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VO L.
47
S yst. Biol. 47(1):1 68± 173, 1998
Partial W arps, Phy logeny, and O nto geny : A Com m ent on Fink and
Z eld itch (1995)
D EA N C . A D A M S
AND
M IC H A E L S. R O S E N B E R G
D epartment of E cology and Evolution, State Un iversity of New York, Stony Brook, New York 11794-5 245, USA ;
E -m ail: dca287 9@ life.bio.sunysb.edu (D.C .A.)
Fin k and Zeld itch (1995) recen tly prop osed a m ethod by w hich one m ay infer
phylo geny from onto genetic tran sform ations of continuous m orphological data.
They coded ontogenetic reg ression s of
sh ap e on size to obtain discre te characters,
w hich they used as input into a parsim ony
ana lysis. A s sh ape variab les, they used
p ar tial warp scores obtained from an an alysis based on thin-plate splines (TPS),
w hich, they had prev iou sly arg ued, could
be considere d hom ologous characters and
could be used to determ ine sy na pom orphies on a phylo genetic tree (Z eld itch et
al., 1995 ). Here we discuss several asp ects
of their protocol that call into question
their assert ion that the ontogeny of sh ap e
(as represen ted by discrete charac teriza tions of reg ression s of par tial warp scores)
is a suitable charac ter set for phy logeny estim ation. A sim ilar note (R ohlf, 19 98) discusses more theoretical objections to their
m ethodology, and challeng es the notion
that par tial warp scores viewed sep arately
are biolo gically hom olo gou s and interp retable charac ters. Additiona lly, we w ill ad dress two issues raise d by Fink and Zeld itch (199 5). First, do es the choice of a
different star ting form (referen ce) result in
a differen t phy lo geny ? Second, does the
choice of an altern ative basis for tang ent
sp ace resu lt in a differen t phylogeny ?
The pro to col of Fink and Z eld itch (199 5)
is as follow s. First, a reference con® gu ration is generat ed as the m ea n of several ju venile sp ecim ens from a chosen outgrou p
sp ecies. Fink and Zeld itch cho se the average of three juven ile specim en s from one
of their outgrou ps, Pygopristis denticulata,
a s t h eir r e fer en ce s p e cim en (h er e a ft er
c a lle d t he r e fe ren c e ou tg r ou p ). T h ey
alig ned the specim en s using sha pe coordinates (Bo okstein, 1986) , choosin g the
long axis of the ® sh as the baseline, and
calculated the size of each sp ecim en as the
square ro ot of the su m m ed squared distances from each land m ark to the centroid
of that sp ecimen (G ower, 19 71). In the absence of allo metry, this m easu re of size,
called ``root cen troid siz e’ ’ (Bookstein,
1991) , is the only size variable that is uncorrelate d w ith sha pe (Bookstein et al.,
1985; Bookstein , 19 91). The difference in
sh ap e from the reference to each alig ned
sp ecim en was then qu an ti® ed usin g the
TPS (Bookstein, 1989, 199 1). TPS allow s
one to m athem atically represent the sh ap e
variatio n presen t in the con® guratio ns of a
set of hom olo gou s la nd m arks as variation
in a set of param eters of an in terpolatin g
function (Bookstein, 19 89, 19 91), w hich
represents the tran sform ation of the reference to each sp ecim en (R ohlf, 1993 ). From
the reference con® guration they calcu lated
the principal warps, w hich are used to de® ne a set of coord in ate axes for tang ent
sp ace, a line ar sp ace ap proxim ating the
curve d sha pe sp ace, in w hich the sh ap es
of sp ecim en s can be com p ared using stan dard linea r statistical m etho ds (see Bo okstein , 19 91; R ohlf, 199 6). By projecting the
x- and y-coord in ate s of the align ed sp ecim en s onto the principal warp axes, Fink
and Z eld itch generat ed a set of sh ap e variables calle d p artial warp scores for each
sp ecim en. These variab les, as well as two
variab les representing uniform sh ape variation, were then ind ividually reg resse d
onto log(centroid size) to calculate ontogenetic sh ape chan ge s for each sp ecies.
Fink and Zeld itch argu ed that because the
p rin cip a l w a r p a xe s r ep re s en t s h a p e
19 98
PO IN TS O F VIEW
chang e at all non in® nite sp atial scales, regressions of sh ap e on siz e describ ed ontogenetic shap e chan ges at all spatial
scales as well.
To obtain discrete charac ters for their
taxa, they coded each onto gene tic sh ape
reg ression as either a 0, 1, or 2. This was
done by determ ining w he ther the reg ression of each p artial warp on siz e was statistically sig ni® can t, and in w hat direction
(i.e., positive/neg ative ) this sh ap e chan ge
occurre d. Sp ecies w ith sim ilar chan ges
were assign ed sim ilar coding , w ith the referen ce outgroup sp ecies, Pygopristis denticulata, always given the character state 0.
For exam ple, two sp ecies (P. denticulata and
Serrasalmus gould ingi) bo th displaye d signi® can t p ositive ontogenetic chan ge for
character 20 (partia l warp 9y). They each
received a 0 for this character, because P.
denticulata was used as the reference outgrou p. The rem ain ing three species (Pygocentrus cariba, P. nattereri, and P. piraya) displaye d no sig ni® can t sh ap e chan ge for
p artial warp 9y and were thus co ded as 1.
Fink and Z eld itch then used these coded
characters, together w ith several m eristic ,
m yological and osteological charac ters, in
a parsim ony ana lysis of the p iran ha genus.
Finally, they asse ssed the phy logene tic in dep endenc e of these characters by iden tifying the p attern s of charac ter chang e on
the clad ogra m . This was done by exam in ing charac ters that chan ged m ore than
once on the clado gram and determ ining if
other characters that chang ed multiple
tim es diag nosed the sam e no des of the
phy logeny. If two charac ters chang ed multiple tim es at the sa m e nodes of the phylogeny, they were consid ere d not phy logenetically indep enden t of one ano ther.
The protocol of Fink and Z eld itch (1995 )
allow s com parison s of sh ape in a m an ner
that seem ingly com bine s the concep ts of
onto geny and phy logeny. In Figure 2 of
their p ap er, Fink and Zeld itch displayed
w hat they de® ne as ``net onto genetic sh ap e
chang es’ ’ for each of their ® ve taxa. These
® gures were gen erated by tran sform ing
the ju ven ile form of each species to the
adu lt form of the sam e sp ecies usin g the
thin-plate spline (Zeld itch, pers. com m .).
169
A lthough we certa inly have no dif® culties
accep ting this as an adequ ate representation of onto geny, their pro tocol do es not
describe ontogeny in the sa m e m ann er as
is dep icted in their Figure 2. Their protocol
explicitly uses the m ea n ju ven ile of one
outgrou p species as the reference form ,
an d thus the p ar tial warp scores obtain ed
describe the sh ap e chang es from a m ean
ju ven ile of the referen ce outgroup species
to adu lts of each of the ing rou p sp ecies.
Becau se the tra nsform ations they are in terested in are chan ges in ontogeny, the prim itive (outgrou p ) condition should not be
thou ght of as a sta rtin g form (Fin k an d
Z eld itch, 199 5:3 47), but rather as a tra jectory in sh ap e sp ace. Therefore, characterization s of onto geny by partial warp s require only the use of a sing le reference
con® guratio n (Z eld itch et al., 1995) , but
not the use of a ju ven ile con® guration.
In a recen t study, Nay lor (199 6) evalu ated w he ther the correct tree top ology
could be obtained usin g par tial warp
scores as data in a phy logen etic an aly sis.
He generate d a set of differen tly sh ap ed
im ag inary ® sh that were relate d by a
know n, predeterm ined phy logeny. At each
node of the phy logeny, a sin gle unique net
sh ap e chan ge was generate d, insu rin g no
hom oplasy. Nay lor calculated partial warp
scores for each ® sh , coded them as multistate charac ters, and used them to estim ate
the phylogeny. He found two m ost parsim onious trees, one of w hich corre sponde d
to the true tree topolog y. However, the retention index (Farris , 19 89) for these topologies was 0.48, ind icatin g a la rg e deg ree of
h o m o p las y (e igh t tax a , 7 0 ch a r ac te rs ).
W hen sha pe characters were m app ed onto
the phylo geny, Nay lor found little corresp onden ce between the partial warp scores
an d the true sh ap e chan ge s that charac terized the taxa. He argu ed that becau se each
p artial warp score represen ts one geom etric asp ect of overall sha pe difference (i.e.,
a decom po sition ), the biological realiz ation
of such sh ap e differences m ay not corre sp ond to the ind ividu al p artial warps, but
to a com bination of p artial warp s. W hen
taken in su m , the p artia l warp scores p erfectly describe all sh ape differences be-
170
SYSTE M AT IC BIOLO GY
tween the variou s taxa, but w hen an alyz ed
ind ividu ally, this relationsh ip is lost.
It is tem p ting to assig n biolo gical m ean in g to p artial warp axes. However, these
axes are sim ply a convenient m athem atical
(i.e., geom etrically orthogonal) descrip tion
of tan gent sp ace; there is no reason to
thin k they should individu ally have any
sp eci® c biological relevanc e (Nay lor, 1996 ).
Biolo gical relevanc e only com es from the
axes taken together, or m ore accurately,
from the m orphological space that they
sp an. This was clearly dem onstrated by
R ohlf (1998 ), w hen he show ed that a sim ple sha pe chan ge between two specim en s
(an expansio n of a su bset of lan dm arks)
was not described by any ind ividual warp,
but was perfectly describ ed w hen all partial warp s were taken to ge ther. Thus the
claim by Fink and Zeld itch (1995 ) that partial warp scores shou ld be ind ividually biologically interp retable is unwarran ted.
C H O O SI N G
A
R EF ER E N C E FO R M
In discussin g evolutionary tran sform ations, Fink and Z eld itch (199 5) stated that
sh ap e deform ation s can be interprete d as
actual evolutionary even ts only if an outgroup specim en is used as the star ting
form . In their protocol, the reference outgroup species served two purpo ses. First,
the average of several juvenile specim en s
from this species was used as the star ting
(referen ce) form for the TPS an alysis . Second, the character state s of the reference
outgrou p sp ecies were used to co de the
charac ters of the other taxa, by codin g all
regressions of sh ap e on siz e for the reference outgrou p species as 0, and codin g
tho se of the ingrou p taxa (as well as o ther
outroup taxa) relative to these scores. Such
a use of outgroup s is com m on in phy logenetic studies (for discu ssion , see M ad dison et al., 198 4; Swofford et al., 1996 ).
A lthough choo sin g an outgrou p as a referenc e specim en sound s app ealin g from
an evolutiona ry persp ective, there are a
num ber of dif® culties w ith such a choice.
First, the term ``reference con® gu ratio n’ ’ in
g e o m e tr ic m o r p h o m e tr ic s is s o m ew h at
m islead ing, as it refers to the p oint of tan gency between sh ap e sp ace and tang ent
VO L.
47
sp ace; it should not be though t of as a referenc e form chosen on biolo gical ground s.
The prin cipal warp axes, on w hich the partial warp scores are base d, are de® ned
solely on the basis of the reference con® guratio n, and are very sensitive to differen t
choices of a reference (see R ohlf, 199 6,
1998). Becau se the p ar tial warp scores are
m erely projections of the sp ecim ens onto
the princip al warp s, use of a differen t referenc e w ill yield differen t p ar tial warp
scores for the ing rou p taxa. Because Fink
and Zeld itch did not specify a m ethod by
w hich to choo se an ap propriate outgrou p
to serve as the reference (if m ore than one
is ava ilable), this p oses som e dif® culties.
To illustrate this, we used Fink and Zeld itch’s pro tocol to gen erate four phylogenetic estim ates for several host races of the
leaf beetle Neoclam isus bebbianae (the Pygocentrus data were not m ade available to us).
These ho st-asso ciated races are kn ow n to
differ both m orphologically (Adam s and
Fu nk, 19 97) and gene tically (Funk, 199 6),
and can thu s be considere d sep arate operatio nal taxonom ic units for the purp oses
of this exam ple. The data used here are
p ar t of a larger study on the relation sh ip
between m orphological sh ap e and hostplan t speci® city (Adam s and Fu nk , 1997).
Eleven la nd m ark s were recorde d on 30
sp ecim ens of N. bebbianae from each of four
host-plan t populatio ns. For each ana lysis,
we cho se one of four closely relate d sp ecies
(N. cham aedaphnes, N. comptoniae, N. gibbosus, and N. platani) to serve as the reference
outgrou p (Funk and Ada m s, unpubl.). A s
in Fink and Z eld itch, three sm all ind ividuals from the reference outgrou p were averag ed to obtain the starting (reference)
sh ap e; the rem aining 27 sp ecim en s of the
reference outgrou p were used to de® ne
sh ap e ontogen ies for that taxon. Sixteen
p ar tial warp scores were generat ed from a
TPS an aly sis, and each was regresse d on
log(centro id size ) to determ ine sh ap e ontogen ies for each taxon. These were co ded
as discrete characters, w hich were used to
generate phylo genetic estim ates using a
heu ristic search and Wagn er parsim ony,
w ith 100 boo tstrap replicate s, in PAU P 3.1
(Swofford , 1993 ). Fina lly, the phy lo genetic
19 98
171
PO IN TS O F VIEW
F IG U R E 1. Top ologies fou nd by Wag ner par simony
for fou r host-associated race s of the Neochla m isus bebbian ae u sing different outgroup sp ecie s (bo otstrap values bas ed on 100 replicates are show n ). Sixteen d iscrete ch aracters were ob taine d from regressions of
par tial warp scores on log(centr oid size) follow ing the
protocol of Fink and Z elditch (1995). A d ifferen t outgrou p was used for each analys is: (a) N. cham aedaphne s
(C I 5 1.000, RI 5 1.000). (b ) N. compton iae (C I 5 1.000,
R I 5 1.000). (c) N. gibbosu s (C I 5 1.000, RI 5 1.000).
(d ) N. platan i (C I 5 1.000, RI 5 1.000).
indep endenc e of the charac ters was assessed follow ing Fink and Zeld itch’s (1995)
protocol.
Figu re 1 sh ow s the sin gle m ost parsim onious tree s (M PT) from each analy sis.
For each M PT, none of the characters exhibiting multiple chan ge s alon g the phylogeny occurred at the sa m e nodes. Thus
usin g Fink and Zeld itch’s (1995) protocol,
all characters were determ ine d to be phylogen etically indep enden t of one ano ther.
From Figure 1, it is eviden t that the choice
of a reference (startin g) form has dram atic
conse quences on the resu ltin g ingrou p to p ology. T here are several p ossible expla nations for this. First, usin g the protocol of
Fink and Zeld itch, one co des the discrete
characters of the ingrou p taxa relative to
the charac ter state s of the reference outgrou p prior to ru nnin g the phylo genetic
an aly sis. If the relatio nship between size
an d sh ap e is not constan t between the po ssible referen ce outgrou ps, then chan ge s in
ing rou p charac ter states w ill occur. To
avoid such dif® culties, one usu ally pola rizes characters by using multiple outgrou p s (for a discussion, see Swofford et
al., 1996 ). A lthou gh multiple outgroup s
can be ana lyze d phy logene tically usin g
Fink and Z eld itch’s protocol, only one referen ce outgroup can be used , as the thin plate spline is based on only a sin gle referen ce form . Therefore, the trad itional so lution of desen sitizin g characters (Swofford et al., 199 6) to the choice of outgroup
can not be ap plied to their protocol. Second, because the prin cipal warps are base d
solely on the land m ark con® guration of
the referen ce specim en, cho osin g a differen t outgrou p to serve as the reference
sp ecim en virtu ally gu aran tees differen ces
in the m ean ing of each par tial warp (for a
discu ssion of choice of reference, see R ohlf,
19 96, 1998 ). There fore, the p artia l warp
scores of the ingrou p taxa are not invaria nt
to chan ge s in reference selection. Such lack
of charac ter state invaria nce is an unde sirable property for data used in phylogenetic
studies.
C H O O S IN G
A
B A SIS
FOR
TAN G EN T SPA CE
It can not be overem phasized that the
sp ace in w hich the specim en s resid e (the
sp ace tan gent to sh ap e space) is biologically imp ortan t, not the ind ividu al axes
that describ e the sp ace (Bookstein, 1991 ;
R ohlf, 1996). Because the relative distanc es
am ong taxa in tan gen t sp ace are of in terest, any orthogonal basis sp an ning tan gen t
sp ace is equally releva nt to the study of
sh ap e. This is becau se m ost statistical resu lts (from , say, princip al com ponen ts
an aly sis or multivariate ana lysis of varian ce) are inva rian t to rig id rotations.
Therefore, one m ay thin k of rotatin g the
sp ace and expressin g the p artial warp
scores in term s of a new orthogonal basis.
Such a rotation does not lose any inform ation about sh ap e, nor does it chang e the
relatio nsh ips of taxa w ithin the space.
172
SYSTE M AT IC BIOLO GY
If the discrete characters generate d from
Fin k and Z eld itch’s (1995) proto col do not
chan ge w hen an altern ative basis for tan gen t space is used, then the sam e ingrou p
tree topology w ill be obtained from differen t ro tation s of tan gen t space. This would
be an im portan t test of their proto col, for
charac ters sen sitive to arbitra ry ro tations
of the orig inal data space are not reliab le
for phylo genetic studies. We therefore to ok
the partial warp scores from a TPS an alysis of the ho st races of N. bebbianae, usin g
N. gibbosus as the reference outgroup, coded the onto genetic sh ap e reg ressio ns follow ing Fin k an d Zeld itch, and generat ed
an estim ate of the phy logenetic relatio nsh ips am ong the taxa , ag ain usin g Wagn er
p arsim ony (Fig. 2a). We then chose three
altern ative, arbitrary base s for tan gent
sp ace, found from three differen t rig id rotation s of the p ar tial warp scores. We coded the ontogenetic sh ape reg ressions for
scores along the axes of each new basis,
and ree stim ate d the phy logeny w ith these
new ly coded characters (Figs. 2b± e). Unfortunately, we found tree topologies to be
very sensitive to different altern ative base s
for tan gen t space w hen usin g their protocol. O ur results show that different choices
of a basis for tan gen t space resu lt in differen t tree topolo gies. Becau se differen t
bases are m erely a rig id rotation of the
p ar tial warp scores, w hich loses no inform ation about the relatio nsh ip s am ong taxa
in tan gent sp ace, we must conclude that
tran sform in g the rotated continu ous data
(regres sions of sh ap e on size ) to discrete
charac ter state s loses in form ation. Further,
we must also conclude that Fink and Zeld itch’s protocol is very sensitive to the
choice of basis for tan gen t space, and in consistently retain s inform ation about the
relationsh ip between siz e and sh ap e.
O nly in recen t ye ars has the TPS been
used to describe sh ape variatio n w ithin
and between populatio ns (e.g., Bo okstein,
1991; Zeld itch et al., 199 2; Sw idersk i, 199 3;
R ohlf et al., 1996 ; Adam s and Fu nk, 1997).
A lthough new applications of the thin plate spline are constan tly bein g investigated (e.g., Morin et al., 199 5), we feel that
the way Fink and Zeld itch (1995 ) used par-
VO L.
47
F IG U R E 2. Top ologies fou nd by Wag ner p ar simony
for fou r hos t-associated races of the Neochla m isus bebbian ae using N. gibbosus as the outgroup species (bo otstrap values b ased on 100 replicates are show n ). Sixte e n d is cr e te ch a rac ters we re o b ta in e d fr om
reg ressions of par tial warp scores on log(centr oid
size ) follow ing the protocol of Fink and Z elditch
(1995). A differ en t b asis for tang ent sp ace was used
as the initial data set fou nd from rigid rotations of the
p ar tial war p scores prior to cod ing discrete ch aracters:
(a) no rotation (or iginal par tial warp scores) (C I 5
1.000, RI 5 1.000) ; (b ) principal com ponen ts rotation
(C I 5 0.900, RI 5 0.667); (c) and (d) Q R decom po sition
rotation (C I 5 0.875, R I 5 0.600); and (e) random rigid
rotation (C I 5 0.889, R I 5 0.714).
tial warp s for phy logeny estim ation has serious dif® culties that must be overcom e. In
the discussion of their paper, they bring up
severa l aspects of the m etho d that warran ted further exam ination and deb ate.
A m ong these, they felt the m ost critical
question was ``w hether cho osin g differen t
sta rtin g form s or even choice of an alternative basis for sh ap e sp ace would resu lt
in differen t phylo genies’ ’ (Fin k and Z eld itch, 199 5:3 58). We have show n throu gh ex-
19 98
PO IN TS O F VIEW
am ple that the cho ice of starting form , as
well as the cho ice of basis, has dram atic
conse quences on the resu ltin g phy logeny,
an d there fore raise s questions concern ing
the reliab ility of their coding pro cedu re.
Brid ging the gap between onto geny and
phy logeny has long been a goal of evolu tionary biologists. The work of Fink and
Z eld itch is an im portan t step toward our
underst and in g the relationsh ip between
thes e two concepts. Because of our ® nd ing s, however, as well as the ® nd ings of
Nay lor (199 6) and R ohlf (199 8), we must
conclude that the charac ters describing ontogenetic sh ap e trajec tories obtaine d from
the protocol of Fink and Zeld itch are not
s u it ab le fo r ch a rac te r-b as e d p a r s im o ny
m etho ds.
A C KN O W LE D GM E N TS
We than k F. Jam e s R oh lf and D en nis Slice for their
su gge stions and com m en ts on earlier versions of the
m anu script. Com m en ts from M iriam Z elditch and an
anony m ou s reviewer are also ackn ow led ged. T his
work was su pported in p ar t by National Science Foun dation grant DE B-9315 72 (to F. Jam es R ohlf) and is
con tribution nu m ber 996 from the Pro gram in Ecolo g y and E volution at the State Un iversity of New York
at Stony B rook.
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Received 14 M arch 1997; accepte d 29 M ay 1997
A ssociate E ditor: D. C ann atella