Problem and Theory GxG Interactionsnitro.biosci.arizona.edu/Nordicpdf/lecture15.pdf · Lecture 15...
Transcript of Problem and Theory GxG Interactionsnitro.biosci.arizona.edu/Nordicpdf/lecture15.pdf · Lecture 15...
Lecture 15
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CompetitionProblem and Theory
GxG Interactions
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Problem
• Competition (Fighting)– Dominance– Limited Space– Limited Food Supply– Peck Order
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Results of Competition• Reduced Gain• Increased Mortality
– Direct• Injuries
– Indirect• Immune response• Diseases susceptibility
• Reduced Feed Efficiency– Energy lost in fighting– Increased Fat
depositionAnimal Well being concernsAnimal Well being concerns
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Effects of Group Size on Pig Growth and Composition
• Group Size:1, 4, 8, 16 or 32 pigs per pen
• Similar Pen and Feeder Space Per Pig
• Average Initial and Final Pig Weights25.7 and 108.5 kg
•Frank, G. R., M. E. Spurlock, S. G. Cornelius, G. M. Willis, and M. McComb. 1997a. J. Anim. Sci. Vol. 75(Suppl. 1):37(abstr.)
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Average Daily Gain
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
1 4 8 16 32
Group Size•Frank, G. R., M. E. Spurlock, S. G. Cornelius, G. M. Willis, and M. McComb. 1997a. J. Anim. Sci. Vol. 75(Suppl. 1):37(abstr.)
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Fat Depth
13.5
14
14.5
15
15.5
16
16.5
1 4 8 16 32
Group SizeFrank, J. W., B. T. Richert, A. P. Schinckel, B. A. Belstra, and A. L. Grant. 1997b.. J. Anim. Sci.(Suppl. 1):38(abstr.).
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They May Look Happy, But Competition is a Real Problem in Swine and Poultry
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Animal Well-being
• Animal Welfare Issues Are Becoming a Major Concern.– Egg Producers Are Asking for a Different
Type of Hen, Specifically Adapted to ‘Animal Friendly’ Production Systems Preisinger (1998).
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The Cause of the Problem
• Environment of Selection– Natural
Unlimited TerritoryLimited FoodMust Attract Mates
• Environment of Production– Domestic
• Limited Territory• Food Provided• Mates Provided
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Examples Of Behavioral Problems
• Susceptibility To Hysteria In Large Groups
• Pacing Before Laying, • Feather Pecking• Cannibalistic Deaths• Fearful Or Panic Responses• Cannibalism• Inter-individual Aggression
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Contributing to The Problem• Individual Selection
– Group Setting– Non Group Setting
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Individual Selection In a Group Setting Selects for the Most Aggressive Animals
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Domestication
• Method To Adapt An Animal To A Production Environments
• Stress Is A Manifestation Of How Well The Bird Is Adapted To That Environment
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AdaptationBirds in Diverse Ecosystems Evolved from a Common Ancestor
Each Would be Stressed in the Other Environment Because they are Not Adapted to it (GxE Interaction).
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Can Genetic Selection Improve Adaptability and Well-being of Birds?
• Appleby and Hughes (1991)– Welfare Problems In
Cages Are Less Likely To Be Alleviated By Genetic Selection Than Those In Alternative Systems
– Welfare Is Compromised If Freedom To Exercise Normal Behavior Is Absent
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Genetic Selection Can Change “Normal Behavior”
• A Bird Can Evolve Through Selection– Prefers To Be In Close
Proximity To A Large Number Of Cage Mates
– By This Definition, Its Natural Behavior Is Not Compromised
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Breeding Cabbages
• Blind Chickens• Ethics
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Solutions?• Management
– Well-being issues– Costly
• Genetics– Continue the Domestication
Process– Get Rid of Unwanted and
Undesirable Characteristics Which Were Needed In Natural Environments (Peck Order, Dominance)
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Direct Selection on Behavior?
– What Traits Needs to Be Measured
• Biting• Fighting• Other?
– At What Cost?– Diverted Selection Intensity
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Link Between Behavior And Stress Can Be Misinterpreted
• Duncan and Filshie (1979)– Flighty Strain Of Birds
• Exhibited Avoidance And Panic Behavior Following Stimulation
• Returned To A Normal Heart Beat Sooner Than A Line Of More Docile Birds
• Docile Birds May Be Too Frightened To Move.
– Is Flightiness Good Or Bad For Well-being
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Indirect Selection To Reduce Undesirable Behaviors
• Group Selection– Based On The Hypothesis That When
Productivity Of The Group Is High, Behavioral Stresses Of The Group Must Be Reduced Or Absent (GxG interaction reduced)
– Does Not• Increase Costs• Divert Selection Intensity• Require Measurement Of Behaviour Traits
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Among Group Selection
• Foundation Established By Griffing (1967)• Extend Usual Gene Model
– Direct Effects Of Its Own Genes– Associate Contributions From Other Genotypes
In The Group (GxG interactions)
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Group Selection• Not to be confuse with individual selection for
the betterment of the group– Wayne Edwards (1962), Hamilton (1964)– Controversial Evolutionary Theory– Appears to have a number of theoretical problems– Even for the case of related individual (usual kin
selection)• Group selection as applied here is among
group selection– The entire group live or dies depending on the
behavior of the group as a whole (pack behavior)
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Pigs in Individual Pens
GxG Interactions Not Possible
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Y1=19
Y2=16 Y3=17
Example Performance in Individual Pens
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Pigs in a Common Pen
GxG Interactions Possible
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9
76
-7 -7
0
0
-4
-4
Y1=µ+D1+A2+A3+ε
Y2=µ+D2+A1+A3+ε Y3=µ+D3+A1+A2+ε
Interacting Effects Y1=10+9+0+-4+0=15
Y2=10+6+-7+-4+0=5 Y3=10+7+-7+0+0=10
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9
99
-7 -7
-7
-7
-7
-7
Y1=µ+D1+A2+A3+ε
Y2=µ+D2+A1+A3+ε Y3=µ+D3+A1+A2+ε
Clone Top PigY1=10+9-7-7+0=5
Y2=10+9-7-7+0=5 Y3=10+9-7-7+0=5
Y1=10+9-7-7+0=5
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6
66
0 0
0
0
0
0
Y1=µ+D1+A2+A3+ε
Y2=µ+D2+A1+A3+ε Y3=µ+D3+A1+A2+ε
Clone Worst Pig Y1=10+6+0+0+0=16
Y2= 10+6+0+0+0=16 Y3= 10+6+0+0+0=16
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Cloning the Best Pig Gave Worst Performance and vice versa
GxG Interaction
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Individual Selection in a Non Group Setting
•• Selection For Aggression May Still Result Due Selection For Aggression May Still Result Due to Genetic Correlation Between Direct and to Genetic Correlation Between Direct and Associative EffectsAssociative Effects
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Individual Selection
( )[ ]AdaAdi σσσµ )(2/ +=∆
2Adσ
Ada σ)(
Additive Genetic Variance of Direct Effects
Covariance between Direct and Associative Effects
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Group Selection
( )∆µ σ σ σ σ= + +
id aA A A
2 2 22 ( )da
σa A
2Variance of Associative Effects
This quantity is always positive
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To Optimize Productivity In Competitive Environments
• Do Not Select Those Individuals That Perform The Best
• Select The Groups That Produces The Best
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N=23 (5.7)
N=15 (15)
N=19 (6.3)
N=26 (6.5)
Group Selection
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A Positive Response To Selection Is Ensured
• If Selection Is Transferred From The Individual To That Of The Group
• Group Selection Operates On Both Direct And Associate Components
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Kin Selection(Not The Usual Definition)
• If The Group Is Composed Of Related Individuals The Efficiency Is Greatly Increased, Particularly As Group Size Increases Griffing (1976)
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Group SelectionApplications
Application
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Eggs per Hen Housed
91
195219 225
237
507090
110130150170190210230250
1 2 3 4 5Generation
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Percent Mortality
67.9
8.814.915.213
01020304050607080
1 2 3 4 5Generations
%
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Survival After Mechanical Failure in First Month
4838
85 79
Colony Cage Single Cage
Percent Survival
SelectedControl
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89
82
9593
Colony Cage Single Cage
Percent Survival
SelectedControl
Survival For Month 2-12
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7th Generation
• Selected (KBG), Control (C), And Commercial (DXL) Lines Were Compared
• All Stocks Housed In Both Single- Or 12-Bird Cages
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Cumulative Mortality
050
100150200250300350400450
18 21 24 27 30 33 36 39 42 45 48 51 54 57
AGE (WEEKS)
CONTROLKGBCOMMERCIAL
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TOTAL EGGS PER CAGE/12
251
198
295
193
266
217
0
50
100
150
200
250
300
350
SINGLE COLONYSTOCK
EG
GS
CONTROLCOMMERCIALSELECTED
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RATE OF LAY
0
10
20
30
40
50
60
70
80
90
COLONY SINGLE
%
CONTROLKGBCOMMERCIAL
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CONCLUSIONS
• Group Selection Is Effective In Improving Well-being Of Layers In A Relatively Short Period Of Time Without Sacrificing Productivity
• Individual Selection Makes the Problem Worse
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Incorporation of Competitive Effects in Breeding Programs
Without GroupSelection
Mixed Model Theory
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Problems With Group
Selection
• Group Selection– Requires
• Families Be Housed Together• Selected As a Group.
– Rate of Inbreeding Increases Rapidly
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Incorporation of Competitive Effects In The Mixed Model
Equations (MME)
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Example
Pen 1 Pen 2 Pen 3
S1 S2D1 D2 D4 D5D3
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Usual Animal Model
εµβ ++= ddZXY
[ ]
+
+
=
9
8
7
6
5
4
3
2
1
9
8
7
6
5
4
3
2
1
9
8
7
6
5
4
3
2
1
100000000010000000001000000000100000000010000000001000000000100000000010000000001
111111111
εεεεεεεεε
µµµµµµµµµ
β
yyyyyyyyy
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D1
D3D2
A1A1
A2
A2
A3
A3
Y1=µ+D1+A2+A3+ε
Y2=µ+D2+A1+A3+ε Y3=µ+D3+A1+A2+ε
Interacting Effects
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Expand Mixed Model Equationsεµµβ +++= aadd ZZXY
Fixed EffectsMeanLocationAge
IncidenceMatrixFixed Effects
Direct Effects
IncidenceMatrixDirect Effects
IncidenceMatrixAssociative Effects
Associative Effects
RandomError
Yield
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Associative Effects Incidence Matrix
εµµβ +++= aadd ZZXY
=
010000100100000100000100010001000010000001001000010001110000000001100000000011000
aZ
Animal 1Pigs 4 and 5 in Same pen
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MME with Competitive Effects
=
++++
−−
−−
a
d
a
d
aadaa
adddd
ad
ZXZXXX
AkZZAkZZXZAkZZAkZZXZ
ZXZXXX
'''
''
'''
13
'12
'
12
'11
'
µµβ
1
2
22
32
21−
=
aad
add
kkkk
σσσσ
σε
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Genetic Parameters
2dσ2aσ
adσ
Direct Effect
Associate Effect
Covariance Between Direct and Associative Effect
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Maximum Likelihood Estimates of Genetic Parameters
PYY'CGR 5.ln5.ln5.ln5. −−−−=L
)ln(
ln)ln(
lnln
2
2
2
e
Ne
e
N σ
σ
σ
=
+=
=
I
IR
= 2
2
AAD
ADD
σσσσ
AAAA
G
∑++
=
−
=
+
=
RNM
iiC
C
1lnln λ
2e
1σGZZ'XZ'ZX'XX'
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Optimal Selection
ad bbI∧∧
+= µµ 21
The optimal weights are found as the partial regression coefficients of mean pen
performance on estimated direct and associative effects
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Example Pedigree
4 5 6 7
8 910 11
Pen 1 Pen 2(5) (6) (20) (10)10
2065
Y
211761107629541854
PenAniDamSire
=
1111
X
=
102065
Y[ ]µ=B
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=
10000000010000000010000000010000
1Z
Animal4 5 6 7 8 9 10 11
102065
Y
211761107629541854
PenAniDamSire
102065
Y
211761107629541854
PenAniDamSire
=
00100000000100001000000001000000
2Z
4 5 6 7 8 9 10 11
10 is with 8 11 is with 9 8 is with 10
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MME
=
++++
−−
−−
yZyZyX
adb
kAZZkAZZXZkAZZkAZZXZ
ZX'ZX'XX'
'2
'1
'
221
2'221
11
'2
'2
121
2'111
11
'1
'1
21
ˆ
ˆˆ
2
1
2
2
2221
1211e
ada
dad
kkkk
σσσσσ
−
=
50105
550 1
2221
1211−
−
−=
kkkk
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proc iml;start main;
y={5,20,6,10};
X={1,1,1,1};
A={1 0 0 0 .5 .5 0 0,0 1 0 0 .5 .5 0 0,0 0 1 0 0 0 .5 .5,0 0 0 1 0 0 .5 .5,.5 .5 0 0 1 .5 0 0,.5 .5 0 0 .5 1 0 0,0 0 .5 .5 0 0 1 .5,0 0 .5 .5 0 0 .5 1};
AINV=INV(A);
Z1={ 0 0 0 0 1 0 0 0,0 0 0 0 0 1 0 0,
0 0 0 0 0 0 1 0,0 0 0 0 0 0 0 1};
Z2={ 0 0 0 0 0 0 1 0,0 0 0 0 0 0 0 1,
0 0 0 0 1 0 0 0,0 0 0 0 0 1 0 0};
P={50 -5,-5 10};
K=inv(P)#50;LHS=((X`*X)||(X`*Z1)||(X`*Z2))//((Z1`*X)||(Z1`*Z1+AINV#K[1,1])||(Z1`*
Z2+AINV#K[1,2]))//((Z2`*X)||(Z2`*Z1+AINV#K[2,1])||(Z2`*
Z2+AINV#K[2,2]));RHS=(X`*Y)//(Z1`*Y)//(Z2`*Y);C=INV(LHS);BU=C*RHS;RMSE=(Y`*Y-BU`*RHS)#(1/3);print BU RMSE;finish main;run;quit;
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Estimates
EffectAnimal Direct Associate4 .798 -.2175 .798 -.2176 -.798 .2177 -.798 .2178 -1.117 -.2429 3.512 -.41010 -1.732 -.07411 -.662 .727
d a25.10ˆ =u
Note animal with best direct effect has worst associative effect
Vice vesra
102065
Y
211761107629541854
PenAniDamSire
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Lab Problem 1 Competition
A B C D
E F
G H
Assume animals are in pens as indicated by the rectangles above. Fit an animal model with competitive effects, assume
J
9 13 4 12
11 11
13 9
10
12
2
=a
e
σσ
1.2
2
=p
e
σσ 152
2
=p
e
σσ
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Lab Problem 2 CompetitionImpact of GxG effects on Breeding program
11
1 2 3
4 5 6 7 8 9 10
12 9 8 5 7 5 6 8
Pen 1 1 2 2 2 1 1 2
Assume animals are in pens as indicated.
a) Fit an animal model with and without competitive effects
b) Rank Individuals for breeding using the following indexes
c) Discuss results relative to breeding program
60104
430 1
2
1
2
2
−
−
−
−
e
ada
dad σσσσσ
adI µµ ˆ3ˆ1 +=
dI µ1= Without Competitive Effects
With Competitive Effects
Index
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Experimental Testing
• Experimental Model– Quail– Trait: 6 Week Weight (wt)
• Methods tested:– Control: Animal Model BLUP
(AM-BLUP)– Competitive Model BLUP: (CE-
BLUP)
• Selected for 25 Hatches
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Estimates of Genetic Parameters
5.124
8.25.55.57.33
2
2
2
=
−
−=
=
e
AAD
ADD
σ
σσσσ
G
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Initial ExperimentGroup Size and Feed Restriction
Quail Mortality (%)
05
1015202530354045
4 12 16 20Group Size
36
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Initial ExperimentGroup Size and Feed Restriction
6 Week Weight (g)
80859095
100105110115120
4 12 16 20Group Size
36
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Results
25 Hatches of Selection
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6 Week Weight
70
80
90
100
110
CE-BLUPAM-BLUP
Initial
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0.0-0.1-0.2-0.3-0.4-0.5-0.6-0.7-0.8-0.9-1.0-1.1
AM-BLUPCE-BLUP
Associative Effects
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Direct Effects
AM-BLUPCE-BLUP
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Mortality At Termination of Experiment (Hatch 25)
3.4
23.8
0
5
10
15
20
25
Line
CE-BLUPAM-BLUP
Initial
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Feed Efficiency Trial
Full FedNo Feed Restriction2-6 Weeks of Age
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Feed Conversion (Feed per Gain)
6.6
6.8
7
7.2
7.4
7.6
CE-BLUP AM-BLUP
Feed
/Gai
n
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Conclusions• Estimation of Direct and Associative
Effects Allows– Mapping of QTL of Unseen But Important
Traits– Increased Efficiency of Utilization of
Limited Resources– Increased Yield Without Increasing Inputs – Does Not Increase Cost of Program
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Conclusions
• Traditional BLUP Selection– Is Not Optimal– Ignores Competitive
Effects– Assumes No Genotypes
x Genotype Interactions
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Conclusions
• BLUP Incorporating Associative Effects– Almost As Good As
Group Selection– Far Superior to
Traditional BLUP– Does Not Increase Rate
of Inbreeding As Fast As Group Selection