Table Of Contentbota:/.al
MISSOURI
JAN
1 4 ?nQ3
American
Fern Journal 92(4):249-269 (2002) PARDEN LIBRARY
The
Morphological and
Genetic
Distinctness
of Botrychium minganense and crenulatum
B.
Assessed by Morphometric
as Analysis
RAPD
and Markers
M. and
Linda Svvartz^ Steven Brunsfeld^
}.
Department Moscow,
of Forest Resources, University of Idaho, ID 83844-1133
—
Two
Abstract. species of Dotrycbium subgenus Botrychium (moonworts, Ophioglossaceae),
Botrycbium minganense Victorin and B. crenulatum W. H. Wagner, can sometimes be confused
in
the field, even by experts, because of their reduced morphology. Botvychlum minganense can
which more They
imitate B. crenulatum, is rare. are afforded different degrees of protection on
making
Federal lands, the distinctness of these species a question of management, conservation,
and systematic interest. The purpose of this study was to compare a morphometric analysis of
DNA
these two species with an analysis of markers from the same individuals, and to assess their
distinctness under each method. Collections were made Washington, Oregon, and
in Idaho,
Montana from seven populations of B. crenulatum and 18 populations of B. minganense. Each
plant was measured, emphasizing characters cited by authors in the original species descriptions.
SAS
Canonical variate analysis performed on separated the samples into two species groups with
32% RAPD
overlap. genetic markers revealed more genetic variation than has previously been
UPGMA
documented moonworts. RAPD showed
in cluster analysis of the similarity of profiles
w^ell-defined B. minganense and B. crenulatum clusters, but no distinct clusters within
B.
minganense that could be correlated with morphological Small samples
its variability. of the
moonwort and
species lunaria included comparison formed
B. B. 5i777p7ex for also distinct clusters.
RAPD
Botrychium crenulatum had seven unique bands, and identification of crenulatum could
5.
RAPD
be confirmed or ruled out with markers from one or two primers. Both crenulatum and
B. B.
lunaria have been suggested as possible diploid parents of tetraploid B, minganense. All R.-\PD
markers absent in B. crenulatum but present in B, minganense were also present or polymorphic in
One
B, lunaria, supporting B. lunaria as a possible parent. very small population oi minganense
B,
RAPD
showed monomorphic
a profile, consistent with inbreeding, but other populations had
all
Some
multiple genotypes. plants of B. minganense clustered most closely with plants from
km
populations up to 400 away, suggesting that variation may be introduced into populations by
occasional colonization by spores from distant sources.
Species of Botrychium subgenus Botrychium (moonworts, Ophioglossaceae)
are an enigmatic part of the temperate flora, notable for their small size,
reduced morphology and moonwort
difficult identification. Several species in
North America are listed as sensitive or rare because of small and/or few
known
populations. Small populations are more vulnerable to extirpation,
human
whether from natural stochastic events or activities. Understanding the
threat species requires accurate information on numbers of individuals and
to
USDA
Hiawatha
Current address: Forest Service, National Forest, Ignace Ranger
^ St. District,
MI
1798 West Highw^ay Ignace, 49781.
2, St.
^ Corresponding author.
AMERICAN FERN VOLUME NUMBER
JOURNAL:
250
92 4
(2002)
populations. species intergrade morphologically, questions can not
arise
If
numbers and
only about actual of individuals populations but also about
and
species boundaries the genetic distinctness of each species.
All moonworts are relatively small and bear a single leaf with a fertile
segment (sporophore) and segment (trophophore) each season from an
sterile
underground bud. They are notoriously hard to find, especially in thick
As
vegetation. increasing emphasis has been focused on rare plants in recent
known
more
decades, concentrated searches have extended the ranges of
common
new
Botrychium species and provided material from which 13
have been endemic
species described since 1980. Several of these are to
western North America: B. crenulotum W. H. Wagner, B. echo W. H. Wagner,
B, lineare W. H. Wagner, B. montanum W. H. Wagner, B, paradoxum W. H.
Wagner, pedunculosum W. H. Wagner, pumicola and
B, B. Coville, B.
pinnatum H. St. John (the latter two described in 1900 and 1929, respectively).
moonwort
Distinguishing depends on
species in the field often subtle
differences in phenology, color, texture, proportions of the parts of the single
and Such
leaf, dissection of the pinnae. species, poorly morphologically
differentiated but evolutionarily distinct, have been called cryptic species
(Stebbins, 1950; Paris, Wagner, and Wagner, 1989; Hauk and Haufler, 1999).
may
Although some
species differences be subtle, species are also quite
among among
variable regions, and even within the same
sites, site
(e.g.,
Wagner and One
Lord, minganense
1956). of those species B. Victorin.
is
was
This study initiated in response to the practical need to distinguish
between crenulatum and minganense. These two have been
5. B. species
confused in the western United by many
States botanists (Zika, 1992).
Although both have been
listed as "sensitive" in the past by National Forests
in the Pacific Northwest Region (Region and the Northern Region (Region
6)
1),
minganense
B. has been delisted in Region 6 in response to the discovery of
many
more
populations, while crenulatum
B. retains status as
official rare.
its
Species designation affects management options where B. crenulatum occurs.
The documented
distribution of B. crenulatum the mountain states of the
is
American
west
(Arizona, California, Idaho, Montana, Oregon, Nevada, Utah,
Washington, and Wyoming), whereas minganense widespread
B. in the
is
western mountains and
across northern North America (Wagner and Wagner,
1993).
Botanists have employed both lumping and splitting approaches to the
conhising
variability of B. minganense. Botrychium minganense has been
many
by
interpreted authors as a variety of lunaria Sw. Wagner and
B. (see
(L.)
Lord, 1956 for discussion). In Flora of the Pacific Northwest (Hitchcock and
Cronquist, only moonworts and which
1973), five are recognized, the taxon to
minganense
B. keys called B. lunaria onongadense (Underw.) House.
is var.
Cronquist minganense
said that B. '*.. .morphologically scarcely separable
is
from
diploid var. onongadense..." and considered with
conspecific B.
it
and
lunaria (Gleason Cronquist, Botrychium minganense
1991). a currently
is
accepted taxon Taxonomic
(International Information System database
http://
www.itis.usda,gov/plantproj/itis, April 15, 2000; Kartesz, 1994). In the most
SWARTZ
& BRUNSFELD: MORPHOMETRIC ANALYSIS OF BOTRYCHIUM
SPECIES
251
recent treatment of North American moonworts (Wagner and Wagner,
1993), B.
minganense
reported be sometimes
is to misidentified as B. dusenii of South
America.
It is also easily confused with B. lunaria (Wagner and Lord, 1956;
ascendens
Farrar,
1998], B. (Zika, 1992; Farrar, 1998), B, pallidum (Zika, 1992),
spathulatum and
B. (Zika, 1992), B. crenulatum (Wagner and Lord, 195G;
Wagner
and
Lellinger, 1985; Devine,
1989; Zika, 1992; Farrar, 1998). Zika (1992)
described minganense
B. as '^treacherously variable". minganense
Just as B.
was
recognized as an independent species from the more widespread and
common
B. lunaria, so too were pallidum and spathulatum
B. 5. formerly
confused with B, minganense. Both Wagner and Wagner and Wagner
(1988),
(1994) have suggested that minganense may
B. represent a species complex.
Unlike B. minganense, B. crenulatum more constant in form when well
is
developed, but with any moonwort,
as the identity of small plants can be
ambiguous. Botrychium minganense
can approach the form of B. crenulatum
Wagner and Wagner
some
closely. (1981) state that of the collections on which
the original description of crenulatum was based were
5.
originally identified
as B. lunaria minganense.
var.
=
Botrychium crenulatum
diploid Wagner, whereas
is (2/7 90, F. S. 1993), B.
=
minganense
Wagner
is tetraploid (2n 180 and Lord, 1956; but see Hauk and
Many
Haufler, 1999). fern species, however, have races with different ploidy
Asplenium
Wagner
levels trichomanes, and
(e.g. et ah, 1993), ideally,
additional evidence of genetic differences would be employed
to separate
species discussion, Gastony and Windham,
(for see
1989).
Molecular techniques
are well suited problems
to clarify of cryptic species,
Hauk
used rbcL sequences
(1995) in a phylogenetic analysis of 20 species of
Botrychium subgenus Hauk
Botrychium. found
samples
that four
of
B.
minganense
(from Michigan, Colorado, and
Ontario) shared
identical
paradoxum
sequences, along with and
B. B. Xwatertonense, and lacked the
synapomorphies
single
that distinguished the simplex and campestre
subclades
of the "simplex-campestre'' clade. Botrychium crenulatum formed
a separate clade with B. lunaria, identical in sequence to the United States 5.
lunaria sample, and well separated from
the "simplex-campestre'' by
clade
nine
a total of substitutions.
which
In contrast to the rbcL data, did not distinguish crenulatum from
B.
B,
lunaria, isozymes differentiated crenulatum from
B. others
all (Farrar, 1998;
Hauk Among
and
sampled
Haufler, 1999). the diploids crenulatum was
B,
most
similar to B, lunaria, but their genetic identity (Nei, 1978) was only 0.53
(Hauk and Haufler, Botrychium minganense
1999). possessed
the highest
western moonworts (Hauk and
variability of the Haufler 1999, Farrar 1998). but
neither study inferred the variation to be indicative of species-level
within minganense.
differentiation B.
DNA
Random
Amplified Polymorphic (RAPD)
markers, a type of genetic
have
fingerprint, revealed a level of genetic variation useful for distinguishing
populations and sometimes and more
species, typically possess variation than
RAPD
isozymes Bachmann.
(for reviews, see 1997; Crawford, 1997). has been
particularly useful in assessing variation in rare plants because, as a PCR-based
VOLUME NUMBER
AMERICAN FERN JOURNAL:
252 92 4 (2002)
DNA
markers
technique, requires only small tissue samples, fresh or dried.
it
RAPD
mo
Morphometric
which
taxon
in a
igic
made
range of morphologic variation because of assumptions in the
assignment specimens Assigning specimens based on genetic
of to that taxon.
shown
markers can provide more robust morphometric insights, as has been in
Hardig
a variety of studies 2000).
(e.g., et al.,
R
Thus, the goals of this study are to determine the genetic distinctness of
1)
RAPD
mingonense and crenulatum, on markers document
B. the basis of to
2]
within minganense and crenulatum, on the
patterns of genetic variation B. B,
RAPD
and morphological
basis of markers, assess quantitatively the
to
3]
on
between minganense and crenulatum
differences plants of B. B. classified
the basis of genetic markers.
Methods
—
Collections, Samples were collected from seven populations oi Botrychium
crenulatum and 18 populations of B. minganense in the states of Washington,
Oregon, Idaho, and Montana (Table Within region populations were
this
1).
chosen to include a full range of habitats and geography. Plants with
when
morphology between two were
intermediate the species collected
found, and small plants were collected as well as large, well-developed ones to
represent a full spectrum of the morphology found in each population. Plants
were collected throughout the spatial extent of each Sample sizes are
site.
R
given in Table In addition, two populations of lunaria and one of
B.
1.
simplex E, Hitchcock (both subgenus Botrycbium) were collected to provide
sample The
a larger of species level molecular comparisons. ecological
associations of B. minganense and B, crenulatum were quite different in
Botrycbium crenulatum Washington
different parts of their ranges. in
is
sometimes found in somewhat wetter and more open habitats than B.
minganense, but the large populations sampled study were growing
for this all
under a Thuja plicata/mixed conifer canopy on subirrigated ground. By
contrast, the Goofy Springs, Oregon, population was growing in heavy
graminoid cover in an opening on seepy ground; the Stewart Creek, Montana,
mowed
was
wet roadside and and Lapover Ranch, Oregon
site a ditch; (the
at
one site on private land), 5. crenulatum and B. minganense were growing
together in grass cover under Pinus contorta with no spring evident. In
Washington, B. minganense was found almost exclusively under riparian
Thuja plicata stands with depauperate understory, but one sampled
population (Mill Gate) came from an herbaceous mountain meadow. The
may
association with Thuja plicata stands be an artifact of the circumstance
that moonworts have mainly been searched for in association with proposed
timber In Oregon, the sampled minganense populations were
sales. B, all
under canopy open enough herb
forest support luxuriant shrub and/or
to a
except Dusty, which was from wet meadow.
layer, a
A
B
SWARTZ & BRUNSFELD: MORPHOMETRIC ANALYSIS OF BOTRYCHIUM SPECIES 253
Table Collection locations of Botrvchiuin used in this study- Collections from some sites were
1.
segregated under more than one collection number. Where more than one analyzed species
=
occurred at a single site, each species is listed as a population with an identifying letter (m B.
~
=
minganense, c B. crenulatum, L B, lunoria]^ Vouchers are deposited in ID.
Site Site
Voucher
Species (no. of plants) abhreviation Location
minganense Watson Point Watson OR, Wheeler Co. Swartz 387
B.
(2)
WA,
Flowery Flowery Stevens Co. Swartz 393
Trail
(6)
Kelsey Creek Kelsey MT, Lincoln Co. Swartz 394
(6)
Rock Bottom Rock Boundary Co Swartz 398
ID,
(7]
PWB
Deer Deer Boundary Co Swartz 399
ID,
(7)
WenT WA,
Wenatchee Ford Chelan Co. Swartz 401
TSHE
(7)
WenR WA,
Wenatchee Ford Chelan Co. Swartz 401
RUPA
(5)
WA
Club Devil Chelan Co. Swartz 402
Devil's
Creek
(7)
WA,
Mill Gate MilL MillB Chelan Co. Swartz 403,
(17)
Swartz 453
WA,
Aladdin Aladdinl Stevens Co Swartz 414
1
(6)
WA,
Bulldog Cabin Bulldog Stevens Co Swartz 420
(5)
Poison Springs Poison OR. Grant Co. Swartz 425
(7)
m
WA,
Hodgson Creek mHodgson Ferry Co. Swartz 466
[7]
m
WA,
Rd. #9576 mRdg576, Ferry Co. Swartz 468,
(6)
ManleyX Swartz 486
m
WA,
mManley
Manley Creek Ferrv Co. Swartz 470
(15)
La Grande 32 LaG32 OR, Union Co. Swartz 504
(6)
Shady Camp Shady OR, Wallowa Co Swartz 506
(7)
Dusty Dustv OR, Union Co. S^vartz/
(6)
Riley 508,
Swartz/
Yanskey 509
crenulatum Goofy Spring Goofy OR, Crook Co. Swartz 388
B.
(7)
MT,
Stew^art Creek Stewart Flathead Co. Swartz 396
(5)
WA.
Okanogan Cabin OKCabin Okanogan Co. Swartz 404
[7]
WA,
Aladdin Aladdin Stevens Co. Swartz 427
Blowdown
(7)
WA,
Deadman Deadman
Creek Ferry Co. Swartz 445
(5)
WA,
Hodgson Creek cHodgson Ferry Co. Swartz 467
c
(7)
Lapover Ranch Lapover OR, Wallowa Co. Swartz 507
(10)
WA,
L Rd. #9576 LRd9576 Ferry Co. Swartz 469
lunaria
B. (5)
WA,
L Manley Creek LManley Ferry Co. Swartz 471
[7]
LGMead
simplex La Grande OR. Union Co. Swartz 505
B.
Meadow
(5)
were by snipping them ground avoid
Plants collected off at level to
disturbing the roots and the next year's below-ground bud. This procedure
is
on
have negative impact survival (Johnson-Groh
not believed a significant
to
Where
Montgomery, were
and 1996; 1990). possible, plants collected
Farrar,
they had shed spores. Plants were pressed, individually numbered,
after
DNA
color photocopied, and digitally imaged before grinding for extraction.
254 AMERICAN FERN JOURNAL: VOLUME NUMBER
92
4 (2002)
The
color photocopies are deposited in the University of Idaho Herbarium
(ID) as facsimile vouchers, along with additional collections from the same
populations.
—
Morphometric As
analysis. a quantitative approach capturing morpho-
to
morphometric
logical subtlety, a analysis of characters that can be scored from
herbarium specimens was
made.
Characters cited by authors in the original
species descriptions were used whenever Some
possible. characters that are
valuable to botanists in the field, such as color, texture, or folding of pinnae,
could not be scored because they are distorted or destroyed by pressing and
drying. Forty-one measurements were
different or recorded each
ratios for
Measurements were made WV-CD20
plant. using a Panasonic video camera
Mocha
and image
analysis software (SigmaScan Pro version 3.0 Jandel
Scientific).
—
Analysis. Canonical
discriminant one more
analysis identifies or canonical
variables that are linear combinations of multiple measured These
characters.
canonical variables can show the morphological between
greatest differences
groups. Statistical calculations were performed using SAS CANDISC
the
SAS
procedure, Release (SAS
6.11 on same samples
Institute Inc.), the of 5.
minganense and
crenulatum used
B. for genetic analysis, excluding three
Two
were
plants that browsed. very unusual plants of Botrychium minganense
also were excluded from the morphological One was
analysis. CvXtremely
large,
and
had
the other only rudimentary One
peg-like pinnae. plant (cLapover.09)
was RAPD
excluded because
it displayed an additive profile, and thus was pos-
ANOVA
sibly a hybrid. Preliminary one-way showed means many
that the of
=
were
characters between
significantly
different the species the alpha
at
0.05 including
level, the ratio of trophophore width to the width of axis
its
mar
average angle of the margins of the four basal-most pinnae
[degree of fanning);
ratio of the length of the space between two
the pinnae
first pairs to greatest
pinna width measure
(a of overlapping of pinnae); ratio of greatest pinna width
pinna
to least width; width
ratio of length to of trophophore; ratio of length to
width
of sporophore; pinna width
ratio of to length; length of the sporophore;
made
average angle by
the four basal-most pinnae with
the height
rachis; total
(ground
level to tip of sporophore); length of trophophore; length of
trophophore and
stalk; length of gap between two pinna Measure-
first pairs.
ments
of these characters
are illustrated in Figure All pinna measurements
1.
made
were
from same
the pinna each one
for plant, of the largest pair. In the
largest plants the lowest pinnae sometimes
are partly transformed into
sporangial branches. In that case one of the untransformed was
largest pair
The
chosen.
ratios of trophophore width: trophophore width and
1) axis
maximum
sporophore was
of square
root-transformed them normal
to bring closer to a
The
distribution.
distribution of all variables used was judged be within the
to
limits of robustness of the procedures
(K. Steinhorst, pers. comm.). Variances
were compared
between
species groups each were
for character to see that they
equal, or if not, the variance of the larger group did not exceed that of the
SWARTZ & BRUNSFELD: MORPHOMETRIC ANALYSIS OF BOTRYCHIUM SPECIES
255
made
Fig. Measurements for characters that were significantly different between Botrychium
1.
minganense and B. crenulatum in morphometric analysis, Length of common Length of
a. stalk, b.
—
sporophore stalk, c. Length of sporangia-bearing part of sporophore (b+c length of sporophore,
a+b + c = total height. These and any other curved lengths were traced directly on the image of the
=
plant), Length of longest sporophore branch (2d sporophore width), Length of trophophore
d. e.
stalk, Distance between centers of first two pinna pairs, Balance of length of trophophore
f. g.
=
(e+f+g length of trophophore). h. Angle of edges of pinna (for average of four basal-most pinnae].
Angle at w^hich pinna meets axis of rachis (for average of four basal-most pinnae], Greatest
i.
j.
width of rachis. Trophophore width. Least width of largest pinna m. Greatest width of largest
k.
1.
pinna, Length of largest pinna.
n.
smaller group by more than a factor of 2.5, a conservative level chosen for
unequal sample sizes. In general, variances were greater for B. minganense.
—
DNA
RAPD mg
analysis. was isolated from 10 samples of each pressed
plant. For those plants that were less than 10 mg, the whole plant was used.
Plants were ground on ceramic well plates with liquid nitrogen, ground further
.
AMERICAN VOLUME NUMBER
256 FERN JOURNAL:
92 4 (2002)
CTAB
with 600 70°C and ml The
buffer, transferred to 1.5 tubes. grinding
|.il
and
buffer subsequent isolation procedures followed Stewart and Via
(1993),
with homogenate was
the following modifications: the incubated 70°C 30
at for
DNA
minutes before the chloroform extraction, the precipitated pellet was
mM
washed with ml cold 76% ethanol with 10 NH4AC, and the dry
1 pellet
resuspended in 50 TE. Of several tested, this protocol was the least likely to
j.d
gummy
yield residues coprecipitating with the DNA, which was a problem
with some The when
samples. residue, occurred, was removed by
it
DNA DNA
centrifugation before quantifying the with a fluorometer. was
IX
amplified (Williams et 1990) in 25 reactions containing buffer
al.,
|.d
mM
mM
(Promega M190A),
0.1 of each deoxynucleotide, 2 MgCls, 0.00005%
bovine serum albumin, 5 pmols 10-mer primer (Operon), 10 ng genomic DNA,
DNA
and Taq
0.5 units polymerase (Promega), overlaid with 25 mineral
oil.
|al
Samples were amplified in an MJ Research PT 100 thermocycler (44 cycles of
min 94°C, min min with min
1 at 1 at 36°C, 2 at 72^C, a final 5 at 72°C). Products
UV
were
electrophoresed 1.5% by
in agarose visualized illumination
gels, after
staining with ethidium bromide, and imaged with Alphalmager
3.2
v.
software. Populations were divided among multiple PCR and
runs, sub-
a
sample was run multiple times confirm band
to repeatability of each chosen.
Bands were scored manually by comparison to standard size markers. Bands
name
are designated by the of the primer with the approximate base
size in
pairs as a subscript, B-II575.
e.g.
—
Primer
screening. ^Primers were screened against two samples each
of B.
minganense and
crenuJatum. Twelve
B. primers (A-11, B-11, B-12, C-6, C-8, C-
9, C-10, C-11, D-11, D-16, D-20, X-1) showing the best well-spaced bands
polymorphic one
both were One
in or species
selected the data
for final
set.
hundred
ninety-four plants were scored manually presence absence
for or of
RAPD
74 bands each. As more species and populations were added, fewer
primers and bands within primers could be used because some new bands
were
close to the position of old bands or amplified with
different intensity,
making them
difficult to score. Therefore, the scoring conservative and
is
minimum
only among many
reflects differences populations, whereas
all
additional
differences that are not included in the data set are readily apparent
amon
data.—UPGMA
)fRAPD
cluster analysis was performed
RAPD
N
with
data
and
Jaccard metrics.
Results
Morphometric
a77o/ys/s.—Optimal separation two on mor-
of the species a
phological
basis requires consideration The
of multiple characters once. six
at
when
variables in Table analyzed
2, together, provided the greatest separation
of the groups The
in this data canonical
set. variate analysis tested the null
hypothesis no
that there are differences between two based on
the species the
chosen =
variables. This hypothesis was
rejected at the p 0.0001 level, with
SWARTZ
& BRUNSFELD: MORPHOMETRIC ANALYSIS OF BOTRYCHIUM SPECIES
257
Table 2. Correlations and coefficients of the six variables that provided the greatest
discrimination between Botrychium minganense and B. crenulotum in Canonical Discriminant
Analysis.
Pooled Within Pooled Within-Class
Canonical Structure Canonical Coefficients
CANl CANl
Variable
AVANGMAR
0.50 0.65
AVANGPIN
0.16 0.40
PWIDLEN
0.20
0.18
MLSPORO
-0.18
0.94
NTWIDAX
0.51 0.51
NPINMAMI
0.41 0.52
AVANGMAR=average AVANGPIN=average
angle of pfnnae margins; angle of pinnae with rachis;
PWIDLEN=ratio MLSPORO=square
of pinna width:pinna length; root transformed length of
sporophore; NTWIDAX^log-transformed ratio of trophophore width greatest width of trophophore
axis; NPINMAMI=log-transformed ratio of greatest pinna widthdeast pinna width.
=
F 35.52 and degrees of freedom numerator and denominator
of 6 164.
may
Canonical scores be computed by taking the original value for each plant
on each measurement, multiplying by the respective canonical coefficient
it
CANl
from (Table and adding these products plus constant adjustment
a
all
2],
for the means. Scores graphed by species form two overlapping groups,
vi^ith
mean mean
crenulatum and minganense —0.71
the for B. at 1.81 the for B. at
CANl
32%,
(Fig. 2). scores of 55 of the total of 171 plants, or fell in the to 2
where
range species identity ambiguous. Scores of 92 plants of
is B.
-4
minganense and
out of 123 (75%) fell in the to range, 23 plants of B.
crenulatum out of 48 (49%) scored from 2 to 4, where each had a high
CANl
Only one minganense had
probability of correct species identity. B. a
above
score
2.
Canonical variates can be interpreted in terms of those variables that
contribute the most the separation of the groups. Although canonical
to
and must
variates are be interpreted with caution, they can be
artificial
identified in terms of their correlations with the original individual variables
(Johnson and Wichern, 1992). These "within" structure coefficients indicate
how
and
closely a variable the canonical variate are related, or the extent
to
which same The
they carry the information (Klecka, 1980). ratio of
trophophore width:trophophore width had
axis the highest correlation, 0.51,
maximum
followed by average angle of pinna margins, and pinna
0.50,
widthrminimum The
width, 0.41. within-class correlation for pinna width;
length was 0.20, average angle of pinnae to rachis 0.16, and length of
sporophore —0.18.
way
Another of looking at the contributions of each individual variable
within classes by comparing coefficients that have been transformed so their
is
standard deviations are equal to These standardized coefficients then
1,
measure the relative contribution of each variable to the canonical variate
score. As a relative measure, the standardized coefficient of each variable will
two
change depending on the contribution of other variables. variables share
If
"
AMERICAN FERN JOURNAL: VOLUME NUMBER
258 92 4 (2002)
50
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CANl
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Fig. 2. Plot of scores using six morphometric variables (Table of 123 Botrychium
2)
minganense and
48 crenulatum whose
B. plants species identity was confirmed
genetically.
some
same
of the information highly
(are correlated), the standardized co-
efficient value will be partly divided between them, but one was not
variable
if
used, the standardized would
coefficient of the other They could be
also
rise.
have
larger but opposite sign, so that one partially cancels out the other. The
within
structure by
coefficients, contrast, are simple
bivariate correlations
