-
Molecular Ecology (2005)
14
, 2525–2537 doi: 10.1111/j.1365-294X.2005.02593.x
© 2005 Blackwell Publishing Ltd
Blackwell Publishing, Ltd.
Parentage versus two-generation analyses for estimating
pollen-mediated gene flow in plant populations
JAROSLAW BURCZYK and TOMASZ E . KORALEWSKI
Department of Genetics, Institute of Biology and Environmental
Protection, University of Bydgoszcz, 85–064 Bydgoszcz, Poland
Abstract
Assessment of contemporary pollen-mediated gene flow in plants
is important for variousaspects of plant population biology,
genetic conservation and breeding. Here, throughsimulations we
compare the two alternative approaches for measuring
pollen-mediatedgene flow: (i) the
NEIGHBORHOOD
model — a representative of parentage analyses, and (ii)
therecently developed
TWOGENER
analysis of pollen pool structure. We investigate their
prop-erties in estimating the effective number of pollen parents
(
N
ep
) and the mean pollen dis-persal distance (δδδδ
). We demonstrate that both methods provide very congruent
estimates of
N
ep
and δδδδ
, when the methods’ assumptions considering the shape of pollen
dispersal curveand the mating system follow those used in data
simulations, although the
NEIGHBORHOOD
model exhibits generally lower variances of the estimates. The
violations of the assumptions,especially increased selfing or
long-distance pollen dispersal, affect the two methodsto a
different degree; however, they are still capable to provide
comparable estimates of
N
ep
. The
NEIGHBORHOOD
model inherently allows to estimate both self-fertilization
andoutcrossing due to the long-distance pollen dispersal; however,
the
TWOGENER
method isparticularly sensitive to inflated selfing levels,
which in turn may confound and sup-press the effects of distant
pollen movement. As a solution we demonstrate that in case of
TWOGENER
it is possible to extract the fraction of intraclass correlation
that results fromoutcrossing only, which seems to be very relevant
for measuring pollen-mediated geneflow. The two approaches differ
in estimation precision and experimental efforts but theyseem to be
complementary depending on the main research focus and type of a
populationstudied.
Keywords
: effective number, gene flow,
neighborhood
model, paternity, pollen dispersal,
twogener
Received 25 November 2004; revision received 16 February 2005;
accepted 1 April 2005
Introduction
Gene flow within and among populations is an importantcomponent
of plant reproductive systems, affectingboth the genetic structure
and adaptation of populations(Rieseberg & Burke 2001; Lenormand
2002). Plants,especially forest trees, can disperse their genes
over largedistances via pollen (Hjelmroos 1991; Lindgren
et al
. 1995;Di-Giovanni
et al
. 1996; Nason
et al
. 1998; Rogers & Levetin1998). Therefore, studies of
pollen-mediated gene flowhave received much attention in recent
decades (Ellstrand1992; Sork
et al
. 1999; Hamrick & Nason 2000; Smouse &
Sork 2004). Direct assessment of contemporary, pollen-mediated
gene flow is important because it can provideinformation on a
population’s current dynamics and mayshed light on the ecological
constraints that affect pollendispersal (Sork
et al
. 1999).Several methods have been developed for directly
measuring pollen-mediated gene flow, most of whichrely on
paternity exclusion (Smith & Adams 1983; Devlin& Ellstrand
1990; Burczyk & Chybicki 2004) or paternityassignment
(Devlin
et al
. 1988; Chase
et al
. 1996; Dow &Ashley 1998; Streiff
et al
. 1999). However, paternity-basedmethods are usually laborious,
require highly variablegenetic markers, and are inherently limited
by not beingable to sample all potential fathers in large
continuouspopulations. Smouse
et al
. (2001) proposed the
twogener
Correspondence: Jaroslaw Burczyk, Fax: (+ 48-52)
360-82-06;E-mail: [email protected]
-
2526
J . B U R C Z Y K and T . E . K O R A L E W S K I
© 2005 Blackwell Publishing Ltd,
Molecular Ecology
, 14, 2525–2537
approach, which attempts to estimate the extent of
pollenmovement based on estimates of genetic differentiationamong
pools of pollen gametes effectively fertilizingovules of different
mother plants. Because the
twogener
approach requires less sampling and genotyping com-pared to
conventional paternity-based methods, it seemsto be an efficient
way to estimate long-distance gene flow incontinuous plant
populations (Sork
et al
. 2002a; Austerlitz
et al
. 2004).Smouse & Sork (2004) recently reviewed the
strengths
and weaknesses of paternity-based and
twogener
methods for estimating pollen-mediated gene flow.
Theseapproaches rely on different assumptions and may
yielddifferent estimates of gene flow. Although applications
ofpaternity-based methods suggest that much of the pollen-mediated
gene flow occurs over large distances (seeAdams & Burczyk 2000;
Hamrick & Nason 2000; Burczyk
et al
. 2004a; DiFazio
et al
. 2004; Smouse & Sork 2004 forreviews), the studies based
on
twogener
method suggestthat pollen-mediated gene flow is more restricted
(Dyer &Sork 2001; Smouse
et al
. 2001; Sork
et al
. 2002a; Smouse &Sork 2004; but see Robledo-Arnuncio
et al
. 2004). Thesedifferences may result from corresponding
differences inthe species or populations studied, assumptions used,
orthe contrasting statistics that were used to judge the degreeof
pollen flow (Smouse & Sork 2004). To resolve these
dis-crepancies, it would be desirable to compare both
approachesusing the same materials. This is difficult,
however,because paternity-based methods work best when largenumbers
of offspring are sampled from a few mothers,whereas the
twogener
approach works best when fewoffspring are sampled from a large
number of mothers(Smouse & Sork 2004). Although some authors
found thatestimates of pollen-mediated gene flow are similar
usingthe two methods (Austerlitz
et al
. 2004), they have not beencompared using computer simulations,
which allow bothmethods to be compared simultaneously under
controlledsettings.
In this study, we used computer simulations to comparethe
neighborhood
model (a representative of the paternity-based methods) (Adams
& Birkes 1991; Burczyk
et al
. 2002)with the
twogener
approach (Smouse
et al
. 2001). Wewere particularly interested in determining whether
bothmethods provide similar estimates of mean pollen disper-sal
distance and effective number of pollen parents. Wealso studied how
violations of the assumptions affected theaccuracy of the pollen
flow estimates. Although the
neigh-borhood
model and
twogener
approach were recentlymodified to address their previous
shortcomings (Austerlitz& Smouse 2002; Burczyk
et al
. 2002; Dyer
et al
. 2004), herewe deal only with the simplest versions of the
neighborhood
and
twogener
models (Adams & Birkes 1991; Smouse
et al
. 2001), which seems sufficient for the
straightforwardcomparison of the two methods.
Materials and methods
Detailed descriptions of the
neighborhood
model and
twogener
approach are available elsewhere (
neighborhood
model: Adams & Birkes 1991; Burczyk
et al
. 1996, 2002;
twogener
: Austerlitz & Smouse 2001a; Smouse
et al
. 2001;Sork
et al
. 2002a). In both methods, the paternal contri-bution (i.e.
pollen gamete haplotype) must be determinedfor a sample of viable
embryos collected from knownmother plants. These pollen haplotypes
must be measuredusing neutral genetic markers such as allozymes
ormicrosatellites. Both methods can be used in cases wherethe
paternal haplotype can be measured directly andunambiguously (e.g.
from the haploid megagametophyteof most conifers), or when the
paternal haplotype isambiguous (e.g. inferred from the genotypes of
the offspringembryo and female parent). In the latter case, the
paternalcontribution will be ambiguous when the mother andoffspring
are both heterozygotes and share the samealleles. To facilitate our
computer simulations, we assumedthat the paternal contributions
could be determinedunambiguously. Nevertheless, the outcomes of the
analysesare relevant to ambiguous assays as well.
NEIGHBORHOOD
model
In the
neighborhood
model, the minimum data setconsists of progeny haplotype arrays
(i.e. pollen gametes)sampled from several mother plants, the
genotypes of allindividuals (and their locations) within the local
populationthat could potentially sire sampled progeny, and
allelefrequencies in the surrounding populations that mightbe the
source of immigrant pollen gametes. In the
neighborhood
model, we assume that a measured pollengamete may originate from
one of three sources: (i) self-fertilization (in monoecious and
self-compatible plants)with probability
s
, (ii) pollination by a distant unknownfather located outside
the local population (neighbourhood)with probability
m
, and (iii) pollination by local andgenotyped father with
probability 1 –
s
–
m
. Therefore, theprobability of observing a particular pollen
gamete havinggenotype
g
i
is defined as:
(eqn
1)
where
P
(
g
i
|
M
),
P
(
g
i
|
B
) and
P
(
g
i
|
F
j
) are Mendelian trans-ition probabilities (Devlin
et al
. 1988; Adams 1992).
P
(
g
i
|
M
)is the probability that the pollen gamete having haplotype
g
i
comes from the mother having genotype
M
;
P
(
g
i
|
B
) isthe probability that the pollen gamete comes from a
distantand unknown father in the background population; and
P
(
g
i
|
F
j
) is the probability that the pollen gamete comesfrom one of
the
r
local fathers having genotype
F
j
.
P
(
g
i
|
B
)
P g s P g M m P g B s m P g Fi i i jj
r
i j( ) ( | ) ( | ) ( ) ( | )= ⋅ + ⋅ + − −=∑1
1
λ
-
P A R E N T A G E V S . T W O G E N E R
2527
© 2005 Blackwell Publishing Ltd,
Molecular Ecology
, 14, 2525–2537
is calculated as the product of the background allelefrequencies
of the alleles forming the pollen gamete haplo-type
g
i
. The parameter
λ
j
, which represents the relativemating success of the
j
-th father growing within theneighbourhood of the mother
plant
M
, is related to thedistance between the father and mother plants
accordingto the exponential distribution:
(eqn 2)
where
d
j
is the distance between the
j
-th father and themother plant, and
β
is the dispersal parameter thatdescribes the relationship
between the distance of pollendispersal within the neighbourhood
and individual malemating success (Adams 1992).
The likelihood function for
K
mother plants is
(eqn 3)
where
n
k
is the number of offspring sampled from the
k
-thmother. The parameters of interest (
s
,
m
,
β
) are estimatedusing maximum-likelihood methods. Once the
pollendispersal parameter (
β
) has been estimated, both the meaneffective pollen dispersal
and effective number of pollenparents within neighbourhoods may be
derived (Adams &Birkes 1991; Burczyk
et al
. 1996). The
neighborhood
modelappears to be useful for estimating gene flow parameters
inisolated and continuous populations (Burczyk
et al
. 1996,2004b; Latouche-Halle
et al
. 2004). Recent versions of the
neighborhood
model are well suited to ambiguous assaysand allow
pollen-mediated gene flow to be estimated simul-taneously with
background pollen pool allele frequencies(Burczyk
et al
. 2002; Burczyk & Chybicki 2004).
TWOGENER
The
twogener
model is a hybrid approach that combinestraditional paternity
analysis and genetic structure analysis(Smouse
et al. 2001). Mother plants scattered throughout thelandscape
are used to ‘sample’ different sets of pollen donors,and the
differentiation of pollen pools among the mothers(pollen structure)
is measured using the intraclass correlationcoefficient (ΦFT). The
intraclass correlation coefficient, whichis the correlation of male
gametes drawn at random fromthe same mother, relative to those
drawn at random fromthe population as a whole, is calculated using
analysisof molecular variance (amova, Excoffier et al. 1992). Ifone
assumes that ΦFT also estimates the probability thattwo paternal
alleles are identical by descent, then it can beused to estimate
the effective number of the pollen parents:
(eqn 4)
Austerlitz & Smouse (2001a) showed that assuming aspecific
function of pollen dispersal (bivariate normal orexponential), the
mean distance of pollen dispersal (δ) canbe estimated directly from
ΦFT provided that the sampledmothers are far enough apart (ideally
¥ > 5δ, yet ¥ > 3δ isreasonable, where ¥ is the mean distance
between mothers).The original twogener model has been recently
modifiedto overcome some of its initial shortcomings (Austerlitz
&Smouse 2002; Austerlitz et al. 2004; Dyer et al. 2004;
Smouse& Sork 2004).
Simulations
The neighborhood model and twogener approach useslightly
different sampling schemes. The optimal schemefor the twogener
approach is to sample a small number ofseeds from each of many
mothers (Austerlitz & Smouse2002), but in the neighborhood
model (and paternity-basedmethods in general), it is better to
sample more seeds fromfewer parents (Burczyk et al. 1996; Streiff
et al. 1999). Weused a sampling scheme that is reasonable for
bothapproaches. We generated 20 (= K) mothers and 50 (=
nk)successful pollen gametes for each mother, for a total of1000
offspring per simulation. All adults were distributedon a grid of 1
× 1 units. The maternal plants were organizedinto five groups
(similarly to Smouse et al. 2001), but thedistance between the
borders of the neighbouring groupswas set to 80 units and the
distance between the motherswithin each group was at least 10
units. In our simulations,the mean distance between the mothers was
¥ ≈ 117 units.Therefore, we met the ¥ > 5δ criterion (Austerlitz
& Smouse2001a) for the range of dispersal parameters used in
oursimulations (see Results) which enables estimating ofmean
distance of pollen dispersal (δ) directly from ΦFT. Forthe
neighborhood model, it would be difficult to use thissampling
density in practice, but it is feasible in computersimulations. For
the genetic data, we simulated fivemicrosatellite-like loci, each
of which had 10 alleles withfrequency of 0.1 (EP = 0.9996).
Genotypes were simulatedassuming Hardy–Weinberg equilibrium (HWE),
no linkage,no mutations, and no genotyping errors.
The generation of pollen gametes assumed that the com-position
of pollen pools from sampled mothers dependssolely on the distances
from the surrounding fathers, andthat pollen dispersal follows an
exponential distribution:
(eqn 5)
where x is the distance of pollen dispersal, and b is theslope
of the dispersal curve. This is a one-parameterexponential model
that can be considered a specific case ofthe more general
two-parameter exponential power modeloften used for pollen
dispersal studies (Austerlitz et al.2004). We chose the
one-parameter exponential distribution
λβ
βj
j
ll
r
d
d
exp
exp
=
=∑
1
L s m L s m P gkk
K
ii
n
k
K k( , , ) ( , , ) ( ),β β= =
= ==∏ ∏∏
1 11
ΦΦFT FT
.≈ ⇒ ≈1
21
2NN
epep
f x b bx( ) exp( ),= −
-
2528 J . B U R C Z Y K and T . E . K O R A L E W S K I
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
for its simplicity, and because this distribution has
alreadybeen integrated into paternity-based methods (equation
2)(Adams & Birkes 1991; Smouse et al. 1999) and the
twogenermodel (Austerlitz & Smouse 2001a; Smouse et al.
2001).Therefore, the method used to generate the data wasidentical
for both methods of gene flow analysis.
The function f (x) is the probability density distributionthat
describes the probability that a successful pollen gam-ete came
from an individual located at distance x. To usethis function for
generating data, we translated it into acumulative distribution
function C(u) that describes theprobability that pollen came from
males located at dis-tances from 0 to u (i.e. what proportion of
pollen pool camefrom males located at distances from 0 to u):
(eqn 6)
where P(x) is the probability density function that pollencame
from any father located at distance x:
(eqn 7)
Then, since
(eqn 8)
therefore
(eqn 9)
and finally
(eqn 10)
For each simulation, the first step was to place the motherson
the grid. The next step was to place the pollen donorson the grid.
While setting a paternal tree’s position, a C(u)value was generated
by choosing a random numberbetween 0 and 0.999999. Then, the
distance u was foundnumerically using equation (10). Next, an angle
was drawnas a random number between 0 and 360. The two values,i.e.
the distance from the maternal tree u, and the angle,were then used
to obtain the Cartesian coordinates of thepollen parent, which were
rounded to integers to matchthe 1 × 1 unit grid. Therefore, the
pollen dispersal distancewas not limited by the size of the virtual
population (e.g.100 × 100 individuals as in Smouse et al. 2001;
Austerlitzet al. 2004), and the maximum pollen dispersal
distancewas determined by the cumulative mating success of
allfathers. In our simulations, the maximum distance wasequal to
the radius of a circle delimiting an area from which
99.9999% of the pollen arrived (100% corresponds to infin-ity),
according to the distribution function.
After assigning the position of every pollen donor, theirdiploid
genotypes were generated as described above. Pol-len haplotypes
from each father were generated based onMendelian rules. When a
pollen parent was selected morethan once, the same diploid genotype
was used to generatenew pollen haplotypes. Because the species was
assumedto be monoecious, a mother was allowed to act as a
pollenparent for itself (self-fertilization) and for other
mothers.To comply with the methodology of the neighborhoodmodel,
the neighbourhood of every mother plant (about5.66 units in radius)
was populated with the remainingadults that were not chosen as
pollen donors during thegamete generation step. Therefore, the
neighbourhood foreach mother consisted of 100 adults as potential
fathers,which is consistent with typical neighborhood
modelanalyses. If the wide spacings we simulated were used inreal
field studies, 2000 adults would need to be genotyped(i.e. 100
adults/neighbourhood × 20 neighbourhoods),plus the offspring. For
the twogener model, in contrast, only20 adults would need to be
genotyped. Nevertheless, be-cause the sampling of mothers is
usually optimized inpaternity-based analyses, and because
overlapping neigh-bourhoods can be used, the number of adult
genotypesneeded is usually much less than 2000 (Burczyk et al.
1996;Streiff et al. 1999). For each combination of parameters,
200simulations were performed. The mean and standard devi-ation of
each parameter estimate was then calculated fromthese 200
replicates.
Offspring samples were generated under the followingscenarios:
(I) variable pollen dispersal (b = 0.1–1.0, by 0.1)with no selfing,
(II) variable pollen dispersal with randomselfing (probability of
selfing equal to the probability ofdispersal at distance 0), (III)
constant pollen dispersal(b = 0.5) but variable selfing (s = 0–0.5,
by 0.1). Finally, weintroduced long-distance pollen dispersal
(LDPD) (scenarioIV), which does not follow the exponential
distributionand whose origin is unknown. Here, because it is
veryunlikely to have two gametes originating from the samemale, we
generated the proportion (M) of pollen gametesrandomly based on the
prior allele frequency distribution,and then the remaining
proportion (1 – M) as describedearlier. M is the proportion of
pollen immigration thatcomes from outside of the local population,
whereas mis the immigration that comes from outside of the
localneighbourhood. Details on parameter values used in
eachscenario are given in the Results.
Parameter estimation
We wished to estimate mating parameters that could beeasily
compared between the two methods of gene flowanalysis. Therefore,
we chose to estimate and compare the
C u P x dx
u
( ) ( )=�0
P xxf x
xf x dx
bx bx
bx bx dx
( ) ( )
( )
exp( )
exp( )
.= =−
−
∞ ∞
� �0 0
�0
01 1
∞
∞− = − −
− =bx bx dx x
bbx
bexp( ) exp( )|
P x b x bx( ) exp( ),= −2
C u P x dx b x bx dx b ub
bu
u u
( ) ( ) exp( ) exp( )= = − = − −
− +� �
0 0
2 1 1
-
P A R E N T A G E V S . T W O G E N E R 2529
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
effective number of pollen parents and the mean pollendispersal
distance (NeNM and δNM for neighborhood model,and NeTG and δTG for
twogener) because these estimatesshould converge given the
assumptions we used. In thetwogener model, the mean pollen
dispersal distance δTGwas calculated using equation (11), which
assumes anexponential distribution and population density (d) of
1.0.Equation (11) was derived from the equations presentedby
Austerlitz & Smouse (2001a).
(eqn 11)
In the neighborhood model, the mean distance ofpollen dispersal
and effective number of pollen parentsare typically estimated using
outcross matings alone(Adams & Birkes 1991; Burczyk et al.
1996). To accountfor the contribution of the paternal trees growing
out-side the neighbourhood area, the mean distance of
pollendispersal (δNM) was extrapolated based on the shape ofpollen
dispersal function estimated within the neighbour-hood (i.e. based
on the estimate of β). Note that β is the esti-mator of b from
equation (5) (β = –b). The parameter δNMmight be calculated for all
matings at distances from 0 toinfinity (thus including selfing), as
the expected value of x:
(eqn 12)
However, for our simulations, we are interested in separ-ating
selfing from calculations of mean pollen dispersal.If t is the mean
distance that differentiates selfing fromoutcrossing, then the mean
distance of outcrossing pollencan be estimated as:
(eqn 13)
However, the distance t varies depending on the directionof the
location of fathers around a mother, and ranges fromt = 0.5, for
cardinal directions (0, 90, 180, 270 degrees), up tot = 0.71, for
noncardinal directions (45, 135, 225, 315). In oursimulations, the
mean t was close to 0.6. The estimates of meandistances of pollen
dispersal were compared to the actualdistances of pollen dispersal
generated in simulations.
In both models, the effective number of pollen parentscan be
estimated as the inverse of the probability of pater-nal identity
within maternal sibships. In the twogenermodel, the effective
number NeTG was calculated based onequation (4). Occasionally, when
the actual pollen disper-sal is extensive, ΦFT estimates might be
negative, which isgenerally interpreted as lack of pollen structure
(Robledo-Arnuncio et al. 2004). Although we preferred not to
restrictour estimates of ΦFT to positive values, it is unclear how
tointerpret estimates of Ne based on negative values of
ΦFT.Therefore, for the twogener model, the effective popula-tion
number of pollen parents NeTG was calculated based
on the mean value of ΦFT over the simulations, and thestandard
deviation of NeTG was calculated based on thestandard deviation of
ΦFT.
In the neighborhood model, we estimated the totaleffective
number of pollen parents (including selfing andpollen immigration
from outside of the neighbourhood)using the extrapolation proposed
by Burczyk et al. (1996):
(eqn 14)
where NeNM(k) is the effective number of pollen parentsaround
the k-th female, λj is the relative mating success ofthe j-th
father in the neighbourhood of that female basedon equation (2)
given the estimate of β, and s and m are thepopulation-wide
estimates of selfing and pollen immigrationfrom outside the
neighbourhood. The NeNM was averagedacross all females.
The NeTG and NeNM estimates were compared to theexpectation of
Nep. For random selfing (simulation scenarioII) and a uniform
distribution of individuals in space (withdensity d = 1), the
probability of paternal identity in asingle maternal sibship is
given by:
(eqn 15)
A more general expectation that would take into accountvariable
selfing (simulation scenarios I and III) and variableextents of
LDPD (scenario IV) can be obtained as follows:
(eqn 16)
where t is the mean distance that differentiates selfing
fromoutcrossing explained above.
The parameters of the neighborhood model were esti-mated based
on maximum-likelihood methods using theNewton–Raphson algorithm,
assuming that the allele fre-quencies in the background pollen pool
are identical to theprior allele frequencies used for generating
the data. Thetwo sets of parameter estimates were compared
betweenthe two methods and with the expected values. All
simu-lations were performed using a specific computer programn2g
written by T. E. K. in Object Pascal (Delphi 7, BorlandSoftware),
and is available from the authors upon request.
Results
Impact of the dispersal parameter
We conducted our first analyses assuming that the specieswas
self-incompatible (scenario I). The dispersal parameter
δπ
TG
FT
.=12
1
Φ
δβNM
( ) .= = −
∞
�0
2xP x dx
δ β ββNM
( ) ( ) .= = − + − + −
∞
−�t
xP x dx t t t1 221 2
N s s me k jNM( ) /[ ( ) ]= + − − ∑1 12 2 2λ
1 12 80
22
N xP x dx
b
ep
( ) .= =
∞
�π π
1 12
1
4
12
21
2 2 2
22 2
N xP x dx s M s
bbt
bts M s
ep t
( ) ( )
exp( ) ( )
=
⋅ − − +
=+
⋅ − − +
∞
�π
π
-
2530 J . B U R C Z Y K and T . E . K O R A L E W S K I
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
Tab
le 1
The
impa
ct o
f dis
pers
al p
aram
eter
b o
n ac
tual
mea
n po
llen
disp
ersa
l dis
tanc
e X,
exp
ecte
d ef
fect
ive
num
ber
of p
olle
n pa
rent
s N
ep a
nd m
atin
g pa
ram
eter
s ob
tain
ed th
roug
h th
en
eigh
borh
oo
d a
nd t
wo
gen
er m
odel
s, w
hen
self
-fer
tiliz
atio
n is
not
allo
wed
bN
epX
nei
ghbo
rho
od
two
gen
er
mβ
NeN
Mδ N
MΦ
FTN
eTG
δ TG
0.1
2530
.10
20.0
5 (0
.44)
0.89
0 (0
.011
)−0
.123
(0.0
62)
8242
.66
(172
7.16
)16
.35
(16.
45)
0.00
020
(0.0
0098
)24
93.3
3 (2
602.
00)
17.1
5 (1
7.49
)0.
264
4.15
10.0
6 (0
.22)
0.68
9 (0
.015
)−0
.205
(0.0
40)
962.
36 (9
4.07
)9.
85 (2
.40)
0.00
088
(0.0
0104
)56
7.21
(201
9.14
)12
.83
(16.
96)
0.3
294.
316.
75 (0
.13)
0.49
9 (0
.015
)−0
.302
(0.0
33)
337.
45 (2
3.15
)6.
72 (0
.81)
0.00
157
(0.0
0103
)31
9.31
(369
.45)
9.16
(8.4
8)0.
417
1.52
5.11
(0.1
1)0.
347
(0.0
15)
−0.3
99 (0
.029
)17
5.82
(11.
24)
5.13
(0.3
9)0.
0029
0 (0
.001
16)
172.
32 (8
2.23
)6.
15 (4
.92)
0.5
114.
494.
15 (0
.08)
0.23
4 (0
.013
)−0
.498
(0.0
26)
110.
29 (5
.75)
4.15
(0.2
2)0.
0046
7 (0
.001
22)
106.
39 (2
9.49
)4.
23 (0
.59)
0.6
83.3
93.
51 (0
.08)
0.15
5 (0
.012
)−0
.591
(0.0
26)
78.1
2 (4
.04)
3.54
(0.1
5)0.
0062
8 (0
.001
39)
79.6
8 (1
8.62
)3.
64 (0
.46)
0.7
64.5
73.
05 (0
.07)
0.10
1 (0
.010
)−0
.693
(0.0
26)
58.1
7 (2
.67)
3.06
(0.1
1)0.
0084
3 (0
.001
48)
59.3
0 (1
0.73
)3.
11 (0
.28)
0.8
52.3
32.
72 (0
.06)
0.06
5 (0
.008
)−0
.793
(0.0
26)
45.6
1 (2
.10)
2.71
(0.0
8)0.
0108
6 (0
.001
64)
46.0
3 (7
.11)
2.73
(0.2
1)0.
943
.93
2.46
(0.0
6)0.
042
(0.0
07)
−0.8
91 (0
.032
)37
.25
(2.0
1)2.
45 (0
.08)
0.01
345
(0.0
0188
)37
.16
(5.2
8)2.
45 (0
.17)
1.0
37.9
32.
26 (0
.04)
0.02
6 (0
.005
)−0
.986
(0.0
28)
31.2
6 (1
.30)
2.25
(0.0
6)0.
0157
0 (0
.001
84)
31.8
4 (3
.79)
2.26
(0.1
4)
NeN
M a
nd N
eTG
are
the
esti
mat
es o
f eff
ecti
ve n
umbe
r of p
olle
n pa
rent
s, δ
NM
and
δT
G a
re th
e es
tim
ates
of m
ean
polle
n di
sper
sal o
btai
ned
thro
ugh
the
nei
ghbo
rho
od
and
tw
oge
ner
mod
els,
re
spec
tive
ly; m
, pro
port
ion
of p
olle
n im
mig
rati
ng fr
om o
utsi
de o
f the
nei
ghbo
urho
ods;
β, t
he e
stim
ate
of d
ispe
rsal
par
amet
er; Φ
FT, i
ntra
clas
s co
rrel
atio
n of
mal
e ga
met
es w
ithi
n fe
mal
es;
stan
dard
dev
iati
ons
over
rep
licat
es in
par
enth
eses
.
(b) used in our simulations ranged from 0.1 to 1, whichcovers
extensive to very restricted pollen movement. Forexample, when b =
0.1, the actual mean dispersal distance(X) is about 20 units, and
nearly 90% of pollen gametes(m = 0.89) come from males located
outside of thedesignated neighbourhood (i.e. further than 5.66
units). Incontrast, when b = 1.0, X = 2.26 and m = 0.026 (Table 1).
Themean distance between mothers (¥ ≈ 117 units) was greaterthan 5X
(= 100.25 units) for the most extensive pollendispersal simulated
(b = 0.1). This allowed us to calculateNeTG directly from ΦFT using
equation (4) (Austerlitz &Smouse 2001a). The estimates of β
from the neighborhoodmodel were very close to b values we simulated
(notsignificantly different). The variance of < increases as
bdecreases because there a lower proportion of the localmatings
occurs within the neighbourhood (1 – m), and thisis the basis for
estimating β.
The mean dispersal distance estimates (>NM and
>TG)obtained through the neighborhood model and two-gener were
very similar to each other and were close to theactual dispersal
distances, X (Table 1). The rate of conver-gence of the estimates
to the actual values increased as bincreased. Nonetheless, as
estimates of >TG approached X(i.e. when b ≥ 0.5), the estimates
of >NM were nearly identi-cal to X, even for b ≥ 0.2 (Table 1).
Notably, the variances ofthe estimates increased as b decreased,
and they werelarger for twogener than for the neighborhood
model.
Our estimates of the effective number of pollen parents(NeNM and
NeTG) ranged from about 31, when b = 1.0, to acouple of thousands
when b = 0.1. The values of NeTG weresimilar to expectations (Nep),
whereas NeNM was significantlyoverestimated when b ≤ 0.2. Except
for b ≤ 0.2, the values ofNeNM and NeTG were very close to one
another and theexpected values (Nep). Nonetheless, the variances of
theestimates were larger for twogener than for the neighbor-hood
model. In addition, the variances of ΦFT were lowand relatively
stable across a range of b values. Given thegenetic information
content of our simulated data sets (i.e.1000 offspring, EP =
0.9996), the mating parameters arereasonably well estimated (i.e.
low coefficients of vari-ation) in the neighborhood model when b ≥
0.2, and intwogener when b ≥ 0.5.
For any given b, our estimates of ΦFT (Table 1) aremuch lower
than those reported by Smouse et al. (2001)(Fig. 3, therein). We
suppose that these authors simulatedtheir data sets in only one
dimension using equation (5), whichdoes not take into account that
(at any given distance) thereis a certain number of individuals
with the same matingprobability. In later publications, Smouse and
coworkersemployed two-dimensional pollen distributions
(Austerlitz& Smouse 2001a) that are comparable to our
simulations.
We repeated our simulations allowing for self-fertilization,the
frequency of which equals the probability of pollen dis-persal at
distance 0 (Table 2) (scenario II). Our simulated
-
P A R E N T A G E V S . T W O G E N E R 2531
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
Tab
le 2
The
im
pact
of
disp
ersa
l pa
ram
eter
b o
n ac
tual
mea
n di
sper
sal
dist
ance
X,
expe
cted
eff
ecti
ve n
umbe
r of
pol
len
pare
nts
Nep
and
mat
ing
para
met
ers
obta
ined
thr
ough
the
nei
ghbo
rho
od
and
tw
oge
ner
mod
els,
whe
n se
lf-f
erti
lizat
ion
is a
llow
ed b
Nep
X
nei
ghbo
rho
od
two
gen
er
sm
βN
eNM
δ NM
ΦFT
NeT
Gδ T
G
0.1
2513
.27
20.0
2 (0
.48)
0.00
2 (0
.001
)0.
889
(0.0
11)
−0.1
14 (0
.062
)80
44.3
7 (1
823.
91)
27.3
6 (2
8.76
)0.
0002
(0.0
010)
2340
.46
(244
5.36
)15
.93
(17.
70)
0.2
628.
329.
99 (0
.21)
0.00
7 (0
.002
)0.
685
(0.0
16)
−0.2
03 (0
.042
)93
5.89
(96.
62)
10.3
0 (2
.28)
0.00
06 (0
.001
0)78
9.91
(136
4.48
)14
.21
(16.
35)
0.3
279.
256.
68 (0
.15)
0.01
3 (0
.003
)0.
494
(0.0
17)
−0.3
02 (0
.033
)32
9.33
(24.
62)
6.71
(0.7
2)0.
0018
(0.0
011)
280.
47 (2
85.1
6)8.
45 (6
.17)
0.4
157.
085.
02 (0
.12)
0.02
2 (0
.004
)0.
341
(0.0
17)
−0.3
98 (0
.030
)16
9.29
(11.
06)
5.06
(0.3
8)0.
0030
(0.0
012)
168.
74 (8
2.73
)5.
67 (1
.78)
0.5
100.
534.
01 (0
.07)
0.03
3 (0
.005
)0.
226
(0.0
13)
−0.4
96 (0
.025
)10
4.44
(5.6
6)4.
04 (0
.19)
0.00
49 (0
.001
3)10
2.77
(30.
16)
4.18
(0.7
4)0.
669
.81
3.34
(0.0
7)0.
046
(0.0
06)
0.14
7 (0
.011
)−0
.595
(0.0
26)
71.9
9 (3
.80)
3.36
(0.1
4)0.
0069
(0.0
014)
72.1
5 (1
5.37
)3.
45 (0
.38)
0.7
51.2
92.
87 (0
.06)
0.05
9 (0
.007
)0.
095
(0.0
10)
−0.6
94 (0
.028
)53
.24
(2.7
1)2.
88 (0
.10)
0.00
93 (0
.001
6)53
.61
(9.3
7)2.
95 (0
.27)
0.8
39.2
72.
51 (0
.05)
0.07
6 (0
.008
)0.
060
(0.0
07)
−0.7
96 (0
.029
)40
.70
(1.9
6)2.
51 (0
.08)
0.01
23 (0
.001
7)40
.79
(5.7
2)2.
57 (0
.18)
0.9
31.0
32.
23 (0
.05)
0.09
3 (0
.008
)0.
038
(0.0
06)
−0.8
95 (0
.028
)32
.31
(1.5
8)2.
22 (0
.06)
0.01
51 (0
.001
9)33
.05
(4.2
2)2.
31 (0
.15)
1.0
25.1
32.
01 (0
.04)
0.10
9 (0
.010
)0.
024
(0.0
05)
−0.9
91 (0
.030
)26
.67
(1.3
5)2.
00 (0
.05)
0.01
85 (0
.002
0)27
.10
(2.9
6)2.
09 (0
.11)
Para
met
er d
escr
ipti
ons
as in
Tab
le 1
; s, t
he e
stim
ate
of s
elf-
fert
iliza
tion
; sta
ndar
d de
viat
ions
ove
r re
plic
ates
in p
aren
thes
es.
rates of self-fertilization ranged from 0.002 (at b = 0.1)
to0.109 (for b = 1.0). Therefore, the actual mean dispersaldistance
(including the fact that self-fertilization occursat the distance
0) decreased faster with increasing b. Ourestimates of the
effective number of pollen parents andmean dispersal distance also
decreased, and convergedclose to the expected values as b
decreased. The estimatesof NeNM were significantly overestimated
when b ≤ 0.2(Table 2). However, the accuracy of δ estimates
wasgreater, and the variances of Ne and δ lower for the
neigh-borhood model.
Impact of self-fertilization
To investigate the effect of self-fertilization upon
theparameter estimates, we simulated data sets with b set to0.5,
and allowed for s to vary from 0 to 0.5 at an interval of0.1
(scenario III). These analyses show that ΦFT increasesdramatically
as s increases (Table 3). The difference in ΦFTbetween s = 0 and s
= 0.5 was 25-fold. This resulted in acorresponding decrease in the
values of NeTG. Nevertheless,the estimates of the effective number
of pollen parents areclose to the expected values and similar
between theneighborhood model and twogener, although
twogenerproduced higher variances (Table 3). Although the
neigh-borhood model provided unbiased estimates of δNM,twogener
gave estimates of δTG that were biased down-wards. This is not
surprising because it is inappropriateto use equation (11) when the
levels of simulated self-fertilization exceed the level of selfing
expected from thedispersal curve at b = 0.5.
Because both s and b have a strong influence on ΦFT, wefurther
investigated their joint impact on the estimates ofΦFT. We
generated data samples for a combination of b(ranging from 0.1 to
1.0 at an interval of 0.1) and s (from 0to 0.5 at an interval of
0.05). We found that self-fertilizationhas a much stronger effect
upon ΦFT than did the mode ofpollen dispersal. ΦFT increased nearly
exponentially as sincreased (Fig. 1a). The proportional impact of
selfingseems to be greater when b is small. Interestingly, the
samevalues of ΦFT may be produced from very different
matingpatterns. For example, ΦFT was about 0.046 when bequalled 0.5
and s equalled 0, but also when b equalled 0.1and s equalled 0.10.
Nonetheless, the estimates of pollendispersal under these scenarios
were quite different (4.15and 17.98, respectively).
Impact of long-distance pollen dispersal
In other simulations, we permitted long-distance pollendispersal
(LDPD) that does not follow the exponentialdistribution and whose
origin is unknown (scenario IV).Assuming no selfing, we generated
data samples for acombination of b (ranging from 0.1 to 1.0 at an
interval of
-
2532 J . B U R C Z Y K and T . E . K O R A L E W S K I
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
Tab
le 3
The
im
pact
of
self
-fer
tiliz
atio
n (S
) on
act
ual
mea
n di
sper
sal
dist
ance
X,
expe
cted
eff
ecti
ve n
umbe
r of
pol
len
pare
nts
Nep
and
mat
ing
para
met
ers
obta
ined
thr
ough
the
nei
ghbo
rho
od
and
tw
oge
ner
mod
els,
whe
n di
sper
sal p
aram
eter
b =
0.5
SN
epX
nei
ghbo
rho
od
two
gen
er
sm
βN
eNM
δ NΜ
ΦFT
NeT
Gδ T
G
0.00
114.
494.
15 (0
.08)
—0.
234
(0.0
13)
−0.4
98 (0
.026
)11
0.29
(5.7
5)4.
15 (0
.22)
0.00
47 (0
.001
2)10
6.39
(29.
49)
4.23
(0.5
9)0.
1058
.56
3.73
(0.0
8)0.
1000
(0.0
005)
0.21
1 (0
.013
)−0
.498
(0.0
32)
57.6
3 (1
.50)
3.75
(0.2
5)0.
0079
(0.0
014)
63.3
2 (1
1.33
)3.
21 (0
.29)
0.20
21.9
33.
33 (0
.08)
0.20
00 (0
.000
5)0.
188
(0.0
11)
−0.4
96 (0
.032
)21
.84
(0.2
0)3.
35 (0
.21)
0.02
12 (0
.001
8)23
.57
(1.9
8)1.
94 (0
.08)
0.30
10.6
12.
90 (0
.08)
0.29
99 (0
.000
4)0.
164
(0.0
12)
−0.5
02 (0
.032
)10
.58
(0.0
4)2.
90 (0
.17)
0.04
52 (0
.002
8)11
.07
(0.6
8)1.
33 (0
.04)
0.40
6.13
2.48
(0.0
7)0.
4000
(0.0
004)
0.13
9 (0
.010
)−0
.493
(0.0
34)
6.12
(0.0
2)2.
53 (0
.16)
0.07
92 (0
.003
8)6.
31 (0
.30)
1.00
(0.0
2)0.
503.
962.
08 (0
.06)
0.49
99 (0
.000
3)0.
117
(0.0
09)
−0.4
95 (0
.038
)3.
96 (0
.01)
2.10
(0.1
5)0.
1238
(0.0
050)
4.04
(0.1
6)0.
80 (0
.02)
Para
met
er d
escr
ipti
ons
as in
Tab
les
1 an
d 2;
sta
ndar
d d
evia
tion
s ov
er r
eplic
ates
in p
aren
thes
es.
0.1) and M (from 0 to 0.5, at an interval of 0.05) (Fig. 2a).
Theimpact of M upon ΦFT is evident, and leads to lowerestimates of
ΦFT. Therefore, if LDPD occurs, this will resultin lower estimates
of ΦFT and increased estimates of Ne.In any case, if LDPD occurs,
the mean dispersal distancecannot be estimated reliably using
either twogener or theneighborhood model.
We also generated data samples for a combination of sand M (both
ranging from 0 to 0.45 at an interval of 0.05)with a constant b (=
0.1; Fig. 2b). Under these conditions,LDPD has a minor effect on
ΦFT, as compared to the effectof selfing. Nevertheless, when we
included either selfing orLDPD in our simulations, the neighborhood
model andtwogener both provided estimates of the effective numberof
pollen parents that were not significantly different fromthe
expected values (Nep) (Tables 3 and 4).
Discussion
Previous applications of twogener focused on theeffective number
of pollen parents and resulting effectivepollen dispersal distance
(Smouse et al. 2001; Sork et al.2002a; Austerlitz et al. 2004). In
contrast, paternity-basedanalyses emphasized the contribution of
long-distancepollen flow and mean pollen dispersal distance
(Burczyket al. 1996; Chase et al. 1996; Streiff et al. 1999; Lian
et al. 2001).Whereas the first perspective is important for
evolutionarygeneticists, the second is more familiar to plant
biologists,conservationists, and plant breeders.
Despite their differences, the neighborhood and two-gener models
provide comparable estimates of effectivenumber of pollen parents.
Furthermore, they may providecomparable estimates of mean pollen
dispersal distance,given the assumptions on modes of pollen
dispersal areappropriate. The neighborhood model provided
lowervariances of the parameter estimates, but more potentialpollen
parents would need to be genotyped (greatergenetic information
content). Under such sampling,maximum-likelihood methods should
always have smallervariances for a given parameter combination.
Estimates of NeNM are biased upwards when pollendispersal is
extensive (b ≤ 0.2, Tables 1 and 2) becausepollen contributions
from outside of the neighbourhoodsare ignored in equation (14).
Equation (14) is based onthe assumption that background pollination
occursrandomly with an infinite number of potential pollenparents.
Therefore, the values derived from equation (14)might be considered
an upper bound of the effectivenumber of pollen parents (Burczyk et
al. 1996). Neverthe-less, because equation (14) appears to be
accurate forestimating the effective numbers reduced due to
selfingor restricted pollen dispersal, it should be appropriatewhen
precise estimates are needed (i.e. genetic conserva-tion
programs).
-
P A R E N T A G E V S . T W O G E N E R 2533
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
Impact of self-fertilization
Self-fertilization might affect the estimates of ΦFT
(Austerlitz& Smouse 2001a, b) because selfing strongly affects
theprobability of identity by descent (IBD). The need tointegrate
selfing into the estimation of ΦFT has already beenemphasized
(Austerlitz et al. 2004; Smouse & Sork 2004).In practice,
self-fertilization might be only weakly relatedto the probability
of pollination at the distance 0. Selfing
in different taxa depends on a number of ecological andgenetic
determinants, including population density, theavailability of
self-pollen, synchronization between maleand female flowering, and
self-fertility (Schnabel 1998;Boshier 2000). Although selfing might
be reduced throughthe post-zygotic selection, several authors
demonstratedthat selfing varies among individuals within
populations.Therefore, we further explored the impact of selfing
levelon the parameter estimates produced by both models.
Fig. 1 Impact of dispersal parameter and self-fertilization upon
the total intraclass correlation, ΦFT (a), and the intraclass
correlationresulted from outcrossing, ( b).′ΦFT
Fig. 2 The impact of long-distance pollen dispersal and
dispersal parameter (a) and selfing (b) upon the total intraclass
correlation, ΦFT.Note the scale difference between the two
graphs.
-
2534 J . B U R C Z Y K and T . E . K O R A L E W S K I
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
It would be interesting to determine the fraction of ΦFTthat
results from outcross matings. The data sets used forthe twogener
method can be readily used to estimate self-ing (Ritland 2002).
These estimates might then be used toadjust the estimates of ΦFT so
they reflect outcross matingsonly. We may use the reasoning
outlined by Burczyk et al.(1996). The effective number of pollen
parents can beestimated as according to Crow & Kimura
(1970):
(eqn 17)
where φj is the contribution of the j-th pollen parent to
theoffspring. Therefore is the probability that two gametescome
from the j-th father, and Σ φj = 1. Let one of the φjdenote the
proportion of selfing (s), and the remaining φjparameters denote
outcrossing: , where isan adjusted outcrossing contribution that
still sum to unity
. Separating selfing from outcrossing, thedenominator of
equation (17) is
(eqn 18)
Since for twogener Ne = 1/(2ΦFT), we may relate the
twodenominators:
(eqn 19)
The last component on the far right-hand side ( )might be used
in equation (17) to estimate the Ne that resultsonly from
outcrossing. Thus, by analogy: ,where is the intraclass correlation
of outcross matings.Substituting it to equation (19), we may
calculate basedon ΦFT and selfing:
(eqn 20)
which might be then used to approximate the mean pollendispersal
for outcross mating, using various types of
dispersal functions (Austerlitz & Smouse 2001a; Austerlitzet
al. 2004). This parameter is comparable to the correlationof
paternity, as presented by Ritland (1989).
We used equation (20) to estimate for simulated datasets shown
on Fig. 1a. Then, the relationship between and b appeared to be
uniform across a range of selfinglevels, and, in fact, it always
approximated the relationshipas when s = 0 (Fig. 1b). Although the
variance of isslightly larger with higher s values, it is primarily
causedby the reduced proportion of outcrossed offspring (1 – s)that
is used for estimating ΦFT.
Self-fertilization rates observed in the seed or seedlingstage
might be reduced at later life stages (Williams &Savolainen
1996). In these cases, the estimates of pollen dis-persal based on
seed samples might underestimate theeffective pollen dispersal that
would reflect the populationstructure at later life stages. For
these reasons, it is valuableto estimate pollen dispersal distance
based on outcrossmatings only. Although this is an inherent feature
of theneighborhood model, it can also be done using twogener.
Robledo-Arnuncio et al. (2004) in one of the studied Scotspine
populations found s = 0.068, while ΦFT = 0.004 (andNe = 125). Based
on equation (20), we can estimate =0.00194, which gives the
effective number of outcrossingpollen parents equal to = 257,
double the estimate of Ne.A contrasting example would be that by
Sork et al. (2002a),who investigated pollen movement in a
population ofQuercus lobata. They estimated ΦFT = 0.136, which
translatesto Ne = 3.68 individuals. The selfing level observed in
theseed sample was low, s = 0.04 (Sork et al. 2002b). Usingequation
(20), we can calculate the that results solelyfrom outcrossing. In
this case, it is even lower than ΦFT( = 0.1467, = 3.41). This is
not surprising becausewe expect an equilibrium stage to exist:
(eqn 21)
Substituting with equation (20), we see that the equi-librium is
attained when
Table 4 The impact of selfing (s) and long-distance pollen
dispersal (M) on expected effective number of pollen parents Nep
and theestimates of mating parameters obtained through the
neighborhood and twotener models, when dispersal parameter b =
0.5
S M Nep
neighborhood twogener
m β NeNM ΦFT NeTG
0.00 0.00 114.49 0.234 (0.013) −0.498 (0.026) 110.29 (5.75)
0.0047 (0.0012) 106.39 (29.49)0.10 0.10 64.14 0.289 (0.013) −0.494
(0.029) 63.43 (1.48) 0.0071 (0.0014) 70.45 (13.97)0.10 0.30 76.08
0.440 (0.011) −0.501 (0.035) 75.21 (1.45) 0.0057 (0.0012) 87.54
(19.30)0.30 0.10 10.74 0.240 (0.010) −0.498 (0.035) 10.72 (0.04)
0.0445 (0.0026) 11.23 (0.66)0.30 0.30 10.94 0.394 (0.009) −0.497
(0.036) 10.93 (0.03) 0.0436 (0.0026) 11.46 (0.70)
Parameter descriptions as in Table 1; standard deviations over
replicates in parentheses.
Ne jj
J
==∑1 2
1
φ
φ j2
φ φj js ( )= − ′1 ′φ j
( )Σ ′ =φ j 1
φ φ φjj
J
jj
J
jj
J
s s s s21
2
1
12 2 2 2
1
1
1 1= =
−
=
−
∑ ∑ ∑= + − ′ = + − ′ [( ) ] ( )
2 12 2 21
1
ΦFT ( )= + − ′=
−
∑s s jj
J
φ
∑ ′=−
jJ
j11 2φ
2 11 2′ = ∑ ′=
−ΦFT jJ
jφ′ΦFT
′ΦFT
′ =−
−Φ
ΦFT
FT
( )22 1
2
2
ss
′ΦFT′ΦFT
′ΦFT
′ΦFT
′N e
′ΦFT
′ΦFT ′N e
∆Φ Φ ΦFT FT FT = − ′ = 0
′ΦFT
-
P A R E N T A G E V S . T W O G E N E R 2535
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
(eqn 22)
The far right-hand side of the equation equals the
inbreedingcoefficient under equilibrium and partial selfing
(Hedrick1999; p. 190). ∆ΦFT will be greater than zero (and
greaterthan Ne) when 2ΦFT < s/(2 – s), as in the example
ofRobledo-Arnuncio et al. (2004). Otherwise, when 2ΦFT > s/(2 –
s), ∆ΦFT will be negative, leading to a decrease in (asin Sork et
al. 2002a, b). The impact of ΦFT and s upon ∆ΦFTis demonstrated in
Fig. 3.
Impact of long-distance pollen dispersal
Several empirical studies demonstrated that the shape ofthe
exponential pollen dispersal curve in local populationscannot
explain the high levels of pollen immigration fromoutside (Burczyk
et al. 1996; Dow & Ashley 1998; Streiffet al. 1999;
Oddou-Muratorio et al. 2003). Pollen dispersalby wind is a complex
phenomenon (Di-Giovanni & Kevan1991). Although some proportion
of the pollen dispersedwithin populations might be described by
mathematicallysimple dispersal curves, some pollen might be
dispersedover large distances at random. In large continuous
popu-lations of wind-pollinated species (such as temperate
foresttrees), pollen movement is partly driven by turbulence
thatlifts pollen over the canopy of a population, where mildwinds
are then able to carry pollen over large distances(Di-Giovanni
& Kevan 1991; Lindgren et al. 1995). Examplesof long and
intensive pollen dispersal are also known
among animal-pollinated trees (Chase et al. 1996; Nason
&Hamrick 1997; Konuma et al. 2000).
Let’s assume that a considerable proportion of the pollencomes
from a very restricted number of fathers, and therest of the pollen
comes from a potentially infinite pool offathers. Based on equation
(17), this situation will lead torelatively low effective numbers
of fathers anyway. Forexample, let five fathers contribute to the
next generationequally (i.e. φj = 0.1 for pollen parent), and let
the rest ofpollen (50%) come from an infinite number of fathers.
Basedon equation (17), the resulting Ne cannot be greater than
20.If 50% of the pollen results from LDPD, then how informativeis
Ne or ΦFT for estimating the extent of pollen movement?
Both Ne and ΦFT are composite summary statistics, whichcan be
the same for very different mating scenarios. Look-ing at estimates
of ΦFT, we do not know the reason for highor low intraclass
correlation. It could be selfing, correlatedpaternity, or LDPD. We
can easily imagine that there mightbe data examples with selfing s
= 0.2 and some proportionof pollen coming from a great distance
(say M = 0.40). ThenΦFT ≈ 0.02 (Fig. 2b), which is equivalent to Ne
= 25. In ourvirtual experiment, the same values of ΦFT and Ne may
beobtained when there is no selfing and no LDPD (s = M = 0)and when
b = 1.15; a pattern of a very restricted pollen dis-persal. Ne is a
parameter of general interest and utility fordemography and
genetics of populations, and it is usefulin a number of theoretical
and practical considerations.However, the estimates of ΦFT or Ne
alone are inadequateto describe the details of mating patterns and
gene flow.The difficulties arise from estimating the average
dispersaldistance from ΦFT, when factors like selfing, LDPD,
oreffective density impose problems. LDPD will certainlypose a
problem for estimating the average distance ofpollen dispersal, not
only in twogener, but also the neigh-borhood model.
We compared the simplest versions of the two methodsunder
optimum assumptions: categorical assignment, largeoffspring
samples, highly informative markers, lack ofgenotyping problems,
uniform male fertility, and an expon-ential dispersal function. In
the real world, the two methodsmight behave differently. Genotyping
problems mightinflate the levels of long-distance pollen dispersal
as esti-mated in the neighborhood model (Burczyk et al. 2004a),but
it might have a minor effect upon ΦFT. Variable malefertility
reduces the ‘effective density’ (sensu Austerlitz &Smouse 2002)
of pollen donors, which in turn affects theestimates of mean
dispersal distance. Variable flowerphenology may further increase
differentiation of pollen poolsamong females, leading to decreased
estimates of Ne andunderestimates of δ. Recent developments of
twogenerallow one to estimate the shape parameter of the
dispersalfunction jointly with the ‘effective density’ (Austerlitz
et al.2004). In the case of Quercus lobata, this yielded a
muchlarger average pollination distance (> = 300 m) compared
22
ΦFT =
−s
s
Fig. 3 The impact of total intraclass correlation, ΦFT, and
selfingupon the difference between the total and outcross
intraclasscorrelations ∆ΦFT (= ΦFT – ). The shaded area indicates
∆ΦFT < 0.′ΦFT
′Ne
′Ne
-
2536 J . B U R C Z Y K and T . E . K O R A L E W S K I
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
to the case in which the density was estimated from popu-lation
counts (> ≅ 100 ÷ 120 m) (Sork et al. 2002a; Austerlitzet al.
2004). On the other hand, some of the male fertilitycovariates can
be incorporated into the neighborhoodmodel to account for the
variable male fertilities (Burczyket al. 1996, 2002; Burczyk &
Prat 1997).
The distribution of pollen dispersal is also generallyunknown,
but the shape of the pollen dispersal functionhas to be assumed for
either model. However, as indicatedby Austerlitz et al. (2004),
testing various dispersal func-tions is feasible in twogener, but
the mating models havethe advantage of making possible the
evaluation of fit ofdata to resulting log-likelihoods, which is not
possible intwogener. Some of the assumptions mentioned above,along
with ambiguous genetic assignment, could be testedin future using
computer simulations.
Acknowledgements
We are grateful to Igor Chybicki, Glenn Howe, Peter Smouse
andJuan Jose Robledo-Arnuncio for helpful discussions, commentsand
suggestions that improved the manuscript.
ReferencesAdams WT (1992) Gene dispersal within forest tree
populations.
New Forests, 6, 217–240.Adams WT, Birkes DS (1991) Estimating
mating patterns in forest
tree populations. In: Biochemical Markers in the
PopulationGenetics of Forest Trees (eds Fineschi S, Malvolti ME,
Cannata F,Hattemer HH), pp. 157–172. SPB Academic Publishing,
TheHague, The Netherlands.
Adams WT, Burczyk J (2000) Magnitude and implications of
geneflow in gene conservation reserves. In: Forest
ConservationGenetics: Principles and Practice (eds Young A, Boshier
D, BoyleT), pp. 215–224. CSIRO Publishing, Collingwood,
Australia.
Austerlitz F, Smouse PE (2001a) Two-generation analysis of
pollenflow across a landscape. II. Relation between ΦFT, pollen
disper-sal and interfemale distance. Genetics, 157, 851–857.
Austerlitz F, Smouse PE (2001b) Two-generation analysis of
pollenflow across a landscape. III. Impact of adult population
struc-ture. Genetic Research, 78, 271–280.
Austerlitz F, Smouse PE (2002) Two-generation analysis of
pollenflow across a landscape. IV. Estimating the dispersal
parameter.Genetics, 161, 355–363.
Austerlitz F, Dick CW, Dutech C et al. (2004) Using
geneticmarkers to estimate the pollen dispersal curve. Molecular
Ecology,13, 937–954.
Boshier DH (2000) Mating systems. In: Forest Conservation
Genetics:Principles and Practice (eds Young A, Boshier D, Boyle T),
pp. 63–79. CSIRO Publishing, Collingwood, Australia.
Burczyk J, Prat D (1997) Male reproductive success in
Pseudotsugamenziesii (Mirb.) Franco: the effect of spatial
structure andflowering characteristics. Heredity, 79, 638–647.
Burczyk J, Chybicki IJ (2004) Cautions on direct gene flow
estima-tion in plant populations. Evolution, 58, 956–963.
Burczyk J, Adams WT, Shimizu JY (1996) Mating patterns andpollen
dispersal in a natural knobcone pine (Pinus attenuataLemmon.)
stand. Heredity, 77, 251–260.
Burczyk J, Adams WT, Moran GF, Griffin AR (2002) Complexpatterns
of mating revealed in a Eucalyptus regnans seed orchardusing
allozyme markers and the neighbourhood model.Molecular Ecology, 11,
2379–2391.
Burczyk J, DiFazio SP, Adams WT (2004a) Gene flow in
foresttrees: how far do genes really travel ? Forest Genetics, 11,
179–192.
Burczyk J, Lewandowski A, Chalupka W (2004b) Local pollen
dis-persal and distant gene flow in Norway spruce (Picea abies
[L.]Karst.). Forest Ecology and Management, 197, 39–48.
Chase M, Kesseli R, Bawa K (1996) Microsatellite markers
forpopulation and conservation genetics of tropical trees.
AmericanJournal of Botany, 83, 51–57.
Crow JF, Kimura M (1970) An Introduction to Population
GeneticsTheory. Harper and Row, New York.
Devlin B, Ellstrand NC (1990) The development and application
ofa refined method for estimating gene flow angiospermpaternity
analysis. Evolution, 44, 248–259.
Devlin B, Roeder K, Ellstrand NC (1988) Fractional
paternityassignment: theoretical development and comparison to
othermethods. Theoretical and Applied Genetics, 76, 369–380.
DiFazio SP, Slavov GT, Burczyk J, Leonardi S, Strauss SH
(2004)Gene flow from tree plantations and implications for
transgenicrisk assessment. In: Plantation Forest Biotechnology for
the 21stCentury (eds Walter C, Carson M), pp. 405–422. Research
Sign-post, Kerala, India.
Di-Giovanni F, Kevan PG (1991) Factors affecting pollen
dynamicsand its importance to pollen contamination: a review.
CanadianJournal of Forest Research, 21, 1155–1170.
Di-Giovanni F, Kevan PG, Arnold J (1996) Lower planetaryboundary
layer profiles of atmospheric conifer pollen above aseed orchard in
northern Ontario, Canada. Forest Ecology andManagement, 83,
87–97.
Dow BD, Ashley MV (1998) High levels of gene flow in bur
oakrevealed by paternity analysis using microsatellites. Journal
ofHeredity, 89, 62–70.
Dyer RJ, Sork VL (2001) Pollen pool heterogeneity in
shortleafpine, Pinus echinata Mill. Molecular Ecology, 10,
859–866.
Dyer RJ, Westfall RD, Sork VL, Smouse PE (2004)
Two-generationanalysis of pollen flow across a landscape V: a
stepwiseapproach for extracting factors contributing to pollen
structure.Heredity, 92, 204–211.
Ellstrand NC (1992) Gene flow by pollen: implications for
plantconservation genetics. Oikos, 63, 77–86.
Excoffier L, Smouse PE, Quattro JM (1992) Analysis of
molecularvariance inferred from metric distances among DNA
haplo-types: application to human mitochondrial DNA
restrictiondata. Genetics, 131, 479–491.
Hamrick JL, Nason JD (2000) Gene flow in forest trees. In:
ForestConservation Genetics: Principles and Practice (eds Young
A,Boshier D, Boyle T), pp. 81–90. CSIRO Publishing, Colling-wood,
Australia.
Hedrick PW (1999) Genetics of Populations. Jones and
BartlettPublishers, Boston.
Hjelmroos M (1991) Evidence of long-distance transport of
Betulapollen. Grana, 30, 215–228.
Konuma A, Tsumura Y, Lee CT, Lee SL, Okuda T (2000) Estima-tion
of gene flow in the tropical-rainforest tree Neobalanocarpusheimii
(Dipterocarpaceae), inferred from paternity analysis.Molecular
Ecology, 9, 1843–1852.
Latouche-Halle C, Ramboier A, Bandou E, Caron H, Kremer A(2004)
Long-distance pollen flow and tolerance to selfing in aNeotropical
tree species. Molecular Ecology, 13, 1055–1226.
-
P A R E N T A G E V S . T W O G E N E R 2537
© 2005 Blackwell Publishing Ltd, Molecular Ecology, 14,
2525–2537
Lenormand T (2002) Gene flow and the limits to natural
selection.Trends in Ecology & Evolution, 17, 183–189.
Lian CL, Miwa M, Hogetsu T (2001) Outcrossing and
paternityanalysis of Pinus densiflora ( Japanese red pine) by
microsatellitepolymorphism. Heredity, 87, 88–98.
Lindgren D, Paule L, Shen XH et al. (1995) Can viable pollen
carryScots pine genes over long distances ? Grana, 34, 64–69.
Nason JD, Hamrick JL (1997) Reproductive and genetic
conse-quences of forest fragmentation: two case studies of
Neotropicalcanopy trees. Journal of Heredity, 88, 264–276.
Nason JD, Herre EA, Hamrick JL (1998) The breeding structure ofa
tropical keystone plant resource. Nature, 391, 685–687.
Oddou-Muratorio S, Houot M-L, Demesure-Musch B, Austerlitz
F(2003) Pollen flow in the wildservice tree, Sorbus torminalis
(L.)Crantz. I. Evaluating the paternity analysis procedure in
contin-uous populations. Molecular Ecology, 12, 3427–3439.
Rieseberg LH, Burke JM (2001) The biological reality of
species:gene flow, selection, and collective evolution. Taxon, 50,
47–67.
Ritland K (1989) Correlated matings in the partial selfer
Mimulusguttatus. Evolution, 43, 848–859.
Ritland K (2002) Extensions of models for the estimation of
matingsystems using n independent loci. Heredity, 88, 221–228.
Robledo-Arnuncio JJ, Smouse PE, Gil L, Alia R (2004)
Pollenmovement under alternative silvicultural practices in
nativepopulations of Scots pine (Pinus sylvestris L.) in central
Spain.Forest Ecology and Management, 197, 245–255.
Rogers CA, Levetin E (1998) Evidence of long-distance
transportof mountain cedar pollen into Tulsa, Oklahoma.
InternationalJournal of Biometeorology, 42, 65–72.
Schnabel A (1998) Parentage analysis in plants: mating
systems,gene flow, and relative fertilities. In: Advances in
MolecularEcology (ed. Carvalho GR), pp. 173–189. IOS Press,
Amsterdam,The Netherlands.
Smith DB, Adams WT (1983) Measuring pollen contamination
inclonal seed orchards with the aid of genetic markers. In:
Proceed-ings of the 20th Southern Forest Tree Improvement
Conference,pp. 69–77, University of Georgia, Athens, Greece.
Smouse PE, Sork VL (2004) Measuring pollen flow in forest
trees:
an exposition of alternative approaches. Forest Ecology
andManagement, 197, 21–38.
Smouse PE, Meagher T, Kobak C (1999) Parentage analysis
inChamaelirium luteum (L.) Gray (Liliaceae): why do some maleshave
higher reproductive contributions? Journal of EvolutionaryBiology,
12 (6), 1069–1077.
Smouse PE, Dyer RJ, Westfall RD, Sork VL (2001)
Two-generationanalysis of pollen flow across a landscape. I. Male
gameteheterogeneity among females. Evolution, 55, 260–271.
Sork VL, Nason J, Campbell DR, Fernandez JF (1999)
Landscapeapproaches to historical and contemporary gene flow in
plants.Trends in Ecology & Evolution, 14 (6), 219–224.
Sork VL, Davis F, Smouse PE et al. (2002a) Pollen movement
indeclining populations of California valley oak, Quercus
lobata:where have all the fathers gone? Molecular Ecology, 11,
1657–1668.
Sork VL, Dyer RJ, Davis FW, Smouse PE (2002b) Mating patternsin
a savanna population of valley oak (Quercus lobata Neé).
In:Proceedings of the Fifth Symposium on Oak Woodlands: Oaks
inCalifornia’s Changing Landscape, October 22–25, 2001 (eds
StandifordR, McCreary D, Purcell KL), pp. 427–439. Pacific SW
ResearchStation, US Forest Service, USDA, San Diego,
California.
Streiff R, Ducousso A, Lexer C, Steinkellner H, Gloessl J,
Kremer A(1999) Pollen dispersal inferred from paternity analysis in
amixed oak stand of Quercus robur L. and Q. petraea (Matt.)
Liebl.Molecular Ecology, 8, 831–841.
Williams CG, Savolainen O (1996) Inbreeding depression in
conifers:implications for breeding strategy. Forest Science, 42,
102–117.
Jarek Burczyk is particularly interested in estimating
andmodelling mating patterns and gene flow in natural and
breedingplant populations. Tomasz Koralewski has interests in
creatingand using computer simulation means to address and
elucidatebiological (population genetics in particular) issues. He
also wrotethe nzg computer program. Anyone wishing to contact
himshould email: [email protected]
-
本文献由“学霸图书馆-文献云下载”收集自网络,仅供学习交流使用。
学霸图书馆(www.xuebalib.com)是一个“整合众多图书馆数据库资源,
提供一站式文献检索和下载服务”的24 小时在线不限IP
图书馆。
图书馆致力于便利、促进学习与科研,提供最强文献下载服务。
图书馆导航:
图书馆首页 文献云下载 图书馆入口 外文数据库大全 疑难文献辅助工具
http://www.xuebalib.com/cloud/http://www.xuebalib.com/http://www.xuebalib.com/cloud/http://www.xuebalib.com/http://www.xuebalib.com/vip.htmlhttp://www.xuebalib.com/db.phphttp://www.xuebalib.com/zixun/2014-08-15/44.htmlhttp://www.xuebalib.com/
Parentage versus two-generation analyses for estimating
pollen-mediated gene flow in plant populations.学霸图书馆link:学霸图书馆