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Hysfrix,
(n.s.)
11 (1)
(2000):
49
-
75
PHYLOGENETIC
ANALYSIS
OF
SKULL
SHAPE
EVOLUTION
IN
MARMOTINE SQUIRRELS USING LANDMARKS
AND THIN
-
PLATE SPLINES
DONALD
L. SWTDERSKT
(*),
MIRIAM
L. ZELDTTCH
(**)
AND
w.
L.
FINK
(***)
(*)
Museum
of
Zoology, University
of
Michignn, Ann Arbor, Michigan, 48109 USA
("*)
Museum
of'
Pnleontology, Universiiy
of
Michigan, Ann Arbor, Michigan,
48109
USA
Pm*)
Department
of
Biology atid Museuni
of
Zoology, University
of
Michigan.
Ann Arbor, Michigan,
48109
USA
Corresponding Author: Donald L. Swiiderski. Museum
of
Zoology, Ann Arbor MI 481 09 USA
e
-
mail: dlswider@umich.edu
ABSTRACT.
-
Sevcral studics havc shown that thc rcccntly dcvclopcd tcchniqucs of gcomctric mor
-
phometrics are extremely powerful descriptive tools. And yet, one potential use
of
thc rcsulting dc
-
scriptions, phylogenetic analysis, has generally been neglected. This neglect is understandable be
-
cause prominent systematists as well
as
prominent inorphometricians have objected to the use of mor
-
phometric data in phylogenetic systematics. We agree that some methods
of
morphometric analysis
produce results that cannot be used in phylogenetic systematics. and that some methods of incorpo
-
rating morphometric results into statements about character transformation are not appropriate. How
-
ever, we do not agree that these objections
to
specific techniques support a blanket rejection
of
the
use of morphometric data in systematic studies.
In
this paper, we review the principles
of
phyloge
-
netic systematics and show that they are equally applicable
to
qualitative descriptions
of
triangles and
to quantitative descriptions (shape coordinates
of
the apex) of those same shapes. Then we show how
these principles would he applied to complex shapes like
skulls
of marmotine squirrels, and that the
resulting analysis leads to legitimate hypotheses about marmotine phylogeny and the evolution of skull
shape in these animals.
Geometric morphometrics has several ad
-
vantages over traditional methods of ana
-
lyzing biological shapes (Bookstein, 1990;
Bookstein, 1991). One advantage is that the
use
of landmarks anchors the descriptions of
shape differences and the explanations for
those shape differences to specific regions
of the organism. When landmarks are cho
-
sen carefully, the tendency of traditional
measurement schemes to overrcprcscnt par
-
ticular regions or dimensions can be dra
-
matically reduced. Another advantage of
this approach is that it provides independent
descriptions
of
size and shape. In addition,
it
provides
a
mechanism for decomposing
shape differences into
a
series
of
compo
-
nents ranging from large
-
scale features
spanning all or most of the form to small
-
scale features localized
to
the vicinity
of
a
few closely spaced landmarks. Empirical
studies have demonstrated the utility
of
these methods
for
the study
of
allometry
(Zelditch and Fink, 1995; Loy et al., 1996;
Taylor and Contrafatto, 1996), morphologi
-
cal integration (Zclditch et al., 1992;
Swiderski, 1993), and the relationship be
-
tween shape and function (Bales, 1996;
Courant
et
al., 1997).
One potential use of geometric morphomet
-
rics that has received relatively little atten-
50
D.
L.
Swiderski
et
al.
tion is the reconstruction
of
phylogenetic re
-
lationships. For example, Courant et al.
(1997) used least squares Procrustes super-
positions of cranial landmarks to describe
similarities
in
skull shape among fossorial
rodents (Arvicolidae) but did not use the
skull shapes in an analysis of arvicolid rela
-
tionships. Consequently, their results sug
-
gest that there could have been convergence,
but do not actually document the indepen
-
dent historical transformations of dissimilar
ancestors into similar descendants. Rohlf et
al. (1996) used UPGMA cluster analysis and
minimum spanning trees
on
canonical vari-
ates of partial warps scores
to
evaluate sim
-
ilarities and differences in skull shape
among European moles. Rohlf et al. com
-
pared their results to the current taxonomy
of the moles, but like Courant et al., did not
attempt to incorporate the shape analysis in
a phylogenetic analysis. Several other biol
-
ogists have performed similar studies in
which geometric morphometrics were used
to
describe similarities among taxa, but no
phylogenetic analysis was performed to in
-
fer the evolutionary relationships of those
taxa (,e.g., Bales, 1996; Capanna et al.,
1996; Taylor and Contrafatto, 1996). One
of the few explicit attempts to reconstruct a
history
of
shape changes
was
performed by
van Dam (1
996), who used the fossil record
to infer the sequence of tooth shapes in
a
group of murid rodents, and then used the
morphometric analysis to describe the im
-
plied shape changes.
As
far as we know,
only Fink and Zelditch (1995) have used
cladistic methods of phylogenetic analysis
to infer genealogical relationships of taxa
from shape differences described by geo
-
metric morphometrics.
The lack of cladistic studies using geomet
-
ric morphometrics is not surprising. Sever
-
al
investigators have argued that cladistic
analysis is an inappropriate use of morpho
-
metric data (Bookstein,
1994;
Adams and
Rosenberg, 1998; Rohlf. 1998). Others
have argued that cladistic analysis of quan
-
titative data requires manipulations that can
-
not be justified (Felsenstein, 1988; Garland
and Adolph, 1994). In addition, some in
-
vestigators have argued that morphometric
data lack the qualities that are necessary to
justify hypotheses of homology, and there
-
fore, are unsuitable for this kind of analysis
(Pimentel and Riggins, 1987: Mickevich
and Weller, 1990). Taken together, these ar
-
guments seem to constitute a daunting ob
-
stacle
to
the cladistic analysis of morpho
-
metric data.
We have argued that this obstacle is not as
formidable as it appears to be. We agree
that many older morphometric methods
produce variables that are unsuitable for
phylogenetic analysis, but we also find that
some of the recently developed landmark-
based methods produce variables that are
suitable (Zelditch et al., 1995). In addition.
we agree that many of the methods used to
code morphometric data for phylogenetic
analysis employ manipulations that are un
-
justified, but we have not found these ma
-
nipulations to be necessary when taxa are
well differentiated (Swiderski et al., 1998).
Consequently, we argue that some quantita
-
tive descriptions of biological shapes can be
coded by using the same criteria that are
used when those shapes are described qual
-
itatively. Perhaps most important, we have
demonstrated that the arguments suggesting
that cladistic analysis is an inappropriate
use of morphometric data are based on in
-
correct interpretations
of
cladistic method
-
ology (Zelditch et al., 1995; Zelditch and
Fink, 1998: Zelditch et al., 1998). Thus,
even though there
is
great need for caution
in the selection of morphometric variables
and in the selection of criteria used for cod
-
ing, it is possible
to
produce valid infer
-
ences of historical shape change by per
-
forming a cladistic analysis of biological
shapes that have been described using geo
-
metric morphometrics.
The purpose of this paper is to demonstrate
how cladistic methods of phylogenetic
analysis can be applied
to
quantitative de
-
scriptions of biological shapes. We begin
Plzjlogenetir,
analysis
of
skull
shape
in
squiri-els
51
with a brief review of cladistic methodolo
-
gy, then present two examples to illustrate
its application. In the first example, we an-
alyze an artificial data set composed of a se-
ries of triangles.
In
the second example, we
analyze differences in skull shape among
several species
of
squirrel
-
like rodents in the
tribe Marmotini.
CLADISTIC
METHODOLOGY
The cladistic approach to inferring phyloge
-
netic history is a logical extension
of
evolu-
tionary theory (Hennig,
1966).
Organisms
are expected to inherit traits from their an
-
cestors, but they are also expected to acquire
modifications
of
those traits. Subsequent
descendants will inherit the modified ver-
sions of the traits, and perhaps acquire ad-
ditional modifications
of
them. When the
lineage branches, the two lines
of
descen-
dants will accumulate different sets
of
de-
rived traits. In the absence
of
convergence,
any similarities between representatives
of
the two lines will be due to the retention of
unmodified ancestral traits in both lines.
As
the lineage continues to branch and other
traits are modified (still without conver-
gence) the distribution
of
derived traits in
descendent taxa will exhibit a hierarchical
arrangement that retlects the sequence of
branching events. Consequently, Hennig ar
-
gued that the goal of phylogenetic analysis
should be to identify nested sets
of
derived
traits and use their distributions
to
infer the
historical sequence
of
branching events.
Hennig recognized that the principal obsta
-
cle to implementing this approach is con-
vergence. Organisms in similar environ-
ments may experience similar selection
pressures. Consequently, some of their fea-
tures may be independently modified in
ways that make those features more similar
in the descendants than they were in the an-
cestors. These homoplasic similarities could
lead to the mistaken inference that the con-
vergent taxa shared a more recent common
ancestor with each other than they did with
the other members
of
their respective lin-
eages. However, Hennig reasoned that ho-
mologous similarities, those due to common
ancestry, would be found throughout the or
-
ganism, whereas the homoplasic similarities
due to
a
particular convergence would be
found in the relatively few traits that were
most directly affected by the similar selec
-
tion pressures. In addition, one species
might be convergent with a second species
in
one set of traits, but convergent with
a
third species in
a
different set
of
traits.
Thus, convergent similarities might be mis-
leading, but they would contradict each oth-
er. This led Hennig to propose the principle
of
phylogenetic parsimony. Each judgement
of
derived similarity supports a hypothesis
of homology and monophyly. The judge-
ments that are correct will support hypothe
-
ses that corroborate one another, but the
judgements that are incorrect due
to
homo-
plasy will support contradictory hypotheses
(intersecting sets
of
monophyletic taxa) and
ad hoc hypotheses of additional transforma-
tions will be necessary to resolve those con-
flicts. Because homoplasic similarities are
not expected to exhibit a coherent pattern,
the phylogenetic hypothesis that most accu
-
rately retlects the genealogical relationships
of
the taxa will be the one that requires the
fewest ad hoc hypotheses, i.e., the one that
is most parsimonious.
Some biologists have claimed that this ap-
proach implies an assumption that evolution
is parsimonious, that convergent similarities
are less common than homologous similari
-
ties, and argued that parsimony methods
will be mislead if this assumption is incor-
rect (e.g., Felsenstein, 1978; Saether,
1986).
However. Farris (1983, 1986) has shown
that parsimony methods
do
not require that
homologous similarities are more common
than homoplasic similarities. but only that
there is more support for the correct phy
-
logeny than for any one of the alternatives
supported by the homoplasies. Thus the re
-
al danger is that a particularly large set of
functionally or developinentally linked char-
52
D.
L.
Swiderski
et
a1
acters has undergone the same series
of
transformations in evolutionarily indepen
-
dent lineages. Accordingly, some systema
-
tists have suggested that the characters
in
these complexes should be assigned lower
weights (Hecht and Edwards, 1976; Neff,
1986) or even coded
as
a
single character
(Winterbottom, 1990: Mabee, 1993; Fink
and Zelditch, 1995) to reduce the influence
of correlated homoplasies on the phyloge-
netic analysis.
The application of Hennig’s approach
is
quite simple. In analyses of qualitatively
described traits, the first step is to identify
the features that can be used to
sort
taxa in
-
to groups that are different from one anoth
-
er. The next step is to describe each feature
and the alternate states found in each group
of taxa. Then, integer codes are applied to
indicate which taxa have which states. Fi
-
nally,
an
analysis is performed to identify
which phylogenetic trees imply the fewest
number of character state transformations.
In analyses of quantitatively described traits,
the protocol is slightly different because the
measurements are specified
a
priori and the
decision of what to measure is often based
Figure
I.
An artificial
clata
set
cornposed
of
a
set
of
triangles
on expectations of what should be informa
-
tive in light of functional models or experi
-
ence with related taxa. Consequently, the
first step
i\
to describe the traits that will be
measured, and the second step is to evaluate
which traits can be used to sort taxa and de
-
scribe the alternate states found in each
group of taxa. (Much of the debate about
coding quantitative data is actually about the
validity
of
alternative criteria proposed for
sorting taxa
-
cf., Farris, 1990; Gift and
Stevens, 1997; Swiderski et
al.,
1998.)
Once the states of the potentially informa
-
tive traits have been described, the subse
-
quent steps are the same
as
in analyses of
qualitatively described traits.
T
R
I
A
N
G
L
E
S
As discussed above. phylogenetic inference
is based on hypotheses of homology and
monophyly, and these hypotheses are based
on judgements of the similarity of the traits
observed in the taxa. In morphometric analy
-
ses, the traits are siLes and shapes. Sizes are
one
-
dimensional scalars. There might be dis
-
agreement concerning which measurement of
size is more appropriate (e.g., surface area or
volume), but not about how to judge the sim
-
ilarity of volumes or areas. In contrast,
shapes are multi
-
dimensional,
so
the evalua
-
tion
of
similarities of shapes is more com
-
plex. In this section, we illustrate the prob
-
lem
of
comparing shapes, and our solution of
the problem, with a set of triangles. Later in
this paper, we show how this solution can be
applied to analyses of more complex shapes
like those of mammalian skulls.
Quulitatiile
Analysis.
Figure
I
shows sever
-
al
triangles, each representing an individual
specimen
of
one of the 5pecies being
ana-
lyzed. For any inferences of homologous
shapes to
be
valid, the triangles must be de
-
fined by the same three points in
all
taxa,
and oriented in the same way for
all
com
-
parisons. For example, the two lower points
might be the anterior end\
of
the zygomatic
Figure
2.
The
triangles from Figure
1
sorted by
shape.
A)
short and relatively symmetrical,
B)
tall
and
relatively symmetrical,
C)
tall
and asym
-
metrical.
arches
on
the left and right sides, and the
apex might be the distal end
of
the mid-line
suture between the two nasal bones. Be-
cause this is a constructed example. we will
assume that
all
of the triangles have been
oriented appropriately.
There are several sets
of
attributes that could
be used to describe the shape of a triangle.
Two
commonly used features are the aspect
ratio, which describes the height
of
the apex
relative
to
the length
of
the base, and skew-
ness, which indicates whether the apex is
centered over the baseline or displaced to-
ward one end. Together, these two features
describe the shape
of
a triangle completely
and without redundancy. In Figure
2,
the
triangles have been sorted into three groups:
A)
relatively short and approximately sym-
metrical, B) relatively tall and approximate
-
ly
symmetrical. and
C)
relatively tall and
skewed to the right.
Now that the three sets of shapes have been
recognized, the next step is to code those
shapes for the phylogenetic analysis. If
there were only two sets of shapes, perhaps
those
in
groups
A
and
B,
this would be sim-
ple. The shape shared by the ingroup (the
taxa of interest) and the outgroup (selected
close relatives) would be assigned state
0
to
reflect the hypothesis that this shape was in
-
herited by both groups from their common
ancestor and therefore primitive. The other
shape would be assigned state
1
to reflect
the hypothesis that this state is derived and
the taxa that share this shape are a mono-
phyletic subgroup
of
the ingroup. If the two
sets of shapes are those in
A
and
C,
we still
have evidence of only a single shape
change, even though it is necessary to de
-
scribe the changes in terms of both the as
-
pect ratio and skewness. Only when all
three shapes are present is there evidence of
shape changes in two different directions.
Unfortunately, there also are nine possible
histories
of
transformations connecting
these three states (Figure
3).
The shapes of
these triangles provide no information that
can be used
to
choose among these nine
character state trees; information from oth
-
er characters is needed. It is possible to re-
duce the set
of
possible character state trees,
but only if there is only one state that is
shared by the ingroup and the outgroup.
A
JL
BC
A
f
B+C
A
*
B+C
A
J
B4C
A
fI
BC
A
Jt
BC
A
L
B+C
A
)t
B+C
A
f
BcC
Figure
3.
Nine
possible transformation series for
three character
states.
54
D.
L.
Swiderski et
al.
Figure
4.
Graphical representation of shape co
-
ordinates.
Under those circumstances, it would be rea
-
sonable to hypothesize that the state shared
by the ingroup and the outgroup is primi
-
tive. Even
so,
there would still be three
equally plausible transformation histories,
and no way to choose among them. Be
-
cause there is no way to choose among the
alternative hypotheses, multistate characters
are analyzed
as
unordered, which means
that no hypothesis is specified.
Quantitative
analysis.
As
in the qualitative
description, there are several combinations
of
variables that could be used
to
quanti
-
tatively describe the shapes
of
triangles.
One particularly convenient set
of
vari
-
ables is the pair
of
shape coordinates of
the apex (Bookstein et al.,
1985).
The first
step of computing \hape coordinates
is
to
rescale each triangle
so
that its baseline
has unit length. The subsequent steps
compute the vectors that describe the or-
thogonal projection of the apex onto the
baseline (Figure
4).
In essence, the shape
coordinates
of
the apex are linear, quanti
-
tative versions of skewness
(x)
and aspect
ratio
(J)
of
the triangle.
The correspondence between shape coordi
-
nates and familiar qualitative descriptors
is
useful, but the real utility of shape coordi
-
nates is that they completely describe the
two
-
dimensional shape of the triangle
in
two
linear and independent variables. Conse
-
quently, the diversity
of
shapes can be dis
-
played as
a
scatter
-
plot of the shape coordi
-
nates. In Figure
5A,
the triangles from Fig
-
ures
2A
and
2B
are aligned by their base
-
lines, which have been rescaled to the same
length. Figure 5B shows only the locations
of the apical points, with ellipses to outline
each group. The two clusters
of
points do
not overlap,
so
the clusters can be coded
as
separate character states. The transforma
-
tion can be described
as
a
shift along the
y
-
axis (i.e.,
a
change in the relative height of
the apex), but the direction of that transfor
-
mation cannot be determined from the in
-
formation given
so
far. However, if the
shape of the outgroup is known, then the di
-
rection can be specified
as
an increase or de
-
crease relative to the shape shared by both
the outgroup and some members of the in-
group. In other words, the hypothesis
of
transformation can be polarized to indicate
Figure
5.
Graphical representation of coding
two sets of triangles,
1.
transformation parallel
to one morphometric axis.
A)
short symmetri
-
cal triangles and tall symmetrical triangles
su
-
perimposed at their baselines,
B)
scatter
-
plot of
shape coordinates
of
the apical points,
C)
scat
-
ter
-
plot with arrow to indicate the inferred di
-
rection
of
transformation.
Phylogeiwtic
analysis
of
skull
shape
in
squirr.els
55
which shape is inferred to be derived and
which group is inferred to be monophyletic.
In Figure
SC,
an arrow is included to indi
-
cate the polarized hypothesis that the shape
change is an increase in the relative height
of the apex.
In Figure
5,
the values of the shape coordi
-
nates are not shown. They were used to
generate the scatter-plot, but they are irrele
-
vant to the subsequent analysis. Only two
pieces of information are used to formulate
the hypothesis of transformation: the pres
-
ence of two distinct groups of shapes, and
the shape of the outgroup. The integers that
'
are assigned
as
character state codes are
nothing more than labels that reflect
the
hy
-
pothesis of transformation. These labels are
not intended to represent the magnitude of
that transformation on any scale.
Figure
6
shows the case in which the trans
-
.
formation
is
not parallel to the axes of the
quantitative description, using the triangles
from Figures
2A
and
2C.
As
in the quali
-
tative analysis, the description of this
Figure
6.
Graphical representation of coding two
sets
of
triangles,
2,
transformation that is not par
-
allel
to either morphometric axis.
A)
short
sym
-
metrical triangles and tall asymmetrical triangles
superimposed at their baselines,
E)
scatter
-
plot of
shape
coordinates of the apical points,
C)
scat-
ter
-
plot with arrow to indicate the inferred direc
-
tion
of transformation.
Figure
7.
Graphical representation of coding
three sets
of
triangles.
A)
all three sets superim
-
posed at their baselines,
B)
scatter
-
plot
of
shape
coordinates of the apical points,
C)
scatter
-
plot
with two-headed arrows to indicate uncertainty
about the directions of transformation.
change
is
more complex because it requires
two variables
(x
and
y),
but that does not
mean that the change occurred in two
steps.
A
different method of quantification
may produce
a
description that requires on-
ly one variable. As in the previous exam-
ple, the hypothesis of
a
transformation is
based on the recognition that there are two
distinct groups of shapes, not on the de-
scription of the difference between those
groups.
Figure
7
shows the quantitative analysis
of
all
three groups of triangles from Figure
2.
As
in the qualitative analysis, the available
information supports the hypothesis that
there are two derived states. Also as before,
that information does not indicate whether
those states are steps in
a
historical se-
quence, nor what that sequence was. Other
characters must be used to infer the phylo-
genetic relationships of the taxa. Then, the
historical sequences
of
these shapes can be
interpreted in the light
of
those relation-
ships. In the absence of any evidence about
the historical sequence, all possible se
-
quences must be considered equally plausi-
ble,
as
indicated by the two
-
headed arrows.
56
D.
L.
Swiderski
et al.
MARMOTINES
We constructed the examples above
so
that
the groups of shapes would be clearly dis
-
tinct. The natural world
is
seldom
so
neat.
Below, we present
a
more realistic example
in
which we produce quantitative descrip
-
tions of skull shape in marmotine squirrels.
then use those descriptions
to
infer what
transfonnations of skull shape occurred dur
-
ing the evolution of marmotines.
Barkgroiitz(f.
The tribe Marmotini is a
monophyletic group that includes marmots
(Marmota).
antelope squirrels
(Ammospe~-
niophilus),
ground squirrels
(Spernzophrlus),
and prairie dogs
(Cyzomys)
(Hafner.
1984).
Several lines of evidence suggest that mar-
motines diverged from primitive tree squir
-
rels in the late Oligocene (Bryant, 1945;
Hight et
al.,
1974; Ellis and Maxson, 1980;
Emry and Thorington, 1982; Hafner,
1984).
Since their origin, marmotines have under
-
gone considerable diversification in adult
body size, diet and foraging habits (Howell,
1938; Bryant, 1945; Black; 1963; Hafner,
1984). Comparable changes in size and be-
havior are associated with the evolution of
skull shape in many mammalian lineages
(cf., Radinsky, 1982; Janis and Ehrhardt,
1988:
MacFadden, 1992). It would not be
surprising to find similar associations
in
the
marmoti nes,
Six marmotine species and three outgroups
are included
in
the analysis below (Appen
-
dix
1).
All four genera and
most
of the
commonly recognked subgenera
of
mar-
motines are included.
In
addition. these six
marniotines span
most
of the range of adult
body size
in
the tribe and exemplify most of
the different diet and foraging habits found
in the tribe. The three outgroup species
(two
tree squirrels,
Sciiirus
niger
and
Tunli-
Figure
8.
Line drawing of
a
representative specimen
of
Sciitr-its
iiiger,
showing locations
of
the land
-
marks.
I
j
tip of the rostrum at the midline suturc.
2)
lateral limit of the dorsal margin of the nares.
3)
antero
-
dorsal end
of
the zygomatic arch and plate,
4)
notch above the lacrimal process.
5)
anteri
-
or end
of
the rnasseter lateralis fossa,
6)
margin of the orbit at the supraorbital notch or foramen,
7)
notch behind the postorbital process,
8)
posterior end of the masseter lateralis
fossa,
9)
anterior end
of
the glenoid fossa,
10)
posterior end
of
the glenoid fossa,
11)
mastoid process,
12)
posterior edge
at
the midline.
usciurus
l7udsorzicus,
and a chipmunk,
Tmnius
striatus)
are included to represent
some of the size and dietary diversity found
among the closely related outgroups.
The six marmotine species included
in
this
example are only about
1/10
of the extant
species recognized by most inarmotine tax
-
onomists. Because this analysis includes on
-
ly
a small fraction of the marmotine species.
it is unlikely that the results will be an accu-
rate reflection of the marmotine phylogeny.
Therefore, the purpose of this demonstration
is not to produce a definitive answer to the
question
of
marmotine relationships, but to
illustrate the methods that would be used in
a more complete analysis. The question
to
be addressed in the analysis of each shape
feature is whether the diversity of shapes
is
distributed in a way that justifies a specific
hypothesis of homology and monophyly.
Shape
Anaiysis.
We began the analysis of
skull shape by digitizing 12 landmarks on
each skull (Figure
8).
These landmarks were
chosen because they mark prominent aspects
of shape that could be compared among
taxa. For example, landmark
1
1,
the mastoid
process, marks the widest point on
the
brain-
case, and with landmark 12 marks the edge
of the occipital region. Another important
consideration in the selection
of
landmarks
was to use points that are easily recogniz
-
able, but not prone
to
breakage. We did not
use the tip of the post-orbital process be-
cause this structure is often broken, and we
did not use the anterior end of the base of the
process because it is smoothly continuous
with the margins of the orbit. We did use the
notch behind the process, which also repre
-
sents the antero
-
medial corner of the tempo
-
ral fossa. We used the supraorbital and
lacrimal notches because both are easy
to
lo
-
cate, and because both have consistent posi
-
tions relative to the orbit. In contrast, we did
not use landmarks on the sutures on the
snout because the locations
of
these sutures
are quite variable within species and often
differ between individuals of the same
species with similar snout shapes. Thus,
landmarks on these sutures might be useful
for describing the shapes of these bones, but
would not be very useful for describing the
shape
of
the snout. For similar reasons, we
used landmarks on the zygomatic arch that
are associated with muscle attachments
or
the jaw joint and in stable locations around
the arch, and did not use sutures of the bones
forming the arch. Several of these features
are easier to see in lateral view than in dor-
sal view,
so
markers were placed
in
the field
of
view adjacent to their locations.
To
eliminate the effects of asymmetry. land-
marks 2-1
1
were digitized on both sides and
shape coordinates were computed for all 22
landmarks using points
1
and
12
to define the
baseline (midline). The signs of the
y
coor-
dinates of landmarks on the right side were
reversed, effectively reflecting the right side
onto the left. Then, the
s
and
y
coordinates
of each pair of corresponding landmarks
were averaged for each specimen. These 12
pairs of symmetrized shape coordinates and
the shape coordinates of the baseline were the
input for thc thin
-
plate spline analysis.
For the spline analysis, one specimen of
S.
niger
was used as the reference form (or
starting form). The symmetrized shape co-
ordinates of each landmark were compared
by rank order to identify a specimen that
does not have an unusual arringement of
landmarks. Our goal was to find a specimen
that has a normal shape for that species,
so
that the other specimens
in
the study would
be described in terms that referred to the
shape of that species. One of the principal
advantages
of
using landmarks is that they
attach descriptions of shape to specific lo
-
cations on the form. Using a reference that
is a representative form of one species en
-
hances this advantage by ensuring that the
descriptions refer to features of
a
biological
form. This advantage can be enhanced fur-
ther if the reference has a primitive
or
juve-
nile form, which makes it possible
to
de-
scribe the other shapes as modifications of
the reference, not simply as different from
58
D.
L.
Swiderski et
al.
the reference. Using
a
reference that is
a
mean
of
several dissimilar species dilutes
the advantages
of
landmarks by allowing
shape description to refer to features of an
artificial construct that may not represent
any biological form.
In
addition, using the
mean shape as the reference form means
that the starting configuration will change
with the addition of each new specimen,
whereas using
a
specific shape as the refer
-
ence means that specimens can be added to
the study and described in the same terms.
In our view, changing inferences about pat
-
terns of shape evolution should reflect
U2
changing hypotheses of what is primitive,
not changing sample sizes.
We compared shapes using partial warps
scores (Bookstein, 1991), and scores for the
uniform component (Bookstein, 1996). Our
reasons for using these scores rather than rel
-
ative warps
are
related to our reasons
for
us
-
ing
a
specific reference rather than a sample
mean. Partial warps describe differences
from the reference in terms
of
features of the
reference. Relative warps are principal com
-
ponents of partial warp scores for all the
specimens in the study. Like the mean, prin
-
cipal components can change every time
-
0.03
-
-
0.03
0,OO
0.03
0.06
U1
S.
tridecemlineatus
7
A
Figure
9.
Variation in the component
of
marmotine skull shape described by the uniform
analysis.
A)
scatter
-
plot
of
uniform component scores.
U1
is
shear,
U2
is dilation and compression.
B)
vec
-
tor diagram
of
the uniform component of the deformation
of
the reference into the configuration of
a
representative specimen
of
S.
triderernlineutus.
Phylogenetic
analysis
of
skull
shape
in
syuiriuls
59
specimens are added and deleted. More im
-
portant, principal components are deter
-
mined by the patterns of variation and co-
variation in the sample,
so
that relative
warps are
a
function of dissimilarity over
all
the landmarks, over all the specimens.
In
our view, these features of principal compo
-
nents make relative warps analysis unsuit
-
able for phylogenetic studies because they
defeat the purpose of using landmark
-
based
morphometrics. (For more discussion of the
issues related to reference choice and the use
of partial warps rather than relative warps,
the reader is referred to the following papers:
Swiderski, 1993; Fink and Zelditch, 1995;
Zelditch and Fink, 1995, 1998; Zelditch et
al;
1995, 1998; Swiderski et
al.,
1998)
The programs TPSSPLIN (Rohlf, 1997) and
TPSRELW (Rohlf, 1998) can both be used
to generate partial warp scores. The refer
-
ence form used by TPSRELW is
a
consen
-
sus
form
(a
mean form constructed by
Pro-
crustes analysis), but the reference used by
TPSSPLIN can be any form the user speci
-
fies. Because
we
were using
a
particular
specimen
as
the reference, we used TPSS-
PLIN to generate partial warp scores.
TPSSPLIN does not compute scores for the
uniform component according to Book
-
stein’s (1996) new protocol,
so
we wrote a
program in QBASIC
to
implement
Book
-
stein’s protocol and compute the uniform
components of our selected reference, and
the scores on those components for each
specimen. To illustrate the uniform defor
-
mations of
a
particular specimen, we used
the scores to compute the landmark dis-
placements that can be attributed to this
component, and we used VECTOR SPEC
-
TOR
(Humphries, 1994) to draw those dis
-
placements.
We
also used VECTOR SPEC
-
TOR
to produce vector diagrams of select
-
ed non
-
uniform deformations. Following
Bookstein (1991), we have numbered the
warps in order of increasing localization,
which reflects the order of their computa
-
tion. Scatter
-
plots of scores (both uniform
and non
-
uniform components) were pro
-
duced
in
SYSTAT. The reference is plotted
at the origin of each graph.
Unfo1.m.-
This feature describes shearing
(Ul), in which medial and lateral landmarks
are displaced in opposite directions, and di
-
lation
-
elongation
(U2).
in which the skull be
-
comes wider and shorter, or longer and nar
-
rower (Figure 9). In the scatter
-
plot of scores
for this component, there is
a
noticeable gap
in the distribution of
A.
leucurus
specimens.
Five specimens
are
on the left with the
T.
hudsonicus
cluster, and one
A.
leucurus
spec
-
imen is on the right with the other taxa.
If
the gap separated
all
A.
leucurus
and
T.
hud-
sonicus
from the others, then we would con
-
sider it reasonable
to
interpret this gap
as
ev
-
idence of evolutionary divergence separating
these two groups. We also might interpret
this gap as evidence of divergence despite the
one unusual specimen
of
A.
leucurus,
if we
had reason to dismiss that individual
as
an
outlier. However, there are similar gaps in
the distributions of several other species, sup
-
porting the inference that sample sizes are
too
small to judge which specimens are outliers.
Because none of the gaps anywhere in this
scatter
-
plot support an unambiguous group
-
ing
of
species (two or more species on each
side of the gap with none spanning the gap),
our judgement is that no informative charac
-
ters can be inferred from this plot.
Wur-p
I
.
-
As
is common for elongate forms,
the largest scale warp describes
a
pattern of
landmark displacement
in
which the land
-
marks near the center of the form move in
one direction and the landmarks near the
ends move in the opposite direction (Figure
10).
When the landmarks are displaced
par
-
allel to the long axis of the form, they pro
-
duce
a
gradient of relative elongation in one
direction. Thus, negative scores on the
x-
axis
(as
in
T.
hudsonicus)
indicate
a
longer
braincase and shorter snout than in the ref
-
erence
(S.
nigeu).
Positive scores, which are
not found in these taxa except for very low
scores in some specimens of
S.
niger,
would
indicate
a
shorter braincase and longer snout
than in the reference specimen. In
T.
stiia-
60
A)
Yl
0 -0%
0
-04
0
-00
B>
D.
L.
Swidcrski et
a1
-
0.08
-
0.04 0
.00
Xl
*+
c
*
7:
hud’sonirus
*
Figure
10.
Variation in the component
of
skull ahape described
by
warp
1.
A)
scatter
-
plot
of
partial
warp scores.
B)
vector diagram
of
the deformation described
by
partial warp
1
for
a
representative
specimen
of
T.
lz~id~onkr~s.
C)
vector diagram
of
the deformation described
by
partial warp
1
for
a
representative specimen
of
T.
S~I-~U~NS.
tits
and the marmotines, negative scores on
the x-axis are combined with positive scores
on
the y-axis. reflecting the fact that their
braincases are wider as wcll as longer, and
their snouts are narrower,
as
well as shorter.
The scatter-plot for this feature shows
sev
-
eral species with ranges that do not overlap
any other.
An
especially large gap separates
S.
rzigei-
from everything else, smaller gaps
separate
T.
hudsonicus.
T.
sti-iutiis,
S.
ti-idc-
cenzlineutits
and
S.
columhiniius.
To
code
this feature, it is necessary
to
consider
whether each of these species is truly dis-
tinct from the four specks with overlapping
ranges.
It
is also necessary to consider
whether any of the species with separate
ranges can be grouped together (i.e., can a
hypothesis
of
shared transformation be jus-
tified despite their differences).
Of
the five non-overlapping species,
S.
Phylogenetic
nnalysis
of
.skull
.shupe
in
squirrels
61
Y2
0.08
0.04
0.00
-
0.04
B)
I
I
I
0.00
0.04
x2
'd
Figure
11.
Variation in the component
of
skull
shape described by
warp
2.
A)
scatter
-
plot
of
partial
warp
scores with an ellipse enclosing
the
scores of
S.
nigw
specimens.
B)
vector diagram
of
the
de
-
formation described
by
partial warp
2
for
a
representative specimen of
C.
Iitdoi*ic,ianus.
coluntbintius
and
S.
taidecemlineatus
are
closest to each other. These two are also
the closest to the four overlapping species.
In fact, a boundary drawn between
S.
colL4nzhiatzus
and the overlapping species
would have some rather sharp bends in it,
suggesting that
S.
columbianics
is not real-
ly
differentiated from the others. If
S.
columbianus
is recognized as divergent,
then both
S.
trYderernlineutus
and
C.
/U-
dovicianus
should be recognized
as
sharing
the same transformation and all three
species should be assigned the same char
-
acter state code. However, one reason for
not doing this is the overlap of
M.
flu
-
vii,entl-is
and
C.
ludoviciaizus,
suggesting
these species
inay
not be differentiated.
Another obstacle is the fact that a different
direction of transformation
(+x)
provides
an equally valid justification for assigning
a
shared character state to
S.
triderenzlin-
earus,
T.
striutus
and
S.
niger.
In
fact,
there are at least two other equally valid,
equally narrow dividing lines that could be
drawn on this scatter
-
plot
to
demarcate
groups.
Given the nuniber
of
conflicting groupings
that can be based
on
this plot, there is good
0.
a
EX
00'0
EO'O
-
90'0-
EO'O
-
63
I
0,OO
4
-04
0.00
x4
Figure
13.
Variation
in
the component
of
skull
shape described
by
warp
4.
A)
scatter
-
plot
of'
partial
warp
scores.
B)
vector diagram
of
the
deformation described
by
partial warp
4
for
a
representative
specimen
of
C.
luclozic-ianus.
end of the zygomatic arch, and also its rel
-
atively broad and square braincase.
The scatter-plot for this feature, like that for
the uniform, appears to have two distinct
clusters of specimens which might reflect
evolutionary divergence except for the fact
that one species has members in both clus-
ters. Here the gap suggests divergence from
the outproup by all marmotines except
A.
leucurus.
The species that spans the gap
is
one
of
the outgroups,
S.
niger.
As before,
we cannot be certain that one particular in-
dividual is an outlier,
so
we
cannot ignore
the one specimen of
S.
niger-
on
the right
side of the gap. Therefore. our judgement
is that
no
informative characters can be in
-
ferred from this plot. either.
Wuip
3.
-
In this feature, the outer (lateral)
portion
of
the zygomatic arch is displaced
relative to its ends (Figure
12).
In
addition,
the posterior end
of
the skull is displaced in
the same direction as the outer portion
of
the
zygomatic arch. Transformations
of
this
feature retlect a relatively triangular
~ygo-
matic arch and tapered braincase
(-x),
espe-
cially
in
representatives
of
A.
Ieiici.~~.~~
and
S.
tl-ideremlineatus,
or a relatively square
zygomatic arch and narrow braincase
(+J]),
as in
C.
liido\icianiis
and
M.
jlavii~entl-is.
At least three groups can be recognized in
64
D.
L.
Swidenki
et
a1
Figure
14.
Variation in the component
of
skull shape described
by
warp
5.
A)
scatter
-
plot
of
partial
warp
scoreb.
B)
vector diagram
of
the deformation described
by
partial warp
5
for a representative
specimen
of
C.
ludoi~icionus.
this scatter-plot. There is unambiguous sep-
aration of
M.
flaviventris
and
C.
liidovi-
cianirs from all other species. Another large
gap separates
S.
tridecemlineatus,
S.
vai-ie-
gutus
and
S.
rolicnihianus from
A.
le1tcul-u~~
and the outgroups. There is one
S.
tr-ide-
cenilineatiis specimen in this gap; but it is
still possible to draw
a
line between the two
groups.
A
third gap separates
A.
leucuriis
from the outgroups.
S.
tl-idecenilineutus ap-
pears
to
diverge from
S.
vui-iegutus
and
S.
columbicznus
in the same direction that
A.
leucul-us
diverges
from
the outgroups
(-A+).
but
S.
ti.iderenzlineatus still overlaps both
S.
~~ai-iegatus
and
S.
rolumhianus.
Without
this overlap,
S.
t~-idecenilineatus
might be
assigned the same character state
as
A.
leii-
ci~i-us,
or even assigned a unique character
state. Because there is overlap here, we
have coded this feature
as
an
unordered
multistate character with
4
states (Table
1).
Warp
4.-In
this feature, the largest dis-
placements are at landmarks
3,
6,
8
and
11
(Figure
13).
The large negative ,I--scores
in
C.
~udovicianus
again reflect the relatively
greater angularity of its zygomatic arch.
The distribution of scores for this feature
has one
obvious
gap separating
C.
Iirdoii-
Phylogenctic
arialysis
of
skull
shape
in
sqrrir
wls
65
C.
ludo
vicianus
Figure
15.
Variation in the component
of
skull
shape
described
by
warp
6.
A)
scatter
-
plot
of
partial
warp
scores.
B)
vector
diagram
of
the deformation
described
by
partial
warp
6
for
a
representative
specimen
of
C.
ludovuciarrus.
ciclnus
from all other species.
It
is
also
pos-
sible to draw a line separating
A.
1c.ucuiu.s
and the outgroups from the other taxa.
There is no overlap, but there is also more
than
one specimen responsible for the nar-
rowness of this gap. In addition, the gap is
smaller than almost all distances between
individuals within species. Consequently,
we only recognize the gap separating
C.
114-
dovicianus
as
clear evidence of an evolu-
tionary transformation. Because the diver-
gence
of
a single species is not phylogenet-
ically informative, we have not included this
character in Table
1.
Wbr-p
5.-In this feature, large displace-
ments at landmarks
5,
6.
7
and
8
are com-
bined with contrasting displacements of the
landmarks at the tips
of
the snout (Figure
14).
Thus this warp describes changes
in
which the elongation of the outer portion of
the zygomatic arch (further contributing
to
its relatively greater angularity) are com-
bined with blunting of the snout. Near the
center of the scatter plot for this feature is
a
dense cluster with several species broadly
overlapping. Two groups of species appear
to diverge from this cluster in two direc
-
tions. One group includes
C.
ludoviciunus.
66
D.
L.
Swiderski
et
al.
5.
tridecemlineatus
Figure
16.
Variation
in
the component
of
skull
shape described by
warp
7.
A)
scatter-plot
of
partial
warp
scores.
B)
vector diagram
of
the
deformation described
by
partial
warp
7
for
a representative
specimen
of
S.
tiidecemlineatus.
M.
flaviventris
and
S.
columbianus
(+-U);
the
other group includes
A.
leucurm
and
S.
tridecendineaius
(+y).
As in the previous
feature, there
is
no overlap between groups,
but the difference between groups is less
than most differences within species.
Again, the only large unambiguous differ-
ence is the one separating
C.
ludovicianus,
so
this phylogenetically uninformative char-
acter
also
is not included in Table
1.
Warp
6.-In this feature, the largest dis-
placements are at landmarks
8,
10
and
11
(Figure
15).
The large negative
s
scores
for
C.
Iudovicianus
reflect posterior exten-
sion
of
the zygomatic arch, reduction of the
posterior root of the arch, and posterior dis-
placement of the mastoid producing
a
more
squared outline for the braincase. The
somewhat smaller positive
,U
scores for
T.
hudsonicus
primarily reflect
a
relatively
broader posterior root of the zygomatic
arch. The scatter
-
plot for this feature also
shows a dense cluster near the center, from
which both
C.
ludovicianus
and
T.
hudson-
icus
are unambiguously differentiated.
Some specimens of
M.
,flaiiventris
have
relatively large
+y
scores, but this species
is not completely differentiated from the
Phylogenetic
analysis
of
skull
shupr
in
squirrels
67
Y8
0.03
-
0.00
-
-
0.03
0.00
0.03
-
xi3
Figure
17.
Variation in the component
of
skull shape described
by
warp
8.
A)
scatter
-
plot
of
partial
warp
scores.
B)
vector diagram
of
the deformation described
by
partial
warp
8
for a representative
specimen
of
C
.
ludo~icianus.
central cluster. Thus we have coded this
feature as
a
three
-
state character
in
which
two states are unique to single species
(Table
1).
Warp
7.--In this feature, the largest dis-
placements are at the tip of the snout and
near the eye (Figure 16). The positive
y
scores for
S.
tridecemlineutus.
A.
leucurus
and
T.
stiiatus
reflect their relatively large
eyes and more tapered snouts. The positive
x
scores for
C.
ludovicianus
reflect a sharp-
er point at the tip
of
the snout (but not a gen
-
eral tapering) and a relatively small contrac
-
tion
of
the base of the post
-
orbital process.
At
first glance the scatter
-
plot for this fea
-
ture appears to have three
or
four distinct
clusters
of
specimens. Closer examination
reveals that each gap runs through the range
of
at least one species. Thus, the gaps ap-
pear to be artifacts of small sample size, not
evidence
of
evolutionary change. In other
words, no character state transformations
can be inferred from this plot.
Warp
8.-In this feature, there is a large dis
-
placement of landmark
4
on the anterior of
the orbit, and contrasting displacements
of
landmarks
5
and
6
on
the lateral and medi-
al sides of the orbit (Figure 17). Positive
x
scores for
C.
ludovicianus
again reflect
greater angularity at the anterior end
of
the
68
D.
L.
Swiderski
et
a1
A)
Y9
0*02
1
0,oo
-
0.04
-0.02
0.00
x9
0.02
Figure
18.
Variation
in
the component
of
skull
shape described by warp
9.
A)
scatter
-
plot
of
partial
warp
scores.
B)
vector diagram of the deformation described
by
partial warp
9
for
a
representative
specimen
of
S.
varirgotus.
C)
vector diagram of the deformation described
by
partial warp
9
for
a
representative specimen
of
A.
Imc.~rr-r.rs.
zygomatic arch
(in
conjunction with slight
reduction
of
the posterior root of the zygo-
matic arch). Positive
y
scores for
S.
tt-ide-
centlineatus
reflect
a
somewhat square zy-
gomatic arch
in
these animals
as
well, but in
this case it is due to medio
-
lateral expansion
of
the anterior end rather than an anterior
displacement of the antero
-
lateral corner.
There is one unambiguous gap separating
C.
ludovicianus
from the other taxa. Some in
-
dividuals
of
S.
c.oluirzhianus
have similar
scores, but there is considerable overlap be-
tween
S.
colirnibianirs
and
S.
variegatus.
Consequently,
S.
aolunihianus
and
S.
iw-ie-
gurus
cannot be differentiated. Similarly, all
specimens of
S.
tr-idecemlineatus
have large
+y
scores, but
a
specimen of
T.
str-iatus
has
an
equivalent score,
4o
these species also
cannot be differentiated. Again, the only
large indisputable difference is the
one
4ep-
Table
1
-
Data
matrix
w1
w3
W6
S.
niger
1
0 0
T.
hudsonicus
2
0
1
T.
striatus
0
0 0
A.
leucurus
0
1
0
M.
jlaviventris
0
3
0
S.
variegatus
0
2
0
S.
tridecemlineatus
0
2
0
S.
columbiunus
0
2
0
C.
ludovicianus
0
3
2
w9
0
0
0
0
1
1
I
1
I
I
'
Vi:3-1
is=
W1-2
VJ1-l
W6-1
C.
ludo
Ucianus
M.
hvivent-ris
S.
tridecemlleatus
S.
columbianus
S.
vsiegatus
A.
leucurus
7:
stratus
7:
hudsonicus
5.
niger
C.
ludo
Wanus
M.
flavivent;rls
S.
tfidscemlmatus
S.
columbtanus
5.
variegatus
A.
lsucunis
7:
stiiatus
7:
hudsonlrus
S.
niger
Figure
19.
Cladograms showing the phylogeneiic relationships that can be inferred from this analysis
of
marinotine
skull
shapes.
A)
Character
W3
interpreted as diagnosing three evolutionarily inde
-
pendent
groups.
B)
Character
W3
interpreted
as
diagnosing three sequentially nested groups.
70
D.
L.
Swiderski
et
al.
arating
C.
Iudovicianus,
so
this phylogenet-
ically uninformative character also is not in
-
cluded in Table
1.
Wurp
9.-This feature describes contrasting
displacements of landmarks
7
and
9
(Figure
18).
In
S.
Iwiegatus
and most other mar-
motines, negative scores on both
x-
and
y-
axes reflect their relatively narrower and
deeper notch behind the post
-
orbital
process. In some
A.
leucurus
and
S.
tride-
cemlineatus,
the
y
scores are nearly zero, in
-
dicating that the notches of these specimens
are simply narrower.
The scatter
-
plot for this feature shows a gap
separating most of the marmotines from
A.
leucurus
and the outgroups.
In
most
places this is a rather broad gap, relative to
the distances between individuals within
species. Only one specimen of
S.
niger
in
-
trudes into this gap, but does not cross it.
Accordingly, we have coded this feature as
a two
-
state character with
A.
leucurus
and
the outgroups sharing state
0
and all other
taxa sharing state
1
(Table
1).
Phylogeneiic analysis.
Table
1
lists the
character state codes for all 9 taxa for the
four features that could be coded. Because
there are
so
few characters, the relation
-
ships of these six taxa cannot be complete
-
ly resolved. However, it is possible to ex
-
tract some information by rooting the tree
among the outgroups, as suggested by pre
-
vious studies of marmotine phylogeny
(Bryant, 1945; Black,
1963;
Hight et al.,
1974: Ellis and Maxson, 1980; Hafner,
1984). Based on this rooting. warp 9 can
be interpreted as supporting a monophylet-
ic group that includes all marmotines ex
-
cept
A.
leucurus.
Within this group, two
subgroups with different states for warp
3
can be recognized. Using only the evidence
at hand, it is not possible to determine
whether one
or
both groups are mono-
phyletic; different trees would be inferred
from different interpretations of the rela
-
tionships
of
the warp's character states.
Figure
19A
shows the relationships that
would be inferred if state
0
is considered
primitive and states 1,
2
and
3
each diag
-
nose a separate lineage. Figure 19B shows
the phylogenetic relationships that would be
inferred if the character states are ordered
from
0
to
3,
with each derived state diag
-
nosing
a
progressively smaller group. Sev
-
eral other trees are equally plausible. Be
-
cause this analysis
is
based
on
only a small
portion of the species
in
the Marmotini, and
because each species is represented by
on
-
ly six specimens, we do not view Figure 19
as
a
meaningful statement of marmotine re
-
lationships. Considerably more work will
be needed before we have a clear picture of
marmotine relationships and the evolution
-
ary history
of
skull shape in this group.
D
I
S
C
U
SS
I
O
N
On
the surface, phylogetxtic analysis of
qualitatively scored traits simply analyzes
the distribution of coded character states
and identifies the tree that implies the
fewest changes between states. However, if
this analysis is performed within the Hen-
nigian paradigm, the states and the tree
have deeper meanings. In this conceptual
framework, the states represent initial hy
-
potheses
of
homology and monophyly pro
-
posed to explain the diversity of traits in the
taxa under investigation. and the tree repre
-
sents the branching pattern that requires the
fewest ad hoc hypotheses to resolve con
-
flicts among the initial hypotheses (i.e., the
most parsimonious tree). Because the char
-
acter states encode hypotheses that explain
diversity, the analysis of their distributions
to
identify the most parsimonious tree is
logically separate and distinct from the
analysis that describes the diversity. It is
this disjunction between the phylogenetic
analysis and the morphological analysis that
allows systematists to
score
morphological
features as categorical variables and com
-
pare them as logically equivalent. Coding
is not a statement that two differences are
equivalent evolutionary changes (e.g., addi-
Phylogenetic
unulysis
of
skull
shape
it1
squirrels
71
tion of a fold
on
a tooth and fusion of two
wrist bones); rather, it is a statement of a
hypothesis that they are equivalent indica-
tors of phylogenetic relationships. The
same logic means that quantitatively de-
scribed traits can be coded to reflect hy
-
potheses about their evolution, and that do-
ing
so
requires more than simply rescaling
the original measures.
To
apply the logic of the Hennigian ap-
proach, the descriptions of the traits must
meet certain requirements. One important
requirement is that the traits must be de
-
scribed in enough detail that it
is
possible to
judge whether they refer
to
comparable fea
-
tures in different organisms (Pimentel and
Riggins,
1987;
Zelditch et al.,
1995).
Only
if the features are comparable does it make
sense to attribute differences to evolutionary
transformations, and to attribute similarities
to a single transformation in a common an
-
cestor.
In
other words, coding can only be
a rational hypothesis of transformation
when there are grounds for interpreting sim-
ilarities and differences in terms of descent
with modification.
Partial warps decomposition of the thin-
plate spline and the new formula for de
-
scribing the uniform component both pro
-
vide the necessary grounds for coding
(Zelditch et al.,
1995;
Swiderski et al.,
1998;
Zelditch et al., 1998). This is because these
components describe specific patterns of
landmark displacement. Consequently, the
scores of any particular component reflect
the variability of a particular region of the
reference form.
If
that reference is
a
single
individual or an average
of
individuals from
a single species (preferably representing a
single age class), then the region is a feature
of an organism, and the diversity in shape
can be interpreted in terms of descent with
modification. Thus, partial warp analysis
and the uniform analysis of an appropriate
reference form provide descriptions of
shape differences that can legitimately be
used in a cladistic analysis
of
phylogenetic
relationships.
In our analysis of skull shape
in
mar-
motines, we used one individual from one
of the outgroups as a starting form. The
shapes
of
all the other individuals were de-
scribed
in
terms of differences from the
reference form (i.e., non
-
zero scores on the
partial warps). Then we proposed hy-
potheses interpreting these scores as evi
-
dence of a change in the underlying mor-
phology, but only if we judged that the
scores could be sorted into two or more
distinct groups.
For
example, partial warp
3
describes
a
pattern of landmark displace-
ment involving large movements at six
landmarks
on
the zygomatic arch and pos-
terior of the braincase. The scores for this
feature indicated considerable diversity in
the ways in which individual specimens
differ from the reference with respect to the
relative positions of these landmarks. We
then moved from the morphometric analy-
sis to the first steps of the phylogenetic
analysis. Based
on
the scores, we inferred
that there was an evolutionary transforma-
tion of the underlying anatomical structures
(the zygomatic arch and braincase) in
which the lineages leading to
C.
ludovi-
ciunus
and
M.
flaviventris
diverged from
the lineages leading to the other species.
In addition, we inferred from the similari-
ty of their scores that this transformation
occurred in the common ancestor of
C.
lu-
dovicianus
and
M.
flavi~~entris,
and that
none of the other species in this study are
derived from that ancestor. Because none
of
the other data at hand contradicts that in
-
terpretation, our phylogenetic tree (based
only
on
these data) suggests that
C.
lu-
dovicianus
and
M.
j7aviventris
represent a
monophyletic group.
Thus, the methods of geometric morphomet-
rics are powerful tools for recognizing dif
-
ferences among biological shapes. This does
not mean that the shape differences de
-
scribed using these methods can be equated
automatically with descriptions of the his-
torical evolutionary transformation.
A
phy-
logenetic analysis of the observed differ-
72
D.
L.
Swiderski
et
a1
ences is needed to infer the history
of
shape
change. This caveat
is
not unique to the
methods of geometric morphometrics.
Rather, the unique feature of some
of
these
methods is that their descriptions of shape
differences can be used in a subsequent
analysis, which proposes and evaluates hy
-
potheses of evolutionary change. When
used in this way, geometric morphornetric
analyses can play an important role in stud
-
ies
of
morphological evolution and phyloge-
neti c relationships.
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A
PPENDIX
1
-
L
I
S
T
O
F
SPECIMENS
.
All specimens are from the University of
Michigan Museum of Zoology, Mammal
Division.
m
=
male, f
=
female,
?
=
un
-
known.
O
U
T
G
R
O
U
P
S
Sciurus
nigel-:
USA, N. Carolina, Anson
C
O
.: 123729,
f.
USA,
N.
Carolina,
Craven
Co.:
123565,
m,
123731,
m.
USA, N. Carolina, Duplin Co.: 123566,
f.
USA,
N.
Carolina, Hoke Co.:
123733,
f.
USA,
S.
Carolina, George-
town
Co.,
125705, m.
Tumiasciui-us hudsonicu;,
:
USA, Michigan,
Clare
Co.:
85195,
m.
USA, Michigan,
Iosco
Co.:
85202,
f.
USA, Michigan,
Presque Isle
C
O
.:
86232,
f.
USA,
Michigan. Van Buren
Co.:
82640, f.
USA, Michigan, Washtenaw
Co.:
79823, m, 79824, m.
Taniias striutus: USA, Michigan, Gogebic
Co.: 53592,
f.
USA, Michigan, Chippe-
wa Co.: 126668, m. USA, Michigan,
Mackinac Co.: 162429, m; 162432, ni;
162433, m; 162434,
f.
MARMOTINES
Ammospermophzlu
y
leucul-us: USA, Cali
-
fornia, Inyo
Co.:
108235. m; 108236,
m;
108237,
f;
108243, m; 108245, m;
108246,
f.
Cynontys
ludoiiciamis: USA, Kansas, Ness
Co.: 67352,
m;
67354,
?.
USA, Ne
-
braska, Sheridan
Co.:
75513,
m.
USA,
New Mexico. Quay
Co.:
108049
f.
USA,
S.
Dakota. Custer
Co.:
96071, m;
97078. f.
Phylogenetic
unalysis
of
SkdI
shape
in
squirrels
75
Marnzota
,flat’iilentris:
USA, Idaho, Butte
Co.:
78814,
f;
78816,
m;
78817,
f.
USA, Idaho, Fremont
Co.:
162546
f.
USA,
Montana, Ravalli Co.:
57974,
f.
USA, Montana, Sweet Grass Co.:
87343,
f.
Sper-nzophilus
columbianus:
Canada.
Al
-
berta,
Rio
Alto Ranch
(50O34‘
N,
114O20’
W):
158291, 158294. 158295,
158302,
f;
158303,
f.
Canada, Alberta,
Hailstone Butte
(50°12’N, 114O27’W):
15 8460
f.
Sper-mophilus tridecenilineatus:
USA, Iowa,
Crawford Co.:
162866,
f;
162872,
f;
162873,
m;
162875,
f;
162878.
f;
162879,
m.
Spermophilus
variegutus:
USA, Arizona,
Cochise
Co.:
66337,
m;
66338,
f;
66340.
m;
77493,
f;
77494,
m;
77495,
m.
