Parental GCA testing: How many crosses per
parent?
G.R. Johnson
i\bstract: The in1pact of increasing the nun1ber of crosses per parent
(k) on the efficiency of roguing seed orchards
(backwm..ds selection, i.e .. reselection of pm_.cntsl was examined by using lvfontc Carlo simulation. Efficiencies \Vere examined
in light of advanced-generation l)ouglas-fir
(Pseudotsuga n7en::.iesii
(fl,firb.) Franco) tree in1proven1ent prograrns where
infonnation is available frorn previous generations, seed orchards have reduced genetic variation as a result of selection, and
dominance variation is s1nall compared \Vith additive variation. Both the efficiency of reselection and its associated vaTiance
leveled off after t\VO or three crosses per parent The infom1ation fron1 previous generations did not significantly increase
reselection efficiency.
Resume:,\ l'aide de sllnulations Monte CmJo, l'autem· a 6tudi6 les effets d'une augn1entation du nombre de croisen1ents par
parent (k) sur l' efficacite des eclaircies dans les vergers a graines (selection a rebours, c.-a-d. selection repetee des parents).
L'etude s'est inscrite dans le cadre des prograrn1nes avances d'anielioration genetique chez le sapin de Douglas (Pseudotsuga
1nenziesii (Mirb.) Franco) et oil !'information est disponible a partir des cycles a11terieurs d'an1elioration. Ces progrannnes
SOnt CaJ_.acterises par des Vergers 3, graineS den10ntrant Une diversite genetique reduite SUite 3, la s61ection, et egale1nent Ulle
preponderance de la variation genetique additive cornparalivernent 8 la varialion de dominance. I .es restlltat<; d€1nontrent que
]'efflcac[te de la seJect[on 3, rebOtlrS a[ns[ que Sa variance Se stabllisent apres deux_ Oll trois croisen1ents par parent.
L 'infonnation decoulant des cycles precedents d' amelioration n 'a pas aug1nente de fagon significative l' efficacite de la
seleclion a rebours.
f_Traduit par la R6daction1
Introduction
Tree
supplyproviding
both treesa selection
and informa­
tion forbreeding
variousprograms
purposes;must
including
base for the next generation, providing breeding value estirnates for the
selection
baseparamerers
and the parents,
andand
providing
estin1ates
genetic
variation
(Burdon
Shelhoume
l97 l).of }.'oflostgenetic
second-generation
progrrunssuchhaveas reasonable
variation pararneters,
heritabilitiesestimates
and ge­
netic
con·einlations,
and thegenerations
primary go<ibylproviding
is most often
to opti­
mize gain
subsequent
an optin1um
selectionforpopulation.
goal of providing
values
roguing seed'fheorchards
is usually parental
secondarybreeding
and is more important in long-rotation species than in short-rotation species.
species,
seed orchar·
ds area longer
lived, andForthelong-rotation
rogued orchard
population
represents
lru·ger proportion
of theorchard
orchardcanlife.somcrimcs
For short-rotation
species,
next-generation
provide seed
soon theaf­
ter Reselection
the current-generation
rogued. in the 1iterat11re of parents orchard
has beenisaddressed
to varying degrees (van .Buijtenen 1976; l.indgren 1977; Pep­
per
and (1977)
runkoongand1978;
van Buijtenen
Lindgren
BurdonBurdon
and vanandBuijtenen
(1990)1990).
dern­
onstratcd
in many
using parcnrs
in ascross)
fc\V asto one or tv,rothatcrosses
yieldssituations,
approxin1ately
70o/C (one
over 85%
(tv,rocrosses.
crosses)Burdon
of the and
gainvanachieved
using each
parent
in eight
Buijtenenby (1990)
fur­
ther exan1ined the impact of types of crossing designs and the Received July 21, 1997. /\_cceptcd January 19, 1998.
G.R. Johnson. LTSI)1\ Forest Service, Pacific North'Nest Research Station, 3200 S\V Jefferson Way, Corvallis, OR
97331-440 l , LT.S.1\. e-1nail: jo1uiso1u@'fsl.orst.edu Can. J. For. Res. 28: 540-545 (1998)
number of crosses per parent and found most mating designs give sitnilar reselection efficiencies, except that s1nall, discon­
nected
to be less
efficient.and van Buijrcncn The factorial
average sets
gaintend
cstimarcs
of Burdon
(1990) are helpful it1 determining an efficient crossit1g design for parental GC;\ testing. but the uncertainties of achieving these gains rnust also be understood. For exarnple, Magnussen and Yanchuk
demonstr<i
selection
age could
be later(1993)
than \Vhat
sin1pletedage-that- -ageoptimum
co1Telation
averages
would infer \Vhen risk (probability of achieving a certain level of gain) \Vas factored into the decision model. L.ikcwise, one needs to understand the probability of achieving a level of gain through roguing \Vhen choosing mating designs.
'Ibe gains and efficiencies presented in the literature are from a first-generation and l..5-generation point of view. They used only it1fonnation frorn crosses arnong the parents arid assumed
that the genetic
variation represented
in theho\vever,
parents v,ras
not truncated.
i\dvanced-generation
orchards,
represent a truncated population arid therefore reduced genetic variarion. Moreover, additional infon11ation from rhc previous generation is available for use in a selection index. I'hese t\VO factors \Vork in different directions; less genetic variation in1plies that
the parents
\Vill be rnore
difficult,
addi­
tionalrar1king
infonnation
used originally
to select
the pru·yetentsthe could
increase the ability to rank parents in subsequent generations. 1he objectives of this paper \'Iv' ere to exa1nine the stochastic variation associated about the mean expected gain fron1 rogu­
ing seed orchards \Vhen differing numbers of crosses per parent arc used and to examine the added usefulness of information fro111 the previous generation. 1·hese questions are exarnined inbreeding
light of\fJouglas-fir
Franco)
Vithin the frame\vork of the Northv,{!Vrlirb.)
est Tree
Im­
provernent Cooperative. ·rhe Cooperative is in the process of (Pseudatsuga lnenziesii
cG 998 NRC Canada
Johnson
developing
strategies
the various
localsecond-generation
foresr tree hreedingbreeding
cooperatives
in the forPacific
orth\vest.
(6l Generate full--sib fan1ily n1cans that represent testing at each of
five sites.
(7a) Calculate es1irna1ed parental breeding values uslng the best ][n­
ear predictlon (BLP) solution for tlie f ull-sib fantily nteans tliat
represents one to six crosses per pai·cnt. The BLP solution \vas
obtained by solving the equation for the index weights (b) as
b - p-1(; where Pis the variance-covariance rnatrix of full-sib
fanrily means (an n x n rnatrix for n fnll-sih fanrilies) and(; is
Methods
1onte Carlo simulations were used to exanrine correlations between
the covariance inatrix of the fuil--sib family mcai1s \Vith the pa­
estimated breeding values a11d actual genetic values of clones in a
rental breeding values (an
sccond--gcncration seed orchard and to examine gains fron1 orchm_.d
roguing. The procedures generally follo\ved those of King and
Johnson (1993) in that faniily means and illdividual phenotypes arc
used SAS sofh.vare (SAS Institute Inc. 1990) to generate lndependent
lutlon, using tlie full-sib fantily ineans, first-generatlon half-sib
family meai1s, and parental phenotypic values.
(8) tions. Phenotypes of indi vidna ls and fan1ily n1ea11s were cons1rncted
by sun1nllng the genotypic values and environn1ental deviations (phe­
notype
= genotype ---;- cnviron1ncnt). The process allo\VS one to esti
T1ie base inodel asswned tliat 24 clones are selected front a first­
genera1ion progrm:n for seed orchard establishrnenL T\velve clones
are randoruly assigned to each of t\:vo sets. Crosslng is h1nited to
Con_.elate the estin1ated breeding values fron1 step
7
\Vith the
actual genetic values for all 24 parents (without adjusting for
differences in breeding group rneans).
(9) Rogue half the clones from the seed orchard, regardless of
breeding group, usillg the cstin1atcd breeding values and exam­
n1ate breeding values using phenotypes and then co1Telate the
esti1nated breeding values \Vith the true genotypes.
12 inatrix. since there aTc 12
(7b) Calculate estirnated parental breeding values using the BLP so­
generated frou1 predetennined variaHce components. The process
nonnal distributions for genotypic values and envirorunental devia­
n x
parents per breeding group).
ine tlte lncrease ln gain.
These steps were repeated 200 tin1es aiid used to generate mem:ts
and standard deviatlons of the 200 correlations and galn estintates.
The increase ln tlie seed orchard's genetic val ne frorn rogulng was
exainined using the n1ean genetic values of the rogued and umogued
\Vithin a set and the inating design is a balanced paitial diallel. Based
orchards. Because the first generation started \Vith a genetic value of
on the results of the paiiial-diallcl progeny test, the worst 12 clones
0, the
lliT
rogued from the orchai·d \Vithout respect to breeding group.
T1ie baseline genetic variance componen1s conform to the general
fonnula is
16 increase in orchard gain ­
ln the Pacific No1tll\vest for growth aHd fonn. The siruple genetic
n1odel assun1cd additive (GC,\) and dominai1cc (SC,\) vai"iation. but
]
[(rogued orchm_.d inean/umogued orchard n1eai1) -- 1
pat1eni of genetic variation found ln J)ouglas-fir breedlng progran1s
The breeding rnodel
x 100
\Vas developed to sinn1late operational
second-generation breeding strategies for the Northwest Tree hn­
no interaction (cpistatic) co1nponents of genetic variation. They rep­
proven1ent Cooperative's Douglas-fir breeding programs. 1n these
resent narro\V sense heritabilitics of 0.25 on a single site and 0.19
programs, second- generation progeny tests ai·e bcll1g designed to in­
across sites. l)onllnance variance \Vas set to 35o/o of the additive vari­
vestigate gcnotypc-by--cnvironmcntal interactions as a secondary ob­
ai1cc, \Vhich is in line \Vith Douglas fir gro\vth trait estimates of
jective. To examine this interaction, it VhlS decided that at least five
Yanchuk ( 1 996). The variance cornponents for the baseline scenario
progeny test sites \Vill be established in any testing zone. Therefore.
(0 -) - 19,
the baseline rnodel asswned tliat the 24 paTents would be tested \Vlth
were set to the follo\ving:
additive genetic variation
additive-by-location variation
(0;j'i- 6.75,
(0 -0y-£) = 6,
doniinance-by-location variation
cnvironn1cntal variation
(CT )= 66.
donrinance v<)riation
(0a_oy-£) -
2.25, and
The model assun1ed the use of single tree plots and the absence of
replication-by-fan1ily variation (none usnally found in cooperative
progeny tests). Because both the location and replication effects can
he ren1oved fron1 individual estinrates and they do not affect family
niean rankings, they \Vere ignored in the rnodel.
The sllnulations first generated a first--generation open --pollinated
population that represented 300 open pollinatcd fainilics. each having
80 individuals. Fainily--1nean heritability for the first generation was
set to 0.70 to represent first generation trials \Vhere field test layout
and design were not as refined as present. The best individuals (phe­
notype adjnsted for location and replication) frorn the best 24 farnilies
\Vere used as the second-generation seed orchard parents, and their
actual (JCA values \ 'ere nsed to generate the farnily rneans that \Vere
later used to csti1natc their brccdillg values. The specific steps were as
follO\VS.
( l ) (fenerate ::HJ() half-sib farnily genetic valnes with a variance of
0.250;
and environniental deviations snch that the heritability
of half--sib family means=
(2) Generate
of
(3) (4) (5) 0.750
80
+
0. 70.
individuals per half sib family \Vith the vai"iation
n?J 0 .750 -hy-T + 0;r_hy-t> + 0 .
Select the best individual fro1n each of best 24 half-sib families.
Randonrly divide the 24 progeny selections (seed orchard par­
ents) into t\VO sets of 12 parents.
Generate a series of crosses (paiiial diailcls) that represents a
parent being involved in one to six crosses
(k).
A parent in­
volved in only one cross represents single-pair rnating and re­
sults in generating six fainilies for a 12--parent set.
2400 progeny over five progeny test locations. \1ariatlons of tlie base­
line prograin \Vere also ex.amlned. These included the following: alter
tlie nun1ber of progeny to
4800, 1200, aiid 600; start \:Vitli 150 fnll-slb
(single-pair cross) fainilies instead of 300 half-sib fan1ilies (heritabil­
ity of fainily meai1s set to
0.75);
set the do1ninance (SCi\) genetic
variance equal to the additive genetic vai·iai1ce; use t11Tee breeding
groups of eight parental selections; inodel a fixed family size (20
progeny per site) ai1d allo\V t11e nu1nber of progeny to increase; ai1d
for the fixed farnily size niodel, increase breeding gronp size to 24 and
the nnn1her of sets to
4, thus increasing the selection populalion to 96.
Results and discussion
1·he added efficiency of rnaking rnore crosses per parent dropped markedly after only tv,ro crosses (Table l) and is in line
\Vithcorrelations
Burdon andofvanLindgren
Buijtenen's
and the
(1977).(1990)
1"11e gain
trendestimates
was the san1e
ere used to\Nhether
estimareonlyof thesecond-generation
hreeding values data
or. in(progeny)
addtion tov,rthe
second-generation
the first-generation
tion
\-Vas also usedinfor1nation,
to estimate breeding
values. I'heinforma­
percent increase
in
orchard
gain
from
roguing
closely
fo11(
n
ved
the con'.elation of estin1ated breeding value \Vith actual genetic
value (r . ·rhis is expected because the correlation is the square
root of the index heritahility and the formula for gain is
ra
[1] Gain
\and
VhereCT isisthe
the additive
selectiongenetic
intensity,variation.
t is the phenotypic variation,
)
(h2)
= ih2ap= iha a= i
i
a
a
cG 998 NRC Canada
Can. ,J. For. :=!c:s. Vol. 28,
-: DDS
Table 1. Correlations bet\veen estimated breeding values and actual genetic values, and percent increase in initial
seed orchard galn frorn roguing half the clones based on estlrnated breeding values.
Crosses
Variable
2
r
3
4
5
6
using only second-generation data
Iviean
0.655
0.849
0.905
0.917
0. 924
0.926
SD
0.1292
0.0674
0.0509
0.0475
0.0456
0.0461
CV
0 179
0.079
0.056
0.052
0.049
0.050
lviin.
0.276
0.57_
0.716
0.735
0.741
0.727
11:b
0.366
0.660
0.739
0.758
0.775
0.780
5qf,
0.418
0.722
0.809
0.833
0.833
0.831
lO':f>
0.482
0.751
0.839
0.852
0.868
0.868
Iviean
0.666
0.848
0.899
0.925
0.935
0.942
SD
0.1214
(J.(1649
0.0523
(J.(1447
0.0425
0.0412
r
using first- and second-generation data*
CV
0.182
0.076
0.058
0.048
0.045
0.044
lviin.
0·""'''
1'7'7
0.596
0.634
0.731
0.758
0.780
J 0(,
IU98
11.6%
11.746
0.787
0.798
1 1 .817
51:b
0.457
0.731
0.798
0.841
0.852
0.858
lO':f>
0.493
0.772
0.833
0.864
0.877
0.887
o/o increase in orchard gain from orchard roguing using only second-generation data
[\;fean
28.2
35.7
37.9
38.3
38.4
38.6
SD
8.69
8.65
8.68
8.50
8.75
8.59 CV
0.31
0.24
0.23
0.22
0.23
0.22 6 ry,
87
1o/o
12.7
19.2
"0
...,...,,£.,
50(,
15.11
22.8
10%·
17.7
25.7
Mln.
13 ..l
14.5
8.9
22.9
22.1
22.4
24 3
24.2
25.9
24.8
27.3
28.l
27.4
28.3
17.2
1 1 increase in orchard gain fro1n orchard roguing u:\.ing fir:\.t- and second-generation data
lviean
28.6
35.4
37.5
38.8
39.0
39.l
SD
9.43
9.04
8.68
8.45
8.60
8.47
CV
0.33
0.26
0.23
0.22
0.22
0.22 Min.
3.9
13.8
12.9
9.6
117
·"')
_, k
1'7
8.7
lg;;,
21.8
22.9
23 0
23.4
50(,
14.3
22.::1
24.2
26.1
26.I
26.I
l Oo/c.
17.5
23.4
26.6
28.5
28.6
28.8
12.5 Note: l\1eans. standard dc;viations. coefficients of variation. r:'jnirn;nns. and the. ; , 5, and O percentile values arc. repo:·tc.d.
*Second-genera:ion data a:·e the dialk l :;:irogeny test of tie parents; first-generation da:a are tie half-sib fa:r.ily values fron :be
fi:·st-generation progeny tests :fro;r. wbc.:·e the pa:·ents \Vere selected and the pa:·ental pbc.notypc. in those tc.sts.
The standard deviation (and variance) and coefficient of variation
the 200for estimates
quicklycoefficients
stabilized after threecalculated
crosses perfro1nparent
the correlation
and after tv,ro crosses for the percent increase in orchard gain ('trends
rable for1 . the1'heineans.
trends for the percentiles were sirnilar to the
VVhile the
percenttheincrease
in orchard
gain differences.
and co1Telations
generally
fo11o\.ved
same trend,
there v,rere
The coefficients
for the This
gainsresulted
\Vere considerably
larger than those forofthevariation
corTelations.
in the percentiles
being sm<i11er proportion of the me<ins for the g<iins compared
\'lv'ith the correlations
percentile
correlations
\Vere 74,('88,fable92,1).93,For94,exa1nple,
and 947,:,, theof the10 ineans
for one ro sixgainscrosses
parent (k).values
For were
the percent
orchard
the 10perpercentile
63, 72, increase
72. 73, 71,in and'111e73%percent
of the means
1-6. gain averaged 28.2% for increaseforink=orchard
)
a
one cross per parent and up to 38.6% for six crosses per parent, when11nrog1
half1theed orchard
ble 1). 'orchard
fhus, if the
orchard clones
had a were
lOo/C rogued
gain, the('l'arogued
v,rould have from 12.8 to 13.9Sf; gain. Jn this exercise the un­
rogued
orchardinaveraged
a gainforoftwo
6.9 units.
cent increase
orchard gain
crosses1'hpere average
parent per­
\Vas 35.
7
·
1i:
:
,
but
fell
belo\V
18
1i:
·
:
in
lOo/
0
of
the
simulations
and
rhe \VOrst case v,ras less than O ii· . Although gain from four orin n1ore
averaged
39c;:sthat
, gain25%1wasin less
in 10%) of the crosses
simulations
and less
5S0 ofthanthe29o/C
simulations
(Table 1).
Exarnination
of theestimates
stochastic\.vould
variation
associated
with the corTelations
and gain
not change
the decision­
making
procedureintoaamanner
large degree
percenrile val­
ues
all stabilized
similarbecause
to the the
means.
can achieve
niore generations
year, andAgronomic
as a result,crops
realized
gain canonebeorexmniued
over nrualtiple
l
cG 998 NRC Canada
543
Johnson
Fig. 1. Percent increase in orchard gain for selecting the best four
Fig. 2. Correlation coefficients between predicted parental breeding
or 48 parents from an orchard (population) of 96, and correlation
values and actual genetic values for four levels of testing (number
between estimated and actual breeding values for differing numbers
of progeny) and differing numbers of crosses per parent.
of crosses per parent.
0.95
.8160
0.9
'i:'
'7;0.85
140
'"d
120
...s::
100
0
.8 80
IJ)
"'
60
0:::
40
(.)
.8 20
0 -F--1---t�+--t----1�-t---+-�1---+--+�+--+ 0
1
2
4
3
0
5
6
0
·.g
0.8
]0.15
0
(.) 0.7
0.65
0.6 +----1�--+-�-+-�+-----+�-+-�-i�--+--I
1
crosses per parent
- - correlation
- best 4 gain
2
3
4
crosses per parent
1--- 600
- best 48 gain
(k)
5
6
1
-- 1200-a- 1200-e- 2400
(1990) where they found that moderate changes in heritability
generations. Unfortunately, forest tree breeders require consid­
had minimal effects on backwards selection efficiency.
erably more time to complete a generation and the fate of a
Using first-generation information from full-sib families in
breeding program can rest on the results of one generation.
addition to the second-generation data (progeny) increased the
Thus, it important that we account for the variation in gain
correlations and percent increase in orchard gain slightly for
estimates because if we fail to meet expectations in a single
single-pair matings
generation, the fate of the breeding program may be in jeop­
ing rose from
ardy. Managers must be aware of the variation associated with
(k 1). The correlation for single-pair mat­
0.645 to 0.685 (Table 2), and percent increase
in orchard gain increased from 27.9 to 29.7%. The first­
gain estimates and should probably use estimates less than the
generation full-sib information did not increase selection effi­
=
k was greater than 1. The minor increase in the
averages for financial forecasting. The greater variation in per­
ciencies when
cent increase in orchard gain compared with the correlations
single-pair matings was because indices generated from full­
suggests that theoretical variation estimates may underesti­
sib families tend to be superior to those generated from half-sib
mate the actual variation associated with realized gain.
families. More of the genetic variation (and therefore, index
A simpler fixed family size model was used to examine
score) is associated with the family mean for full-sibs than for
whether these trends held true for higher selection intensities.
half-sibs. Family means are more stable than individual phe­
When the selection base (orchard population) was increased to
notypes, hence the greater stability of the full-sib indices. The
96 parents, the percent increase in orchard gain from reselect­
ing the best four or 48 showed the same trends, although gains
were higher for the higher selection intensity (Fig. 1). As be­
(0.64 x
0.12 x phenotype) and breeding value
for the seed orchard parents increased to 0.42 and ranged from
-0.07 to 0.77.
fore, gains from both selection intensities followed the same
trend as the correlation between the estimated and actual
1).
breeding value (Fig.
correlation between the first-generation full-sib index
full-sib family mean+
Changing the number of progeny tested had little effect on
the rate at which efficiency plateaued, but did affect the level
The use of the first-generation information to increase se­
at which it plateaued (Table
2; Fig. 2). Doubling the number
lection efficiency was of little value because the correlation
of progeny never doubled the efficiency of selection. After
coefficient and percent increase in orchard gain increased
2400 progeny, very little increase in efficieny was noted. It
scarcely at all for all values of
k (Table 1).
should be noted that three crosses per parent with a given
One reason that the first generation data added little infor­
mation was because it did not have a strong correlation with
the parental breeding values. The correlation between the first­
generation index
notype)
and
(0.59 x half-sib family mean+ 0.16 x phe­
the
actual
values
for
the
Reducing the breeding group size to eight parents and using
three sets did not reduce the efficiency of reselection (Table
2).
total
At five and six crosses per parent, the correlations between
first-generation population averaged 0.56 and ranged from
0.53 to 0.59. The seed orchard population, however, was a
truncated population with less genetic variation (75% of the
relative to the baseline scenario. These increases are probably
original), and the correlation between the index and the breed­
values in a diallel. Sampling does not play a significant role
ing value for the
24 orchard selections averaged 0.31 and
-0.17 to 0.66. While the truncated genetic vari­
when moderately sized diallels are complete. For each parent
ranged from
in the diallel, both its effect and the effect of the other parents
ation affected forward selection efficiency in the first genera­
that it is crossed with can be well estimated. For example, in
tion for the subset of orchard parents, it had little effect on the
a complete six-parent half diallel with no selfs, the five full-sib
backwards selection efficiency. This is in line with the obser­
families in which a parent is represented represent one-half its
(1977) and Burdon and van Buijtenen
breeding value and one-half the average of the other five
vations of Lindgren
breeding
number of progeny was always superior to two crosses per
parent with twice the number of progeny.
estimated breeding values and actual genetic values increased
due to being able to accurately estimate most of the full-sib
© 1998 NRC Canada
Can. ,J. For. :=!c:s. Vol. 28, -: DDS
Table 2. Correlations of esti1nated breeding values \Vith actual genetic values for inodifications of the baseline model.
Standard deviations arc in parentheses.
Crosses
:">, odification
2
Baseline (2400 progeny)
0.655
0.849
(0 0674)
(().1292)
4800 total progeny
0648
0.857
(0 1194)
1200 total progeny
600 total progeny
n;i G
(0.0615)
0.641
0.832
(0.1229)
(0 0691)
Start with 150 ft1ll-slh fan1ilics
11 842
(0.0739)
0.685
families and use first and
0.887
0.852
0.645
0.843
(0 1021)
(0 0641)
iO 0458)
0.901
(0 05.'51
(0 0578)
(0 0581)
0.805
0.922
0.907
0 78.'
(0.0795)
0.917
(IHl475)
(0 0499)
(0 0807)
(0 1100)
Start with 150 ft1ll-slb
0.905
0.620
(0.1256)
4
(().0509)
(0 1194)
0.620
=
3
0.869
(0.0588)
0.870
0.893
(0.0578)
(0 0504)
11.896
11.912
iO 0534)
(0 0543)
0.898
0 92.l
(0 0512)
(0 0448)
5
0.924
(0 0456)
0.928
(0.04601
0.909
i0.0509)
0.874
iO 0563)
0.907
(0 0477)
11.919
(0.05061
() 935
i0.0429)
6
0.926
(().(1461)
0.931
(0 0471)
0.911
(0 0500)
0.879
(0.0549)
0.914
(0.0479)
11.924
(0 0512)
0.942
(0 0425)
second-generation data
Three eight--parent breeding
0.613
groups
0.845
(0 1139)
(0.0609)
0.634
Fixed faintly size
0.858
(().1137)
(0 0601)
0.888
0.906
(0 0526)
(0 0548)
0.908
0.924
(().0542)
(IHl509)
0.974
(0 0109)
0.932
(0 0496)
0.982
(0.0072)
0.937
(().(1486)
ote: U11le:ss of:1e:rwise: intlica:etl, values are for ctsi11g seeuntl-generacion infonnatio11 011ly.
parents. Theprecision
avenige byof thetheother
five parents
is estin1ated
with reasonable
ren1aining
10 families.
The actual
solution is easily obtained using a BL.P solution. •'or moderate­
sizcd dia11c1svariation
rhc effectis ofnotsan1pling
dominance
extren1e.ls prohahly unimportant if Increasing
the do1ninance
additive
variation
decreased
the overallvariation
efficiencytoofequal
GCi\thetesting
and slightly
rateclatlon
at \Nhichcoefficients
the con·elations
plateaued
(Tahlc 2).decreased
Still, thethecon·
plateaued
afrcr three
per parent.
standardanddeviations
the corTe­
lationscrosses
were higher
than theI'hebaseline
plateauedoflater.
'Vith only two crosses per parent, there v,ras a notice<ihle decrease in reselection
baselinedecreased
scenario (0.805
versus efficiency
0,849, Tablecornpared
2), butwith
the the
difference
with
eachinsuccessive
crossdecrease
per parcnr.inThree
crosses\Vithpertheparent
resulted
only a minor
efficiency
in­
creased dominance
siderable
arnount ofvariation:
do1ninar1cetherefore,
var·iationittoseerns
requireto take
inorea con­
than three crosses per parent to effectively estin1ate the hreeding value
ents. ii\.lthat
thoughthe atvar·first.
inay seem
one mustof par·rernember
iancethisof full-sib
familyincorrect,
rneans for
trialisv,rith sires and n replicates of single-tree plots at eacha site
, l , by + 4-"°j
l , by )i
[,1'"' Cfu, -sibs= 2"°l , +4°d, + 1,2"°
3 +2°
1 '-by-e +:f1
3 :i-by-e +a;) n
+[(l2° +4°;i
J
'nance
rhe additive
ahnostof full-sib
t\-vice thefarnilies
effectVv'ith
of domi­
variationvariation
on the var·hasiance
lar·ge l
s
l
l
0
c
c
0
'
S
'\
_
I
s
n. Consider also that for the vari<ince of "half-sib'" family inear1s
cornposed
single site
is of equal arnounts of c full-sib fa1nilies for a I '1
'
1 /c)J+l
l1 1 c)Jal
[3] a!;,,,b,= ['l2(l
1(c-l)/cl)t;+l1(1/
+ (ren1aining variationin)
When ca=a a d three crosses arc made per parent, the vari­
ar1ce of the half-sib family for a single site is
l4J al;,1,,,,= ;+ 1 +[( a;+*31 +a;}"]
Ininfluence
this casethanthetheadditive
variance
h<is <ifor
ln1ostlargefourn. times n1ore
don1inance
variance
'l'hese results appear counterintuitive in light of the rela­
rivcly
large numhcr
of crosses per
hrccd­
ing progran1s
(e.g., six-parent
halfparcnr
dia11e1s)usedandin then1anyliterature
\changes
Vhich reports
one crossingsignificantly
designs or thedifferent
nu1nberefficiencies
of crosses \-perVhenparent
(e.g., Ken1pthorne
Cu111toov,cxisring
r 1961; Cun1ov.:
· 1963;
Narain
1990). VVirhandregard
programs.
oneArya
mustand
rc­ 1nernber that crossing designs ar·e selected for rnore than the reselection
of parents.
The
studiesdesigns
that shov,
rnumber
substantiaof 1differ­
ences
in
efficiency
for
crossing
and
crosses
per
parent
exmniued
the
variances
of
the
breeding
value
esti­
1nates, not necessarily the irnpact that they have on a testing program
Decreasing
rhc variance
of anv.:·ocsrimatc
one half doespernotsc.n1ean
that selection
efficiency
uld increase
double.1'
hese l\ilonteand
Cm'the
lo sirnulations,
's (1977)
es­
tilnated correlations,
Burdon aridLindgren
var1 Buijtenen
(1990)
r
n
cG 998 NRC Canada
Johnson
gain estimates
report that(r one0.6),cross
parenthothgivesparents
sur­
evenperthough
prising
accurateallestin1ates
in a cross
receivebetterthethan
same60%estirnated
breeding gain
value.fromIf one
cross
can yield
of the potential
the reselection
of parents,because
it is impossible
double the effi­
r=
istotheevenn1aximum.
ciency
of reselection
>
LO
Conclusions
The expected gains from backv,rards selection increase very little
three crosses
parent.quickly
'fhe variation
ciatedafter
\Vithtv,rogainor esti1nates
alsoperplateaus
after twoasso­
or three
crosses
per
parent;
therefore,
the
trends
in
stocastic
vari­
ation \Vould not alter decisions on the nun1ber of crosses with regard to back\vards selection. l-Iowever, the variation associ­
ated
ith breeding
estimates
needsfortosingle-pair
be considered
when\Vprojecting
gainvalue
estimares.
especially
mat­
ings
which haveof thesubstantial
largest coefficients
variation.(ad=
Evena;),in the presence
do1ninance ofvariation
three
crosses
p<irent <ippe<irs
sufficientof toparents.
providetrsereli<iof bin­
le breeding
valueperestimates
for reselection
fonnation from the previous generation did little to improve breeding value esrimates.
Acknowledgements
Thanks
due to N.and
I\1andel,
Dr. R.fJ. Burdon,
[Jr. G.forR.reading
Hodge, Dr. T.S.areAnekonda,
t\VO anonyn1ous
reviewers
and cornmenting on drafts of the manuscript.
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cG 998 NRC Canada