used since it alone was consistently derived from a non-spherical data set.
3. Results
The comparison of the degree of emergence, as AVGD, for the three different aged needles,
young, middle age and old, are presented in Table 1. In no case is the difference between the sub-
groups and the whole data set AVGD for any one age of needle primordia great, nor is differ-
ence in AVGD among the differently-aged needle primordia great. Even so, all are statistically sig-
nificantly different, even given a highly conserva- tive probability level for rejection of the null
hypothesis of similarity, 0.0001.
Table 2 presents the relationship between the degree of emergence, AVGD, and variation in
size, SIZEVAR, and variation in integration, SHAPEVAR. This is a comparison similar to that
presented in Maze 1999. Both estimates of varia- tion show a significant relationship with the de-
gree of emergence AVGD, with variation in size having the larger absolute effect. In addition, the
signs of the two estimates of variation are differ- ent, with the average degree of emergence declin-
ing with variation in size but increasing with variation in integration.
Table 3 shows the eigenvectors and percent variation accounted for by the first PCA axis for
each entire data set describing young, middle age and older needle primordia, respectively. The pur-
pose of this table is to offer insight into how the variable interrelationships change with age, giving
more information on patterns of change as emer- gence occurs. The eigenvector elements for each
needle variable measured, b width at base, m width at midpoint and l length, decline with
age, with the greatest decline being in m and l. First axis eigenvalues also decline with age, an
indication that the variables become less strongly polarized with age.
Fig. 2 presents the notched box plots. All three variables become larger with age, an expected
observation. There are also differences in time-re- lated variation as expressed in the size of the
boxes and presence of outliers. The most variable
Table 1 Average AVGD, standard deviations below, for young, middle
age and old needle primordia
a
Old Young
Middle age 1.1
2.8 0.4
0.1 0.6
0.5
a
All are significantly different at PB0.0001. Table 2
Results of multiple regression analysis
a
Variable Coefficient
Prob −
1.151 SIZEVAR
0.000 SHAPEVAR
0.913 0.000
a
AVGD, average degree of emergence; SIZEVAR, varia- tion of needle primordia as measured by variance in PCA axis
scores for young, middle age and old needle primordia; SHAPEVAR, variation in integration for each tree as mea-
sured by variance in loadings on first eigenvector. First axis r
2
= 0.834.
Table 3 Eigenvalues and eigenvectors for young, middle age and older
needle primordia
a
Old Young
Middle age Eigenvalues
1.5 1.7
2.4 0.819
0.796 b
0.778 m
0.697 0.935
0.766 l
0.724 0.910
0.655
a
b, width at base; m, width of needle primordia at midpoint; l, length of needle primordia.
measurements for width at the base of the needle primordia b are in the oldest largest amount of
central variation defined by the notched box and youngest most outliers expressed needles. The
least amount of variation for b is seen in the middle age needle primordia. For the width at the
midpoint m and the length of the needles l, the most variable primordia were the youngest, with
the middle age and older primordia appearing less variable.
The patterns seen in Fig. 2 illustrate the level of within-structure needle variation where the
greater variation in the youngest primordia grad- ually becomes more constrained through time.
This constraint may be related to the loss of potential that accompanies development. At a
more abstract level, this constraint may result as growing needles access information from a higher
level phylogenetic clock. This ‘higher level infor- mation’ may be the reason why differences among
species become more pronounced at later develop- ment stages.
These changes in variation, while based on notched box plots, were confirmed by Bartlett’s
test for homoscedasity Wilkinson, 1988 and co- efficients of variation. The results of those tests
were not included.
4. Discussion
Kategori