Deployment of related clo nes into seed orchards

DaDa work 2001-2007Deployment Deployment of of

related clorelated clonesnes into into seed orchardsseed orchards

The road to The road to efficientefficient breeding breeding

Seed orchard conference, Umea, Sept. 26-29 2007

Darius Danusevicius (LFRI),Darius Danusevicius (LFRI),Dag LindgrenDag Lindgren ( (SLU), SLU),

Ola Rosvall (SkogForsk)Ola Rosvall (SkogForsk)

I try to mark changes in red I try to mark changes in red Darius my responce Darius my responce in greenin green

Dag Lindgren

Main findingsMain findings•Tools are developed to handle situations with related orchard candidates

•Large diversity available: Make a subset of the best unrelated candidates and deploy proportionally to their BVs (“linear deployment”).

•Small diversity:Small diversity: allow relatives in seed orchard allow relatives in seed orchard and use computer optimization, e.g. (for small and use computer optimization, e.g. (for small materials) materials) Optimal proportionsOptimal proportions in ourin our EXCEL EXCEL software “Orchard optimizer” software “Orchard optimizer”

Dag Lindgren

ProblemProblem

Progeny testsProgeny tests

How to deploy clones to seed orchards How to deploy clones to seed orchards where candidates are tested relatives?where candidates are tested relatives?

Fam1Fam1

Fam3Fam3

Fam4Fam4

Fam2Fam2

How many How many famsfams? ?

Individuals per Individuals per famfam.?, ramets .?, ramets

from individual?from individual?

Ibreeding

Dag Lindgren

ObjectiveObjective•To compare To compare Net gainNet gain from alternative from alternative deployment strategies based on simulated deployment strategies based on simulated data (“half sibs”) or real data (“full sibs”).data (“half sibs”) or real data (“full sibs”).

•To develop methodology for seed orchard To develop methodology for seed orchard designers calculations to design seed orchards designers calculations to design seed orchards in an efficient way when candidates are in an efficient way when candidates are related? related?

Half sibsHalf sibs:: more general study, more scenarios and more general study, more scenarios and parameters. parameters. Full sibs:Full sibs: case-study with complex case-study with complex relatedness structure, but less scenarios and relatedness structure, but less scenarios and alternatives. alternatives.

Optimal selection is best by definition, other Optimal selection is best by definition, other alternatives are to check how inferior they are - if not alternatives are to check how inferior they are - if not very inferior they can be used as they are simplervery inferior they can be used as they are simpler??

M&MM&M

ParametersParameters

• We want to maximize Net gain at a We want to maximize Net gain at a given status numbergiven status number

•Net gainNet gain== average Breeding Value of average Breeding Value of seeds reduced by expected inbreeding seeds reduced by expected inbreeding depressiondepression

•Status number= 0.5 /(group Status number= 0.5 /(group coancestry)coancestry)

•Group coancestry = Pair coancestry Group coancestry = Pair coancestry (among sibs) + self(among sibs) + self coancestry coancestry (within (within clone)clone)

amongfam12out126out6 24out2448out481.629 1.267 1.948 2.2331.116 0.642 1.503 1.8370.793 0.202 1.239 1.6090.537 -0.202 1.041 1.4420.312 -0.642 0.877 1.3080.103 -1.267 0.734 1.194

-0.103 0.604 1.094-0.312 0.484 1.004-0.537 0.37 0.921

-1.116 0.156 0.772-1.629 0.052 0.704

-0.052 0.639

Simulated data Simulated data withwith half- half-sibs sibs

withinFam5out5 5of10 5out20 5out40 5of80 5of1201.163 1.539 1.867 2.161 2.427 2.5720.495 1.001 1.408 1.753 2.057 2.22

0 0.656 1.131 1.517 1.848 2.024-0.495 0.376 0.921 1.344 1.698 1.884-1.163 0.123 0.745 1.203 1.578 1.773

•Selection forward in unrelated half sib familiesSelection forward in unrelated half sib families

•Individual BVs generated from normal order statisticsIndividual BVs generated from normal order statistics..

)(, *75.0*25.0* ijiAji CVBV

BVBV=10*(SQRT(1/4)*O5+SQRT(3/4)*P5)+100=10*(SQRT(1/4)*O5+SQRT(3/4)*P5)+100

AmongAmong WithinWithin

BV expressed as std from mean 0 based on ND (Dag’s program) and expressed in units of CVa by x 10.

Real data Real data withwith full-sibs full-sibsBV of 19 short listed field-tested clones BV of 19 short listed field-tested clones from 11 fams (8 unrelated), from 11 fams (8 unrelated), maxmax 2 sibs 2 sibs per famper familyily

Types of Types of relatedness: - half relatedness: - half sibssibs θθ=0.125=0.125

-full sibs-full sibs θθ =0.25 =0.25

TTruncation Deploymentruncation DeploymentTruncation related: individual above certain threshold are selected regardless of their relatives; equal number of ramets from each

Fam1Fam1

Fam3Fam3

Fam4Fam4

Fam2Fam2

Truncation unrelated: one individual is selected from good families; equal number of ramets from each

Fam5Fam5

Fam1Fam1

Fam3Fam3

Fam4Fam4

Fam2Fam2

Fam5Fam5

= = commoncommon approach approach

used todayused today

Linear deploymentLinear deployment

Fam1Fam1

Fam3Fam3

Fam4Fam4

Fam2Fam2

Fam5Fam5

LD related: individuals above certain threshold are selected regardless of their relatives; no of ramets deployed proportionally the BV

LD unrelated: the best clone is selected in the good families and deployed proportionally the BV

Fam1Fam1

Fam3Fam3

Fam4Fam4

Fam2Fam2

Fam5Fam5pi = (gi – g0)/g0 where:

pi =proportion of i-th individual;

gi = breeding value of i-th individual

g0 = intercept of linear relationship (the threshold breeding value)

Optimal proportionsOptimal proportions Individuals are deployed in the proportions which Individuals are deployed in the proportions which maximize the net gain at a given status number. maximize the net gain at a given status number.

Fam1Fam1

Fam3Fam3

Fam4Fam4

Fam2Fam2

Fam5Fam5

Inpu

ts

Results

ggive it all to a ive it all to a computercomputer

(”solver” in EXCEL)(”solver” in EXCEL)

ScenariosScenarios ( (””half sibshalf sibs””))Parameter Main

ScenarioAlternative scenarios

Low budgetscenario

Number of half-sib families

24 6, 12, 48

12

Family size 40 20 5

Status number in seed orchard 12 3, 6, 24 12

Inbreeding depression Important Not Important

Important

Number of clones As found As found As found

The simulatorThe simulator

Adjust the Adjust the truncation BV truncation BV

to get the to get the desired Ns, and desired Ns, and

see the see the resulting Net resulting Net

gaingain

Seed orchard deployed (developed by Seed orchard deployed (developed by Dag)Dag)

Results (half-sibs)Results (half-sibs)

Strategies comparedStrategies compared

•““Optimal prop.” is Optimal prop.” is best best

•““Linear unrelated” Linear unrelated” ~~ “Otimal prop.” if “Otimal prop.” if fam. no > 20fam. no > 20

•““Truncation Truncation related” & “Linear related” & “Linear related” are inferior: related” are inferior: they they sampsamplele relatives when relatives when unrelated cand.’s unrelated cand.’s with high BV are with high BV are available.available.

•Low diversity of Low diversity of candidates favors candidates favors strategies which strategies which allow relativesallow relatives

Optimal proportions Linear unrelated Truncation unrelated Linear related Truncation related

Ordered by rank

Strategies comparedStrategies compared

Increasing demand of diversity Increasing demand of diversity

•Increasing Ns means Increasing Ns means more diversity is more diversity is needed in the orchard.needed in the orchard.

•Net gain is lower as Net gain is lower as more inferior has to more inferior has to enterenter

•““Optimal prop.” is at Optimal prop.” is at its best when the its best when the demand for diversity is demand for diversity is highhigh““Optimal prop.” is best; Optimal prop.” is best; “Linear unrelated” may “Linear unrelated” may be used when diversity be used when diversity is high; Truncation to be is high; Truncation to be left to the pastleft to the past

You phrase as we should use Linear unrelated when You phrase as we should use Linear unrelated when diversity is high. Linear unrelated is enough but it is diversity is high. Linear unrelated is enough but it is by definition never better than optimal, and have we by definition never better than optimal, and have we developed optimal we can use it always. So there is developed optimal we can use it always. So there is

no need to develop optimal if diversity is high! But we no need to develop optimal if diversity is high! But we should not directly recommend to forget about it, it is should not directly recommend to forget about it, it is

just unneeded.just unneeded.

OK I have rephrased it OK I have rephrased it

Optimal proportions Linear unrelatedTruncation unrelated Linear related Truncation related

Ordered by rank

When is OK with Linear When is OK with Linear Deploy.Deploy.

10

15

20

25

30

0 4 8 12 16 20Ratio Ns availabe / Ns desired

Nu

mb

er

of

de

plo

ye

d c

lon

es

Use Optumum proprtions

Use Linear Deployment unrelated

a)Dependence of the no. of Dependence of the no. of deployed clones on the deployed clones on the diversity available for diversity available for deployment (expressed deployment (expressed as ratio as ratio NsaNsa / / NsdNsd). ).

When number of When number of deployed clones is deployed clones is constant, one best constant, one best individual was selected individual was selected from certain number of from certain number of superior families and superior families and then “Optimal prop” then “Optimal prop” =“Linear unrelated”;=“Linear unrelated”;

Increase of Nsa/Nsd ration Increase of Nsa/Nsd ration means high diversity available means high diversity available

for selectionfor selection

Optimal deployment strategy

00

55

1414 1818

No of No of fams with fams with

one one individual individual Here I will not go into Here I will not go into

details just will show the details just will show the slide and say that it may be slide and say that it may be possible for particular cases possible for particular cases

to find a threshold value to find a threshold value when to use whatwhen to use what

Effect of parametersEffect of parametersInbreeding Inbreeding depressiondepression had weak effect on had weak effect on Net gainNet gain, , because the gene diversity in of candidates was high because the gene diversity in of candidates was high enough to maintain low degree of relatedness in the enough to maintain low degree of relatedness in the deployed population. deployed population.


Ordered by rank


Ordered by rank

No chance you can remember legends, but it is enough No chance you can remember legends, but it is enough to give legends for the two main competers. The to give legends for the two main competers. The

conclusion on the bottom is more important and easier conclusion on the bottom is more important and easier to see than the one on the top, can you in some way to see than the one on the top, can you in some way

change the emphasischange the emphasis

I moved the bottom sentence to the slide 15 last I moved the bottom sentence to the slide 15 last paragraph, because namely there strategies are paragraph, because namely there strategies are

compared and it is shown that reduction of diversity of compared and it is shown that reduction of diversity of candidates favors strategies allowing relatives. Here we candidates favors strategies allowing relatives. Here we

just show the effect of parameters.just show the effect of parameters.

Family sizeFamily size

120

121

122

123

124

125

126

6 8 10 12 14 16 18 20119

120

121

122

123

124

15 20 25 30 35 40

12 fam .s, Inbreeding=1, Ns=12

110

111

112

113

114

115

116

117

118

119

120

0 5 10 15 20 25 30 35 40

Family size

Ne

t g

ain

, %

24 fam.s, Inbreeding=1, Fam size=40

120

121

122

123

124

125

126

6 8 10 12 14 16 18 20

Status number

Net

gai

n, %

Optimal proportions

Linear related

Linear unrelated

Truncation related

Truncation unrelated

e)

Ranking of deployment strategies is Ranking of deployment strategies is independent of family size.independent of family size.

Short lists of fam. membersShort lists of fam. membersNo of families from which the number of

individuals given in table heading is selected

5 best 4 best 3 best 2 best 1 best

Parameter Number of families

(ratio Nsa/Nsd)

Family size

Status number desired (Nsd)

Inbreeding

depression

No. of clones

Best families

Not taken

6 (2) 40 12 1 28 4 2 0 0 0 0 12 (4) 40 12 1 21 0 0 2 5 5 0

24 (8) 40 12 1 18 0 0 0 2 14 8

Family number

48 (16) 40 12 1 18 0 0 0 0 18 30

Family size

24 (8) 20 12 1 18 0 0 0 1 16 7

24 (12) 40 8 1 12 0 0 0 0 12 12 24 (8) 40 12 1 18 0 0 0 2 14 8

Status number desired (Nsd)

24 (5) 40 18 1 29 0 0 1 7 12 4

6 (8) 40 3 1 4 0 0 0 0 4 2 12 (8) 40 6 1 8 0 0 0 0 8 4 24 (8) 40 12 1 18 0 0 0 2 14 8

Nsd with variable family number

48 (8) 40 24 1 39 0 0 1 7 22 18

6 (2) 40 12 0 27 4 1 1 0 0 0

12 (4) 40 12 0 25 1 1 2 3 4 1

24 (8) 40 12 0 22 0 0 2 4 8 10

Inbreeding

48 (16) 40 12 0 21 0 0 1 3 12 32

OP strategyOP strategy

Increasing Increasing diversity leads diversity leads to selection of to selection of one best from one best from ca. half of best ca. half of best

famsfams

Results (“full-sibs”)Results (“full-sibs”)

13

14

15

16

17

18

19

20

2 3 4 5 6 7

Status number

Maximizing net gain, V

Linear deployment - no relatives, IV

Truncation - no relatives, II

Linear Deployment - allowing relatives, III

Truncation - allowing relatives, I

Net

gai

n (

%)

Comparison of strategiesComparison of strategiesLinear Linear unrelated is as unrelated is as good as good as Optimal Optimal proportions= proportions= it does not it does not want more want more than one from than one from certain no. certain no. best fams!best fams!

Thus often we Thus often we do not need to do not need to try to apply try to apply the higher the higher degree of degree of sophistication!sophistication!

Model to optimize deploymentModel to optimize deploymentTo keep track of gene diversity To keep track of gene diversity

Group coancestry = Pair Group coancestry = Pair coancestrycoancestry (among relatives) + self (among relatives) + self coancestrycoancestry (within clone(within clone))

Nsd= 0.5 /(group coancestry)Nsd= 0.5 /(group coancestry)CandidatesCandidates

OrchardOrchard

Deployment by Optimal prop Deployment by Optimal prop or – if or – if group coancestry low -group coancestry low - Linear Linear

Deployment UnrelatedDeployment Unrelated

ForestsForests

Net gain is the parameter to be Net gain is the parameter to be maximizedmaximized

ConclusionsConclusions•Truncation is usually inefficient, thus today Truncation is usually inefficient, thus today most advanced seed orchards are probably not most advanced seed orchards are probably not efficiently establishedefficiently established

•If large number of unrelated individuals (half If large number of unrelated individuals (half sibs) available: short listsibs) available: short list the single best the single best candidate from the best families and deploy candidate from the best families and deploy with ramet number linearly related to breeding with ramet number linearly related to breeding values.values.

•If such large reduction of diversity is not If such large reduction of diversity is not tolerable or the short-list tend to be related, tolerable or the short-list tend to be related, optimize with the optimize with the Optimal proportionsOptimal proportions. .

Do we need different conclusions for half Do we need different conclusions for half and full sibs, is it not enough with one and full sibs, is it not enough with one

conclusion slide? conclusion slide? Yes you are right they Yes you are right they duplicate each other I left this one duplicate each other I left this one

Dag Lindgren

EndEnd

Conclusion: “full sibs”Conclusion: “full sibs”

Linear deployment of unrelated is an Linear deployment of unrelated is an efficient approach when there is limited efficient approach when there is limited relatedness among the candidatesrelatedness among the candidates

If there is much relatedness among If there is much relatedness among candidates a sophisticated program is candidates a sophisticated program is needed to get high efficiencyneeded to get high efficiency

Continents of Continents of 1515 min min

•Deployment of full sibs (real data) Deployment of full sibs (real data) (Dag(Dag Lindgren Lindgren, Ola, Ola Rosvall Rosvall, Darius, Darius D. D.) )

•Deployment of half sibs (Dag and Deployment of half sibs (Dag and Darius) (simulated data) Darius) (simulated data)

ParametersParametersGroup coancestry = Pair (among h-sibs) Group coancestry = Pair (among h-sibs) + self (among ramets)+ self (among ramets)

Ns= 0.5 /(group coancestry)Ns= 0.5 /(group coancestry)

NsaNsa (for large HS fam) (for large HS fam) ~~ 4 4

ppiiggii- BV of clone (g) and its proportion (p, ramets) - BV of clone (g) and its proportion (p, ramets)

ID is a weight coef. for diversity: if IDID is a weight coef. for diversity: if ID==1 and all are 1 and all are inbreed (Op inbreed (Op ==1), then Net gain 1), then Net gain == 0. 0.

Net gain

Parameter to maximize: Parameter to maximize: average BV of seeds average BV of seeds produced from the orchard with a deduction for the produced from the orchard with a deduction for the expected inbreedingexpected inbreeding

Spare slides full sibsSpare slides full sibs

0

0,01

0,02

0,03

0,04

0,05

2 3 4 5 6 7Status number

Truncation- allowing relatives, I

Linear deployment - allowing relatives, III

Maximizing net gain, V

Pa

ir c

oa

nc

es

try

How deployment strategies cope with How deployment strategies cope with increased demand for diversity in the orchardincreased demand for diversity in the orchard

How NHow Nstatusstatus is related to Ns? is related to Ns? Helps to understand the Helps to understand the

conceptsconcepts

0

4

8

12

16

20

0 4 8 12 16 20

Clone number

Truncation - allowing relatives, I

Truncation - no relatives, II

Sta

tus

nu

mb

er

For Unrelated For Unrelated NNcensuscensus=Ns;=Ns;

For related , For related , they depart they depart when relatives when relatives are sampledare sampled

Spare slides half sibsSpare slides half sibs

Net gain (%) from different deployment strategies

Parame ter

Fami ly

num ber

Fami ly size

Nsd Inbreed

ing weight

Optimal proportion

s

Linear Deployme

nt

Linear Deployment

Unrelated

Truncation

Truncation

Unrelated

Superiority of Optimal proportions

, %

Main scenario 24 40 12 1 123.2 121.6 123.2 121.6 122.6 100.0

6 40 12 1 115.1 114.4 no value 113.9 no value 105.1 12 40 12 1 120.1 118.5 118.9 118.3 118.7 106.4

Family number

48 40 12 1 125.5 124.1 125.5 123.9 124.9 100.0 Family

size 24 20 12 1 120.7 119.3 120.7 119.2 120.0 100.0

24 40 8 1 124.6 122.6 124.5 122.9 124.0 100.1 Status number 24 40 18 1 121.8 120.6 121.5 120.4 120.8 101.2

6 40 12 0 117.0 116.7 no value 116.1 no value 101.9 12 40 12 0 120.9 120.5 118.9 120.1 118.7 102.1 24 40 12 0 123.6 123.2 123.2 122.9 122.6 101.5

Inbreeding weight

48 40 12 0 125.7 125.4 125.5 125.0 124.9 100.7 Family number and size

12 5 12 1 111.2 110.3 110.3 110.0 110.1 108.4

Why Optimal prop. is Why Optimal prop. is efficientefficient


0.0000

0.0050

0.0100

0.0150

0.0200

5 9 13 17 21 25

Status number

Pai

r-c

oan

cest

ry

Optimal proportions

Linear related

Truncation related

Variation in pair coancestry in the deployed material Variation in pair coancestry in the deployed material depending on Nsd. depending on Nsd. Increase of pair-coancestry - Increase of pair-coancestry - selection of relatives.selection of relatives.LD samples individuals with high BV regardless of relatedness leading to high pair-coancestry.

OP favors less sampling of relatives (relatively less relatives from the few top ranking families).

When Nsd is increased, OP deploys more individuals from better fams and optimizes their proportions to maximize Net gain (leads to increase of pair-coancestry)

TR & LR sample the top ranking individuals from the families of a lower rank, which are unrelated to the already sampled. This causes reduction in pair-coancestry. Increased demand on diversity

(Nsd)

Self coancestrySelf coancestryIs coancestry among the ramets of Is coancestry among the ramets of oneone cloneclone

Included in desired Ns and effective clone Included in desired Ns and effective clone no.no.

Not included in Net gain, but assumed Not included in Net gain, but assumed that its negative effect can be handled by that its negative effect can be handled by placing the ramets some 30 m apart from, placing the ramets some 30 m apart from, each othereach other

Proportion of selected famsProportion of selected fams

10

15

20

25

30

0 4 8 12 16 20

0.0

0.2

0.4

0.6

0.8

1.0

0 4 8 12 16 20

Ratio Ns availabe / Ns desiredP

rop

ort

ion

of

fam

ilie

s n

ot

se

lec

ted

b)

(b) how much diversity we need for (b) how much diversity we need for NsdNsd of 12 (usual case)? When of 12 (usual case)? When NsaNsa is for 4 times greater than is for 4 times greater than NsdNsd, all families are needed (12 , all families are needed (12 half-sibs families at half-sibs families at NsdNsd of 12). of 12).

Deployment strategies Deployment strategies reduce relatednessreduce relatedness


0.0000

0.0050

0.0100

0.0150

0.0200

5 9 13 17 21 25

Status number

Pa

ir-c

oan

ces

try

Optimal proportions

Linear related

Truncation related

Note, there is large Note, there is large diversity to select diversity to select form and that form and that deployment strategies deployment strategies are aimed to are aimed to maximize net gain so maximize net gain so they trend to reduce they trend to reduce relatedness. relatedness. Therefore, relatedness Therefore, relatedness figures are rather figures are rather small small

4: BP size optimised

3: Ph/Prog amplified (pine), effect of J-M.

Seminar 2004.03.02

1-2: Best testing strategy

The Road to this semianrThe Road to this semianr

Breeding cycler

Hungry shark

Time compnentsTime compnents

TRecomb

TBefore

Stage 2. Time after: from selection of new individuals to start of their

flowering (crosses for the next cycle can be made). If the selected

individuals flower, Time after = 0.

Recombination time:pollen collection, crossing, seed

maturation…

Stage 1. Time before: test plant production

Breeding cycle

Time components of complete breeding cycle

Ttest

TAfterTBefore

Ttest

TAfter

Stage 1. Time after: from selection of candidates to their reproductive

maturity. If the candidates are reproductively mature, Time after = 0.


Stage 2. Testing: from establishment to

selection


selection

TRecomb

TBefore








maturation…


maturation…



Breeding cycle

Time components of complete breeding cycle

Ttest

TAfterTBefore

Ttest

TAfter

Stage 1. Time after: from selection of candidates to their reproductive

maturity. If the candidates are reproductively mature, Time after = 0.




selection


selection


selection


selection

Why selection forward?Why selection forward?

•The study is thought to serve for long term breedingThe study is thought to serve for long term breeding

•Long term breeding is usually based on selection Long term breeding is usually based on selection forwardforward

•If select back say ½ best mothers based on OP fam. If select back say ½ best mothers based on OP fam. trial, the selections may miss good recombinant trial, the selections may miss good recombinant progeny which may return higher gain (Dag do you progeny which may return higher gain (Dag do you know reference??) know reference??)

Deployment of related clo nes into seed orchards

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