| 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?
Premise:
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
tall.
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 |
dbhg-@comcast.net |
|
May
17, 2005 04:28 PDT |
Ed:
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.
Bob |
| ENTS
and science |
Edward
Frank |
|
May
17, 2005 11:15 PDT |
Bob, ENTS
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 |
Ed:
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.
Bob
|
| Question
to Dale Luthringer |
Robert
Leverett |
|
May
18, 2005 09:19 PDT |
Dale:
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.
Bob
|
| Re:
Question to Dale Luthringer |
Edward
Frank |
|
May
18, 2005 12:37 PDT |
Bob,
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
Earth.
Darian
|
| Continuing
dialog with Darian |
Robert
Leverett |
|
May
19, 2005 10:16 PDT |
Darian:
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.
Bob |
| 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 |
Ed:
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.
Bob
|
| Back
to dialog with Bob Leverett |
Edward
Frank |
|
May
20, 2005 18:12 PDT |
Bob,
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
maturity.
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
distribution?
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 |
wad-@comcast.net |
|
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.
Scott
|
| Flukes:
modular vs. unitary |
tpdig-@ysu.edu |
|
May
21, 2005 16:44 PDT |
ENTS,
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!
Tom
|
| Re:
Flukes: modular vs. unitary |
Edward
Frank |
|
May
22, 2005 18:05 PDT |
Tom,
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 |
Ed,
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.
Darian
|
| Outstanding
performers |
Robert
Leverett |
|
May
23, 2005 07:42 PDT |
Darian:
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.
Bob
|
| RE:
Flukes: modular vs. unitary |
Edward
Frank |
|
May
23, 2005 18:44 PDT |
Darian,
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.
Ed |
| 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 |
ED:
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
persistent.
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.
Bob
|
| RE:
Flukes: modular vs. unitary |
Edward
Frank |
|
May
24, 2005 08:31 PDT |
Bob,
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.
Ed
|
| 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.
Bob |
| Back
to Don Bragg |
Robert
Leverett |
| Feb
22, 2006 09:57 PST |
Don,
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.
Bob
|
|