To Rucker or not to Rucker, what's in an index?   Robert Leverett
  May 24, 2006 12:42 PDT 

     In a "behind the list" exchange of communications, several of us
are discussing the expansion of Rucker indexing in two distinct ways.
Colby would be surprised and I hope proud.

     We are looking at adopting a compact system of notation to identify
the different kinds of indices we are now using, planning to use, or
thinking about using. We are also looking at expanding the number of
site indices that we typically post for a site on the ENTS website. Some
of us compute several kinds of indices now, but usually don't report
them in list communications. The kinds of indices that could be computed
based on our collective interests include the following:

     1. Regular 10-species height index, [THIS IS THE STANDARD]
     2. Regular height index, but based on a different number of
     3. Iterated height index for either of the above,

     4. Regular 10-species circumference index,
     5. Regular circumference index, but based on a different number of
     6. Iterated circumference index for either of the above,

     7. Regular 10-species crown spread index,
     8. Regular crown spread index, but based on a different number of
     9. Iterated crown spread index for either of the above,

     10. Regular 10-species volume index,
     11. Regular volume index, but based on a different number of
     12. Iterated volume index for either of the above,

     In all the above, a particular species can contribute to an index
calculation only once. However, suppose we were to lift that restriction
and compute a second family of indices where species repetition is
allowed. In the case of 1. above, it would be just the 10 tallest trees
regardless of species. This is admittedly a less valuable kind of index,
but it would add information about species and tree height distribution
for a site. Under both systems, 24 different kinds of indices arise.

   We don't have to go all the way. A system of regular reporting might
include 1and 4 from the above choices for both non-repetition of species
and for repetition. That would be 4 indices per site. We could add crown
spread, but I doubt that we'd ever keep up the crown index. So the 4
could become our standard for site reporting.

   A sample of a compact system of notation that some of us are
experimenting with follows in the examples below, where RHI stands for
Rucker Height Index, RCI for Rucker Circumference Index.

    1. RHI-10-N indicates a height index using 10 species (no species
    2. RHI-7-N   would be a 7-species index with no repetition of
    3. RHI-10-N-3 would indicate the 3rd iteration of a RHI-10-N type
    4. RCI-10-R would indicate a 10-tree circumference index with
species repetition allowed.
    5. RCI-8-N-2 would indicate the second iteration of a 8-species
circumference index with no repetition allowed

   A symbolic way of incorporating these index attributes that utilizes
the power of mathematics and of computer meta-language methodology


   To use the above template, a selection is made from the choices in
braces and the actual number of trees in the calculation is substituted
for n. If iteration is allowed, the above form becomes:

    R{H,C,S}I-n-{N,R}-j where j is the number of the iteration.

   This looks worse than it is. Using the meta-language, we would
recognize RHI-10-N-4 as the 4th iteration of a non-repeating 10 species
height index. To simplify matters, we could agree by convention that
RHI-10 will be shorthand for RHI-10-N. This is the form recommended by
Ed Frank. In most list communications, there isn't a need to utilize the
full notation, but it is there for more rigorous discussions of

    We are mercifully keeping most of these technical discussions to
private e-mails among the few of us, with the intention of periodically
reporting where we stand. If others among you want to participate,
please let us know. If enough do, we'll discuss the topic on the list,
but I suspect that most of you would vigorously exercise the message
delete button.

Re: To Rucker or not to Rucker, what's in an index?   Edward Frank
  May 24, 2006 15:08 PDT 

With your broach of the nomenclature of the various indexes to the ENTS
list, I thought I would make a post to the ENTS list rather than to you
individually. I had hoped for more behind the scenes discussion before
making a broader presentation.

Rucker Indexes strike me a special kind of index that includes a composite
of measurements each from a different species. For example the RI or RHI is
the average of the height of the tallest individual of each of the ten
tallest species on the site. Similarly we can have a Rucker Girth Index, Or
Rucker Volume Index, or any of a variety of indexes including one
representative from each species. I would rather see Rucker refer to just
this type of index as opposed to just any assortment of species.

The nomenclature for these types of lists needs to be clearly stated
initially and follow a logical pattern, to keep from needing to revise it in
the future. I would like to suggest the following naming protocols, instead
of the structure you have cited below and in the MTSF 2006 report.

Rucker Index

The Rucker index was initially devised to characterize the maximum heights
found in a particular area or plot. It is essentially a foreshortened
version of a tree height profile listing in order the maximum heights of all
the species found there. The Rucker Index in its basic form consists of the
numeric average of the ten tallest individuals of the ten tallest species on
the site. It can be used to compare sites in different areas that include
different assortments of species. Other measurements can used to generate
Rucker Indexes following the same format. A Rucker Girth Index would be the
numeric average of the ten fattest individuals in each of the ten fattest
species in the site or area. I can envision Rucker Indexes from a variety of
measurements that may be devised in the future with more data: Rucker
Volume Index, Rucker Canopy Index, Rucker Age Index, Rucker Anything Index.
I would use Girth rather than Circumference. The terms are synonymous and
can be used interchangeably. Why I want to use girth is because G is a
distinctive letter that is not used by any of the other hypothetical indexes
I can think of. The next most common measurement after height and girth is
some for of crown spread or canopy. I can't think of another initial to use
for crown spread or canopy other than C, so I would like to reserve the RCI
for crown spread, and call the circumference or girth measure the Rucker
Girth Index or RGI


RI or RHI: Rucker Height Index Either form is fine, if more than 1 type of
index is being presented then the expanded RHI form should be used

RGI: Rucker Girth Index

In some cases it may be useful to derive a Rucker Index using some number of
species greater or less than 10. Whenever possible a ten species Rucker
should be calculated. Some reasons for using a smaller number of species in
a Rucker Index might include: 1) A limited number of measurements in one or
more sample sets, 2) a strongly bimodal distribution of heights (or other
measured value) among the species in the population, 3) a limited number of
species present in the population in the sample area. Where possible I
would suggest using a five species Rucker index. Fewer numbers than this
would limit the probative value of the index. In addition a mixture of 5,
6, 7, and 8 species numbers would be hard to compare and contrast between
sites. Using a single number, 5 is my suggestion, would facilitate these
comparisons. In other cases a more in depth analysis of a particular site
might be warranted and a larger number of species included in the index. A
Rucker index of twenty species would be an example. Again twenty would be a
good number because it could be standardized to facilitate comparisons
between different areas with more in depth measurements, and it is different
enough from the basic ten species index to give a broader picture of values
in the area under consideration. These numbers would be used as a modifying
suffix to the basic Rucker Initials. For example a Rucker Height index
using 5 species would be RI5 or RHI5. A Rucker girth index of 20 species
would be listed as RGI20


RH5 or RI5: Five species Rucker Height Index
RGI20: Twenty Species Rucker Girth Index

In Bob's recent report he used an average of the heights of the ten tallest
trees in the plot and called it a Rucker Height Index-2. This nomenclature
conflicts with the above protocol for indicating the number of species in
the index. In addition, I do not believe these should be called Rucker
Indexes. And third, I do not believe Bob's proposed nomenclature is
distinctive or can clearly be understood based upon the letters and number
combinations alone. These values may be of importance is some situations
and I am not opposed to gathering them. In general an index of these
measurements should include ten specimens to make it comparable to standard
Rucker Indexes. Fewer than ten values for a numerical average suggests that
there is not enough data for the average to even be meaningful. I would
suggest the numerical average of the ten tallest trees on the site simply be
called a Height Index: or HI, the numerical average of the ten fattest trees
be called a Girth Index or GI. Again if fewer or more than the standard
number of ten specimens were included in the index it could be modified as
noted above for the Rucker Indexes, but I do not think this is something
that should be done except under extraordinary circumstances.


HI: Height Index - numerical average of the heights of the ten tallest
trees in a plot
GI: Girth Index - numerical average of the girths of the ten fattest trees
in a plot.

Species Index: In past analysis Bob has used a species height index which
consisted of the numerical average of the ten tallest individuals of a
particular species on a site. This can be expanded to include other
parameters than just height. The nomenclature should be straight forward.
A Species Height Index would be designated SHI, As noted above some
situations may require that fewer than 10 or more than 10 individuals be
used when calculating the species index, this can be noted as explained
above for the Rucker Index. One example of why a lower number might be
used, would be if a series of species indexes were calculated for multiple
species at a site. For common species ten individuals would be easy to
include. For other less common species ten mature individuals might not be
present . I can only think of the locations of three Sassafras Trees at Cook
Forest, while Dale has dozens of white pines over 150 feet tall.


SHI: Species Height Index - numerical average of the ten tallest
individuals of a particular species in a population
SGI: Species Girth Index

There are a number of other indexes being used by ENTS. One is the Tree
Dimension Index which has been described elsewhere. It is in two forms.
One form includes Height, Girth, and Maximum Crown Spread. The other form,
like the one used by Bob in his most recent MTSF Forest Research Report,
consists of just Height and Girth. Each value is expressed as a percentage
of the maximum dimension of the parameter know for that species. These
percentages are then summed to calculate the TDI. The TDI with height and
girth has a maximum value of 200% for a tree that is both the tallest and
fattest of the species.

Another measure that has been discussed are multiple iterations of various
indexes. ...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.

These are suggestions for general discussion. I believe they are
reasonable, more straight forward to interpret, and simpler to implement
than the nomenclature suggested by Bob L. below.

Ed Frank

RE: To Rucker or not to Rucker, what's in an index?   Robert Leverett
  May 25, 2006 06:27 PDT 


   You've done your customary thorough job of presenting the
alternatives. Thanks as always. I decided to post the discussion to the
list to test the level of interest on the topic and to insure that folks
like Anthony Kelly, Carl Harting, Darian Copiz, Michael Davie, etc.
aren't left out. The limited list of addressees in the off-list
communications was growing quite long.     

   Actually, I can live with any of these forms: RHI, RI, RHI10, RI10,
RHI-10, or RI-10. G for girth as opposed to C for circumference is fine.
I prefer girth to circumference since the latter implies a circle and
misleads people into thinking that circumference and diameter really do
apply to the shapes of tree trunks.

    In terms of HI or HI10 for overall 10 tallest tree height index,
that's fine. In terms of my original definitions, this implies that
species repetition is allowed, i.e. the 10 tallest. GI or GI10 for the
10 fattest, is fine.

    Ed, what I'm really arguing for in all this is for us to move toward
the use of multiple indices so that we get a clearer idea about the
maximums achieved by a site's trees. That is what Rucker indexing is all
about. What are the best ways to profile a site from the top down. Thus,
when I presented a combination of indices for MTSF, the choices looked
as follows:

Site    RHI10-N   RHI10-R     RCI10-N    RCI10-R

MTSF     136.0     161.0       12.4       13.7

    Simplifying the above notation, per your recommendations, we get:

Site     RHI       HI          RGI        GI

MTSF     136.0     161.0       12.4       13.7

     The second notation is simpler (obviously). The simpler the better.


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: To Rucker or not to Rucker, what's in an index?   Edward Frank
  May 26, 2006 17:13 PDT 


Colby was a participant in early discussion on expanding the basic Rucker
Height Index to also include A Rucker Girth Index, and he even looked at an
index of the girth x height, all using ten different species.

Pushing the Envelope Further: