BIOLOGY
Plumage as a Measure of Quality in Eastern Bluebirds
Andrea Mitchell
ABSTRACT
The males of many animal species use bright colors and ornaments to attract potential
mates. In this paper I examined studies of how plumage color in eastern bluebirds (Sialia
sialis) affects mate choice. I compared findings on this species with findings on European
starlings, zebra finches, and blue grosbeaks to identify which visual cues are commonly
used by songbirds to identify possible mates. I found that plumage color in all four of
these species was linked to individual health, offspring quality, and reproductive fitness .
Two ideas that remain unknown are exactly how these visual cues evolve, and how birds
learn to assess potential mates.
INTRODUCTION
Many species of male songbirds sing to attract females, but both males and females send "visual
signals" via their plumage. These signals are secondary sexual characteristics, sex-specific traits
in males or females that are not directly involved in reproduction (Molles 2008). Bright colors
and ornaments, such as large body size in male gorillas, antlers in moose, and bright colors in
tails of male guppies, are all examples of secondary sex characteristics (Keyser and Hill 2000).
Studies on guppies have shown that females prefer brightly-colored males. In guppies this choice
is not merely aesthetic; rather, bright males sire more broods than unattractive males (Molles
2008).
The importance of secondary sexual characteristics of the eastern bluebird, Sialia sialis, has been
studied extensively over the past decade. Eastern
bluebirds range from Canada to Mexico and from
the Atlantic Ocean to the Rocky Mountains, and
are easily recognizable for the males' brilliant
blue wings, back, and head, and orange chest
(Figure l; Gowaty and Plissner 1998). Bluebirds
usually mate in monogamous pairs, with both
parents taking time to watch over and feed the
young (Siefferman and Hill 2003). They were
once threatened by nest-site competition from
invasive species such as European starlings and
house sparrows, but conservation efforts of groups
such as the American Bluebird Society have
nursed the population back to health (Stokes and
Stokes 1991 , Gowaty and Plissner 1998). My
family has aided the efforts by feeding birds in our
backyard and putting up nestboxes that only
bluebirds can access. As such, I have developed a
fascination with the species, and have witnessed
many bluebirds interacting and raising their young.
Fi gure I. Mal e eastern bluebird (from Stokes &
Stokes 1991)
16
As with the guppies menti1
may be linked with individ
examined the implications
bluebirds (Figure 1), testin
competition for nesting sit1
evidence that plumage coli
visual signals used by blue
I compared the findings in
other songbird species.
CONNECTIONS BETWEEN
Songbirds are sexually die
it is duller (Gowaty and Pl
songbird species- reflects
range of humans, but the l
have shown that eastern bl
dichromatic in both light r:
Feathers have barbs that re
thicker in female bluebirdE
amount of light that can p2
to appear dull in the visibl
In addition, male bluebird~
than females in both their 1
(McGraw et al. 2004), cau
Plumage coloration of botl
influence mate choice, and
bird's reproductive quality
Between 1999 and 2005, ~
a series of studies on plum
test whether there was a re
male bluebirds and mate q
advantage, they began a m
captured female and male
released them (Siefferman
breeding season they teste'
male provisioning rate via
for UV chroma and reflect
with more intense UV-blu'
laid eggs earlier. Second, t
broods than dull males. n
These results suggest that
more likely to survive (Sie
BIOLOGY
:ern Bluebirds
naments to attract potential
r in eastern bluebirds (Sialia
s with findings on European
li visual cues are commonly
>lumage color in all four of
ty, and reproductive fitness.
cues evolve, and how birds
iles and females send "visual
acteristics, sex-specific traits
t1olles 2008). Bright colors
10ose, and bright colors in
:ics (Keyser and Hill 2000).
males. In guppies this choice
nattractive males (Molles
.uebird, Sialia sialis, has been
)Ver the past decade . Eastern
1 Canada to Mexico and from
o the Rocky Mountains, and
)le for the males' brilliant
d head, and orange chest
nd Plissner 1998). Bluebirds
ogamous pairs, with both
.o watch over and feed the
.nd Hill 2003). They were
test-site competition from
h as European starlings and
conservation efforts of groups
n Bluebird Society have
n back to health (Stokes and
y and Plissner 1998). My
efforts by feeding birds in our
~ up nestboxes that only
. As such, I have developed a
species, and have witnessed
·acting and raising their young.
As with the guppies mentioned above, the secondary sexual characteristic of plumage in bluebirds
may be linked with individual quality and reproductive success. Several recent reports have
examined the implications of color signals. I begin with a series of studies on male eastern
bluebirds (Figure 1), testing the connection between plumage and male parental effort,
competition for nesting sites, or offspring survival. I also investigated whether there is any
evidence that plumage color affects female bluebird fitness (Figure 2). To determine whether the
visual signals used by bluebirds are specific to this species or common to many songbird species,
1 compared the findings in bluebirds with studies of secondary sexual characteristics in three
other songbird species.
CONNECTIONS BETWEEN PLUMAGE COLOR AND REPRODUCTIVE SUCCESS IN BLUEBIRDS
Songbirds are sexually dichromatic; female birds have plumage in the same color as the male, but
it is duller (Gowaty and Plissner 1998; McGraw et al. 2004). Plumage- in bluebirds and other
songbird species- reflects not only in the visible light
range of humans, but the UV range as well. Studies
have shown that eastern bluebirds are sexually
dichromatic in both light ranges (Shawkey et al. 2005).
Feathers have barbs that reflect light; these barbs are
thicker in female bluebirds, therefore decreasing the
amount of light that can pass through and causing them
to appear dull in the visible range (Shawkey et al. 2005).
In addition, male bluebirds have more melanin pigment
than females in both their orange and blue plumage
(McGraw et al. 2004), causing males to appear brighter.
Plumage coloration of both sexes has been shown to
influence mate choice, and potentially indicates the
bird ' s reproductive quality (Shawkey et al. 2005) .
Between 1999 and 2005 , Siefferman and Hill conducted
a series of studies on plumage in eastern bluebirds. To
test whether there was a relationship between color of
male bluebirds and mate quality or reproductive
advantage, they began a monitoring study in which they
captured female and male bluebirds, tagged and then
Figure 2. Female eastern bluebird (from Stokes
released them (Siefferman and Hill 2003). Over the
& Stokes 199 1)
breeding season they tested nestling weight and number of offspring per brood, and also observed
male provisioning rate via video camera. They also collected feather samples from each adult bird
for UV chroma and reflectance analysis. The study had several important results. First, males
with more intense UV-blue coloration and larger orange breast patches paired with females that
laid eggs earlier. Second, these same brighter males fed offspring more often and fledged heavier
broods than dull males. Third, males with more UV color fledged a greater number of offspring.
These results suggest that offspring of brighter males are in better physical condition and are
more likely to survive (Siefferman and Hill 2003).
17
BIOLOGY
Another aspect of reproductive success is
success in establishing nest sites. Bluebirds
nest only in secondary cavities (dead tree
holes and holes made by other animals) or
I
boxes, so the number of nesting spots
1
available is always limited (Gowaty and
I
"0
E
Plissner 1998, Siefferman and Hill 2005a).
..cu
Males without a nesting cavity cannot attract
a mate . Siefferman and Hill (2005a) tested
..
whether male plumage color was associated
I
with success in competing for nest sites.
!!>
Fifteen nestboxes were added to two study
~'
sites without previously-established bluebird
populations, and then the areas were
monitored for male-male fights, territory
establishment, nest building, and date of first
egg-laying. As in the previous study, males
were banded and feathers were collected for
10
.ft
analysis. They found that males with feathers
that had high UV reflectance established
Fi gure 3. Relation of male UV chroma and reproductive
nestboxes earlier than males with low
success (number of offspring fled ged) Log Scale.
reflectance; these same high-reflectance birds
also had more body fat than their competitors (Siefferman and Hill 2005a). Both of these factors
contributed to a brightly-plumaged male's ability to produce more offspring (Figure 3). Based on
these results, Siefferman and Hill suggest that male coloration serves as a signal to potential
competitor males (and males of other cavity-nesting bird species), but they did not directly test
whether plumage color (or a related trait such as differences in energy or aggression) is the cue
that determines the outcome of male-male competition.
••
5
•·
•
••
"' • ••• ••
1
•
• •
Life history theory suggests that reproduction is energetically costly, and there must be tradeoffs
between current reproductive effort and production of future ornamentation (Siefferman and Hill
2005b ). To test whether there was a cost to males that had high parental effort, Siefferman and
Hill (2005b) manipulated brood size and effect on male plumage the following season. Plumage
was compared for males with reduced broods (2 nestlings) and males with enlarged broods (6
nestlings). Males with small broods invested little in caring for the nestlings, and as a
consequence had very bright plumage in the following season. These bright second-year males
then mated with better-quality females that laid eggs earlier. Males that had large broods in the
first experimental year provisioned their offspring more often, then in the following year
expressed duller coloration (Siefferman and Hill 2005b). Thus, males that began with only 2
nestlings likely "made up for" their lack of offspring by mating sooner and attracting better mates
the subsequent year, while males that began with 6 nestlings invested more in caring for young
and did not reproduce as well in the second season.
18
Age of males has also been ~
be correlated with plumage
coloration (Siefferman and I
2003, 2005a). Age was estin
by the shape of primary feat]
and the cycle of molt. The
researchers found that both 1
blue coloration and body co1
increased with age, and the I
difference was between year
and two-year-old males
(Siefferman et al. 2005). Thi
studies show that plumage
coloration can provide fema
information on a male ' s age
and parental ability. In addit
males with brighter colorati<
UV chroma fed incubating f
often (Figure 4) (Siefferman
time foraging, indicating tha
offspring fitness, but also be
Although it is now clear tha1
that female plumage also si~
of the male due to less mela
is still observed in females (
low food versus adequate fo
stressed females were duller
females with brighter tail co
earlier in the season; female
offspring more often (Sieffe
those in better body conditic
pigmentation (Siefferman 21
reproductive quality. Most i
coloration, males can also ic
COMPARISON OF VISUAL (
To assess whether visual cu
reviewed studies of seconda
zebra finches. Blue grosbea
to bluebirds), zebra finches
least color dimorphism betv
was related to male quality
and weighed the males, ther
correlation with mass, phys
per hour (Keyser and Hill 2
body size than dull males (I
breeding territories, and blu
offspring at a six-fold highe
visits per hour (Keyser and
BIOLOGY
:ct of reproductive success is
tablishing nest sites. Bluebirds
:econdary cavities (dead tree
les made by other animals) or
number of nesting spots
!ways limited (Gowaty and
l, Siefferman and Hill 2005a).
it a nesting cavity cannot attract
~rman and Hill (2005a) tested
: plumage color was associated
in competing for nest sites.
oxes were added to two study
previously-established bluebird
and then the areas were
r male-male fights, territory
t, nest building, and date of first
•S in the previous study, males
and feathers were collected for
y found that males with feathers
UV reflectance established
·lier than males with low
hese same high-reflectance birds
ll 2005a). Both of these factors
: offspring (Figure 3). Based on
ves as a signal to potential
. but they did not directly test
ergy or aggression) is the cue
:ly, and there must be tradeoffs
mentation (Siefferman and Hill
sental effort, Siefferman and
he following season. Plumage
ties with enlarged broods (6
: nestlings, and as a
ese bright second-year males
s that had large broods in the
n in the following year
lies that began with only 2
oner and attracting better mates
:ted more in caring for young
1
Age of males has also been shown to
be correlated with plumage
a!
coloration (Siefferman and Hill
t'5
2003, 2005a). Age was estimated
E:
by the shape of primary feathers
•
l!!I
and the cycle of molt. The
2
e0(
researchers found that both UVc:
blue coloration and body condition
·;:
0
·;;;
increased with age, and the largest
·;;:
difference was between yearling
e0.
and two-year-old males
c:
"'
(Siefferman et al. 2005). These
~
studies show that plumage
14
16
18
20
22 24
26
28
30
coloration can provide females with
Mean male bri ghtness (% li ght)
information on a male's age, health,
and parental ability. In addition,
Fi gure 4. Correlation between male provisioning rate of
incubating females and male bri ghtness.
males with brighter coloration and greater
UV chroma fed incubating females more
often (Figure 4) (Siefferman and Hill 2005c). Females that were better provisioned spent less
time foraging, indicating that male bluebird plumage coloration has consequences not only for
offspring fitness, but also benefits females.
.,
s
Q)
•
•
.,•
Although it is now clear that male plumage provides information on male quality, is it possible
that female plumage also signals female quality? Female plumage is noticeably duller than that
of the male due to less melanin pigmentation (McGraw et al. 2004), but significant color diversity
is still observed in females (Shawkey et al. 2005). Siefferman and Hill (2005d) tested the effect of
low food versus adequate food on plumage, body mass, and nestling provisioning behavior. Foodstressed females were duller, but did not have less body mass compared to control females . Also,
females with brighter tail coloring, better body condition, and older females began to lay eggs
earlier in the season; females with more colorful rumps and-better body condition provisioned
offspring more often (Siefferman and Hill 2005d). It has also been shown that older females and
those in better body condition are less susceptible to diseases and lay eggs with more
pigmentation (Siefferman 2006). These data imply that female color can indicate female
reproductive quality. Most importantly, in the same way females can assess male quality by
coloration, males can also identify quality f emales by their color.
COMPARISON OF VISUAL CUES AND MATE CHOICE IN OTHER SONGBIRD SPECIES
To assess whether visual cues are equally important in mate choice in other songbird species, I
reviewed studies of secondary sexual characteristics in blue grosbeaks, European starlings, and
zebra finches . Blue grosbeaks have strong color dimorphism between males and females (similar
to bluebirds), zebra finches have moderate color dimorphism, and European starlings have the
least color dimorphism between the sexes. Keyser and Hill (2000) tested whether plumage color
was related to male quality in blue grosbeaks (Guiraca caerulea). They collected feathers, banded,
and weighed the males, then kept records throughout a breeding season to observe color
correlation with mass, physical condition, territory size/quality, and male feedin g rate of nestlings
per hour (Keyser and Hill 2000). They found that males with a higher blueness score had a larger
body size than dull males (Figure 5). Second, two-thirds of the monitored males established
breeding territories, and bluer males had larger territories . Third, although female grosbeaks fed
offspring at a six-fold higher rate than males, the bluest males had the highest rate of feeding
visits per hour (Keyser and Hill 2000). However, Keyser and Hill did not test whether plumage
19
BIOLOGY
~
o
~~~~~~~~~~~~~
.,
920
900
e
ss o
E
86 0
·=
toc:
~
84 0
82 0
•
.• '· T.:
~ ..
• -- !& • • - •'·: •
••
••
color is a signal between rival males, potential
mates, or both. Based upon bluebird studies
(Siefferman and Hill 2005a-c) it is probable that
both occur, but grosbeaks might react to plumage
"signals" in a different way than their smaller
counterparts.
A study on European starlings (Sturnus vulgaris)
suggested that coloration signals are most
important to females of the species (Bennett et al.
•
1997). Although starlings appear black and drab to
••
•
•
human eyes, their feathers reflect in the UV range
••
86 0
in the same way as bluebirds and grosbeaks
84 0
•
(Shawkey
et al. 2005). Bennett et al. (1997)
•
82.0
investigated whether female starlings could detect
80 0
•
differences in plumage coloration, based upon UV
Rump
78 0
reflectance.
Each female was allowed to visually
10
15
20
25
30
35
assess
four
males,
and her preference was
Blueness score
measured as the length of time she spent with each
: Figure 5. Correlati on between male blueness and
male. In the first trial , no variables were
, body size measured as wing chord length (mm).
manipulated, but in the second trial the same set of
males were subject to a light that filtered out UV reflectance. They found that female starlings
ranked males differently under the two treatments (Bennett et al. 1997), suggesting that both light
environment and the amount of variation in UV reflectance is extremely important in mate choice
decisions. Despite the minimal sexual dimorphism in plumage color (at least as apparent to
humans), this study shows that female starlings do rank males based on differences in the UV
reflectance of their plumage. More studies are needed to determine whether this plumage cue is
correlated with health, siring ability, or parental behavior as in the bluebirds.
..,_..
.
.
.
.
.
..
.
.
.
-.. · :l ·
SUMMARY
Studies by Siefferman and Hi
multiple ways to individual q
healthier and sired healthier c
starlings, and zebra finches a•
starling, that have less sexual
potential mate via their color.
his plumage.
However, it remains to be se<
advantageous. Burley did not
or why males preferred black
( 1997) showed how female b
reflectance. Certainly mate cl
al. (2005) showed that health
how do potential mates kno'-"
lf the behavior is learned, do
females? To my knowledge
conduct studies linking durat
and reproductive fitness. Or J
that have not yet been tested
extent to which these prefere
REFERENCES
A study by Burley (1986) showed that mate choice was linked to reproductive success in zebra
finches in ways similar to the bluebirds. Zebra finches (Poephila guttata), like bluebirds, are
socially monogamous with both parents feeding the young. Instead of assessing plumage, Burley
put different colored leg bands on each bird to test the role of visual cues in mate choice. Males
were randomly banded with orange, red, or green, while females were not color-banded (The
selected aesthetically-pleasing colors were known from previous experiments on finches .) Burley
found that, out of20 females, 11 mated to red-banded males, 4 to green-banded males, and 5 to
orange-banded males. "Red" males mated with females that laid more eggs per clutch, and
produced twice as many offspring as the other colors (Burley 1986).
Bennett, A. T. D. , I. C. Cuthi
predict mate preferer
94: 8618-8621.
In a second trial, Burley randomly banded females with blue, black, or orange bands and left
males unhanded. As in the banded-male experiment, colors were determined from previous finch
studies. Burley found that black-banded females produced an average of I 8 offspring, while
orange-banded females produced 12 and blue-banded 8 offspring. " Black" females also had the
highest offspring survival rate (Burley 1986). Clearly female finches deemed red-banded males
the most attractive (with the best potential reproductive benefit), and male finches deemed blackbanded females the most attractive. As a result, the sexually-selected "preferable" colors did
produce offspring with the best fitness. Even though the aesthetic trait was human-manipulated
rather than natural as in the bluebird, grosbeak, and starling studies, it shows that birds of both
sexes will select for certain traits more than others, and their discerning judgment is usually
rewarded.
Keyser, A. J., and G. E. Hill.
quality in male blue
20
Burley, N. 1986. Sexual sele•
American Naturalist
Gowaty, P.A. , and J. H . Plis
America 381: 1-31.
McGraw, K.J., K. Wakamats
Safran, L. Siefferma1
its color: carotenoid
bluebirds, penguins,
Molles, M. C. 2008. Ecology
BIOLOGY
ween rival males, potential
ed upon bluebird studies
ll 2005a-c) it is probable that
beaks might react to plumage
ent way than their smaller
m starlings (Sturnus vulgaris)
·ation signals are most
s of the species (Bennett et al.
rlings appear black and drab to
:athers reflect in the UV range
bluebirds and grosbeaks
5). Bennett et al. ( 1997)
r female starlings could detect
1ge coloration, based upon UV
male was allowed to visually
1d her preference was
5th of time she spent with each
11, no variables were
the second trial the same set of
found that female starlings
1
97), suggesting that both light
mely important in mate choice
r (at least as apparent to
i on differences in the UV
whether this plumage cue is
1luebirds.
SUMMARY
Studies by Siefferman and Hill found that plumage color in eastern bluebirds were linked in
multiple ways to individual quality and reproductive fitness. Birds with brighter plumage were
healthier and sired healthier offspring. Analogous studies on aesthetic traits in grosbeaks,
starlings, and zebra finches add weight to this claim. Interestingly, even species, such as the
starling, that have less sexual dimorphism still showed that males and females can assess a
potential mate via their color. In bluebirds, even rival males can predict a competitor's fitness by
his plumage.
However, it remains to be seen just how birds know to find mates with traits that are
advantageous. Burley did not determine why female finches preferred males with red leg bands,
or why males preferred black-banded females; neither Siefferman and Hill nor Bennett et al.
(1997) showed how female bluebirds and female starlings chose males with the greatest UV
reflectance. Certainly mate choice cannot be based solely upon subjective judgment. Shawkey et
al. (2005) showed that healthier birds produced more proteins for melanin in their feathers, but
how do potential mates know to look for this quality? Selectiveness may be instinctive or learned.
If the behavior is learned, do younger female bluebirds have less reproductive success than older
females? To my knowledge this has not yet been studied. Perhaps future researchers also need to
conduct studies linking duration or strength of a male bird ' s mating calls with plumage quality
and reproductive fitness. Or perhaps there are traits such as pheromones or other chemical cues
that have not yet been tested in birds. Determining how mate choice preferences evolve and the
extent to which these preferences are learned or instinctive seems to be the next challenge.
REFERENCES
productive success in zebra
ttata), like bluebirds, are
of assessing plumage, Burley
cues in mate choice. Males
Te not color-banded (The
periments on finches .) Burley
een-banded males, and 5 to
re eggs per clutch, and
Bennett, A. T. 0., I. C. Cuthill, J. C. Partridge, and K . Lunau. 1997. Ultraviolet plumage colors
predict mate preferences in starlings. Proceedings of the National Academy of Sciences
94: 8618-8621.
or orange bands and left
ermined from previous finch
:e of 18 offspring, while
3lack" females also had the
. deemed red-banded males
male finches deemed black, "preferable" colors did
it was human-manipulated
it shows that birds of both
ngjudgment is usually
Keyser, A. J., and G. E. Hill. 2000. Structurally based plumage coloration is an honest signal of
quality in male blue grosbeaks. Behavioral Ecology 11 : 202-209.
Burley, N. 1986. Sexual selection for aesthetic traits in species with biparental care. The
American Naturalist 127: 415-445.
Gowaty, P.A., and J. H. Plissner. 1998. Eastern bluebird (Sialia sialis). The Birds ofNorth
America 381: 1-31.
McGraw, K.J., K. Wakamatsu, S. Ito, P. M. Nolan, P. Jouventin, F. S. Dobson, R. E. Austic, R. J.
Safran, L. Siefferman, G. E. Hill , and R. S. Parker. 2004. You can' t judge a pigment by
its color: carotenoid and melanin content of yellow and brown feathers in swallows,
bluebirds, penguins, and domestic chickens. The Condor 106: 390-395.
Molles, M. C. 2008. Ecology: Concepts and Applications. McGraw Hill, New York, NY, USA .
21
BIOLOGY
Shawkey, M. D., A. M . Estes, L. Siefferman, and G. E. Hill. 2005 . The anatomical basis of sexual
dichromatism in non-iridescent ultraviolet-blue structural coloration of feathers .
Biological Journal of the Linnean Society 84: 259-271.
Analysis of the '
Siefferman L. 2006. Egg coloration and recognition of conspecific brood parasitism in eastern
bluebirds. Ethology 112: 833-838.
Siefferman, L. and G. E. Hill. 2003. Structural and melanin coloration indicate parental effort and
reproductive success in male eastern bluebirds. Behavioral Ecology 14: 855-861 .
Siefferman, L. and G. E. Hill. 2005a. UV-blue structural coloration and competition for nestboxes
in male eastern bluebirds. Animal Behaviour 69: 67-72 .
Siefferman, L. and G. E. Hill. 2005b. Male eastern bluebirds trade future ornamentation for
current reproductive investment. Biology Letters 1: 208-211.
Siefferman, L. and G. E. Hill. 2005c. Blue structural coloration of male eastern bluebirds Sialia
sialis predicts incubation provisioning to females . Journal ofAvian Biology 36: 488-493.
Siefferman, L. and G. E. Hill. 2005d. Evidence for sexual selection on structural plumage
coloration in female eastern bluebirds (Sialia sialis). Evolution 59: 1819-1828.
Siefferman, L., G. E. Hill, and F. S. Dobson. 2005 . Ornamental plumage coloration and condition
are dependent on age in eastern bluebirds Sialia sialis. Journal of Avian Biology 36: 428435 .
Stokes, D.W. and L.Q. Stokes. 1991. Stokes Bluebird Book. Little Brown, New York, NY, USA.
Understanding the inhibi
pharmaceutical ingredients
procedure of industrial tab!
hydrate transformation of
differences in solubility co
be inhibited through the us
caffeine was analyzed in a
added to the slurries to det
was monitored using in-lin
calibration was used to co
amounts of hydrate and an
in the Raman spectra. The
the transformation at cone<
least 400 min at a PAA cc
hydroxypropyl methyl cell
showed little to no inhibit
were performed to determi
inhibition. Analysis of kim
the growth of caffeine hyd1
INTRODUCTION
Andrea is a senior and will graduate in 2008 with a BS in Biology. She wrote this paper for Dr.
Marr' s BIOL L473.
A common method for the
mixing the active pharmac<
mixture is sprayed with wa
APL After several other pri
It is not uncommon for an i
often an anhydrous crystal
has specific properties, wh
of the physical properties c
altered by this transformati
the bioavailability and effe
The anhydrate to hydrate t1
This process includes three
second is the nucleation of
dissolved material is above
themselves properly. After
growth is accomplished by
22