Multiple Iterations   Robert Leverett
  May 25, 2006 06:27 PDT 

     In terms of iteration, we can agree to continue disagreeing. You
see no value in it, but I do. And there isn't much doubt in my mind
about that - at least in terms of showing species patterns more clearly.
The dependency of a site's RHI on a few extraordinary individuals can
never be revealed through RHI alone. In making the case to the
Commonwealth of Massachusetts that MTSF is a very special place, it is
important that they understand that we're not dealing with a scattering
of isolated tall trees.

    Looking beyond my specific objective for MTSF, I like to distinguish
which sites are deep in tall trees of a single species, versus several
species, versus many species -ala the Smokies. The patterns revealed by
the iteration process for MTSF clearly show the roles played by the
constituent species. I grant you that we can get at the same information
in other ways, but the iteration process is one way of doing it and a
fairly good one. Should other Ents use iteration? Well, that is entirely
up to them. Do we need lists based on itrations maintained on the
website? No, I don't see that as necessary. But where an in-depth
analysis of a site is needed, iteration is useful to whatever level the
researcher needs to go to reveal the height/girth patterns. In the case
of MTSF, 20 iterations probably tells the whole story. That represents
200 trees and a heck of a lot of work.     

   Another way of approaching the problem of examining patterns is to
compute an average of the n tallest individuals of the n tallest species
and then compute an average of the (n)(n) total number. If n=10, then
the measurer is in for a lot of work, i.e. 100 trees. This approach does
reflect depth, but leads to a different result from iteration. A
particular species might have say two very tall members and no others.
Were the 10 tallest of the species averaged, the result would include
the 2 tall memebers and 8 short ones. Those eight trees would also be in
the overall average. They might or might not be in the iterated index.

   Here is another way to look at iteration, taking an analogy from
baseball. Identify the best player for each of the nine positions.
That's an RH9 index. They all get hurt and have to be removed. Do you
still have a good team (tall, diverse forest), i.e. what do you have
left to work with? You form a new team of 9 using the next best at each
position. That would by RH9(2) - just to express the idea symbolically.
Do we know more about the team's depth than we did? How far can we go
before we run out of say shortstops and can no longer field a team of 9?
Does this tell us more overall about the team? Yes, of course it does.
We get a picture of depth. If we assigned a numeric value to each
individual player, say batting average, then we can see very clearly how
the overall team average depends of position and player. Could we get
that level of understanding in other ways? Yes, we could. But in terms
of forming teams, the removal of the top members of a team and formation
of another from what is left provides insight. Now, the 64 dollar
question is do we need the insight? Certainly baseball managers do, but
do we in ENTS for our forest purposes? For my particular purposes, I
believe that I need to understand the role of each species at a site
beyond its contribution to RHI10 and iteration clearly helps me in that

   I would be interested in John Eichholz's current views on iteration.
John is my sidekick (or I am his) in measuring the forests of Mohawk.


Ed Frank wrote:
Another measure that has been discussed are multiple iterations of various
indexes. I do not believe these are of value, and would rather not see them
used at all, but I will suggest a format for nomenclature. For example the
10th iteration of a 10 species Rucker Height Index would be listed as
RHI10-IT10. Other indexes for which multiple iterations are calculated
could use a similar naming format.


RE: To Rucker or not to Rucker, what's in an index?   John Knuerr
  May 25, 2006 17:06 PDT 

I'd like to throw in my two cents on this one from the perspective of not
forgetting who came up with the Rucker Index. Colby saw this as a way to
profile the forest canopy champions and through iterations of the index to
get a sense of the "height robustness". When comparing different sites, the
value of the multiple iterations become clearly evident.

Another point to keep in mind is that the Rucker Index caught on amongst
many of us and generated lot's of energy and friendly competition among our
ENTS colleagues and continues to do so.
I would like to see us honor the memory of Colby and only use the "Rucker"
label in its original formulation.

Re: Multiple Iterations of the Rucker Index   Edward Frank
  May 25, 2006 17:08 PDT 

ENTS and Bob,

The question of the merits of multiple iterations of the Rucker Index has
been a topic of discussion before between Bob and I and others. A copy of
these discussion threads appears on the website at:


My major concerns with the use of multiple iterations are discussed in the
second thread above. Since Bob outlined why he thought multiple iterations
were useful, I will summarize my objections. For more detailed discussion
read the above threads. When a multiple iteration of a Rucker Height index
(or other parameter) is generated -the first number is a standard Rucker
Index - the numerical average of the ten tallest trees from each of the ten
tallest species on the site. When a second iteration is done, these
specific trees from the first iteration are eliminated from the analysis
pool, and the next ten tallest trees from each of ten different species are
averaged to generate a second iteration. This process continues for each
additional iteration. My objection is that for each tree of a given height,
the next size smaller tree in a population will have more members. So in a
successive iteration of a Rucker index all of the trees in the first Rucker
Index of the tallest trees should be present in each size step smaller. The
number of trees making up canopy of the forest at a particular site is large
compared to the number of trees for which heights have been measured
(excluding extremely tiny yards and patches), therefore all the trees
represented in the Rucker Index and in the multiple iterations of the Rucker
index are trees in the canopy of the forest. Some trees reach the lower
parts of the canopy but not the upper portions. Bob has suggested when
these trees appear in the series of multiple iterations implies some
information about the structure of the forest. My objection is that when a
new species to appears on the list that implies that every individual of the
species it has replaced on the entire site has been measured and/or found to
be shorter than this specimen from the new species. We know from regular
posts to the list that Bob is finding new trees of height every trip. So
what does it really mean if a new tree appears on the list in a particular
iteration? It means that the observer choose to measure that particular
tree, and that other trees of the replaced species may or may not be on the
site and may or may not have additional individuals that are taller that the
specimen replacing them. When a new species appears on a list , at what
iteration, and with what other species are on the list at that time, its
simply a reflection of what trees the observer choose to measure. A high
Rucker Index or consistent Rucker index over multiple iterations simply
reflects that there were many trees measured, but by no means all of them.

Bob suggests that where these species appear in, the iterations reflects
what he sees in the forest. Of course they do. They are a reflection of
the sampling bias in what he choose to measure, so they do match what he
sees in the woods also as indicated by his sampling choices. I see no
logical relationship to when these species appear in the list to any
naturally occurring distribution within the forest canopy. I want materials
published under the ENTS name to reflect the highest standard of scientific
veracity, and I can't see any probative value in multiple iterations. For a
more expanded discussion see the links listed above. I feel better
information would be generated by simply plotting the maximum heights of all
of the tree species on the site - a tree profile - would be simpler and
provide real information.

I would encourage anyone who has something to contribute with regard to the
initials used to represent various types of measurements or insight into the
question of multiple iterations, please feel free to participate and post to
the discussion list. My tone sounds at times dictatorial, but I am really
just trying to present my viewpoint in as straight forward and
understandable way as possible. Unlike some technical writers seem to
think, the purpose of language is to communicate ideas, not to confuse the

Ed Frank
RE: Multiple Iterations of the Rucker Index   John Knuerr
  May 25, 2006 17:19 PDT 

Unless I'm missing something here, every tree that's in any index or in any
table in our ENTS database is a measured tree. The whosle point of the
Rucker Index IS to have it constantly change as we find and measure new
trees that surpass the height of whatever is currently in our lists as the
height champion. The more we scour an area the more our confidence level on
what the tallest tree species can achieve increases. So the more
"Eicholzing" we do the more our confidence level increases that we are
reaching the maximum on our Rucker Index number.
Re: Multiple Iterations of the Rucker Index   Edward Frank
  May 25, 2006 17:50 PDT 


Yes and No... All of the trees on the lists have been measured. The first
iteration of the Rucker index reflects the tallest of these trees. With
more measurement, the index typically increases as a reflection of better
coverage in the forest. More of the tallest trees are found over time.
That is all good. Over time the Rucker Index approaches the true maximum
for the site.

The successive iterations are also measured trees. The question is how well
do the changes in these subsequent iterations reflect true changes in the
canopy structure? You know and I know and everyone else knows that when
measuring trees the goal is to find the tallest individual of a species. So
these are the trees most measured. Once the tallest white ash is found,
there is not the same dilligence paid to measuring what would be the
twentieth tallest ash in the forest. If the next tallest tree species was a
sugar maple, there would be much searching for the tallest Sugar Maple.
Certainly more so than the 13th tallest ash. So when you get to the
thirteenth iteration and Sugar Maple replaces ash for last spot on the list,
is it a milestone? No because not as much time or effort was spent finding
the 12th tallest ash, which may in fact be taller than the tallest sugar
maple. The sugar maple likely should not have replaced the ash on the
thirteenth iteration,maybe not on the 50th iteration. What the iterations
are indicating is not the pattern of appearence in the canopy, but pattern
of trees that were selected to be measured. So while these number used in
the iterations are actual measurements, how well they reflect the forest
structure is not so much related to these measured heights, but what was not
measured. Multiple iterations provide an analysis of measurement bias - not
canopy structure. If they do not reflect canopy structure, what if anything
do they indicate?

Ed Frank
Re: Multiple Iterations of the Rucker Index   Edward Frank
  May 25, 2006 17:53 PDT 


One additional point. The more thouroughly a canopy is measured, typically
the greater the number of iterations will be required befoer one species is
replaced by another species. The more measurements that are taken, the
slower the Rucker Index will decline from one iteration to the next. Both
are reflections of the measurement process rather than anything to do with
the forest or the trees themselves.

RE: Multiple Iterations of the Rucker Index   John Knuerr
  May 25, 2006 18:59 PDT 

A little kidding here. When you said: "Once the tallest white ash is found,
there is not the same diligence paid to measuring what would be the
twentieth tallest ash in the forest", I would have to reply by saying: have
you ever been out with Bob?
But all kidding aside, we do scour the areas such as Mohawk Trail State
Forest with a lot of diligence. And the iterations of the index when you
compare different sites does give you descriptive information. In MTSF we
have a good handle on a variety of species and their heights (or height
ranges) in certain stands. In multiple iterations of the index it is
interesting to see what species remain and what species drop through
multiple iterations and the rate at which the index drops over the
iterations. The measurement bias you mention below, I see as an intentional
bias. We are trying to measure the tallest trees. It would be interesting to
see if we could graphically represent what's being shown by the multiple
iterations. I think of it something like the equivalent of a spectrograph
where certain markers are reflective of certain stand characteristics
Re: Multiple Iterations of the Rucker Index   Edward Frank
  May 25, 2006 17:53 PDT 


One additional point. The more thouroughly a canopy is measured, typically
the greater the number of iterations will be required befoer one species is
replaced by another species. The more measurements that are taken, the
slower the Rucker Index will decline from one iteration to the next. Both
are reflections of the measurement process rather than anything to do with
the forest or the trees themselves.

RE: Multiple Iterations of the Rucker Index   John Knuerr
  May 25, 2006 19:29 PDT 

Good point. So, if we're interested in observing the decline in the index,
in theory the more trees we've measured, the more iterations of the index
would be needed to achieve the same decline in the index value.

Re: Multiple Iterations of the Rucker Index   Edward Frank
  May 25, 2006 19:51 PDT 

Yes you may know the heights of a variety of trees (or ranges). This is
because you have measured alot of trees, not information gained by multiple
iterations. The "intentional bias" means that where and when species drop
out of an iteration set is dependant on a choice you have made by what you
measured not because of what is present in the forest.

If one Species A replaces Species B in the 5th iteration of a Rucker Height
Index, can you tell me that there is not another example of Species B in the
entire forest that is not taller than this example of Species A? If there
is, then one species should not have dropped out at iteration 5 and the
other should not have appeared. So what does it tell you when one species
replaces another in a particular iteration? Nothing. It tells you at what
height the tallest example of a species appears, but you already knew that
because you measured the tree. Tell me one new thing a multiple iteration
has told you about the forest, that you did not already know, or should have
known, from the raw measurement data. How many trees are there in MTSF above
125 feet tall, and how many of them have you measured? That is the number
for the shortest species in the Rucker Index for the site. Until that
number approaches 90 to 100%, the iterations will reflect numbers that are
more dependant on your sampling selections rather than objective portrayals
of the forest structure.

Bob used a baseball analogy to represent forests.   In the baseball team
analogy he knows the "batting average" of every player in the pool. He knows
how many positions he must fill. He knows all kinds of things that limit
the variability within the baseball player pool. It is not valid analogy.
In the case of the forest is not clear that beyond the first iteration that
the with each subsequent iteration that next tallest are being removed from
the data set, or even that the next tallest trees have even been measured.
You are eliminating the next tallest trees you have measured. But if you
have chosen which trees to measure, particularly whether the umpteenth
member of one species was hunted for as hard as the tallest member of
another species, that is enough sampling bias to skew your data beyond

{material deleted}


Re: Multiple Iterations of the Rucker Index   Edward Frank
  May 26, 2006 03:11 PDT 

John and Bob,

I am sorry I have gotten into a rant about the issue of multiple iterations.
We have discussed this before and still we do not agree. You have collected
the data and think they are worthwhile. I think they detract from the
presentations of you information. As Bob said, we can agree to disagree.
Too many interesting things are going on now to spend time focusing on this
issue that I don't see being resolved.   I will give you the last word on
the subject if you have additional comments to make.

RE: Multiple Iterations of the Rucker Index   Robert Leverett
  May 26, 2006 09:42 PDT 


   Okay, Ed. I'll take you up on that last word. We’ve devoted a lot of
time in to thinking about what the iteration process is doing, or more
to your point, not doing, and in terms of what it specifically doesn't
do, there is little disagreement between us. I certainly don’t see the
iteration process as some highly revealing technique that needs to be
adopted by everyone who computes a Rucker index. However, as long as the
results are carefully interpreted, iteration has value.

    With respect to Mohawk, iteration has provided me with a better view
of the canopy from the top down -something I cannot easily get by
establishing conventional plots unless I have a heck of a lot of them.
Yes, John Eichholz and I are always finding new tall trees in MTSF, but
not by much, and most of the Rucker additional points come from tree
growth of what we’ve already measured. We have the property pretty well

RE: Multiple Iterations of the Rucker Index   John Eichholz
  May 29, 2006 21:48 PDT 

I am kind of late to the party here, but...

The question of the purpose of multiple iterations is an interesting and
controversial topic, which I will summarize as: If a tree grows in the
forest, but is not measured, is it really taller?

What does this mean for the iterations of the Rucker index? Not much,
but we can describe the sorts of questions we are looking to answer.

What are the dominant canopy species in the best subsites? How does this
compare to other forests we have studied? What is it about the site
that makes this so?

How much taller are the outliers than the common examples from the upper
canopy? Where are the examples found? Are they from a single exceptional
grove, are there multiple pockets of high growth, or is widespread high
growth the norm? (Bigtooth aspen, white ash and white pine respectively
at MTSF.) To answer this question, we have to measure lots of trees, and
multiple Rucker iterations help organize our data.

Are the relative rankings of a species consistent throughout a series of
iterations? If so, how does this compare to other forests? At MTSF for
20 iterations white pine is always at the top, white ash next, sugar
maple number three, northern red oak number four and eastern hemlock
number five, except when hemlock is replaced by bitternut hickory. They
are widely distributed and heavily measured species. They really seem to
earn their rankings. The remaining ten or so species found in the top 20
iterations are more sparsely distributed and do not form orderly ranks.

When we have not yet visited a site, we can learn something about the
habitat by looking at a single Rucker index.   The questions above could
not be answered by a single iteration. Add in some trip reports and we
get more insight into the interplay between canopy species. Once ten or
twenty iterations have been compiled, a picture emerges, at least for
the measurer.

And, what can we learn about the measurers of so many trees? Do they
measure in multiples or singly, moving on? If they stop measuring, will
they or the forest be forgotten?

John Eichholz
RE: Multiple Iterations of the Rucker Index   Robert Leverett
  May 30, 2006 09:19 PDT 


You raise provocative questions in your last paragraph. In a one word
answer to all - yes. Of that I haven't much doubt.