**MAT 7310
Summer 2002**

Constructing a Dichotomous Key

*freely adapted from Perry, Morton, Perry 2002*

To classify
organisms, you must first identify them. A
taxomonic key is a device for identifying an object unknown to you but that someone else
has described. The user chooses between
alternative characteristic of the unknown object, and by making the correct choices,
arrives at the name of the object.

Keys that
are based on successive choices between two alternatives are known dichotomous keys
(dichotomous means to fork into two equal parts). The
set of choices may be regarded as a flow chart with each step as a branch. In graph theory, diagrams of these choices are
called binary trees. Searching algorithms can
be built this way. The identification
procedure is deterministic, and terminates after a finite number of steps. So this process goes by many different names in
various science disciplines.

Suppose the
geometric objects below have unfamiliar names. Look
at the dichotomous key following the figures. Notice
there is a 1a and a 1b. Start with 1a. If the description in 1a fits the figure you are
observing better than the description in 1b, then proceed to the choices listed under 2,
as shown at the end of line 1a. If 1a does not
describe the figure in question, 1b does. Looking
at the end of line 1b, you see the figure’s name is Eric.

Using the
key provided, determine the name for each object. Write
the name beneath the object and then check with your instructor to see if you have used
the key correctly.

__ ______________ __ ___________
_________
_________
_________

Key |
||

1a |
Figure with
distinct corners |
2 |

1b |
Figure without
corners |
Eric |

2a |
Figure with 3
sides |
3 |

2b |
Figure with
more than 3 sides |
4 |

3a |
All sides equal
length |
Gina |

3b |
Sides not all
equal length |
Stan |

4a |
Figure with
only right angles |
Sue |

4b |
Figure with
angle other than right |
Pots |

This is not
the only such key; there are lots of others. Can
you make one that is longer (requires more than four decisions)? Can you make one that is shorter (requires less
than four decisions)?

Now we will
construct a dichotomous key for the participants in this workshop. We will work in two groups.

To plan a
dichotomous key, we need to set up binary (two choice) categories that will differentiate
members in your group. The most obvious split
it male/female, but this need not be used, even as a first cut. Look at the sample branch diagram below.

Select
characteristics for your group (they must be distinguishable by visual inspection), and
construct a branch diagram; condense it into a dichotomous key. (Every member of your group will carry the same
key.) Once both groups have complete keys,
exchange your key with an individual in the other group.
Key out the individuals in the other group without speaking until you believe you
know the name of the individual you are examining. Ask
that individual if you are correct. If not, go
back and find out where you made a mistake, or possibly where the key was misleading.