The next step for MTSF   Bob Leverett
  4/16/2004 &  4/19/2004
Private Emails 

The attached Excel spreadsheet takes the Rucker indexing to the next level by computing the index on each species and then an overall. At present, this incorporates 128 trees in Mohawk. The single index for 13 species is 129.6. The composite index is 121.6. Both will drop with the addition of the white birch, but we need to add the white birch to paint a better picture of the MTSF canopy potential.


   My full dataset for MTSF currently includes 712 trees. I'll soon send
another spreadsheet in a form more appropriate to web posting. I usually
send a "limited edition" to a small group of you who are more apt to think
about it and make suggestions for improvement.


RE: The next step for MTSF   Edward Frank
  Apr 19, 2004 17:21 PDT 

Thanks for the information. I plotted the height versus cbh for all of the
white pines in the dataset you sent and all of the white pine from Dale's
PA data set. The results are pretty noisy but shows a couple of clear
trends. Overall the pines at Cook Forest have a slightly greater diameter
at any given height than do the ones at MTSF and Mass. In general you see
only a slight, but clear, increase in diameter as the tree height
increases. At the lower end of the height scale you also see an increase
of diameter. I think this is partially because of selective sampling.
There are few trees at the lower heights measured, and those likely were
selected to be measured because they seemed unusually fat with respect to
others of their height category. Over a broader perspective it might be
expected that there would be a bimodal distribution of height versus cbh
plots. I am thinking there is the primary trend of trees getting fatter as
they get higher, but a second bump might occur as open-grown trees put more
growth into diameter and crown-spread and less into overall height. There
is insufficient data yet to actually see if this is true.

There is less data for the other species. Using Dale's Pa dataset, similar
trends can be seen in Black Cherry, Tuliptree. Interestingly a plot of
Eastern Hemlock actually shows a decrease of diameter with increasing
height.   This may reflect the idea that trees in a tighter stand grow
taller at the expense of diameter.

Your chart shows a h/d ratio and a circ x height calculation for the groups
of ten trees in each species rucker index. I am not sure that these
numbers mean anything of importance, but since they are easy to calculate
we can see. There is such a high degree of variation from tree to tree
with respect to various height diameter ratios the results of the average
is highly dependant on which individual trees are included in the index.
But I don't know how to do anything better.

<<the rucker index for a particular species is a new idea that has not been
discussed in detail yet and is still being played with. Essentially it is
the average of the tallest 10 specimens of each particular species in a
study area. If there are enough of them then they can be used to calculate
an average multispecies rucker index for the site by averaging the average
heights of the average heights of the top ten species.>>


RE: The next step for MTSF
   Apr 19, 2004 19:27 PDT 


   The populations of pines in Cook Forest are quite a bit older than those in Mohawk and that accounts for the differences in average diameter between the two sites.

   There are a number of separate populations of pines being sampled in Mohawk that vary in age from 100 to 175 years. Stands that are growing exceptionally fast can reach significant heights and still have small diameters. The Pocumtuck Pines are in this class. We can divide the Pocumtuck Pines into six sets with each pine belonging to 3 sets. We have the set of older pines and the set of younger pines. We have the set of pines that receive more light and the set that receive less light. We have the set that receive the most water and the set that receives the least. The pines that are the oldest, receive the most light, and receive the most water are both the largest and slightly the tallest. The pines that are the youngest, receive the least light and water are the smallest and shortest. Some pines fall into each combination of age, light, and water. Of course other factors such as injury and disease enter the picture to slow growth, but discounting those factors, competition with neighbors enters the picture to allow some slender pines to gain great height.

RE: The next step for MTSF    Ed Frank
   Apr 19, 2004 19:49 PDT 


So you have eight possible combinations (2 x 2 x 2). How many trees are
in the Pocumtuck Pines? Are there enough trees to fit into each subset
to do a meaningful comparison? Given the broad variation in diameter
versus height plot, you will need significant numbers of trees in each
box in order to make comparisons.   I would guess a bare minimum of ten
in each category would be needed to do anything at all, with a number
more like twenty to get any reasonable projection. I am just estimating
based upon the series of height versus cbh plots I did for a variety of
species using your data and Dale' datasets. If the variation from tree
to tree is lower within these more strictly defined categories then you
can get away with fewer samples, but I am not encouraged looking at the
datasets I have in hand.. Good luck and keep me posted on how things
are working out.

RE: The next step for MTSF
   Apr 20, 2004 04:16 PDT 


   There are probably 200 pines in what we call the Pocumtuck area. The dense clusters of white pine there create an almost uniform canopy in places with trees varying in height on the order of 12 feet and circumference of 3 feet for the same moisture and soil condition and moderate changes in light exposure and ages varying between 5 and 10 years. Variations in age and height each run between 7 and 9%, while variations in circumference run between 35 and 40%. In the older Elders grove, the age range varies by about 9 to 11%, height by 12 to 14%, and circumference by 25 to 30%. This is the first crack at testing stand limits. More to come.

Range of WP dimensions    Robert Leverett
   Apr 20, 2004 09:12 PDT 

Lee, Ed, Colby, et al.:

   Based on current data, what might we expect from a 125 to 135-year
old white pine stand in MTSF in terms of the range of tree dimensions?
Do we have enough data to compute the ranges? Yes.

    Circumference: 6.5 - 10.5 feet
    Height:         135 - 155 feet
    H/D Ratio:       40 - 75

    Circumferences can vary by almost 40% for living trees.
    Heights can vary by about 13% for living trees.
    Age variation is 7%.

   How will these numbers change with added aging, say 40 years? What
would the broadest range of height to diameter ratios likely be
throughout the life of the stand?

   How do these ratios compare with white pines in the Connecticut River
Valley? Holding age constant, the Valley ratios will be a little less,
reflecting less height for the same diameters. Calculating exactly how
much less requires more data though. That will be one of the objectives
of this summer, i.e. broaden the base of white pine data across a large
area of southern and central New England.

RE: The next step for MTSF    Edward Frank
   Apr 20, 2004 11:40 PDT 


I am not convinced this is the reasons for the disparity is diameter per
given height. First I included the entire dataset for both sites. Are you
sure that the majority of trees at all heights from Cook Forest are older
than the majority of trees from all height classes from MTSF? If there is
a range of ages in the data set, with the older trees at Cook just
dominating the upper end of the scale, it does not explain the
disparity between diameters at all of the lower ranges either. You can see
from the raw scatter plot that overall the MTSF trees have a smaller
diameter per given height than those at Cook Forest. I used a polynomial
line fit to plot the average values and they tended to be just less than a
foot smaller in diameter at virtually all height across the sampling set.

If many of the trees Dale sampled are not that old, and their inclusion in
the plot still results in fatter trees at Cook Forest, what does that say?
Assuming the trees are on average older at Cook than at MTSF, why should
they have a different shape just because they are older? If the trees are
growing more slowly upward, why shouldn't they be growing more slowly in
diameter as well, all other factors being equal. I think at this stage the
only valid conclusion that can be drawn is that the trees at Cook are on
average fatter. The cause for the difference may be a disparity in average
ages, but may be some other factor.

I have been wondering. There seems to be a change in the maximum height of
 a species with latitude, a surrogate for growing season, with the maximum
height for white pine decreasing as you go northward. What if that pattern
is reflected in the diameter of the trees, with trees also being skinnier
as you go north. One way to test this would be to see if a plot of trees
from GSMNP or other southern sites are both taller overall, and fatter for
a given height.

Ed Frank
RE: The next step for MTSF    Robert Leverett
   Apr 20, 2004 13:05 PDT 


   Yes, the population set from Cook represents a considerably older
forest. The Mohawk trees are more slender on the average because they
are at least 100 years younger. At 1/20 inch average radial growth for
the next 100 years, the Mohawk pines will put on close to another foot
which would bring them into the size range of the Cook pines. Many of
the Cook Forest trees have flat crowns and are putting on very little
height growth because they are 250+ year old trees with some at least
350. The oldest of the Mohawk Pines are 175 years and there are only 18
in that age range. Most are 125 to 150. In one area they are barely 100
years old.

   If Dale can choose the younger pines and give us an approximate age
for them, I expect will see a more Mohawk profile, at least based on the
younger pines I saw at Cook. I'll put together a better distribution in
the coming week that adds columns for age, terrain, and light
availability. The initial sample will be smaller, because I'll need to
revisit the sample trees and compute a terrain index. I should have been
doing this all along.

   Incidentally, Lee Frelich believes that the height potential of
Mohawks trees to be about 170 feet. I think he is right in his range
assessment. I few might possibly make it to 175. In terms of radial
growth, I'll be taking a few cores over the next several weeks to get at
the present growth rates. Maybe we can come up with some neat


RE: The next step for MTSF    Edward Frank
   Apr 20, 2004 14:14 PDT 


Why would the trees at Cook Forest in heights, from say 125 feet tall and
155 feet tall, stop growing upward as much and put their energy into
getting fatter while those younger trees at MTSF put their energy into
growing taller? Neither are yet reaching their projected maximum heights.
Why did they not continue to their height potential before getting fatter?
Are the trees at MTSF going to slow getting taller and start to fatten-up
over the next hundred years? Why are some trees growing to a certain
height and then becoming fatter rather than becoming fatter at some other
height? Do they grow tall until a certain age then fatten-up? Is upward
growth versus increasing diameter age dependant? and why? I remain
unconvinced that the operative factor is age.

RE: The next step for MTSF    Edward Frank
   Apr 20, 2004 14:19 PDT 


What about it? Are there any significant number of younger trees in the
pine data set you sent to me for the website or are they all older? If so,
can you delineate which ones might be younger trees from your notes and
estimate some ages? It would give us something to compare with Bob's data
at MTSF. I understand that more measurements would be great, but is there
any that can be pulled from the existing data at this time to play with?


RE: The next step for MTSF, coming to conclusions....    Paul Jost
   Apr 20, 2004 15:10 PDT 

The tendency that I see is that trees often get shorter AND fatter as you go
north, particularly in virgin stands. As mentioned before, the past record
white pine trees in Wisconsin and Michigan were approaching 18' in girth
while "only" around 150' tall. The taller trees in Wisconsin were about
165' tall and 13.5' in girth while most of the taller Smokies pines were
much taller and slightly smaller if I recall correctly. Cook is a nearly
virgin area while Mohawk is an old growth recovery area, therefore
accounting for some of the difference in age structure and size
distribution. There are too many other variables involved to make a
sweeping overgeneralization of a simple relationship for height to diameter
ratios. In addition to regional variations, stand age and origin can be a

In the old growth pine areas that I have visited, especially the Nicolet
National Forest's Cathedral Pines Grove, I have noticed a h/d disparity.
Remembering that usually pine enters an area after a disturbance, I have
noticed that the oldest and fattest trees in many of the larger old pine
groves often tend to be shorter. They probably were the pioneer trees and
entered a gap or larger opening following some apparent disturbance. In
larger disturbance areas, they maxed out at a lower height because of
limited competition or damage during the disturbance and put on bulk instead
of height before getting to the stage of slow growth due to old age. The
tallest trees were clearly younger than the short, fat, old fellows. They
had a better h/d ratio and were probably seeded by the older pioneer trees.
There could be many other scenarios.

Be careful when trying to come to conclusions when analyzing datasets that
have limited numbers of variables. H/d ratios of individuals and
distributions within a stand are dependent to varying degrees upon many
factors including but not limited to: stand age, stand density, species
content, soil characteristics, topography, extent of exposure to insects and
pathogens, meteorological variations, genetic variation, etc.

Paul Jost
RE: The next step for MTSF    Dale J. Luthringer
   Apr 20, 2004 


All the Cook Forest white pine on that data set are definitely over 150,
probably even over 175. I'd say roughly 50% of those measured should
easily go over 200 years. Max age would be close to 350.

At Cook Forest, I believe I've been observing the trend that once the
pines lack significant competition for sunlight from surrounding trees
(get above the canopy), they tend to slow down in terms of height and
start to put on girth. Most are so old at this point, that they may
also be showing that they don't grow tall as fast when they were a
"teenager", as compared to how slow when they're "senior citizens".

Paul's comments about the largest CBH pines being shorter, holds true at
Cook Forest also. A majority of our "fattest" white pines are very old
275+, probably ~350 years, but their tops have been knocked off due to
natural disturbance, such as wind or lightning.


RE: The next step for MTSF, coming to conclusions....    Bruce Allen
   Apr 21, 2004 05:59 PDT 


I would add tree growth rate to your list of factors that influence H:D
ratios (although a lot of the factors that influence growth were on your
list). The maximum height a tree attains will depend on height growth rate.

RE: The next step for MTSF    Lee E. Frelich
   Apr 21, 2004 06:31 PDT 

Bob, Ed et al.:

I am very sure that had the trees at Cook forest been measured when they
were the same age as MTSF trees are now, they would have had higher H:D
ratios. They are at a lower latitude, and soils are not much different, so
H:D as well as height at a given age would be higher at Cook Forest. The
Cook trees have reached their asymptotic height but continue to put on
dbh. H:D ratios always go down as stands advance from young age to
maturity and old growth. If you really want to compare sites in detail, you
need to find trees of all dbh's and/or ages (say from 50-300 years old, and
from 5 inches to 45 inches dbh), and compare the elevations of the
regression lines (height on Y-axis, age or dbh on X-axis). There is no
doubt that the regression line for Cook would be higher across the range of
dbhs and ages.