iteration may also show that some species have a much greater
spread between maximum and common height than others.

7) Loss of a species from the list would either indicate that while it is
tall at its maximum, it is not among the ten tallest at commonly reached
heights. It may also indicate that there simply were not enough examples
of the species in the dataset for it to remain in the index. Is this
because it really is that rare, or is it a problem that there simply
haven't been enough of them measured? Maybe only the tallest individuals
of the species were measured, especially if it is an uncommon tree, and
those of common height simply were not sampled. If this is the case, then
the iterations are not so much an analysis of forest structure, as it is an
analysis of the sampling protocols.

There is more I want to ask or speculate, but it is late and I will close
for now.

Ed Frank
Re: Rucker Index Multiple Iterations
   May 17, 2005 04:28 PDT 
   You have done a yeoman job thinking through the process. I will respond with more thoughts and analysis in a couple of days. I need to first think carefully about what you've said.
ENTS and science    Edward Frank
   May 17, 2005 11:15 PDT 


When I pose questions, like the recent post about multiple Rucker Index
iterations, I am not being critical. I have found in school that if I did
not understand something, chances were good that many others in the class
did not understand it either, or were so lost they could not even pose a
good question. With regard to the multiple iterations, the light bulb
simply doesn't light. If Bob and other statisticians and mathematicians in
the group feel the concept has merit, I can believe that, but I obsessively
still need to understand what is happening. It drives me nuts.
Generalizations only frustrate me and feed the obsession. So if I offend
anyone, I do not mean to do so, but I am not sure I have any choice without
making myself crazier than I already am.

If any of you have tries to write formal scientific reports, you will
understand that half the time is spent in writing the report, and the other
half is spent tracking down various loose ends - what is that citation,
where is that specific number, I need to make the letters bigger in this
graph, I need to rework that explanation... ENTS is both a hobby for many
of us and an outlet for pursuing scientific interests. If as an
organization we are to be viewed as more than a group of hobbyists, as a
credible scientific resource, it is imperative that we try to tie up
various loose ends. The loose ends in our methodologies are many, but
mostly consist of minor details that can be easily fixed. We need to
better define our terms. An excellent step in this direction is the
inclusion of Will Blozan's tree measuring guidelines on the website.

When I first started working on the website, there was discussions of the
Rucker Index for this site or that site. The only place that I found any
type of a description of what was a Rucker Index was a partial explanation
in the introduction of one of Colby Rucker's tree lists. Posts between
Colby and I, and materials from Bob Leverett and others enabled me to
generate a good description of the mechanics and application of the Rucker
Index. The Multiple Iteration concept is one area that needs better
explanations. In many other areas there are minor details that still need
to be addressed.

For example, Colby talked about the base of the tree, the lower point at
which we should start measuring the tree's height, should be "where the
acorn sprouted." This catch phrase meant to frame and address the problems
when the upper side of a tree on a sloping surface was at a much different
elevation than the base of the tree on the downslope side of the tree.   It
seems to be a clear explanation, but it is not perfect. Bob Van Pelt
pointed out nurse logs as an example. Trees would sprout on the surface of
a fallen log, sending roots into the ground on each side of the tree.
Eventually as the nurse log rotted, stilt roots would form. At the same
time what was initially the tap root would extend downward to the actual
ground surface, becoming a perfectly good trunk for the tree. If the nurse
log was large, as is the case in many western trees, the difference in
elevation between where the "acorn sprouted" atop the nurse log, and the
true ground surface may be several meters. The question is whether this
trunk length between where the acorn sprouted and the ground surface is to
be counted as part of the height of the tree. I would say yes - the point
of measurement for the base of the tree should be where the plane of the
surface of the ground intersects the center or oldest portion of the tree
trunk. The problem from scientific angle is that the thread ended with
BVP's comments. The issue was never addresses. It remains as on of the
loose ends that still needs to be tied up.

I bring these points to the discussions to try and reach a consensus on
what the correct methodology should be, we have the discussions, and then
we need to formalize the results. We are often missing this last crucial
step, leaving these loose ends.

Ed Frank
RE: ENTS and science    Robert Leverett
   May 17, 2005 13:02 PDT 


   No need to be concerned about the persistence with which you pursue
these ENTS issues. I for one, and I have no doubt the others, appreciate
your devotion to ENTS and your desire for our efforts to be seen as more
than just the exercise of an intense tree measuring hobby.

   One reason our definitions have stayed a little loose is that we
represent several professions with different interests in trees. There
is forestry, forest ecology, dendrochronology, arborculture, and
landscaping, to name a few. Forestry had the greatest influence in
shaping our original approach to measuring, but the other professions,
plus mathematics for its own purposes, have come to figure prominently
into the equation - no pun intended.

   We're still in the sorting out stage of where we want to go and why
with the quantitative side of ENTS. I have a good idea of the direction
I want to go from a political perspective and often a historical one,
and certainly a sporting one, but I am wide open when it comes to
science. I basically leave that to Lee Frelich.

   Ed, personally, I welcome your challenge to us to buckle down and
define our terms and put our methodologies on a sound scientific
footing. You are absolutely right.

   I am presently thinking critically about the value of multiple
iterations of the Rucker index and will have a post in a day or two. In
the interim, thanks again for your unwavering commitment to ENTS and
its mission. In the future when we want to cut out the ambiguities and
generalizations, maybe we should begin our sentences with - "frankly
speaking". Okay, I'll stop with that one.   


Question to Dale Luthringer    Robert Leverett
   May 18, 2005 09:19 PDT 


   For the Cook Forest data you currently have, how many Rucker
iterations can you run and what do you believe you gain personally in
the way of insight, if anything, by running multiple Rucker index
iterations? Ed has presented us with a challenge to think through the
iteration process and explain what we gain by doing it. As a proponent
of iterations, I'm taking Ed's questions seriously and I am rethinking
the whole site documentation process.

   One immediate benefit of iterations to me is that they tell me how
dependent an index value is on a particular subset of trees or a
particular species. The question I ask myself is what would the site
look like were a specific subset of trees not there. Another question
that comes to my mind is whether there is a perceivable site norm in
terms of overall canopy appearance/behavior. Or does a site consist of a
heterogeneous mix of subsites - so much so that combining them into one
large site for the purposes of computing an index would give a
misleading impression by suggesting perhaps a uniformity that just does
not exist.

    I'm fumbling with these ideas now, including a more sophisticated
model in my head that includes:

    1. An iterated cross-species Rucker index (what we do now)
    2. Density measures such as # of trees in a height range (e.g. >=100
feet) per unit area.
    3. Individual species Rucker index

   Any thoughts? Same question to everyone else.

Re: Question to Dale Luthringer    Edward Frank
   May 18, 2005 12:37 PDT 


When you are thinking about site models, I want to point out the enormous
value of descriptive narratives of a site. The numbers help quantify
various aspects of a site characteristics, but a well thought out
description ties everything together into a cohesive whole.

Ed Frank
RE: Question to Dale Luthringer    Darian Copiz
   May 19, 2005 07:58 PDT 

Bob, ENTS,

Great ideas! I like the additions because they add more of a control to
the data.

I like the idea for density of trees over a certain height. The tree
heights per unit area would be very useful for comparing large and small
sites. I think it would be a step toward standardizing the data.
However, this could be very difficult. On a large site where tulip
trees get over 160', would anyone really measure every tree over 100'
tall? If not, we would not be able to get a true density. Sample plots
could also be used, but I don't know if anyone would really do that
either and they would not necessarily be representative of the entire
site. Density calculations could possibly be easiest for small sites or
for single species tree heights at the edge of their height range.

I really like a single species Rucker Index. I expect for many sites
there is already enough data for this. It allows apples to be compared
to apples (although apple trees don't get that tall). This would shift
the focus of attention from the site to the actual species on the site
and what we can learn about those species. It would increase the
importance of some sites with low diversity but many impressive trees of
a single species. It would be easier to see that this site has tall
trees of this species whereas another site has tall trees of another
species. It reduces the weight of "fluke" trees (which multiple
iterations also does). I think it would also open the door for
competition and thus more data for trees which are generally of shorter
heights (There must be something Mohawk State Forest could beat the
Smokies at). How often do we see dogwood on a Rucker Index? How often
is it even measured? From the reports, it appears that Colby was one of
the only ones measuring the shorter stuff - even spicebush! I think
this would be a great practice to continue. I imagine there could be a
site that has an RI under 100, yet has some of the tallest dogwoods on

Continuing dialog with Darian    Robert Leverett
   May 19, 2005 10:16 PDT 


   Excellent points. They reinforce the thinking of many of us and on
the direction that Rucker analysis should take. However, before getting
into that, first some comments about a couple of points you made.

      (1) You are 100% right in observing that Colby Rucker had a more
balanced approach to a site evaluation by including the shorter species.
I have been highly negligent in measuring the understory and shrub
layers. Gotta change that.

      (2) I am with you. I always worry about "flukes" and a single
iteration of the Rucker index is highly vulnerable to just that concern.
If for no other reason, I would always want to measure enough trees to
do two iterations of the Rucker. Three is better than two, but beyond
three, arguments can be made for going on to other kinds of indices.

   Because of the abundance of data we have on Mohawk, I'll use it to
discuss the direction that I think we should take. Mohawk's common
multiple species Rucker index presently stands at 135.4. Its historical
index stands at 135.8. I would doubt that it ever reached 136, however
far back into the past we might go. The following table shows the
species composition for the current index.

wp    166.4 10.2
wa    151.5   6.2
sm    133.8   5.0
nro   133.5   9.3
hm    131.0 10.7
ab    130.0   7.8
bnh   128.4   4.1
bta   127.7   3.5
rm    126.1   6.2
abw   125.4   5.9
Rucker Index 135.4, 6.9

    We would all agree that the simple publishing of this index tells us
little about Mohawk's forests. For example, is the 166.4-foot white pine
a fluke? We could turn to the Rucker index for that species to answer
the question. Mohawk's white pine index is (160.2, 9.6). In addition,
Mohawk is 73 deep in 150-foot white pines, at least 207 deep in
140-footers, and 130-footers are too numerous to measure. It takes
little time to recognize that in terms of indexing, the white pine's
dominance is so commanding that Mohawk without the white pine would,
indeed, be a very different place. Yet, that's not the end of the story.
Since the tall white pines grow in relatively pure groves, one can see
the great whites as distinct - islands unto themselves. If one's
attention turns away from the pines, what does one see?

    There's a second class of forest in Mohawk, the vast majority of the
wooded acres. That second forest forms the hardwood-hemlock zones. Is
there a dominant in those zones, comparable to the white pine? No there
isn't. However, the white ash is clearly dominate as the tall tree.
Yet, it does not dominate its environment anywhere close to the extent
that the whites do. There are several small clusters of white ash trees
and it is widely distributed among other hardwoods, but where it is
abundant, it does not dominate like the white pine. A Rucker index on
white ash yields (144.7, 7.7). In terms of a height distribution, Mohawk
is 1 deep in 150s, 15 deep in 140s, and 52 deep in 130s. In terms of
height, the ash's closest rival is the sugar maple which has a Rucker
index of (130.5, 8.4). Beyond that come N. red oak at (126.3, 7.3),
hemlock at (124.6, 8.3), and oddly, bigtooth aspen at 120.4, 4.4). There
are 12 native species that reach 120 feet and 13 over all, including
Norway spruce. The common 10-species Rucker index stays above 120 for 16
iterations. A 23-species index yields 120.2.

    It's clear that there are a lot of tall trees in Mohawk, yet
something is missing. Despite all this analysis, it is unclear how
prevalent trees are in different areas of Mohawk that fall within
different height ranges. Are there areas where one can walk among trees
that commonly exceed 100 feet, 120, 130, 140, etc.? So expressions of
tall tree density become important. If we start simply, this may not be
quite so labor intensive as it sounds. Taking two height thresholds: 100
and 120 feet, within the white pine stands that are 60 years and older,
virtually every tree exceeds 100 feet. Figuring 100-footers per unit
area is more a matter of simple counting with an occasional laser shot
than complex measuring. Identify the boundaries of an area of known size
and count pines.

    More work is required in the hardwood areas, but following a similar
plan, computing densities of 100-footer in hardwood-hemlock areas is
doable -or at least, so I say. This Sunday several of us intend to go to
Ice Glen and Bullard Woods. These sites will provide us with tests of
the effort involved to compute densities of 100-footers.

Dialog with Darian and Bob    Edward Frank
   May 19, 2005 18:30 PDT 

Darian and Bob,

Pardon my interruption but I felt I needed to comment on one aspect of this
discussion. Both of you talk about trees that may be "flukes" in terms of
size. I would argue that these are real trees. They may be a fortunate
combination of genetics, environmental conditions, and timing, but as they
actually exist their heights are perfectly valid heights and can not be
construed as flukes, no matter what the expected size range for the species.

If I were to accept the premise that these trees, falling out of the
expected statistical distribution for the high end of the tree height
graph, Bob's suggestion that multiple iterations would be a better
indication of true tree heights still is not satisfactory. Given that the
first iteration contains one or two "fluke" heights (a concept I am
unwilling to concede), and nine or ten species maximums that fit the normal
height distribution pattern, you have a mixture of flukes and first tier
heights. If you run a second iteration, now you are making a composite of
the one or two true maximum heights - replacing the flukes - with eight or
nine second tier heights for the other species. You are not getting a true
index because you are not making a composite of all of the first tier
heights for all of the species. There may be a significant drop-off in the
height between the tallest and second tallest individual of a particular
species, especially if you have a limited number of examples from that
species. Multiple iterations may get rid of "flukes" - if they actually
exist - but introduces a different type of a problem into the analysis.

The species index requires more thought on my part. I see you give a
species index for white pine for MTSF. But the examples you actually use
in your argument are a tabulation of numbers of the species per given
height category.

I certainly agree that more species should be measured. There may actually
be a site with spicebush is spectacular for the species, and I think that
is worth knowing. I had been on Dale's case about measuring several
smaller species found at Cook Forest that he hadn't gotten around to
measuring. The speculations about other types investigations are
intriguing. I find the white ash/hardwood speculations to be a worthwhile
and thoughtful.

Ed Frank

Back to dialog with Ed Frank    Robert Leverett
   May 20, 2005 06:01 PDT 


   You certainly aren't interrupting. You're input is absolutely
indispensable to these discussions. For the present, it's just you, me,
and Darian, but hopefully, Lee, John Eichholz, Will, and others will
weigh in because we've got a lot of discussing left to do.

   With respect to the use of the term "fluke", maybe that's a bit
strong, but not too much so. If we recall the thin scattering of humans
that have grown past the 8-foot tall mark, while acknowledging their
existence, we would not want to include the few 8-footers if that skewed
our calculations and gave us a misleading picture of the more typical.
So, while we wouldn't want to call the 8-foot folks "flukes", at least
not to their faces, we wouldn't necessarily want them included in the
human equivalent of a Rucker index without considering the impact of
their inclusion to our understanding of human physical height.

   In rethinking the importance of the iterated Rucker index, I still
like its role in drawing attention to the depth of tall trees at a site.
However, I don't want to rely on iterations beyond that and I don't.
Iterations is not an end all - just another tool.

   For a new site, my current methodology is to begin by computing a
single Rucker index. If the site is interesting enough, I move to
multiple iterations, which follows somewhat naturally as a consequence
of identifying the top 10. I then turn to computing individual species
indices. For instance, in Monica's Woods, I've measured every single
tuliptree. If the site is extraordinary, I may want to take the
documentation and analysis to the next level. I will consider computing
the density of tall trees by some definition over one or more subsites
within the site.

    Well, I'm jumping the gun a little. I should say that computing
densities is where I would like to now head. But computing them is going
to be labor intensive. I can't just measure one conspicuous tree here or
there and then move on. I have to focus on delineating a subsite and
then concentrating on it. If I'm just looking to verify trees over say
100 feet, I can be less precise in my measurements. For example, I can
shoot straight up on many trees and rule them into or out of the count.
The ones that don't appear to make it on the quick and dirty first pass
get extra attention.

    This weekend will mark my starting point for making density
calculations. Ice Glen and Bullard Woods are the target sites. Wish me
luck. Or I should say wish us luck. As a minimum, Holly Post, Susan
Scott, and Monica Jakuc will be with me.

Back to dialog with Bob Leverett    Edward Frank
   May 20, 2005 18:12 PDT 


If you want to talk about 8-foot humans as "flukes" rather than simply the
upper end of the spectrum - I can see it either way. 8-foot humans
typically suffer from acromegaly - and overactive pituitary gland producing
too much growth hormone, or it does not stop producing it upon reaching

1) Do you have any evidence of trees suffering a similar type of
over-active growth?

2) What is the cause of this anomaly, and how can it be distinguished from
normal growth?

3) Can you give any examples of any trees that ENTS has measured that are
by their size a "fluke," outside of the normal statisticlly expected size

4) If you can't give examples of any "flukes" with all the measuring that
has been done, why do you believe it to be a problem with the single
iteration Rucker Index?

5) If you can give an example, would it not be better to exclude the
"flukes" from the first iteration on a case by case basis, rather than
throwing out all of the trees represented by the first iteration of the
Rucker Index?

I want to expand on my thoughts concerning 8-foot tall humans. There are
about 6 billion people on Earth 6,000,000,000. Most people are between 5
feet and 6 feet in height. There are a lot, but still a smaller number
between 6 feet and 7 feet. If 1/100th of 1% of the human population was
over 7 feet, that would still be 600,000 people. You see them everyday in
the NBA and basketball. At one time the average height of the male in the
Watusi tribe in Africa was over 7 feet. If 1/100 of 1% of the number of 7
footers, were over 8 feet tall you would still have 60 of them. If that is
too high still, the 1/1000th of 1% would still yield 6 people at any one
time being over 8-feet tall. That does not to me seem to be a curve
breaking number for 1 in a billion to be over 8-feet tall, no matter the
cause, acromegaly or whatever. I don't think the 8-foot tall people would
be out of place in calculations, but agree a sampling that happened to
include them could potentially be higher average. But at what point does
throwing out numbers because they don't fit your pattern, become selecting
only those numbers that bear out your predetermined hypothesis?

Ed Frank

Re: Back to dialog with Bob Leverett
   May 21, 2005 05:22 PDT 
Bob and Ed

I am not a scientist, but thought I would chime in. Humans used to exist in separate tribes all over the world, where the DNA pools were small, and not much, if any, new DNA was introduced. You mentioned the Watusi tribe. This tribe still has tall people because of isolation. Once they reproduce with humans outside their tribe the height will come down. I am 6'1" and I am from a family where the shortest person was my Grandmother at 5'8", the tallest at 6'7". I study family trees, and from that have found, the Wade (Teutonic) and Templeton (Scottish) clans were "Giants" in historic times. Since those times other "tribes" have reproduced with our "tribes" to the point that I am a complicated hybrid. This all happens at a much faster pace with humans, as we are mobile.

Trees on the other hand would be much slower. They would have to grow their range to the point of coming in contact with another species that had traits similar enough to breed with them. Then things would change for both species. I think of variety for a tree as compared to the Watusi tribe. An isolated remaining group with specific traits. I think someday certain tree families will be indistinguishable from each other. The black oak family may hybridize to the point where they all look alike. Black maple and sugar maple will become one, and so forth. It may never get to the point where different plant families interbreed, but who knows.

Maybe the local group of tulip poplar retain some gene for height from some ancient magnolia "tribe", and others have hybridized themselves out of the height race? I have also read about whitetail deer populations having larger antlers in certain areas based on the food available to them. This could correlate to trees also.

Thanks for listening. Ramble over.

Flukes: modular vs. unitary
   May 21, 2005 16:44 PDT 


When considering any growth form or size as a "fluke" (i.e., outside the norm)
we have to be careful when comparing humans to trees. Trees are "modular"
organisms - a series of repeated units. We are "unitary" - a singular body plan
from which we cannot deviate too far. Environmental control of morphology in
modular organisms can be much more pronounced than in unitary organisms. Think
of a gardener pruning a bonsai. Don't try to make a chihuahua that way!


Re: Flukes: modular vs. unitary    Edward Frank
   May 22, 2005 18:05 PDT 


I understand the argument you present. I guess the point I was trying to
make is that I don't think it is correct to call exceptionally tall people
or trees "flukes." If there was some way to determine a biologically
distinctive criteria that could be used to determine that a particular tall
tree was significantly different physiologically from other trees of that
species, aside from just height, there might be a reason to consider it to
be an abnormality and exclude it from the Rucker Index. Otherwise I think
the tallest tree of a species on a site is a perfectly valid tree for the
Rucker Index.

Bob is developing arguments supporting the multi-iterative process. I am
anxious to read them. One argument suggested in recent posts was that the
second iteration "weeds out" trees that are "flukes" or exceptions to the
normal height limits. I am arguing, somewhat preemptively, that I don't
think these are flukes. I also am posing the argument that a second
iteration of the index creates a mixed index of the first order tallest
trees (where the "flukes" were eliminated) and second order of not quite as
tall trees. I do not believe this mixture is indicative of anything. If
there really are "flukes," the criteria to determine which trees are flukes
must be demonstratable by strict definable biological standards.

Ed Frank
RE: Flukes: modular vs. unitary    Darian Copiz
   May 23, 2005 06:49 PDT 

I agree with your points on flukes. As far as I am aware, there is
nothing that would make a tree being taller than others of its species
something unnatural. What I originally meant by using the term "fluke"
was that a single particular tree might not be representative of the
site. A site could have one remnant old age tree, but have mostly
younger, far shorter ones. There wouldn't be anything abnormal about
the one large tree, but it could cause misleading conclusions under a
single Rucker Index iteration.

If there was a site with one 150' tulip tree I might come to the
conclusion that this site had tall tulip trees. Although unlikely, if
the next tallest tulip tree was 100' then my conclusion would have been
very misfounded. The site would have one tall tulip tree, but over all
be very short. This is what I meant with the term "fluke". I do agree
that such trees should not be eliminated or discounted. However, these
sort of trees would exemplify the usefulness of multiple iterations or
single species indexes.

Outstanding performers    Robert Leverett
   May 23, 2005 07:42 PDT 


   Your use of the term "fluke" is well stated. I hadn't thought through
the genetic argument very well. So fluke is probably inappropriate in
terms of tree morphology. But at a site, a tiny remnant, may only one,
or at most 2 or 3 trees of lingering giants could skew the perception of
others toward what the site exhibits as the norm. Several iterations of
the Rucker index provides a better picture of what each species is doing
at a site. Individual species indexes would add another level of
understanding. And then there is density.

RE: Flukes: modular vs. unitary    Edward Frank
   May 23, 2005 18:44 PDT 


I would not come to the conclusion that the site had many tall trees of a
species simply because there was a tall example in the Rucker Index. If
you are looking at site potential - one of the presumed applications of the
Rucker Index - a remnant 150 foot tree would be far more indicative of the
site than any number of younger 100 foot trees.

My point with the entire thread is that I don't see ANY use for the second
or multiple iterations, or that it tells me ANYTHING. The example you cite
does not "exemplify the usefulness of multiple iterations." I still fail
to see any useful information gained by the process.

RE: Flukes: modular vs. unitary    Edward Frank
   May 23, 2005 19:39 PDT 

Darien and Bob,

The last post sounded a bit harsh. I guess I am getting frustrated by this
line of argument. The examples that each of you have cited, do not, from
my perspective, demonstrate the utility of multiple iterations. While to
each of you the same arguments seem to be irrefutable.   The first
suggestions posed was that the second and multiple iterations helped
eliminate flukes. I counter-argued that these trees were not flukes, and
should not be eliminated or discounted. I also argued that if these were
indeed biological exceptions then the second iteration was not an
improvement on the first iteration as it would mix first and second order
trees in the same index.

In this post Darien's point, as I understand it, was that the tallest of a
species might be an older remnant, and the Rucker Index including that
tree might not be representative of the site. See my argument in the
previous post.

However suppose there was a single 150 foot tuliptree and all the 
rest were100 feet or so tall. The maximum change in the Rucker Index from the
subtraction of this tree in the second iteration would occur if the
tuliptree dropped from the tallest on the site to the tenth tallest on the
site. the difference in height of 50 feet divided by the 10 trees in the
iteration would all by itself drop the index by 5 points. Is this a
dramatic drop from a first iteration to a second iteration? (That is a
question - I don't know) 

A general expectation is that the tulip tree in
the first iteration would be replaced by a tulip tree somewhere in the
second iteration. So what happens when it drops off completely? Because
it is not there, most of the the other trees are bumped up one slot. Trees
in the second iteration that would have been taller than the second
iteration tulip tree would be unaffected. They would retain the same
position. All of the tree that are shorter than the expected second
iteration tulip tree would be bumped up one slot. What would have been the
expected 11th tallest species in the second interation, instead now becomes
the 10th species of the second iteration. The difference would be that the
expected second iteration tulip tree height is replaced by what would have
been expected to have been the eleventh tallest species height. The other
species on the list remain the same. So the affect of the tulip dropping
out is equal to the difference in the height of the missing second iteration
tulip tree and the new tenth species on the 2nd iteration Rucker Index
divided by 10. 

In the example cited this tenth species can not be shorter
than 100 feet or that slot will be retained by the tulip tree - the maximum
change would be 50/10 with a second tulip tree of 150 feet, and the tenth
slot taken by a 100 foot tulip tree. The actual variance would be less
than 5 feet as stated below, but the upper number could be something less
than 150 feet.  The drop from this individual may actually only be a couple
of points. In addition to the drop caused by this individuals removal from
the index, there would be the drops caused by the difference between the
first tier of tallest trees from the second iteration of second rank trees.
I am not sure if the drop from this single tree would stand out within
this broader context.

You could look at the differences in the species present. You would see in
the second iteration that tulip tree dropped out. It would likely reappear
in later iterations. I really don't see how this would jump out at you and
indicate a bimodal size distribution for the species based upon the
multiple iteration data. It would be seen in a single species analysis,
but... If you believe this would be made clear through the multiple
iteration series, is this the best way to find this information? Or would
another type of listing or analysis demonstrate the conclusion in a
simpler, less intensive, process? What might that process be?

Ed Frank

RE: Flukes: modular vs. unitary    Robert Leverett
   May 24, 2005 07:49 PDT 


   Perhaps we're all straining too much either defending or refuting the
value of multiple iterations of the Rucker index. There is definitely a
use for multiple iterations in answering certain questions about the
behavior of the Rucker index for a site, especially when the index is
used in comparisons to other sites. Also, multiple iterations is
important when investigating indexes above a threshold value. For
instance, Ice Glen's 1st order index is 126.2. Does this suggest to us
that Ice glen is sufficiently deep in tall trees of at least 10 species
to keep the index above 120 for some number of iterations? Ice Glen's
2nd order index is 121.8, and its 3rd order index is 119.2. Its 4th
order index drops to 115.6. Ice Glen's high index is dependent on a
small number of super trees, a couple of pines, a couple of hemlocks, a
couple of white ash trees, and a single shagbark hickory. We can see the
effects the super trees on a sustained high index by removing them from
consideration. Remove the top 20 performers, and Ice Glen drops below
the 120 threshold. By contrast, MTSF stays above 120 for 16 iterations.
More searching would unquestionably raise the number of iterations over
120 in Mohawk to over 20.

   However, the Rucker process should not be done with blinders on. For
instance, in MTSF bigtooth aspen is a strong performer, but that is
courtesy of one small stand of clonal aspens. So, the aspen's role in
bolstering the Rucker index is greatly diminished if we ignore the
single small stand. Our conclusion is that the aspen's persistence in
Mohawk as a very high performer is low. By contrast, the roles of the
white pine, white ash, sugar maple, n. red oak, and hemlock are

   I use multiple iterations as a tool to examine the long term
influence of each species and what would happen to the index were
certain individual trees lost. Computing an individual species index is
equally important to me to better comprehend how a particular species is
performing. But the numbers and the patterns should be kept accompanied
by an examination of the spatial relationships among the species and
their overall distributions. For instance, the black cherry is thinly
distributed in MTSF. There are no major concentrations of it like we see
for other species. Yet it is a consistent performer within the Rucker
index. Black cherry appears in 15 out of the first 16 iterations. If we
increase the iterations to 20, we still find the black cherry present in
19 out of the 20. Its performance also seems relatively independent of
the surrounding species.   

   What I am alluding to is that given the amount of searching,
measuring, and comparing we do, it is always reasonable to wonder what
effect an individual tree or subset of trees has on the Rucker index.
More on this line of investigation in the next e-mail.

RE: Flukes: modular vs. unitary    Edward Frank
   May 24, 2005 08:31 PDT 


I don't really have anything to add concerning multiple iterations. I can see
that manipulating the numbers helps you get a feel for the dynamics of a
particular site. I am not convinced yet that it is the most appropriate or
best way to draw the inferences you are making. I am going to drop this
thread, let things ride for awhile, and think about the process. I am
still interested in hearing whatever additional thoughts you might have on
the subject.

RE: Flukes: modular vs. unitary    Robert Leverett
   May 24, 2005 11:16 PDT 
   Okay, Ed, sounds good. I do enjoy these discussions and value your
input very much.

   I'll probably send a few more e-mails before I get it all out of my
system. But if I get sloppy in my thinking, don't hesitate to pounce on
me. In the end, we want to have thought the process through from every
conceivable perspective.

   To continue the line of analysis developed in the last e-mail, about
2 years ago, I sat out to determine what red oak is doing in MTSF and up
and down the Deerfield River valley and gorge nd compare the results to
what I was finding in the valley provinces. In terms of size, the
northern reds of the Deerfield commonly reach diameters of 2 to 3 feet.
Trees 3.5 to 4 feet in diameter are found on occasion and on rare
occasion, a little larger, but 2 to 3 feet is the norm.

   In terms of height, Deerfield northern reds over 100 feet are common,
but they are thinly distributed above 120 and very rare over 130. I
presently judge the probability of the region producing a 140-footer to
be near zero. So by this comparison, the Zoar Valley NY oaks are off the
charts. The Cook Forest oaks are comparable in height, but slightly
larger in girth.

   I should also add that the above diameter and height dimensions span
trees ranging in age from 60 to 250 years and are scattered over steep
slopes, in ravines, and on river terraces. The densest northern reds are
concentrated in areas of past large scale disturbance. The reds are
isolated trees at the periphery of the ridge aspect going from south to
north; i.e. we run out of them on the northern exposures.

   Through the extensive Rucker analysis that we've performed, we have
the height distribution of the northern reds dialed in pretty well over
a large area. We know what is ordinary and what is exceptional. Our next
step in the oak survey is to do density analysis. How dense are trees
that reach a particular height threshold, e.g. 100 feet? Where are the
regions of maximum density? What is the northern red's response to the
proximity of other species? Do we find the tallest mixed among the white
pine, white ash, and sugar maple in our neck of the woods? Can northern
reds reach as great height when the species competes against itself?
What are the patterns that we observe?

    On a wider geographical scale, how does the best of the Deerfield
River Gorge oak compare with the best growing within the Connecticut
River Valley region, the Housatonic and Hoosic River Valley regions,
other high growth sites like Ice Glen, Bullard Woods, Laurel Hill, etc.?

    Many questions can be raised relative to the growth of the northern
red oaks over a period of 100 years - say 50 to 150. With Gary Beluzo's
GIS expertise and now with the use of terrain indexing, it pushes some
of us to collect data from as many oak sites as possible and then turn
it over to others for correlation to spatial and terrain variables.

    Analysis to determine maximum species potential will be done
principally by Lee Frelich with assistance from Tom Diggins and Gary
Beluzo. Inter-regional height models based on a minimum of independent
variables is the initial goal. Eventually the model will be tighten by
introducing additional independent variables. It's all exciting stuff.

Back to Don Bragg   Robert Leverett
  Feb 22, 2006 09:57 PST 


   You've said it perfectly. You've identified the essence of Rucker
indexing. The operative challenge is for us to agree on how to apply
indexing and to extend it.

   Presently, I can go through the 10-species iteration process for a
full 38 iterationsfor MTSF. I'd like to get up to 50. Remembering that a
particular species can enter an iteration only once, I have thought
about examining the patterns that indices assume when generated by
single species. I've done a little of this, but have drawn no
conclusions. For instance, the 10-species Rucker index of MTSF currently
rests at 135.4 if exclusively native species are used. If I let Norway
spruce sneak into the process, the index rises slightly to 135.6. If
Norway spruce stays in the mix, the Rucker index stays above 130 through
4 iterations. If only native species are included, the index stays above
130 for 3 iterations. The index stays above 120 for 16 iterations for
the data on native species that I presently have. To take the iteration
process much farther, I need many more measurements of the shorter
species. If more birch trees of all species, more black cherries,
basswoods, red maples, bigtooth aspens, etc. are added, for how long
will the index stay above 120?

   If I focus on white pine alone, the Rucker index is 160.4 for the
first iteration and stays over 150 for 7 iterations. In addition, the
single species index includes trees located in 5 distinctly separate
locations, so all the super trees are not bunched at the same location.

   If I apply the iteration process to this single species, the Rucker
index stays above the 135.4 standard or 10-species index for 25
iterations. If I apply the index iteratively to white ash, the single
species index stays above the 10-species index for 3 iterations. No
other species provides an index above the 10-species index for even a
single iteration. The high Rucker index of MTSF is clearly dependent on
two species.

   The requirement of this kind of analysis clearly requires that a lot
of trees be measured for a site. One focus of our discussions might be
how to get the most mileage for the least amount of expended field time.
As a tradeoff between lots of measurement time on site and the best
understanding of the composition and structure of a site, I've thought
of a 5-index system:

   1. Regular 10-species height index
   2. Single species height index for the species that produces the
highest index
   3. Regular 10-species circumference index
   4. Single species circumference index for the species that produces
the highest index
   5. Iterated 10-species index through 3 iterations.

   I offer no special defense of this combination. It is just one that
quickly came to mind, as I thought about how to better understand the
overall structure of a site. Intuitively, it seems necessary at some
juncture for us to include the physical areas of our sites when
comparing them to develop tall tree density factors, especially where
multiple species are involved. It is a kind of a given that white pines
in a stand grow tall together. In terms of comparing sites of similar
area, I do this now, but in a very undisciplined way.

   The "bunching" of tall species together is interesting - to be
expected at one level. Put red oaks among the white pines and the former
try to keep up with the latter. Substitute white ash for white pine and
the same is true. Then there is black cherry and American basswood, both
of which seem to do their own thing regardless of the nature of the
composition. Lots to think about.