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USDA FOREST SERVICE
RESEARCH NOTE
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THE SEED ORCHARD TREE AS A POLLEN SAMPLER:
A MODEL AND EXAMPLE
-----1'
by
Frank C. Sorensen,
I,
...
?'
Prineipal Plant Gen -t cist
·,
,,
,,,
·
ABSTRACT
A model is developed which uses the seed
tree as a pollen sampler and attempts to parti­
tion the pollen it receives into self pollen,
pollen from immediately surrounding neighbors,
pollen from slightly more distant neighbors,
and background pollen.
An example, using data
from several sources, is introduced to illus­
trate the use of the model.
KEYWORDS:
Pollen dissemination,
seed orchards, Douglas-fir.
;EST SERVICE - U.S. DEPARTMENT OF AGRICULTURE - PORTLAND, QREGON
··
\
INTRODUCTION
Discovery of two Douglas-fir
trees with an albino single-gene
marker at the same chromosomal
locus has provided a means to sam­
ple distribution patterns of pollen
in Northwest seed orchards. The
method involves grafting scions of
the trees into the orchards in pat­
terns permitting detection of their
cross pollination at various dis­
tances and relating this to total seed
yield of the sample tree. To utilize
this possibility requires development
of both the layout patterns of such
grafts in an orchard and a mathemat­
ical model that would interpret re­
sults in terms of the most important
questions from such sampling. A
mathematical model developed for
the simplest assumptions that appear
to partition total pollen into these
classes is presented in this paper.
Source of pollen falling onto fe­
male strobili of trees may be arbi­
trarily divided into four categories:
(1) that coming from the tree itself,
(2) that coming from the immediate
neighboring trees or trees within
about 50 feet, (3) that from trees 50
to several hundred feet away, and (4)
that from further away, or what will
be called here "background pollen. "
In the seed orchard, the last three
categories may be thought of as
"near-neighbor, " "other-orchard, "
and "nonorchard" pollens.
of frequency-distance curves pro­
ceeding away from the source of
the object (Colwell 1951, Silen
1962, Strand 1957, Wang, Perry,
and Johnson 1960, and Wright 1952
for conifer pollen; Bateman 1947a
and 1947b, Hodgson 1949, and
Meinders and Jones 1950 for agri­
cultural crop pollen; and Dahms
1963, Fowells and Schubert 1956,
Roe 1967, Shearer 1960, and Yocom
1968 for coniferous seeds of various
sizes). Almost always the curves
associated with the deposition
of wind-distributed objects have
been curvilinear and show the great
majority of the objects to be depos­
ited near the source. In the case
of pollen, this has led to the calcu­
lation of mostly small- to moderate­
sized neighborhood s!/ (Wang, Perry,
and Johnson 1960, Wright 1962) or
to the conclusion that most pollina­
tion is by near neighbors (Colwell
1951, Ehrlich and Raven 1969,
Langner 1953, and Strand 1957).
On the other hand,. there have
also been observations that much
pollen goes up rather than down,
that this pollen ("background pol­
len") may travel long distances
before it is deposited, and that it
.!/ Neighborhood refers
trees.
to a group of
'
Small- to moderate-sized indicates
a group of 10 to 300 trees, which at most
orchard spacings would include trees in
The movement of objects which
are wind dispersed in nature has
usually been reported in the form
2
categories
(2)
immediate neighboring trees,
and (3) trees 50 to several hundred feet
away.
672
may contribute considerably to local
pollen loads (Koski 1970, Sarvas
1967, Silen 1962, and Squillace
1967). Silen (1962) rationalized the
two vieWIJoints by showing his dis­
tribution curve partitioned into a
curvilinear portion from the sampled
tree plus a highly uniform count of
pollen from distant sources.
Part of this conflict in observa­
tion or interpretation may be due to
different pollen sampling methods;
part may be due to real differences
in pollen dispersal under varied
stand conditions. It is also thought
that part of the difficulty may be a
tendency to view pollen dispersal in
terms of its distribution away from
a source. Pollen sampling, by its
very nature, emphasizes this view
of the distribution pattern. In this
note attention is focused on the pol­
len receptor (rather than on the pol­
len source) and on distribution to­
ward the receptor (rather than away
from the source). A model has been
developed which treats the seed
tree as a pollen sampler and then
attempts to apportion the pollen
catch among the various sources of
the pollen. An example based on
the model is also presented, and
some of the assumptions associated
with the example are discussed.
5
way, it could also be applied to
natural stands, but their irregular­
ity of spacing and age makes them
harder to analyze than seed orchards.
Assumptions associated with the
model are given and discussed in
table 2.
Although the model is simple in
concept, because of the array of
symbols it is rather difficult to de­
cipher. Readers who are not inter­
ested in the fine points of pollen
dispersion may wish to omit table 1
and go directly to the example
(table 3).
Table 3 is meant to be as repre­
sentative as possible of a Douglas­
fir orchard of seed-pro ducing age.
Estimates of the relative amount
of pollen contributed by the sample
tree itself and the first nine ranks
of trees surrounding it (table 3)
were read from a plot of the data
given in table 1 of Wang, Perry,
and Johnson (1960) for slash pine. /
V
See footnote 1, table 1.
/ The pollen dispersal curve for slash
pine was used because it was based on a
tree of producing seed orchard size grow­
ing within its natural range.
This is not
meant to imply that Douglas-fir pollen and
slash pine pollen would have the same dis­
persal properties.
However, among the
pollen dispersal curves given in the liter­
ature, this one seemed to be the most
MODEL AND EXAMPLE
The model, which relates direct­
ly to pollen-frequency curves of the
type cited above, is described in
table 1 where it is applied to a
seed orchard situation. In a general
suitable because of tree size and because
the tree was growing within the species
range.
The available pollen curves for
Douglas-fir were either from much larger
trees (which had, however, pollen dispers­
al curves of the same form as the curve
for slash pine) or from trees growing out­
side the natural range.
3
Table 1.--GeneraZ model for partitioning the poZZen received by any seed tree in a producing orchard
(see table 2 for assumptions for model)
Ran1J/
Distance1/
Pollen
frequencyl/
Relative
pollen
frequency
Fraction
of pollen
pass in /
Amount of pollen received,
self pollen included
Calculated
I
Percent
Self /
0
f
s
f /f
s s
1
f
s
f
s
1
T
1
d
f
l
f /f
l s
1
f
f
l
l
/
f
s
p
/ fs
p
2
d
z
f
2
f
3
d
3
f
3
f
n
d
f
n
f /f
n s
Background
Total
n
f
2
n-1
p
l
TT
s
s
Amount of pollen received,
self pollen excluded
Calculated
f
l
f(T-1)
s
f p
2
f (T-1)
s
f p
2
f T
s
f p
2
f
s
2
f p
3- f
s
2
f p
3
f T
s
f p
3
-f s
n-1
f
f
b
f
s
f
n-1
_!!P__
f T
s
s
T
2
n-1
f
_!!P__
f
s
T
b
f
100
T-1
b
Percent
f
l
- f
s
f p
2
f
s
_!!P__
I
s
2
f p
3
f (T-1)
s
f
n-1
_!!P__
f (T-1)
s
b
(T-1)
100
1./ Rank refers to the "rings" of trees which surround the sample tree.
In a regularly spaced orchard there will be
8 trees in the first rank. The next surrounding ring will contain 16 trees and is designated here as rank 2. The remain­
ing ranks are analogous.
!:_/ Distance is used in reading pollen frequency from frequency-distance curve but is not used in calculations.
3/ To
. be read from frequency-distance curve.
-
4
-/ Fraction of pollen which passes through the ranks of trees intervening between the pollen source and the seed tree.
See assumption 4, table 2, for further explanation.
5
-/ Sample or seed tree itself.
Table 2.--Asswnptions for model in table 1
1. Sample tree is in an evenly spaced orchard.
2. All trees in each rank.!/ of trees are assumed to be equidistant from the
3. 4. 5. 6. 7. 8. 9. sample tree. The distance used is the average distance between that
rank and the sample tree.
If only pollen release is considered and the effect of distance is neglected,
the pollen which the sample tree receives from itself (self pollen) is
assumed equal to the pollen received from all trees within any one rank.
The reason for this can be seen if one assumes rings of trees surrounding
a sample, or target, tree with all trees of equal size and crowns touching.
Then, assume the pollen travels in straight horizontal lines. At any one
time the pollen that is released from the ring and travels toward the tar­
get comes from the equivalent of a single tree, no matter how large the
ring. At the same time, and no matter what the direction of the wind, the
sample tree will be contributing pollen to itself. In other words, it par­
ticipates with all surrounding trees.
A portion of the pollen coming from second and subsequent ranks of trees
surrounding the sample tree is sequentially intercepted or filtered out by
intervening ranks. When a row of trees is standing between the pollen
tree and the sample tree, it is going to capture or cause the loss of some
of the pollen which is moving from more distant trees to the sample tree.
In the model it is assumed that the same proportion of the incoming pollen
is intercepted or otherwise diverted by each intervening row of trees.
The same proportion of trees in each rank produces pollen.
Producing trees yield pollen in equal quantities.
Time curves for pollen release are the same for all trees inside and out­
side the orchard.
Female flower receptivity and pollen shed are synchronous.
All pollen except self pollen is equally effective in producing seedlings.
(The role of self pollen will be noted again in the discussion. )
.!/ See footnote 1, table 1.
5
Table 3.--Proportions of poZZen received by any seed orchard tree from surrounding orchard and nonorchard trees.
O':>
ExampZe is for a hypotheticaZ DougZas-fir orchard
Rank!/
Self
Distarice.Y
( feet )
0
Pollen
frequency}/
327
Relative
pollen
frequency
1.0
1
30
151
.462
2
58
81
.248
3
87
so
.153
4
ll 5
35
.107
5
144
26
.080
6
172
20
.061
7
200
16
.049
8
229
13
.040
9
257
11
.034
Background
Total
Fraction
of pollen
passin /
Amount of pollen received,
self pollen included
Calculated
I
Percent
Amount of pollen received,
self pollen excluded
Calculated
I
Percent
1
1.000
52.7
1
.462
24.4
0.462
51.7
.124
6.6
.124
13.9
.038
2.0
.038
4.3
.013
.7
.013
1.5
1/2
2
(1/ 2)
3
(1/2)
4
(1 /2)
5
(1/2)
6
(1/ 2)
7
(1/2)
8
(1/ 2)
.005
.3
.005
.6
.001
.1
.001
.1
(<. 001)
(<. l )
(<. 001)
(< .1)
(<. 001)
(<. 001)
( <.1)
( <. 001)
(<. l )
(<.1)
(<. 001)
�_/ .250
13.2
1.893
.250
(< .1)
27.9
.893
]) See footnote 1, table 1.
]j Average distance between sample tree and surrounding ranks when orchard spacing is 25 feet.
]/ From a hand plot of data in table 1 in Wang, Perry, and Johnson (1960).
!±_/ Fraction of pollen which passes through the ranks of trees intervening between the pollen source and the seed tree.
In this example it is assumed that one-half of the incoming pollen is intercepted by each intervening row of trees.
'j_/ Background p ollen = 0.25 x self pollen frequency; 0.25 averaged from figures 6 and 7 of Silen (1962).
Level of background pollen was
estimated from figures 6 and 7 in
Silen (1962). A seed orchard spacing
of 25 feet was used in the example.
Trees in the first two surrounding
ranks were considered to be near­
neighbors.
Table 3 estimates the relative
contribution of various pollen
sources when self pollen is included
or excluded. In the case of Douglas­
fir, which usually has a low self
fertility (Sorensen 1971), the self
pollen will probably not sire more
than 5 to 10 percent of the viable
seeds. !/ Consequently, the best
picture of seedling parentage
should be obtained from the column
where self pollen is omitted. In
this hypothetical example, approxi­
mately 65 percent of the seeds were
sired by pollen from the first two
surrounding ranks of trees (near­
neighbors), about 5 percent by other
trees in the orchard, and about 30
percent by the background pollen.
DISCUSSION
The main purpose of the model
is to provide a basis for numerically
relating the contribution of various
pollen sources. Because the fre­
quency-distance curves are almost
always characterized by high pollen
frequency near the source and a
rapid decrease in frequency with
distance, the model offers the addi­
tional advantage of being moderately
.1/
Frank C. Sorensen.
in coastal Douglas-fir.
Natural selfing
In preparation.
stable, even when the other assump­
tions are altered considerably. Per­
haps this can best be seen by making
changes in some assumptions and
examining the effect on the example.
1. Form of the frequency-dis­
tance curve can differ from that
used without greatly changing the
proportion of pollen received from
the various sources provideo that,
in all cases, there is a rapid de­
crease in pollen frequency with dis­
tance. For example, Wright's
(1952) plot of the pollen dispersal
curve for young Douglas-fir growing
outside the natural range of the
species was linear and showed no
pollen capture beyond 150 feet.
Using Wright's curve, Silen's (1962)
estimate of background pollen, and
the other assumptions in table 2, the
pollen contribution (omitting self
pollen) of the first two ranks was
75 percent, of the next seven ranks
10 percent, and of the other ranks
(background) 15 percent. The
example in table 3 which gave pollen
contributions of 65 percent, 5 per­
cent, and 30 percent was based on
a dispersal curve which was strong­
ly curvilinear and includeq pollen
capture up to 250 feet.
2. Silen (1962) estimated back­
ground pollen for Douglas-fir in a
large open area to be about 25 per­
cent of that received by the sampling
station at the peak of the frequency­
distance curve. In the present ex­
ample, a background-pollen density
of 25 percent of the self-pollen den­
sity was used. Omitting self pollen,
this gave estimates of orchard and
7
nonorchard pollen of 70 percent and
30 percent, respectively. If a back­
ground-pollen density of 5 percent of
self-pollen density is used and other
assumptions left unchanged, the pro­
portions of orchard and nonorchard
pollen would be about 95 percent and
5 percent, respectively. If a back­
ground-pollen density of 50 percent
of self-pollen density is used, or­
chard and nonorchard proportions
would be, respectively, about 60
percent and 40 percent. If incidence
of background pollen and self pollen
is assumed to be equal, the percent­
ages of orchard and nonorchard pol­
len which a seed orchard tree re­
ceived would be 40 and 60 percent,
respectively.
3. In assumption 3, table 2, it
was proposed that if the effect of
distance is neglected, the sample
tree receives as much pollen from
itself as it does from all the trees in
any one surrounding rank. However,
it might also be assumed that the
delivery system for self pollen is
less efficient because some of the
self pollen is blown directly out of
the crown without opportunity to con­
tact female strobili, whereas pollen
coming from a neighboring tree will
have the opportunity to pass through
the entire crown of the sample tree.
If self-pollen frequency in table 3 is
'
reduced by half and other pollen fre­
quencies are not changed, the contri­
bution of self pollen would be reduced
from about 55 percent to 35 percent.
If self pollen is omitted, the propor­
tions of near-neighbor, other-orchard,
and nonorchard pollens would remain
unchanged.
8
4. Intervening rows of trees
between the sample tree and the trees
from which it is receiving pollen are
assumed to intercept or cause the
settling-out of half of the incoming
pollen (assumption 4, table 2).
Changes in this fraction have their
greatest effect on the proportions of
near-neighbor and other-orchard
pollen. Relative proportions of or­
chard and nonorchard pollen are
affected to a lesser extent. F<;>r ex­
ample, if three-fourths of the in­
coming pollen were intercepted per
intervening row, then the estimates
would be 55 percent selfing or, with
selfing excluded, about 70 percent
near-neighbor, less than 1 percent
other-orchard, and about 30 percent
nonorchard. If only one-fourth of
the incoming pollen were intercepted
per intervening row, selfing would
be estimated at 50 percent, near­
neighbor, other-orchard, and non­
orchard estimates (excluding selfing)
would be about 60 , 25, and 15 percent,
respectively.
Other factors which may affect the
accuracy of the example are indicated
in assumptions 5 through 9 (table 2).
They include flowering time (do flower
receptivity and pollen release coin­
cide on the sample tree, betwe n the
seed tree and other-orchard trees,
and between orchard trees and trees
in the surrounding stands?), relative
proportions of orchard and nonorchard
trees which are flowering, and possi­
ble deposition of massed pollen clouds
(Lanner 1966). These influences may
vary greatly from area to area and
some of them from year to year, so
it is probably not necessary to
consider them in this general
situation. However, any of these
factors which can be estimated can
be fitted into the model.
Tree size and proportion of space
occupied by tree crowns will also
have to be considered if the model is
used to coordinate and interpret re­
sults of pollen sampling. Both pol­
len production and pollen interception
will be affected by crown size and
density. For the present, it can only
be assumed that the proportion of or­
chard pollen will increase rapidly
after the orchard comes into produc­
tion.
Selfing has . been considered at
the two extremes in tables 1 and 3:
first, with self pollen fully as effec­
tive as cross pollen in producing
viable seeds, and second, with the
sample tree being self-sterile. The
actual situation will usually be be­
tween these extremes.
In the example, the sample tree
has been treated as receiving pollen
equally from all sides. However,
pollen movement may be predomi­
nantly in one direction (Dyson and
Freeman 1968). In this case, the
sample tree should receive pollen
from a smaller number of the sur­
rounding trees, but the relative pro­
portions of self, near-neighbor,
other-orchard, and nonorchard pol­
lens should remain about the same
as when wind movement is variable.
The example and discussion have
centered on the model in relation to
a seed orchard situation. This was
due to the relevance of pollen dis­
persal to the management of seed
orchards, in which pollen contamina­
tion is a serious question, and be­
cause the uniformity of a seed or­
chard plantation made the presenta­
tion of the model and example easier.
In natural stands there will be more
variability in factors such as dis­
tance between ranks of trees and
number of trees per rank. But if
reasonable averages can be obtained
for each of these factors, it appears
that the model could be employed
satisfactorily to partition pollen
sources for trees in a variety of
natural situations.
CONCLUSION
The pollen which trees receive
comes from many different sources
and distances. The model presented
here divides these sources into self
pollen, pollen from immediate neigh­
bors, pollen from slightly more dis­
tant neighbors, and background pol­
len. Data were brought together
from the literature in an attempt to
get a picture of pollen source as
related to seed orchard trees, and
also to determine what additional
information might be most useful in
testing the model.
Of course, the model was quite
simplified. The real situation is
expected to be much more complex.
Nevertheless, in determining what
would be the most valuable addition­
al information, two observations
seemed to be of primary importance.
First, except for large depositions
9
of background pollen, the tree itself
and its immediate neighbors appear
to contribute the
_ majority of pollen
which the tree receives. Second,
the interception of pollen by inter­
vening ranks of trees appears to be
a very influential factor in local pol­
len movement. Its importance is
now largely unknown.
With these two observations in
mind, it appears that estimates of
self-pollen contribution and pollen
contribution from the neighboring two,
or better three, ranks of trees would
be most important for developing a
picture of the pollen distribution in
a seed orchard.
LITERATURE CITED
Bateman, A. J.
1947a. Contamination of seed
crops. II. Wind pollina­
tion. Heredity 1: 235-246.
1947b. Contamination in seed
crops. III. Relation with
isolation distance.
Heredity 1: 30 3-336.
Colwell, R. N.
1951. The use of radioactive
isotopes in determining
spore distribution patterns.
Am. J. Bot. 38: 511-523.
Dahms, Walter G.
1963. Dispersal of lodgepole pine
seed into clear-cut patches.
USDA Forest Serv. Res.
Note PNW-3, 7 p. , illus.
Pac. Northwest Forest &
Range Exp. Stn., Portland,
Oreg.
10
Dyson, W. G. , and G. H. Freeman
1968. Seed orchard designs for
sites with a constant pre­
vailing wind. Silvae Genet.
17: 12-15.
Ehrlich, Paul R. , and Peter H. Raven
1969. Differentiation of popula­
tions. Science 165: 1228 ­
1232.
Fowells, H. A. , and G. H. Schubert
1956. Seed crops of forest trees
in the pine region of Cal­
ifornia. U.S. Dep. Agric.
Tech. Bull. 1150, 48 p.,
illus.
Hodgson, H. J.
1949. Flowering habits and pollen
dispersal in Pensacola
Bahia grass, Paspalum
nota tum Flugge. Agron.
J. 41: 337-343, illus.
Koski, Veikko
1970. A study of pollen dispersal
as a mechanism of gene
flow in conifers. Commun.
Inst. For. Fenn. 70. 4,
78 p. , illus.
Langner, W.
1953. Eine Mendelspaltung bei
Aurea- Formen von Picea
Abies (L) Karst. als
Mittel zur Klarung der
Befruchtungsverhaltnis se
im Walde. Z. Forstgenetik
Forstpflanzenzuecht. 2:
49-51.
Lanner, Ronald M.
1966. Needed: a new approach
to the study of pollen dis­
persion. Sil vae Genet.
15: 50-52.
Meinders, Hadley C., and Melvin
D. Jones
1950. Pollen shedding and dis­
persal in the castor plant,
Riainus communis L.
Agron. J. 42: 206-209,
illus.
Roe, Arthur L.
1967. Seed dispersal in a bumper
spruce seed year. USDA
Forest Serv. Res. Pap.
INT-39, 10 p., illus.
Intermountain Forest &
Range Exp. Stn., Ogden,
Utah.
Sarvas, Risto
1967. Pollen dispersal within
and between subpopulations;
role of isolation and mi­
gration in microevolution
of forest tree species.
XIV Congr. Int. Union
For. Res. Organ. Proc.,
Vol. 3, Sect. 22, p. 332­
345.
Shearer, R. C.
1960. Western larch seed dis­
persal over clear-cut
blocks in Northwestern
Montana. Mont. Acad.
Sci. Proc. 19: 130-134.
Silen, Roy R.
1962. Pollen dispersal consid­
erations for Douglas-fir.
J. For. 60: 790-795, illus.
Sorensen, Frank C.
1971. Estimate of self-fertility
in coastal Douglas-fir
from inbreeding studies.
Silvae Genet. 20: 115-120,
illus.
Squillace, A. E.
1967. Effectiveness of 400-foot
isolation around a slash
pine seed orchard. J.
For. 65: 823-824.
Strand, Lars
1957. Pollen dispersal. Sil vae
Genet. 6: 129-146.
Wang, Chi-Wu, Thomas 0. Perry,
and Albert G. Johnson
1960. Polfen dispersion of slash
pine (Pinus eUiottii
Engelm.) with special
reference to seed orchard
management. Sil vae Genet.
9: 78-86.
Wright, Jonathan W.
1952. Pollen dispersion of some
forest trees. USDA Forest
Serv. Northeast. Forest
Exp. Stn. Pap. 46, 42 p.,
illus. Upper Darby, Pa.
1962. Genetics of forest tree
improvement. FAO For.
& Forest Prod. Stud. No.
16, 399 p., illus. Food
& Agr. Organ. United
Nations, Rome.
Yocom, Herbert A.
1968. Shortleaf pine seed dis­
persal. J. For. 66: 442.
11
The mission of the PACIFIC NORTHWEST FOREST
AND RANGE EXP ERIMENT STATION is to provide the
knowledge, technology,
and alternatives for present and
future protection, management, and use of forest, range, and
related environments.
Within this overall mission, the Station conducts and
stimulates research to facilitate and to accelerate progress
toward the following goals:
1. Providing safe and efficient technology for inventory,
protection, and use of resources.
2. Development and evaluation of alternative methods
and levels of resource management.
3. Achievement of o ptimum sustained resource produc·
tivity consistent with maintaining a high quaHty forest
environment.
The area of research encompasses Oregon, Washington,
Alaska, and, in some cases, California, Hawaii, the Western
States, and the Nation. Results of the research will be made
available promptly. Project headquarters are at:
Fairbanks, Alaska
Portland, Oregon
Juneau, Alaska
Olympia, Washington
Bend, Oregon
Seattle, Washington
Corvallis, Oregon
Wenatchee, Washington
La Grande, Oregon