dichotomy

[Mr Fortuner connection modem]

Mike Dallwitz wrote:
"A deterministic procedure is one in which the only
probabilities considered are 0 and 1. A probabilistic procedure is one which
can deal with any probabilities."

OK, I can live with this. Now, you must
agree that a procedure which can deal with ANY probabilities is by nature
"better" (i.e., more general) than one which is restricted to the extreme of
the range. This is one of the aspect of the "rigidity" (i.e., lack of
flexibility) of any dichotomous system.

Then you said:
"DELTA can deal with
non-dichotomous characters - multistate characters, numeric characters, and
text `characters'."

I believe we have another problem of terminology here.
Multistate, numeric, and text are types of characters. Dichotomy is a method
of identification. You can use dichotomy with any type of character. For
example, if a flower can be red, white, or blue: this is a multistate
character. Here is a dichotomous key to go with it:
1 - If flower is red,
species is Red herring
   - If flower is not red, go to line 2
2 - If flower
is white, species is White trash
  - If flower is not white, go to line 3
3 -
If flower is blue, species is Blue funk
  - If flower is not blue, then you
are in trouble Mister, because I am dichotomous.

Your example of how the
red-white-blue flower character is treated in Delta is exactly what I had in
mind when I said "rigidity" or lack of flexibility. If I understand correctly,
you have to code, separately and beforehand, all possible states or
combination of states, and you have to decide, again beforehand, if they are
going to be used for identification or for natural language (NL) description.
In my system, you would define the character as : structure = flower,
descriptor = color, states = red, white, blue, pink. Then species X (all pink)
would be coded pink (100%), and species Y would be coded white (75%), red
(25%). It's a WYSIWYWD system: what you see is what you write down! If the
unknown has spotted flower, the user just adds "spotted" to the list of
states. The point is that all the states are entered separately, as they
appear in a NL description or as the user sees them in the specimens, and that
each type of metadata (here, the percentages) are in a field of their own,
available for any algorithm that needs them.

The Delta "error tolerance"
parameter is a clever way to make the best of a bad method (dichotomy), but it
is far from perfect. If the threshold is set at 2 you will have:
first error =
0% degradation
second error  0% degradation
third error = 100%
degradation
You have diminished the risk of having degradation occur (at the
expense of a loss in discrimination, obviously), but when the user goes over
the threshold, degradation is total. This is hardly what I would call
graceful.

By contrast, a similarity coefficient degrades gracefully because
of its very nature.

Another quote from Mike:
"At any stage, the user has
access to the number of differences
between any taxon and the specimen, and
the actual character values which have given rise to these differences. Surely
this is more helpful than knowing that a taxon is `99% similar' to the
specimen."

Once you know that species B is 99% similar to the unknown, of
course the next step is to get a list of the similar and dissimilar
characters. Such a list can be provided (should be) by any identification
method, including similarity, so this cannot be used as an argument in favor
of dichotomy. An argument in favor of similarity is that, in addition to the
straight list of differences, it gives you an idea of the overall
resemblance.

Now, I want to make it clear that I do use dichotomy. It is
great for eliminating all the taxa that are obviously wrong for the unknown,
using the most reliable characters (of course, the system cannot know which
are the reliable characters unless it has access to metadata about
reliability). A typical identification session would go like this:
Focus on a
large group by immediate recognition, use dichotomy to eliminate the species
obviously wrong, use similarity to rank the remaining species, and use a
browser to check the most likely answers. Once a particular biocenosis is
completely identified, bayesian probabilities could be used for future
identification in the same biotope.

The point is that you need an "expert
workstation" for identification, i.e., a set of related and integrated tools
which gives you the possibility of using different approaches as you wish,
depending of what you want to do.

Renaud Fortuner
fortuner at math.u-bordeaux.fr