Botany(1978) 3(2): pp. 159-178
Systematu
? Copyright1978 by the American Societyof Plant Taxonomists
Cladistics for the Practicing Plant
Taxonomist
VICKI
A. FUNK
AND TOD
F. STUESSYI
Abstract. Two of the prinicipalgoals of plant systematicsare: (1) to pr-ovidepredictivesystemsof classificationand (2) to develop phylogenies.Traditionally,both
of these goals have been sought by conventionalphyleticapproaches. HoWever,the
and phylogenies,especially
assumptionsand methodsof ai-rivingat the classifications
as portrayedin phylogenetictree diagrams, are frequientlynot evident. Cladistics
has recentlyevolved as a methodof more preciselyachievingthese goals. Beginning
withHennig's methodologyover two decades ago, several approaches, some involving computertechniques,have been developed. These include Parsimony(including
FarrisTrees and Networks),and CharacterCompatibility.The efficacyof thesemethfrom the
ods to plant systematicshas not yet been fullyappr-eciated,par-ticular-ly
viewpointof the practicingtaxonomist.We recommend the routinetise of cladistics
in revisionar-y
studies or in any other type of investigationWhichfocuiseson the
development of phylogenetictrees. For the pr-acticingplant taxonomist,claclistics
phylogeniesby objectiveand r-epeatablemeans. This
offersa methodof constructinig
presentscertainadvantages over inferringphylogenyby the convenitionalimethocd,
of
the most importantof which is to facilitatediscussion by a clear-presenitationi
assumptions.
procedures and evoluitionary
Since the publicationof Darwin'sOn theOrigin ofSpecies byMeans ofNatuhas developed towardunral Selection(1859), interestamong systematists
derstanding the evolutionaryhistoriesof organisms. This interesthas
continued and intensifieduntil,at the present time,attemptsto reconstruct phylogenies are regarded by most workers as a necessary and
importantpart of systematicinvestigations.At the same time,much use
has been made of the ideas inherentin the developmentof phylogenies
for constructingclassifications.These two activitiesusually go hand in
hand and are togetherregarded by many workersas inseparable parts
of the concepts and methodsof modern phylogeneticsystematics.
In the past two decades, interesthas arisen towav-dlookingcriticallyat
Some
thiesetime-testedideas and procedures of phylogeneticsystematics.
critics,in fact(e.g., Sokal and Sneath, 1963; Colless, 1967) have suggested
thatphylogeneticevaluationsbe leftapart fromattemptsto achieve m-axThis viewpointhas led to the well-known
imallypredictiveclassifications.
and useful area of "numericaltaxonomy,"whichalready has made many
importantcontributionsto systematicbiology(cf.Sneath and Sokal, 1973,
for a review).Other workershave focused on the logical and philosophical aspects of phylogeneticsystematics(e.g., Buck and Hull, 1966; Hull,
1967, 1974). Stillotherworkershave become conerned withthe concepts
and methodsof assessing phylogeneticrelationships,and especiallywith
the production of phylogenetictrees (for a historyof the development
1
Botany,Ohio State University,Columbus, OH 43210.
159
160
SYSTEMATIC
[Volume 3
BOTANY
of phylogenetictreesin biology(cf.Voss, 1952). These laterattemptsto determinemore clearlythe phylogenyof organisms,and in particulartheir
evolutionarybranching patterns,have been given the label "cladistics"
(Mayr, 1965, 1969).
Differentcladisticapproaches have been developed over the past 20
years, and one of the earliest and most influentialwas that of Hennig
(1950, 1966a). His ideas, although difficultto follow,provided a strong
basis for futurework. At about the same time,a method was developed
by Wagner at the Universityof Michigan in the late 1950's, which
has now become known as the Wagner Groundplan/Divergencemethod (Wagner, 1961, 1966). From these two initialapproaches have come
several others, most of which can be viewed as belonging to two
basic types (Estabrook, this volume): (1) Parsimony,and (2) Character
Compatibility.These two approaches represent the principal options
available at the presenttimewhich are mostuseful for the plant systematist.
Because cladisticshas great potentialfor aiding in the discernmentof
the branchingpatternsof phylogenetictrees and in the constructionof
and because practicingplant taxonomistsare
phylogeneticclassifications,
engaged in these activities,we believe it helpful to offera discussion of
cladisticsthatis directedtoward these workers.While manyphylogenies
have been produced by workersusing informalmethods, the assumptionsand procedures behind these schemes are usuallynot statedclearly.
Although the end-productsmay be useful, a full understandingof the
portrayedrelationshipsis oftenimpeded because of a lack of information
on how the scheme was devised. Use of explicitcladisticmethodsallows
for improved communicationon all aspects of the process of making a
phylogenyas well as of the relationshipsit portrays.The purposes of
our paper, therefore,are to: (1) explain the specificprocedures involved
with differentcladistic methods; and (2) evaluate the utilityof these
procedures for the practicingplant taxonomist.
PROCEDURES
OF SELECTED
CLADISTIC
METHODS
A number of differentcladisticmethodsfordeterminingrelationships
already have been developed. These methods provide an objectivebasis
fordeterminingbranchingpatternswhichcan then be used in constructing phylogenies.The concepts and ideas of these differentcladisticapproaches have been discussed in the previouspaper by Estabrook(1978).
It is our intent,therefore,to present the procedures of the different
methods that we believe are most applicable to practicingplant systematists.Some methods,such as the statisticaltechniques of Edwards and
Cavalli-Sforza(1964; see also furtherrefinementsby Felsenstein,1973)
and those used in studies of macromolecularevolution (e.g., Fitch and
Margoliash, 1967; Dickerson, 1971; Fitch, 1971, 1975; Boulter, 1973,
1974; Beyer et al., 1974; Penny, 1976; Goodman and Pechere, 1977;
Moore and Goodman, 1977) will not be discussed here.
1978]
FUNK & STUESSY:
CLADISTICS
161
IN PRACTICE
TABLE
1. Basic data matrixof hypotheticaltaxa (1-8) withcharacters(A-H) shown
in two-state(O or 1) configuration.
Characters
Taxa
A
B
C
D
E
F
G
H
1
0
0
1
0
0
0
0
0
2
3
4
5
6
7
8
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
Due to the many overlapping similaritiesand the historicaldevelopmentof the differentcladisticmethods,there are several ways that they
can be grouped. One way is to separate them on whethertheyare based
on similaritiesor differencesof characterstates.For instance,the methNelson and Van Horn, Prim, and Wiffin
ods of Farris (tree/network),
and Bierner are based on Manhattan Distance. The resultingnetwork/
tree is formed by using in some manner the minimumamount of distance between OTU's.2 Because these methods are the result of differences, it is often not necessaryto specifyprimitiveand advanced character states. On the other hand, methods such as those of Hennig,
Wagner, Camin and Sokal, Farris (WISS), and Estabrook are based in
some manneron shared derived characterstates.Because theyare based
on the maximum number of these shared derived states,it is usually
necessaryto determine the primitiveand advanced conditionsof each
character.Those two groups of methodsgive two differentwaysof looking at the same taxa.
Another way of grouping the differentcladistictechniques (following
This
Estabrook,thisnumber)is intoParsimonyor CharacterCompatibility.
grouping is used here to facilitatecomparison withthe previous paper.
For employmentof eitherof these general cladisticapproaches to produce a directionalevolutionarytree, the charactersused in an analysis
mustbe divisibleinto states,and eitherprimitiveand advanced character
statesor an ancestraltaxon withinthe group mustbe selected.Two basic
matricesare necessary for most of these methods. The firstis a basic
data matrix(Table 1) in which the numerical values representthe state
of each character for each taxon. The second matrix is one showing
ManhattanDistance (Table 2), whichis simplythe sum of the differences
of the absolute values of all the characterstates for which any two taxa
differ.
2 Also referredto as "OTU's," operational taxonomic units, or "EU's," Evolutionary
Units. For convenience,OTU is used throughoutthe rest of this paper.
162
SYSTEMATIC
TABLE
Table 1.
2.
[Volume 3
BOTANY
Manhattan Distances between pairs of taxa based upon data presented in
Taxa
Taxa
1
2
3
1
2
3
4
5
6
7
8
0
1
0
2
1
0
4
5
6
7
8
3
2
1
2
5
0
1
2
3
2
3
0
3
3
4
5
0
2
1
6
3
4
0
2
1
6
3
4
2
0
Methods Minimizingthe Amount of Evolution (Parsimony)
Because the taxonomistrarelyknows all aspects of the course of evolution fora particulargroup (even if fossilsare available), some assumptions about how evolution proceeds must be made before phylogenies
can be constructed.Although evolution has undoubtedly proceded in
differentways and at differentrates withinvarious taxa, in the absence
of evidence to the contrary,one alternativeis to assume the shortestand
most feasible pathway.Withinthis context,two kinds of methods have
been developed: those which do not allow reversal of charactertr-ends,
and those which do.
No Reversals of CharacterTrendsPermitted.-This alternative assumes not
only that evolution has proceded in the shortestway, but also that no
reversals in character trends have resulted. This concept has been discussed by several workersin detail (e.g., Camin and Sokal, 1965; Wilson,
1965), and it clearlyis an assumption that is valid for some characters,
but not for others.
Camin and Sokal (1965) developed a method thatassumes: (1) thatwe
have knowledge of the directionof the evolutionarytrendswithincharacters, and that the character states can be arrayed in an evolutionary
sequence fromprimitiveto derived; (2) thatthe ancestralstatearose only
once in the taxa at hand; and (3) thatevolutionis irreversible.The primitivestate of each characteris coded as zero and the derived statespositiveor negative.A linear sequence is constructedforeach character,the
patternsof whichare irreversible.The patternof one characteris drawn
based on the statesof each OTU, and then all the remainingcharacters
are fittedto this pattern.The number of extra steps for-each patternis
calculated, and the tree with the smallest number of extra steps is the
most parsimonious.This method resultsin the "optimal pattern"cladogram. There are two additional methods for refiningthe cladogram and
making it more parsimonious. One removes charactersand OTU's by
trialand errorand the otherremovesbranchesto search fora cladogram
1978]
FUNK & STUESSY:
CLADISTICS
IN PRACTICE
163
witheven fewersteps. These techniques are infrequentlyused, although
one application to a plant group does exist (Baum, 1975). Directionsare
available for makingcomputationsby hand (Camin and Sokal, 1965) but
theyare cumbersomein large groups. Computer programsare also available (CLADON I, II, and III, respectively,used in sequence; Bartcher,
by
Estabrook (1968) refinedthe programns
1966) but theyare inefficient.
limitingthe number of nodes to be considered. The most efficientprogram for drawing cladograms based on the principles of Camin and
Sokal, however, has been devised by Nastansky,Selkow, and Stewart
(1974).
Farris, Kluge, and Eckhardt (1970) developed a method called the
Weighted Invariant Step Strategy(WISS) which also assumes that no
reversals have taken place. This method is based on the idea that the
larger the number of derived character states shared by a group of
OTU's, the more likelyit representsa monophyleticgroup. The method
involvesselectinga group of OTU's that has the largestnumber of derived steps. These are determined by constructinga data matrix and
characterstatetree foreach character,and by thencountingthe number
of derived steps each pair of OTU's has in common. Once a group of
OTU's has been chosen, it is removed from furtherconsiderationand
replaced by the calculated mostrecentcommon ancestorto findthe next
mostcloselyrelatedOTU, and so on, untila treeis constructed.Although
this method can be done manually, a computer program is available
(Farris et al., 1970) that will handle larger numbers of charactersand
OTU's. The technique also includes an option of using character state
networks (in which the direction of evolution has not been stated)
instead of trees. Neither approach has yet been used with any plant
group.
Reversal of Character Trends Permittedl.-These methods seek the most
parsimoniousroute forbranchingpatterns,but theyalso permitthe reversal of character trends. Character reversal is an importantfactorin
plant systematicsbecause reversalsin mosttypesof charactersare known
to have occurred (Eyde, 1975).
The least complicatedof thistype of parsimonious methodsis that of
Kruskal (1956) and Prim (1957). There is no biological theoryattached
to this type of program; it was developed in order to determine the
shortestpossible networkof directlinksbetweena given set of telephone
terminals.It simplyattaches taxa togetherthat have the least distance
fromone another.The procedures of the method as presentedby Farris
(1970) are simple: (1) pick an OTU as a startingpoint; (2) findthe OTU
that is closest to it (smallestManhattan Distance) and connect them; (3)
compute the ManhattanDistance between each of the remainingOTU's
and the OTU mostrecentlyadded to the network;(4) findthe OTU that
is closestto the mostrecentlyadded OTU and add it by connectingit to
the node from which it differsleast; (5) continue until all OTU's have
164
SYSTEMATIC
BOTANY
[Volume 3
been placed. An example of the resultantnetworkof relationshipsis
shown in Figure 1. For additional details of both the algorithmand the
Fortran IV program to performit, referto Farris (1970).
Wagner developed a simpleoperational methodforestimatingbranching patternsin the 1950's and it was used several times (e.g., Hardin,
1957; Iltis, 1959) before he published it in 1961. His method assumes
thatthereis a basic groundplan of similarityunderlyingall phylogenetic
groupings,that plants which have in common a majorityof similaradvanced characteristicshave the same common ancestry,and that evolution usually proceeds in various directionsand in differentlines. The
primitivestates of characters (and hence also the advanced states) are
determinedby assuming that they are likelyto be widespread withina
group (cf. Estabrook, 1977, for commentson this criterion),to be associated with primitivestates of other characters known from other evidence, and to be presentin manyof the representativesof closelyrelated
groups (out-groupcomparison).
There are fourmajor procedural steps in the Wagner Groundplan/Divergence method: (1) studythe taxa and select a primitivestatefor each
character (usually only those characters are selected for which there is
a strongindication of evolutionarydirectionality);(2) constructa basic
data matrixassigninga value of zero to the primitivestate and a value
of one to the derived state[a value of 0.5 or any otherintermediatevalue
can be assigned to an intermediatestate(or states)if so desired]; (3) sum
the values of the charactersfor each OTU to find the total divergence
value; (4) place each OTU on a diagram consistingof concentrichemicircles (Fig. 2) on the line that corresponds to its total divergencevalue
(the level of divergence increases from the center outward on the diagram); and (5) join OTU's on differentcircleswiththe maximumnumber of shared derived character states. Hypothetical taxa (sometimes
called HTU's, "hypotheticaltaxonomic units," Farris, 1970) are often
postulated to provide needed branching points on the diagram. Examples of thismethodare available in Hardin (1957), Benson (1962), Mickel
(1962), Scora (1967), Wagner (1969), Solbrig (1970), and Bacon (1978).
Afterthe developmentof Wagner's Groundplan/Divergencemethod,
several programs were writtenso that large groups of characters and
FIG. 1. Graphic presentationof the cladisticrelationshipsof Gutierrezia
(Compositae)
constructedby the method of Prim-Kruskal(from Solbrig, 1970, p. 227). Shaded area
indicatesNorth American species.
FIG. 2. Graphic presentationof the cladisticsof Gossypium
(Malvaceae) using the Wagner Groundplan/Divergencemethod (fromFryxell,1971, p. 558). Lettersreferto shared
derived characterstates; open circlesindicate hypotheticaltaxonomicunits (HTU's).
FIG.3. Three Farristreesobtained by Baum (1975, p. 2125) forthe hexaploid species
of Avena (Gramineae). The differencesin the trees result from differentHTU's being
chosen as the ancestor.The numberson the branches referto cladisticdistance.
1978]
FUNK & STUESSY:
CLADISTICS
165
IN PRACTICE
GI vnsa
I~~~~~~~~~~~~~~~~~~~
Ga ana
ssp. isernhl
Mandonii
otina
ssp.gilliesi
ssp.mandoan
Spathullata
Bracteata
Ameghinoi
Giandis
Ruix-Lealil
Ruiz/Lealii
Californ ca
Sarerhrae
Neaena\
Re pens
Baccharides
Mlcracephala
Espinosae
Taltalensis
Resinosa
A LI.4
JUSTR
2
'%e
-
.-
14~~~~~~~~~~~~~~~~~~1
:13
:12
11
10
;9
,7
e
6
,S
_ '4
,J
.2_
'I
o
1'
1,
3
~~'
4
5,
6,
7t
6
9'
10'
11'
of Divergenc----L-vel
3
OCCIDENTALIS
SATIVA
X
/43;3
LI
TRICHOPHYLLA
~~
X~
X
ATHE RANTHA
/ATHE
STERILIS
FAU
FATUA\,
OCCIDENTALIS
SATIVA
RANTHA/
FATUA
STERILIS
.12
ATHERANTHA1
TRICHOPHYLLA
6
6/
H
7
HYRIA21
A HYBRIDA
q3
6)
HYBRIDA
64
.11
TRICH
PHYLLA
TERILIS
FATUOID
2
FATUA
8
SATIVA
OCCIDENTALIS
10
6
121
13,
166
SYSTEMATIC
BOTANY
[Volume 3
taxa could be handled by computers. Because each of these programs
gives a somewhatdifferentcladogram fromthe same data, it is necessary
to understand the basic assumptionsof the programs so that the result
can be intelligentlyevaluated. Two of the programs will be mentioned
here: Farris (Wagner) Networks3and Farris (Wagner) Trees3 (Kluge
and Farris, 1969; Farris, 1970).
A Farris Network for a set of OTU's is that which has the smallest
numericalvalue forthe sum of the lengthsbetweenall the internodesin
the network.Such a networkis formedby beginningwiththe two OTU's
that have the greatestdistance fromone another (based on the Manhattan Distance) and adding OTU's to the networkstartingwiththose with
the largest distance. To constructthe most parsimonious network,it is
sometimesnecessaryto use hypotheticaltaxonomic units (HTU's), the
characterstatesof which are determinedby the program. A Farris Network of a particulargroup can be changed to a tree withno change in
lengthby selectingone OTU (or HTU) as the ancestor. One method of
makingsuch a selectionis given by Lundberg (1972).
A Farris Tree is the same as a Networkexcept that directionalityof
linkage is implied (i.e., the networkis "rooted"; Fig. 3).A Farris Tree is
formed by adding OTU's one at a time to a network which initially
consistsof a single node, the ancestor. The order in which OTU's are
added is determined by the Manhattan Distance of each OTU to the
ancestor. OTU's with small distances are added firstand at each stage
an HTU is added. The internodal distance is also calculated. Methods
are available for increasing the parsimony of the trees (Farris, 1970).
Refer to Kluge and Farris (1969) and Farris (1970) for a detailed discussion of the principleson which the trees and networksof Farris are
based and to Solbrig (1970), Baum (1975), and Brothers (1975) for examples of theirapplication.
Several methods have been developed that are variationson Farris'
Networksor Trees, and one of the mostimportantis thatof Nelson and
van Horn (1975; Fig. 4). In thisapplication the amount of computation
required is minimal,and the number of states for each characteris not
limited.The networkis formedbyjoing the two OTU's withthe smallest
Manhattan Distance and adding subsequent OTU's that are the closest
to the average values of the growing network.Between the OTU's are
HTU's, the character states of which are intermediateto those of the
surroundingtaxa. This method is differentfromthose of Farris in that
it simplifiesthe selectionof characterstates for the HTU's, and it eliminates the complex internodaldistance formula.Several networkscan be
generated, and the one witha minimumnumber of evolutionarysteps
may be preferred (cf. Lundberg, 1972, for criteriato select the most
3 Although these methodshave been called by other workers"Wagncer
Networks"an-id
"Wagner Trees" (Kluge and Farris, 1969), theyare called 'Farris Networks"and Facrr-is
miiethod.
Trees" here to avoid confusionwiththe "Wagner Groundplan/Divergenice"
1978]
FUNK & STUESSY:
4
167
IN PRACTICE
CLADISTICS
a I si noid e s
auure a
17
0-11
0-1
B
o-1
0o-I
b
exilis
~~~~~~~~alsinoides
b e l lidtflora
ea
f
e
O-1 0-1
D
exills
e
aasrn
(2)
l
ojde
40
s
aolca
exls
s/
rfara
on
ork
n
T
a
n
f
e
(eg
t POALE
ANCESTOR
H
exilis exilis
HTU's
(p)arD
cs
s/eet
(2)
(pha
bellidHflora
beoin
exills
exills
n
edifferexilis
aeoh,alsnode
41
alsenoides
els
(from
b
bellidiflora
the
n
b
aunrea
aurea
hD
(?)
fragilis
OBABLE
ANCESTOR
1-2
exills
DbeIdiftlore
/a
1-2
exiIisaeoIica
eexls aeolica
A N C E STOR
ly o
9
19
eI Iid i f I o ra
an
e
tt PRO BA BLE
(0)
0-
7 10 14 19HTU920
E (2)
(4)
(2)
cah
0-1
0-i
exills
i
XJ
1-2
0-1
(2)
agiIis
fr
frag;l
NT U
C o- 0-1 0-1 0-1
HT U 3
8
A
(2)
17
(1)
0-
2
15-
(5) 13-
6 -0-i
(1)
(2) 4
(1
exilis
exilis
lyonii
B;
(4
/
TE
yonl
I
O
X
U
H
E
t
ROBABLE
ANCESTOR
FIG. 4. A networkgenerated for Pentalchaevta
(Compositae) by Nelson and van Horn
of characterstate
(1975, p. 368). The numbersin parenthesesreferto the total nuimbeichanges from one taxon to another on the network. The assigniednuimbeirof each
characterand the designationof state-changes(e.g., 0-1) are also shown on each branch.
FIG. 5. Four possible treesbased on one Nelso)nand van Horn network.The differdifferentHTU's being chosen as the ancestoi-(fic)m Nelsonland vain
ences airisefromn
Horn, 1975, p. 37 1). Character statechanges between taxa are indicated by the numbers
in parentheses.
168
SYSTEMATIC
BOTANY
[Volume 3
meaningfulnetworks).To turn the networkinto a tree, one OTU (or
HTU) is selected as the ancestor (Fig. 5). This application of the parsimony method has recentlybeen used by Bierner, Dennis and Wofford
(1977) and can easilybe performedby followingthe directionsgiven by
Nelson and van Horn (1975).
Whiffinand Bierner (1972) have reduced parsimonyto its simplest
level. Their method for constructinga cladogram uses the same characters as one would normally use in a tree, but does not make
any assumptions as to which state of each character is primitiveand
which is advanced. The only assumption necessary is that one taxon
representsthe most primitiveconditionin all features.The method can
handle ten to twentycharacters,is simple to understand,has verylittle
and is easy to use. The basic steps are as follows:(1) a basic data
statistics,
matrixis drawn using zero or one for the character states; (2) a Manhattan Distance matrixis constructed;(3) one taxon is designated as the
most primitive;(4) the remaining taxa are listed in order of their increasing differencefrom the ancestral taxon; (5) the taxon that is first
on the listis added to the tree above the ancestraltaxon; and (6) the next
taxon fromthe list is taken and added to the OTU which is the closest
(i.e., has the smallestManhattan Distance). There are no internodaldistances, no HTU's, and no formulas.The program actuallyis similarto
the Prim Networkexcept that OTU's are added in order of their similarityto a specific(ancestral)OTU ratherthan to the whole network.
Methods Maximizingthe Amount of Character Compatibility
These methodsrequire assumptionson whichstatesare primitiveand
which are advanced, and seek to find the evolutionarytree that is supported by the maximum number of characters. As with evolutionary
parsimony,thisprocedure maybe done eitherby hand, or by computer
if many taxa and charactersare involved.
One of the firstapproaches to cladisticmethodologyof any type was
by Hennig (1950). Because of the place and language of publication,
Hennig's ideas received very littleattentionuntil a revised version was
published in English in 1966. Since that time, more attentionhas been
given to Hennig's work,and manyauthorshave commentedon the basic
concepts (e.g., Cain, 1967; Colless, 1967, 1969a, b; Watt, 1968; Bock,
1968; Byers, 1969; Mayr, 1969; Schlee, 1969, 1975; Darlington, 1970;
Farris, Kluge, and Eckardt, 1970; Nelson, 1971, 1972a, b, 1973; Estabrook, 1972; LeQuesne, 1972, 1974; Ashlock, 1974; Cracraft,1975; Hill,
1975; Lovtrup, 1975; Hecht, 1976; Engelman and Wiley, 1977; Farris,
1977; Szalay, 1977). In addition,two useful summariesof Hennig's ideas
have been presented: one by Hennig himself(1965), and the other by
Kavanaugh (1972).
Hennig's cladisticmethod is reallyquite simple, although much space
is devoted to it and related side issues in his book. First,primitiveand
1978]
c~~~~~ ~
a'
cs )
derived
-~
FUNK & STUESSY: CLADISTICS
c~~~~~
-
5
u
~r~cQ
'~-
-
-
-
'
o -
oc
~>
>0
~
o
E a
Q0t
LO
(D
-@
t
C,)
a
E
X-
a
C,)
clsl
q
a'a)
C)IuJ
"
cs
to
C:10
-0
tq
c
E3
gL
D
0
0
w0 c
-
OUz
E- ree
Lo-
reate
taa
Fro
Brme
-
u
X
c:
CO
c
)
C:
a')
a)
pat
T
C4
C\J
C)"
U)
O
(
C
o
N
O
0
O
Ib
C
a sz
(176
-
C
distriu-iona
a
i
v
i
=~~~~
-
a e'C: 0
I
tv
x
r_ co
oo
o
st
0
C)
"T
cariance)
E
r
0
169
IN PRACTICE
P.
25).~
,
u
Q
c
Q
r
~~~~~~~~~~~~~~~~~~~~~p
FIG. 6. Hennig-type cladogram of relationships in Reihania (Compositae). Bars indicate shared derived character states (synapomorphies); letters correspond to particular
derived character states; and thicker lines refer to allopatiric distributional patterns (vicarianc'e) in closely related taxa. From Bremer (1976, p. 25).
170
SYSTEMATIC
BOTANY
[Volume 3
derived character states must be determined. This is done by making
assumptions from data on morphology,chemistry,physiology,etc. (=
holomorphology),distribution(=chorology), paleontology,and parasitology.Once advanced statesare decided, theyare used to suggestevolutionary character state trends (transformationalseries). The more
shared advanced characterstates(synapomorphies)thattaxa possess, the
strongerthe phylogenyis believed to be. Basically, one begins with a
number of charactersthat are believed to show evolutionarydirectionality,and the taxa are joined in tree-fashionbased on the maximum
number of shared derived character states (Fig. 6). The most complete
examples of how the methodmightworkhave been providedby Brundin
(1966), Hennig (1966b), Brothers (1975), Bremer (1976), Ehrendorfer
et al. (1977), and Bremer and Wanntorp (1978).
In the last few years, Estabrook and coworkers(Estabrook,Johnson,
and McMorris,1975, 1976a, b) have developed a new programthatquantifiesmany of the principles of Hennig (1966ca). First,the pattern of
evolutionis drawn in tree formforeach character;the resultingdiagram
can branch in a varietyof ways and can handle hypotheticalcharacter
states. Next, each taxon is coded as to which character state it has for
each character.Then the taxa are assigned to the proper characterstate
on each characterstatetree and the resultingdendrogram can be called
a taxa characterstatetree. Finally,each of these taxa characterstatetrees
is compared against other such trees. The cladogram in agreementwith
the largestcollectionof these trees can be considered as the most likely
representationof the phylogenyof the group. Referto the followingtwo
papers for examples of the application of this method (Estabrook and
Anderson, 1978; Gardner and La Duke, this number).
ConstructingClassifications
Cladisticmethodsnot onlyare useful in the productionof phylogenies,
but also in grouping and rankingof taxa (based on the phylogenies)for
purposes of classification.Taxa in sections of a cladogram are simply
referredto appropriate levels in the hierarchysuch as species, genera,
families,etc. Althoughany of the described methodsare potentiallyhelpful in thisway,Hennig (1966a) proposes a formalmethod,especiallyfor
ranking.With this procedure the lower and higher level grouping (the
lattercalled "relativeranking" by Hennig) is based on the criterionof
monophyly,i.e., a group of taxa coming from the same "stem" or ancestral species in the phylogeny.The hierarchicalrank ("absolute ranking" of Hennig) that each group should have is preciselydetermined
by its geological age of origin: for divisions(or phyla) the Precambrian;
for classes, the Devonian; for orders, the Permian; for families,Lower
Cretaceous; for tribes,Oligocene; and forgenera, Miocene. Such a rigid
approach to ranking deserves serious attention,but in plant groups it
does not hold up well in comparison to existingdata. For example, most
1978]
FUNK & STUESSY:
CLADISTICS
IN PRACTICE
171
of the divisionsof land plants or-iginatedin the Devonian ratherthan in
the Precambrian (Banks, 1970), although for the divisionsof algae the
concepts may be correct.The idea that the higher one goes in the taxonomic hierarchythe older the groups become mustbe generallycorrect,
but differencesin rates of evolutioncause this not to hold true in many
specificinstances. Hence, the clearlydefined procedure of Hennig for
absolute rankingof taxa is not suitableforeitherhighertaxonomicrianks,
or infragenericcategories (due to widely differingages of particular
species and varieties) where much of the activityof classificationand
makingof phylogeniestakes place.
EVALUATION
OF DIFFERENT
CLADISTIC
METHODS
Having introducedthe differentcladisticinethodsin the previous section of the paper, we now turnto an evaluation of these approaches for
the practicingplant taxonomist.Because classical taxonomistsmay be
less than enthusiasticabout any method involvingcomputers, man-ual
procedures are discussed firstfollowed by computer applications. Published examples, primarilyfrom the botanical literature,also are given.
Manual Procedures
Several methods have been developed which allow phylogeniesto be
constructedin an objectiveand well-definedmanner,and whichare relativelysimple to use and can be done by hand (i.e., withoutuse of a
computer). These manual procedur-eswork best with small numbers of
taxa and fewcharacters(up to a maximumof 20 taxa and 20 characters).
This is not a serious limitation,however, for many ievisionarystudies
deal with this number or fewer taxa, and many workers may find it
difficultto select even 20 charactersfor which primitiveand advanced
states can be satisfactorily
assigned. For those workers experienced in
making phylogenies by the conventional phyleticmethod, we recommend beginningwitha small group of taxa and workingthroughone of
the procedures manually before turningto the computer applications.
The latterare conceptuallyas simple as the former,but there are difficulties involved in obtaininga computer program and gettingit to run
on a new system.
Probably the simplestand most easily understood manual procedure
of cladisticsis Wagner's Groundplan/Divergencemethod. The simplicity
of thismethod derivesfromthe absence of complicatedassumptionsand
difficultprocedures as described above. This method has been used already to good effectby many workers(e.g., Hardin, 1957; Iltis, 1959;
Stern, 1961; Mickel, 1962; Myint, 1966; Scora, 1967; Solbrig, 1970;
Fryxell,1971).
Another manual procedure that is easy to use is that of Henn-ig
(1966a). The graphic display is a conventionaltree diagram withall recent taxa in the same plane (Fig. 6), whichavoids the undesirable impli-
172
SYSTEMATIC
BOTANY
[Volume3
cation that modern-daytaxa have given rise to other extant taxa (Stebbins, 1975). Although it is theoreticallypossible to use any number of
taxa and characters,withlarge numbers the amount of parallelismsand
reversalsincreases untilit is difficultto constructa tree. There is, therefore,a tendencyto decrease the number of charactersas the number of
taxa increases,and the cladogram becomes based upon less information.
The only published uses of thismethod forplants are by Bremer (1976),
Ehrendorfer et al. (1977), and Bremer and Wanntorp (1978). More
detailed examples, but of animal groups, can be found in Brundin
(1966), Hennig (1966b), and Brothers(1975). A modificationof the Hennig procedure has been developed byJohnson and Briggs (1975) under
the titleof a "comparativemethod." In thisanalysis,whichdeals withthe
Proteaceae, a less rigid procedure for devising a phylogenybased on
shared derived characterstatesis presented. It is not described in great
detail, but it deserves attentionfrom the taxonomistinterestedin the
Hennig-typemethodology.
The Whiffinand Bierner (1972) method also can be done by hand.
Because of simplicityof calculationand absence of determiningancestral
and derived characterstates(a single taxon is selected as the progenitor),
this method is very easy to use. It is helpful in revealing preliminary
branchingpatternsin a particulargroup, especiallyif a fullunderstanding of charactertrends has not yet been attained. T he selectionof one
OTU as the ancestor,however, automaticallydeterminesthat all character states of that taxon are primitive,which may not always be true.
This procedure allows for ease of constructionof a cladogram, but the
informationcontentis less than in other methods.
The most useful manual method to evolve fromthe Farris programs
is that of Nelson and van Horn (1975; Figs. 4 and 5). Aside from the
limitationsinherentin most cladisticmethods such as assuming that all
evolution must be dichotomous and that the evolution of character
trends must be unidirectional,this method has much to recommend it.
The resultantnetworksand trees are generated in the same fashion as
with Farris' Networkprogram,but the technique is much easier to use
and without difficultcalculations. All extant taxa are put at the end
points of the branches,which avoids the undesirable implicationsof the
Wagner Groundplan/Divergencemethod which has livingtaxa evolving
from each other on the tree. A recent application of the method is
by Bierner, Dennis and Wofford(1977).
Computer Procedures
All the computer procedures can be calculated by hand with a small
data set. Before running the program, therefore,it is helpful to work
through the algorithmmanually to learn what is actuallyhappening to
the data. Once a basic understandinghas been attained,large numbers
of OTUs and characterscan be handled.
1978]
FUNK & STUESSY:
CLADISTICS
IN PRACTICE
173
Programs for Prim-KruskalNetworks,although simple and easy to
use, are infrequentlyemployedin cladisticanalysis.These programsproduce a less accurate diagram than many of the others,because theyare
designed to find the shortestroute between taxa withoutconsideration
of the charactertrendsinvolved.The shortcomingsof these methodsare
similarto those of the Whiffinand Bierner approach (1972; see previous
discussion).The techniquesare useful,however,in givinga general idea
of the cladisticsof a group, such as was done by Solbrig (1970).
The programs of Farris (1970; Kluge and Farris, 1969; and Farris,
Kluge, and Eckardt, 1970) eliminate the need for making a priori assumptionsabout primitiveand advanced characterstatesexcept for one
of the options of WISS). These techniques allow use of large numbers
of OTUs and characters.Also, phenetic relationshipsare shown by the
internodal distances, which result in an informativecladogram. However, the procedures in the program are difficultfor the non-mathematicallyoriented person to comprehend, because the explanations rely
heavilyon formulas(Kluge and Farris, 1969; Farris, 1970; Farris,Kluge
and Eckardt, 1970). In some of these programs,weightingoccurs so that
the more conservativecharactersare more influentialin developing the
network/trees.The characters are coded in a linear fashion and although no primitiveand derived statesare chosen, one must eventually
select an ancestor, the character states of which become the primitive
statesfor the group. Solbrig (1970) has used this method to good effect
as a supplement to cytologicaland distributionalconsiderationsin Gutierrezia(Compositae). See also Luteyn (1976) for an application with
another group of floweringplants. Although not a botanical example,
Brothers(1975) has an interestingtreatmentusing both FarrisTree and
Hennig methods to determinethe phylogenyof a group of Hymenoptera. The inconsistenciesof the results were compared, which located
problems in the data and theircoding.
The programby Camin and Sokal (1965), while historicallyimportant,
is rarely used because of the availabilityof more efficientprocedures.
Two papers exist, however,which compare the method of Farris with
that of Camin and Sokal. Baum (1975, 1977a) uses these two cladistic
methodsto understandthe phylogeniesof diploid and hexaploid species
of Avena, and he found thatthe totalnumberof steps in the FarrisTrees
was considerablyless than in the Camin and Sokal method. Each tree
had its own meritsand the most parsimonious was chosen as the most
plausible. Another paper using both programscompares the theoriesas
well as the procedures (Smith and Koehn, 1971).
Estabrook's method of Character Compatibilityis stillsomehwatnew,
but it has already been used several times (Bau, 1977b; Estabrook,
Strauch, and Fiala, 1971; Baum and Estabrook, 1978; Estabrook and
Anderson,thisnumber;and Gardnerand La Duke, thisnumber).Character Compatibilityhas at least twoadvantages: (1) evolutioncan proceed in
many directionsin each character, not just linearlyas in most of the
174
SYSTEMATIC
BOTANY
[Volume3
other methods; and (2) inconsistenciesin the data which may be due to
incorrectcoding, incorrectinterpretationof data, or parallelisms and
reversals,are more easily detectable.
CONCLUSION
The differentavailable cladisticmethods provide the practicingplant
taxonomistwith a selection of techniques from which to choose. It is
thereforeimportantto understandthe strengthsand weaknessesof each
of the methods,because some willbe more appropriate forspecificproblems and for certainworkersthan will others. For instance,some of the
methods such as those by Hennig, Estabrook,Wagner, and Camin and
Sokal require the indicationof primitiveand advanced characterstates.
Others such as Nelson and van Horn and Farris do not, but to form a
tree one mustselect the most primitivetaxon and thus indirectlychoose
the primitivecondition.Some of the cladogramscan be easilyconstructed
by hand and work well for small numbers of taxa. However, the larger
the number of taxa and charactersbeing considered, the more cumbersome and time-consumingthe manual operations become. A problem
involvingmore than 20 taxa or characterswould be more easilyhandled
by a computerprogram.One should also recognize the basic differences
betweenthe two methodsof parsimonyand charactercompatibility.
Parsimonymethods arc guessing procedures thatuse differentstrategiesin
order to findthe shortestcladogram. Character Compatibilitymethods
stresscoordination of the charactersto find the cladogram that agrees
withthe largestnumberof possible tr-ees.The decision on whichof these
ideas to followwill depend upon the background of evolutionarythinking of the individual worker,and which alternativeseems most appropriate for a particular problem. As no mathematicaltheory for constructingphylogenies exists at present, either approach is likely to
provide an acceptable representationof the true phylogeny.Perhaps a
useful goal is to understand and employ a number of the methodswell,
so that the results can be compared and explanations sought for any
discrepancies.
One deficiencywith all cladistic methods is that reticulateevolution
cannot be detected or demonstrated graphically (Sneath, 1975). In
plants,this is a serious difficulty,
because many species have evolved by
allopolyploidy(Grant, 1971). If information(such as cytogeneticdata) is
available thatsuggestsallopolyploidy,or even evolutionby hybridization
at the diploid level, then adjustments must be made in the resultant
diagrams to reflectthese known facts.
For the practicingplant taxonomist,cladisticsoffersa method of constructingphylogenies by objective and repeatable means. Because the
development of phylogeniesby traditionalmethods often involvespersonal or "intuitive"judgements, differencesbetween phyleticschemes
for the same plant taxa are difficultto resolve because of a lack of un-
1978]
FUNK & STUESSY:
CLADISTICS
IN PRACTICE
175
derstandingof the evolutionaryassumptionsused and the waysin which
the trees were generated. In contrast,cladistic methodologyfacilitates
discussion by a clear presentationof evolutionaryassumptionsand operational procedures.
Acknowledgments.-We are pleasecl to acknowledge the help of George Estabrook
who made many useful commentson an earlier draftof this paper, and Who aided the
development of our outline of the differentclaclisticmethods. We also appreciate the
ideas and viewpointstowaardcladisticsof colleagues in the Plant SystematicsSemiialr in
the Departmentof Botany at Ohio State. Permissionto republish the claclogramsin Figs.
1-6 was generouslygranted by the respectiveauthors and the curreniteditors or managers of Brittonia,CaanadianJournalof Botany,Evolution,and Opera Botanica. Suppor-t
fromNSF Grant DEB75-20819 (to T.F.S.) is also gratefullyacknowledged.
LITERATURE
CITFD
1974. The uses of cladistics. Ann. Rev. Ecol. Syst. 5: 81-99.
ASHLOCK, P. D.
BACON, J. D. 1978. Taxonomy of Ncrisyrentia
(Crucifer-ae).Rhodoria80: 159-227.
BANKS, H. 1970. Evolution and Plants of the Past. Belmont, Calif.
BARTCHER, R. L. 1966. For-tran IV program for estimation of tla(listic Irelationiships
using the IBM 7040. Kansas Geol. Surv., Computer Contrib.6: 1-54.
B. R. 1975. Cladisticanalysisof the diploid and hexaploicioats (Avelal, Poaceae)
using numericaltechniques. Canaci. J. Bot. 53: 2115-2127.
1977a. Oats, Wild and Cultivated:a monograph of the genus AveilaL. (Poaceae).
Canad. Dept. Agric. Res. Branch Publ. No. 14.
1977b. Assessmentof cladograms obtained for four-teeni species of Avella by two
methods of numericalanalysis.Syst.Bot. 2:141-150.
& G. F. Estabrook. 1978. Application of compatibilityanalysisin numeric-alcladisticsat the infraspecificlevel. Canad. J. Bot. 56: 1130-1135.
BENSON, L. 1962. Plant Taxonomy. New York.
BLYER, W. A., M. L. STEIN, T. F. SMITH & S. M. ULAM. 1974. A imiolecuilar
sequllenlce
metricand evolutionarytrees. Math. Biosci. 19: 9-26.
BIERNER, M. W., W. M. DENNIS & B. E. WOFFORD.
1977. Flavonoid chemistry,chr()mosome number and phylogeneticrelationiships
of Helenhiml,zl
(hihltahUfltl.si.
Biochem. Syst.Ecol. 5: 23-29.
evolution.Evolutioni22: 646BOCK,W. J. 1968. Phylogeneticsystematics,
claclistics, andcl
648.
of amino acids as a taxonomic tool, pp.
BOULTLR, D. 1973. Comparative seqtuencinig
199-229. In L. Reinhold & Y. Liwschitz(ecis.), "Progress in Phytochei-nistry.'
Vol. 3. New York.
c and plastocyaninsin phylogenetic
1974. Amino acid sequences of cytochroimie
studies of higher plants. Syst.Zool. 22: 549-553.
BREMER, K. 1976. The genus RlhAaiia (Compositae). Opera Bot. 40: 1-85.
in botany.Taxon 27: 317-329.
& H.-E. WANNTORP. 1978. Phylogeneticsystematics
of the aculeate Hymenoptera,x\ith
BROTHERS, D. J. 1975. Phylogenyand classificationi
special referenceto Mutillidae. Univ. Kansas Sci. Bull. 50: 483-648.
as evidenced by
BRUNDIN, L. 1966. Transanitarctic
relationshipsand theirsignificanice,
chironomidmidges. Kongl. Svenska Vetensk. Handl. 11: 1-472.
of the Linnaean hieiai-chy.Syst.
BUCK, R. C. & D. L. HULL. 1966. The logical structur-e
Zool. 15: 97-111.
BYERS, G. WV.1969. Reviewof Phylogeneticsystematics
andcl
tranisantai-ctic
relationiships
an-dtheirsignificance,as evidenced bythii-onomidmiclges."Syst.Zool. 18: 105107.
BAUM,
176
SYSTEMATIC
BOTANY
[Volume 3
CAIN, A. J. 1967. On e phylogeneticsystem.Nature 216: 412-413.
CAMIN, J. H. & R. R. SOKAL. 1965. A method for deducing branching sequences in
phylogeny.Evolution 19: 311-326.
COLLESS, D. H. 1967. The phylogeneticfallacy.Syst.Zool. 16: 289-295.
1969a. The phylogeneticfallacyrevisited.Syst.Zool. 18: 115-126.
1969b. The interpretationof Hennig's "phylogeneticsystematics"-a reply to
Dr. Schlee. Syst. Zool. 18: 134-144.
CRACRAFT,J. 1975. Historicalbiogeographyand earth history:perspectivesfora futur-e
synthesis.Ann. Mo. Bot. Gard. 62: 227-250.
1970. A practicalcriticismof Hennig-Brundin"phylogeneticsystem-
DARLINGTON,P. J.
atics" and
DARWIN,C. 1859.
DICKERSON, R. E.
evolution.
antarctic biogeography. Syst. Zool. 19: 1-18.
On the Origin of Species by Means of Natural Selection. London.
1971. The structureof cytochromec and the rates of molecular
J. Molec. Evol. 1: 26-45.
1964. Reconstruction of evolutionary trees,
A. W. F. & L. L. CAVALLI-SFORZA.
Pp. 67-76. In V. H. Heywood and J. McNeill (eds.), "Pheneticand Phylogenetic
EDWARDS,
Classification." Syst. Assoc. Publ. No. 6, London.
EHRENDORFER, F., D. SCHWEIZER, H. GREGOR & C. HUMPHRIES. 1977. Chromosome
(Asteraceae-Anthemideae). Taxbanding and synthetic systematics in Anacyc-lu.s
on 26: 387-394.
ENGELMANN, G. F. & E. 0. WILEY.
1977. Place of ancestor-descendent relationship in
phylogenyreconstruction.Syst.Zool. 26: 1-1 1.
ESTABROOK,G. F. 1968. A general solutionin partialorders for the Camin-Sokal model
in phylogeny. J. Theor. Biol. 21: 421-438.
1972. Cladistic methodology: a discussion of the theoretical basis for the induction of evolutionary history. Ann. Rev. Ecol. Syst. 3: 427-456.
1977. Does common equal primitive? Syst. Bot. 2: 36-42.
C. S. JOHNSON & F. R. MCMoRRIs. 1975. An idealized concept of the true
cladistic character. Math. Biosci. 23: 263-272.
. 1976a. A mathematicalfoundationfor the analysisof cladistic
&
charactercompatibility.Math. Biosci. 29: 181-187.
. 1976b. An algebraic analysis of cladisticcharacters.Discrete
&
Math. 16: 141-147.
J. G. STRAUCH & K. L. FIALA. 1977. An application of compatibility analysis to
the Blackith's data on orthopteroid insects. Syst. Zool. 26: 269-276.
EYDE, R. H. 1975. The bases of angiosperm phylogeny:floralanatomy.Ann. Mo. Bot.
Gard. 62: 521-537.
FARRIS,J. S. 1970. Methods for computing Wagner trees. Syst. Zool. 19: 83-92.
1977. Phylogenetic analysis under Dollo's Law. Syst. Zool. 26: 77-88.
A. G. KLUGE & M. J. ECKARDT. 1970. A numerical approach to phylogenetic
systematics.Syst.Zool. 19: 172-191.
J. 1973. Maximum likelihood and minimum-stepsmethodsforestimating
evolutionarytrees fromdata on discretecharacters.Syst.Zool. 22: 240-249.
FITCH, W. M. 1971. Toward definingthe course of evolution: minimumchange for a
specifictree topology.Syst.Zool. 20: 406-416.
1975. The relationshipbetween Prim Networksand trees of maximum parsimony,pp. 189-230. In G. F. Estabrook (ed.), Proc. 8th Intern. Confer. Numer.
Taxon. W. H. Freeman, San Francisco.
& E. MARGOLIASH. 1967. Constructionof phylogenetictrees. Science 155: 279284.
FRYXELL, P. A. 1971. Phenetic analysis and the phylogenyof the diploid species of
L. (Malvaceae). Evolution 25: 554-562.
Gossypium
GOODMAN, M. & J. PECHERE. 1977. The evolution of muscularparvalbuminsinvestigated
by the maximum parsimonymethod.J. Molec. Evol. 9: 131-158.
FELSENSTEIN,
1978]
FUNK & STUESSY:
CLADISTICS
IN PRACTICE
GRANT, V. 1971. Plant Speciation. New York.
HARDIN, J. W. 1957. A revisionof the AmericainHippocastanaceace.Brittonia9:
177
145171.
HECHT, M. K. 1976. Phylogeneticinferenceand methodologyas applied to the vertebrate record. Evol. Biol. 9: 335-363.
HENNIG, W. 1950. Grundziige einer Theorie der phylogenetischenSystematik.Berlin.
1965. Phylogeneticsystematics.Ann. Rev. Entomol. 10: 97-116.
[transl.D. D. Davis & P. Zangerl.] 1966a. PhylogeneticSystematics.Urbana.
[transl.P. Wygodzinski.] 1966b. The Diptera fauna of New Zealan-das a proband zoogeography.PacificInsects. Monograph 9. B. P. Bishop
lem in systematics
Museum, Honolulu, Hawaii.
HILL, L. R. 1975. Problems arising fromsome testsof LeQuesne's concept of unilquely
derived characters,Pp. 375-398. In G. F. Estabrook (ed.), "Proc. 8th Intern.
Confer. Numer. Taxon." San Francisco.
HULL, D. L. 1967. Certaintyand circularityin evolutionai-ytaxoi-omy.Evolution 21:
174-189.
1974. Philosophyof Biological Science. Englewood Cliffs.
taxonCleomesect. Phyosteiiioii:
ILTIS, H. H. 1959. Studies in the Capparidaceae-VI.
omy,geography,and evolution. Brittonia11: 123-162.
JOHNSON, L. A. S. & B. G. BRIGGS. 1975. On the Proteaceae-the evolution and classificationof a southernfamily.Bot. J. Linn. Soc. 70: 83-182.
KAVANAUGH, D. H. 1972. Hennig's principlesand methodsof phylogeneticsystematics.
The Biologist 54: 115-127.
KLUGE, A. G. & J. S. FARRIS. 1969. Quantitativephyleticsanidthe evolutionof anurans.
Syst.Zool. 18: 1-32.
KRUSKAL, J. B. 1956. On the shortestspanning subtree of a graph and the triaveling
salesman problem. Proc. Amer. Math. Soc. 7: 48-50.
concept.
LEQUESNE, W. J. 1972. Furtherstudiesbased on the uniquely derived char-acter
Syst.Zool. 21: 281-288.
1974. The uniquely evolved characterconcept and itscladisticapplication. Syst.
Zool. 23: 513-517.
LOVTRUP, S. 1975. On phylogeneticclassification.Acta Zool. Cracoviensia 20: 499-523.
LUNDBERG, J. G. 1972. Wagner networksand ancestors.Syst.Zool. 21: 398-413.
LUTEYN, J. L. 1976. A revisionof the Mexican-CentralAmerican species of Cavenlishia
(Vacciniaceae). Mem. New York Bot. Gard. 28(3): 1-138.
MAYR, E. 1965. Numerical pheneticsand taxonomic theory.Syst.Zool. 14: 73-97.
. 1969. Principlesof SystematicZoology. McGraw-Hill,N.Y.
subgenus CoptoMICKEL, J. T. 1962. A monographic study of the fern genus Aniemia,
phyllum.Iowa StateJ. Sci. 36: 349-382.
related protein
MOORE, G. W. & M. GOODMAN. 1977. Alignmentstatisticfor identifying
sequences. J. Molec. Evol. 9: 121-130.
(Convolvulaceae). Brittonia18: 97-117.
MYINT, T. 1966. Revisionof the genus Stylisma
NASTANSKY, L., S. M. SELKOW & N. F. STEWART. 1974. An improved solution to the
generalized Camin-Sokalmodel fornumericalcladistics.J. Theor. Biol. 48: 413424.
1975. A new simplifiedmethod for constructing
NELSON, C. H. & G. S. VAN HORN.
(Compositae, Astereae). BritWagner networksand the cladisticsof Pentac-haeta
tonia 27: 362-372.
NELSON, G. J. 1971. "Cladism" as a philosophyof classification.Syst.Zool. 20: 373-376.
1972a. Phylogeneticrelationshipand classification.Syst.Zool. 21: 227-231.
1972b. Comments on Hennig's "phylogeneticsystematics"and its influenceon
ichthyology.Syst.Zool. 21: 364-374.
1973. Classificationas an expression of phylogeneticrelationships.Syst. Zool.
22: 344-359.
178
SYSTEMATIC
BOTANY
[Volume 3
PENNY, D. 1976. Criteria for optimisingphylogenetictrees al(c the problem of dleter-
miningthe root of a tree.J. Molec. Evol. 8: 95-116.
Bell Syst.
PRIM, R. C. 1957. Shortestconnection netxorks and some gener-alizationis.
Tech. J. 36: 1389-1401.
an "intuitive,statisticoSCHLEL, D. 1969. Hennig's principleof phylogeneticsystematics,
phenetic taxonomy"?Syst.Zool. 18: 127-134.
1975. Numerical phyletics:an analysis fromthe viewpointof phylogeneticsystematics.Entomol. Scand. 6: 193-208.
SCORA, R. W. 1967. Divergence in Moiiarda (Labiatae). Taxon 16: 499-505.
SMITH, G. R. & R. K. KOEHN. 1971. Phenetic and cladisticstudies of biochemicaland
Syst. Zool. 20: 282-297.
morphological characteristics of Cato.stomtius.
SNEATH, P. H. A. 1975. Cladistic representationof rieticulate evolution. Syst. Zool. 24:
360-368.
& R. R. SOKAL. 1973. Numerical Taxonomny:the principlesand practiceof n1umericalclassification.San Francisco.
SOKAL, R. R. & P. H. SNEATH. 1963. Principlesof Numerical Taxonomy. Sall Franicisco.
SOLBRIG, 0. 1970. The phylogenyof Gitilerrezia: ain eclectic appr-oach. Britton-ia 22:
217-229.
STEBBINS, G. L. 1975. Deductions about transspecificevolution throughextrapolation
from processes at the population and species level. Ann. Mo. Bot. Gard. 62:
825-834.
STERN, K. R. 1961. Revision of Dientra (Fumariaceae). Brittonia13: 1-57.
SZALAY, F. S. 1977. Ancestors,descendents, sistergroups and testing of phylogeinetic
hypotheses. Syst. Zool. 26: 12-18.
Voss, E. 1952. The historyof keysand phylogenetictrees in systematicbiology.J. Sci.
Lab., Denison Univ. 43(1): 1-25.
of ferns,pp.841-844. ITl Recenlt
WAGNER,W. H.,JR. 1961. Problemsin the classification
Advances in Botany. Univ. Toronto Press, Montreal.
1966. Modern researchon evolutionin ferns,Pp. 164-184. In W. A. Jensenand
I. G. Kavaljian (eds.), "Plant Biology Today: Advan-cesand Challenges," ed. 2.
Belmont.
1969. The constructionof a classification,Pp. 67-90. In G. Sibley (Chairman),
"SystematicBiology." Natl. Acad. Sci. U.S.A. Publ. 1692.
WATT, J.C. 1968. Grades, clades, phenetics,and phylogeny.Syst.Zool. 17: 350-353.
WHIFFIN, T. & M. W. BIERNER. 1972. A quick method for-computing Wagner tr-ees.
Taxon 21: 83-90.
WILSON, E. 0. 1965. A consistencytest for phylogenies based on contemporaneous
species. Syst.Zool. 14: 214-220.