Rucker Index Application   Robert Leverett
  May 24, 2005 07:49 PDT 

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   Robert Leverett
  May 24, 2005 11:16 PDT 
   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.