5- analysis of reproductive biology poa annua...
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5- ANALYSIS OF REPRODUCTIVE BIOLOGY OF POA ANNUA
5.1. OBJECTIVE
To determine selfing and outcrossing potentials in Poa
annua by observation of morphology, anthesis, pollen tube
development, apomixis, and seed yield from self, sib, and
cross pollination.
5.2. OBSERVATIONS
Anthesis in Poa annua has been reported to proceed from
the uppermost florets of the uppermost spikelets down the
panicle (Lynch, 1903; Hackel, 1904; Hovin, 1957; and Tutin,
1957). Deviations from this pattern were noted on biotypes
in the University of Minnesota collection.
5.2.1.1. Materials and Methods
Observations of anthesis behavior of individual Poa
annua culms were made on selected greenhouse and floral pic
isolation samples. The opening of the first spikelet to
expose stigmas, pollen dehiscence, the site of anthesis,
and/or direction of anthesis on a panicle were recorded.
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5.2.1.2. Results and Discussion
Anthesis of individual culms varied both within and
among genotypes. Most genotypes underwent anthesis as cited
in section 5.2.1. Dichogamy has been observed in the
investigated selections of Poa annua, with respect to
individual inflorescences. Some samples had entire
inflorescences exhibiting protogyny (Plate 3) , although
partial dichogamy was most common (CAN321, FRA15105, NY2061,
NY4093, NY84253215, NY84253220, and OH84073), with anthesis
progressing from the distal end toward the proximal end of
the inflorescence. Stigmas of male sterile florets in the
uppermost spikelets of a panicle were exposed from less than
one hour (NY1605) to more than one day (NY6, NY118, NY11804,
and NY11805) prior to dehiscence. In some instances, an
entire panicle had stigmas from male sterile florets of each
spikelet exerted prior to any dehiscence from the same culm.
A gradation of exposed stigmas of male sterile florets
occurred between these extremes. Pollen shed typically
occurred next from perfect florets below the male sterile
florets in each spikelet.
Individual culms of some genotypes deviated from typical
anthesis patterns. Dehiscence was usually basipetal, though
progress from the middle of the panicle either basipetally
or both acropetally and basipetally was observed in some
genotypes (ITA11699, SWE01, IL85Q004, IL850006r NY10,
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NY3024, NY5041, and NY5081). This phenomenon occurs in corn
where pollen matures and dehisces from the middle of the
inflorescence outward in both directions. One inflorescence
each of OH84074, NY1861, NY4062, and NY5033 even began
anther dehiscence from the bottom spikelets, with anthesis
progressing upward. Protandry, with pollen shed prior to
stigma exertion, was rare, being observed once on NY1861.
A completely male sterile inflorescence was occasionally
observed on Poa annua (CAN321). The same plants also had
panicles with both male sterile and perfect florets. Thus,
the use of male sterility as a breeding option was not
likely with any genotypes observed. However, variation for
male sterility in Poa annua suggests that selection for
complete male sterility or maximizing male sterility
expression by manipulating environmental conditions may be
possible. Based on these observations, physical outcrossing
mechanisms exist within Poa annua.
5.2.2. Pollen Tube Growth
Pollen tube development may be examined to evaluate
compatibility of specific selfs and crosses as early as one
day after pollination. This makes it possible to visualize
compatibility and incompatibility responses for rapid
identification of successful crosses.
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5.2.2.1. Materials and Methods
Pollen tube growth was studied using staining techniques
described by Kho and Baer (1966). These rapid methods could
be used to observe pollen tube growth into styles and ovary.
The procedure was based on secondary fluorescence after
selective uptake of fluorochromes by cells. Only fixed
material was used, although fresh material may also be
examined. A careful maceration in NaOH was not necessary
with this species. The stain was 0.1 percent aniline w.s.
dissolved in 0.1N K3P04. The ultraviolet wavelength source
was 350 to 400 millimicrons.
For the observations reported here, inflorescences were
emasculated prior to anthesis, as described in 4.2.1, and
placed in isolation for self, sib or outcross pollination.
After incubation times of 2 to 48 hours after pollination,
inflorescences were fixed in CRAF for a minimum of 2 hours.
Each flower was dissected to expose the pollinated pistil.
Excised pistils were placed on a glass slide to which 1 to
2 drops of aniline blue stain was added. A cover slip was
placed over the pistils, which were then gently squashed.
Pollen germination and pollen tube growth observations were
completed using both light and fluorescent microscopy.
Callose is found in walls of pollen tubes, but not
usually in stylar tissue. Pollen tubes are outlined by
callose and callose plugs formed at irregular distances in
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the tube. The callose takes up aniline blue and fluoresces
a bright yellow green when illuminated by blue or
ultraviolet light.
5.2.2.2. Results and Discussion
Pollen tube growth was observed extending through the
stigma toward the ovary in both self and cross pollination.
Pollen grains which did not germinate, or which had pollen
tubes that stopped growing immediately upon germination,
were observed for both self and cross pollination. Self
incompatibility, as expressed by differential pollen tube
growth, was not apparent.
5.2.3. Apomixis
Apomixis has been reported for several polyploid Poa
species, such as Poa pratensis (Beard, 1973), and has been
questioned for Poa annua (Koshy, 1969,- Ellis et al 1973).
This phenomenon may be exemplified by uniform progenies of
open-pollinated parents (Hanna and Bashaw, 1987).
5.2.3.1. Materials and Methods
Seed set on selfed panicles isolated alone versus in
pairs and selfed versus outcrossed panicles were compared
using paired t-tests. Selected progeny were also observed
for morphological uniformity.
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5.2.3.2. Results and Discussion
Among genotypes examined, apomixis was not apparent.
As noted in section 4.3., single, selfed inflorescences in
isolation, set less seed per inflorescence than selfed
inflorescences paired with another culm from the same
genotype. If apomixis was occurring, seed set would be
expected to be similar between the two kinds of selfed
inflorescences. No seed was set on several isolated culms
(genotypes NY3091, NY3074, NY4045, OH84074, CAN311, and
CAN313) with exposed stigmas, but no pollen present.
Other evidence for the lack of apomixis within Poa annua
included the significant differences in seed set between
self and outcross pollination (Section 5.3.2.). Seed
production on apomictic species should be unaffected by the
genotype of the external pollen source. In addition,
progeny from open pollination of selected genotypes varied
for germination rate, leaf width, vigor, and/or color.
Apomictic populations would have identical phenotypes
because of clonal propagation. Koshy (1969) and Ellis, et
al (1973) also found none of the meiotic irregularities
associated with apomixis.
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5.3. COMPARISONS OF SELF, SIB, AND OUTCROSS SEED SET
Based on observations of the current collection of
diverse genotypes and conflicting published reports,
reproductive biology of Poa annua may not be easily
classified into either self or outcross fertilization.
Further clarification was pursued by seed yield analyses of
selected isolations.
5.3.1. Materials and Methods
Twenty-five hundred isolations included 1 to 74
inflorescences each of 180 genotypes from 67 families of Poa
annua collected from the United States, Canada, and Europe.
Appendices Al, A2, and A3 contain descriptions of accessions
and progeny. Collection sites and morphological
characterizations are included. Poa annua self, sib, and
outcrosses were made in diallel, when possible, using the
floral pic isolation method described in 4.2.1. Seed was
collected from each inflorescence at maturity and counted.
Seed counts from selected self, sib, and outcross
pollination were analyzed using t-tests. Factors related
to reproductive biology, which could affect seed set,
included potential incongruity as related to geographic
distance between origins of paired accessions (MILE); days
elapsed between panicle excision and anthesis (BPOL);
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asynchrony of anthesis between paired culms (ASYN); and
number of open spikelets per inflorescence (OSPK). Effects
of these factors were evaluated by t-tests, histogram
analyses, and multiple linear regression analyses.
Data used for regression analyses included
inflorescences least influenced by extraneous variables,
such as differing sucrose and/or 8 HQC concentrations. The
master data set, consisting of seed counts from 868 self,
sib, and outcross pollination, was randomly split in half
to form 2 subsets with 4 34 cases each. One to 17
inflorescences from 109 genotypes were unequally represented
among the 3 pollination types in one subset. The other
group included 1 to 18 inflorescences from 103 genotypes,
also unequally distributed among pollination groups. These
subsets were again subdivided into self and cross
pollination (sib pollination were not considered in these
analyses).
Several subsets were randomly and non-randoraly generated
for regression comparisons between and within pollination
types. One subset produced Files 7 and 8, while the other
subset consisted of files 9 and 10. File 5 was generated
from the combined Files 7 and 8. File 6 was similarly
produced from combined files 9 and 10. Files 11, 12, 13,
and 14 were subsampled from files 7, 8, 9, and 10,
respectively. Files 3 and 4 were stratified to have equal
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representation of self and outcross pollination,
respectively from 3 6 genotypes (1 to 16 panicles per
genotype). Files 1 and 2, generated from Files 3 and 4,
respectively, contained one pollination randomly selected
from each genotype. Self- and cross-pollinated subset
derivations are described in more detail in Table 3.
Model building initially used a step-up format.
Variables were added as long as the t-test for the last
added variable was significant at p < 0.05. Other models
tested adding variables of interest (e.g. MILE in subsets
using outcross pollination only) without regard to step-up
procedure. Square root, Freeman-Tukey, log10, inverse, and
squared transformations were tested for potential
improvement of normality and residuals. No data were
deleted as potential outliers (studentized residuals > 2.5)
since results were already screened to eliminate suspect
data.
5.3.2. Results and Discussion
5.3.2.1. Grand Means for Self, Sib and Outcross Pairings
There were no significant differences between self and
outcross seed set in a sample averaged across genotypes
(Table 4). The similarity of seed set between culms paired
with culms from itself, sib, and/or unrelated genotypes
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seemingly affirmed the previously reported self
compatibility. since genotypes could influence potential
seed production, self and outcross samples were paired by
genotype for t-test analysis which was significant to p <
0.001 (Table 5). These results suggest that Poa annua is
not an exclusively self-compatible species.
5.3.2.2. Examples of Specific Genotypes Illustrating
Outcrossing
Two plant families (NY842532## and NY16###) were fairly
consistent in producing greater numbers of seed in sib
pairings than in outcross or self pairings (Table 6). sib
seed set was as much as two times greater than some self
pollination. A finding of self seed set lower than sib or
outcross seed set may be an indication of self
incompatibility occurring within Poa annua.
The percent decrease in self seed set compared to
outcross seed production (l-[mean self/mean outcross seed
set] X 100), was calculated (Table 7). CAN320 and MN66 had
significantly reduced self seed set of 42 and 55 percent,
respectively. The relatively high percent of self
fertilization could be the result of one or more factors,
including pseudo-self compatibility (Ascher, 1976) .
A genetic basis for variation in seed number was
observed by the similar performance of full sibs (Table 6).
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In some genotypes, with data expressed as seed set perinflorescence or per open spikelet, self seed numbers weregreater than or equal to outcross seed set, with sib seedset either greater or less than self or outcross seed set(NYII0002 and NYII0005). For other genotypes (NY84253205and NY84253206), outcross seed set was greater than selfseed set with sib seed set variable in relation to selfs,but less than outcrosses. This demonstrated the range ofpossible responses (from selfing to outcrossing) amonggenotypes for seed set.
In other pairings, outcross seed set was significantlyless than self seed set (Table 8). Data included only seedset on inflorescences where anthesis asynchrony betweenpaired culms was 2 days or less to assure pollenavailability from both culms of each pair during themajority of the anthesis period. since self pollination waspossible for these culms, reduction of seed set inoutcrosses suggests a post-fertilization phenomenon, or
incongruity, which reduces seed yield.Reduction in seed yield in these pairings, then,
reflects the degree of outcrossing. To better visualizethis outcrossing phenomenon, percent outcrossing wascalculated from the formula, l-(mean seed set of outcrosspollinated inflorescences/mean seed set of self pollinatedinflorescences) X 100. For genotypes with significant t-
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tests (p < 0.05), outcross pollination seed set for NY10,
MN21, and AZ1716 was 37, 58, and 83 percent less,
respectively, than self seed set (Table 8). Other
genotypes, without statistically significant t-tests, had
varying levels of potential outcrossing from 2 percent
(AZ1719) to 53 percent (NY604).
Some accessions, such as AZ1716 and IL850006, yielded
nearly equal seeds per open spikelet for self and outcross
pollination, indicating that these genotypes could be self
compatible (Table 9) . When each accession was compared
individually to each different genotype with which it was
paired, however, variable results were observed. Outcross
seed set was greater in some cases and less in other cases.
An interesting note was that male biotypes collected nearest
to the Arizona or Illinois accessions produced the greatest
seed set.
Reproductive barriers may be active prior to
pollination, between pollination and fertilization, and
after fertilization (Levin, 1971). One such barrier may be
a by-product of divergent evolution, resulting from
incongruities in reproductive formats of isolated
populations. The longer genotypes are isolated, (e.g. by
geographic distance) , the longer they can evolve separately,
which could result in stabilization of genetic barriers.
This phenomenon of evolutionary divergence is termed
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incongruity (Hogenboom, 1975). Possible evidence of this
type of barrier in Poa annua may be found in genotypes from
Minnesota (MN44), Ohio (OH84074), and New York (NY10)
(8/16/87 date in Table 10).
Since given female genotypes, with apparently equal
outcross and self seed set, varied in outcross seed set when
different males were used, the data were separated for each
male genotype. Results of seven partial or complete
diallels appear in Table 10. Self seed set was greater than
outcross seed set in many cases, indicating the likelihood
of male interference when unrelated inflorescences were
matched for mutual anthesis. In other examples, self seed
set was less than outcross seed set, which could result from
some level of self incompatibility.
Differences between self- and outcross-pollinated seed
set may represent reduction in self seed set due to
reproductive failure of incongruous outcross fertilizations.
It may also indicate the percent of potential outcrossing
if there was no incongruity. If any seed resulted from
outcross pollination, the outcrossing percentage would be
even higher.
Genotype variation in response to selfing and
outcrossing may contribute to an explanation for the
worldwide adaptability of Poa annua. One implication for
a breeding program is that each genotype must be evaluated
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for selfing and/or outcrossing, rather than assuming that
the response of one biotype is typical for the species.
5.3.2.3. Effects of Days between Panicle Excision and
Anthesis
The last inflorescences paired on a particular date were
most likely to have unequal or uneven pollen shed. An
increasing number of days elapsed between excision and
pollination negatively affected seed production (Table 11} .
Both self and outcross seed set decreased as days between
panicle excision and anthesis increased. To avoid potential
confounding by genotypic differences in response to outcross
pollination, only self seed production was compared.
Overall, seed set was not significantly affected when 4 or
fewer days elapsed between stem excision and pollen shed.
Genotype CAN320 had seed production drop off with only 2
days elapsing between excision and anthesis, while genotypes
AZ1716 and AZ1719 were not affected by 5 days (Table 12).
Seed set decreased for most genotypes when 3 or 4 days
elapsed between excision and anthesis (Table 12).
The mean and standard error for seed production per
inflorescence decreased as days from pollen shed increased
(Table 11) . The square root of seed set and square root of
open spikelets (Tables 11, 12) stabilized the variances best
of all transformations previously examined with regression
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analysis. Results indicated the potential to either account
for fluctuations in anthesis timing with regression models,
to discard isolations when anthesis is too severely delayed,
or to be extremely critical in selecting inflorescences for
isolation. Although the latter method is preferable, it
would also limit the number of inflorescences suitable for
collection from a single plant on a given day. Clonal plant
increases could provide additional flowering culms of
similar maturity at the same time.
5.3.2.4. Effects of Anthesis Asynchrony between Paired Culms
Although every attempt was made to match culms of
similar anthesis dates, asynchrony occurred in several
paired Poa annua pic isolations. A similar situation
probably exists for bagged inflorescences and could have
profound effects on resulting seed set. The occurrence of
asynchronous anthesis, while not intentional, provided
useful information on reproductive biology.
Start of anthesis was recorded at first observation of
anther dehiscence. First stigmas usually exerted no more
than 24 hours before dehiscence. Effects of anthesis
asynchrony between paired panicles on seed set were
significant (p < .05), with highest seed yields resulting
when anthesis of paired culms occurred within 2 days of each
other (Tables 13, 14? Figures 1-4).
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Self seed set was enhanced on culms opening 1 or 2 days
prior to their matched culm (Tables 13, 14; Figures 1, 3).
More stigmas would have been receptive to pollination on the
earlier opening culm when the latter culm began dehiscing,
while stigmas from latter culms would not have been exerted
during initial dehiscence from the early-opening culm. The
first culms to open received more pollen from both culms,
compared to later-opening culms, and yielded more seed,
suggesting a pollen load effect.
For outcross pollination pairings (Tables 13, 14;
Figures 2, 4), culms which opened prior to culms with which
they were matched (culms with positive anthesis asynchrony
values), often produced greater seed than when pollen was
immediately available from the unrelated matched
inflorescence (culms with negative anthesis asynchrony
values) . This may be interpreted as an indication of
incongruity in the form of male interference with self seed
production, resulting from a post-fertilization barrier
developed through divergent evolution. These differences
were observable whether self versus outcross comparisons
were matched by genotypes (Table 14,* Figures 3, 4) or were
pooled across several genotypes unequally represented in
each pollination type (Table 13; Figures 1, 2).
Higher outcross-pollinated seed set on culms opening
before their partners (positive asynchronous anthesis
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values) may reflect self fertilization prior to potential
male interference from the unrelated mated panicle. If
there was no incongruity, this higher seed yield may also
reflect selfing plus outcrossing, since stigmas from culms
with positive asynchronous anthesis values would be exposed
to both self and outcross pollination for longer periods
than later opening culms.
Simultaneous pollen shed ensures maximal pollen load
containing a mixture of pollen from each culm (i.e. self and
outcross pollen would be present with respect to any
inflorescence). In the case of partially overlapping
anthesis, some stigmas would be exposed only to self pollen
(culms with negative anthesis asynchrony), while others
would be exposed to both self and outcross pollen (culms
with positive anthesis asynchrony). Each culm would only
be exposed to self pollen during discontinuous anthesis,
with pollen load being only a fraction of the maximum
potential (e.g. 1/2 if two culms are paired) . If male
interference occurred between self and outcross pollen,
simultaneous anthesis of paired culms would result in
reduced seed set compared to culms with negative anthesis
asynchrony.
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5.3.2.5. Effects of Number of Open Spikelets per
Inflorescence
Open spikelet numbers per inflorescence on Poa annua
biotypes were influenced genetically and environmentally for
total potential spikelets which could open and for the
number which actually opened, As stock plants matured,
panicle size decreased due to increasing vegetative
competition and clipping. Increased days elapsed between
culm excision and anthesis also seemed to reduce the number
of open spikelets per inflorescence. These open spikelets
represented total potential seed yield.
After observing variability on the first 100 isolations,
open spikelets were counted on subsequent samples. Open
spikelet numbers fluctuated among and within genotypes
(Table 15) . Computations of seeds per open spikelet
minimized effects of variability in number of open spikelets
per inflorescence. Similar diversity in floret number has
been reported between species and between and within plants
of a particular species (Mulford, 1937,* Boyle and Stimart,
1986).
5.3.2.6. Multiple Regression Analyses
Multiple regression analyses estimated the partial
influences of genetic isolation as measured by geographic
distance between origins of paired accessions (MILE) , number
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of open spikelets per inflorescence (OSPK), days elapsing
from excision to anthesis (BPOL), and anthesis asynchrony
between mated culms (ASYN) on seed set, using actual or
transformed data. Transformations which improved normality
of data included square roots of seed set per inflorescence
(SSDS) and number of open spikelets per inflorescence
(SSPK).
Data from self and outcross pollination were originally
combined because the original hypothesis was that BPOL,
OSPK, and ASYN would interact similarly with seed set
regardless of pollination type. The geographic separation
factor (MILE) was initially the only element considered to
be testable for evidence of incongruity in Poa annua.
When variability, due to incongruity based on geographic
distance between accession origins (MILE), was not
significant in many models, subsets were derived containing
either self or outcross pollination data (Tables 3, 16).
The rationale was that data sets combining self and outcross
data may have resulted in masked incongruity expression of
outcross pollination by greater representation of self
pollinations. If Poa annua is fully self compatible, models
constructed from the two subset types would have similar
included variables and coefficients.
For all subsets using self-pollination data only, the
best models contained SSDS regressed on SSPK, BPOL with an
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R2 from 0.35 to 0.39 (Table 16, Files 3, 1, 9). Similar
coefficients of the largest files (7 and 9), with no data
in common, indicated good model fit for approximately one-
third of the variability in self seed production in Poa
annua. The model for the smaller subset 3 contained the
same variables as larger sets, but different coefficients.
The smaller file with fewer samples and genotypes, reflects
a more restrictive predictive model. The remaining 65
percent variability in seed yield not explained by these
models may represent genotypic and/or self incompatibility
interactions, for example.
Data subsets using only outcross pollinations also
resulted in models containing SSDS regressed on SSPK and
BPOL (Table 16, files 4, 8 10). They differed, however, in
that MILE could also be included at a significant level (p
< 0.05) for some files (e.g. Table 16, File 10). In
addition to examples in Table 16, models were also
constructed to test whether variables which could be
incongruity indicators (MILE, ASYN, OSPK) were
interchangeable based on the order they were added.
Files 3 and 4 (self and outcross pollinated seed set,
respectively, and represented by the same genotypes)
resulted in similar models with different coefficients. No
difference in coefficients or R2 would be expected if Poa
annua were self compatible. Incongruity is one possible
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explanation for the twelve percent more variability of
outcross-produced data compared to selfed results.
Comparing self- and outcross-pollinated groups, with
files containing the same variables, 10 is more similar to
7 and 9 than 8 is. File 10 is also the only example listed
which included MILE at a significant level after the
variables SSPK and BPOL. Four to 5 percent variability may
be explained by MILE, a potential indicator of incongruity
in outcross fertilization. One explanation for not fitting
MILE into the File 8 model may be that variability
attributable to MILE in File 8 is already partly included
in the model as contributed by SSPK and/or BPOL, such that
MILE is no longer significant when added after the first two
variables.
Considering the R2 of Files 8 and 10, 4 to 12 percent
more variability is attributable to SSPK and BPOL than for
Files 7 and 9. All or part of this may be attributable to
incongruity between divergent genotypes. The low percentage
indicated here does not necessarily conflict with examples
in Table 7, since incongruity expression here may be
confounded with factors other than MILE (e.g. by genotypes
which are cross compatible, or by divergence resulting from
separations other than geographic distance). Asynchronous
anthesis (ASYN) , which may also be an indicator for
incongruity, did not fit outcross data files unless either
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SSPK or BPOL were omitted. There may have been confounding
of variability assignable to ASYN with SSPK or BPOL as was
suggested for MILE. Another reason may be low variation in
ASYN in the smaller subsets generated, since ASYN did fit
in models of larger data sets with self- and outcross-
pollinated seed set.
5.3.2.6.1. Days between Excision and Anthesis
The days elapsed between culm excision and anthesis
contributed significantly to most regression models,
regardless of pollination type. Of the 4 factors included
in the multiple regression modeling, this factor was the
only one inversely correlated with seed set. No
transformations of this variable improved models from any
data sets.
5.3.2.6.2. Asynchronous Anthesis between Paired Culms
Regression models generally were not improved by
including the ASYN variable in data subsets containing self
pollinations only, possibly due to minimal asynchronous
anthesis between selfed culms. Since these culms opened
similarly, they were often much easier to pair for
simultaneous anthesis, Asynchronous anthesis may also be
less critical to selfed seed production compared to
outcrossed seed production. In the latter case, incongruity
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may be expressed when asynchrony occurs and may affect
apparent pollen load.
Using data from outcross pollinations, the asynchronous
anthesis element was added to some models at a significant
level before and/or after number of open spikeiets or days
between excision and anthesis, partially contributing to an
explanation of seed set variability. Interestingly, either
anthesis asynchrony or geographic distance could be added
to models based on data from outcross pollinations, but not
both. This result would be logical if both variables are
at least partially attributable to the same phenomenon, e.g.
incongruity. The low contribution to R2 (0,01 or less for
some models) when these variables were added after number
of open spikeiets could be due to some of the same
incongruity factored into number of open spikeiets.
Subsequent isolations were chosen to minimize anthesis
asynchrony between matched culms and days elapsing between
excision and anthesis. A model, using 2 00 self and cross
pollinations generated from these isolations, resulted in
a low amount of variability attributable to these factors
(R2 < 0.20), indicating success in decreasing undesirable
seed set variation.
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5.3.2.6.3. Number of Open Spikelets per Inflorescence
For most data sets, open spikelet numbers, or their
square roots, were most highly correlated to seed set.
There were reservations, however, about using number of open
spikelets per inflorescence in the regression modeling. If
number of open spikelets affected total possible seed set,
then use of this factor would be appropriate in the modeling
process. Alternatively, if an inflorescence had a maximum
seed set confounded by one or more factors, such as source-
sink capacity or incongruity, then factoring of numbers of
open spikelets could erroneously separate equal seed set or
result in overestimation of predicted seed set. Any
incongruity expressed through an interaction with open
spikelet number and seed set per inflorescence could also
affect identification of incongruity with other variables,
such as asynchronous anthesis and geographic separation.
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