Genetic thinning of clonal seed orchards using linear

deployment

Forest Genetics and Tree Breeding in the Age of Genomics: Progress and Future

November 1-5, 2004 Charleston

Wednesday 1:30-5:40 PMConcurrent Session II: Advances in

Reproductive Biology and Seed OrchardsModerator: Clem Lambeth

4:25-4:50 Seed orchard Thinning Using Linear Deployment of Clones

Dag Lindgren, SLU, Sweden

The authors

Mohan Varghese Dag Lindgren Finnvid Prescher

Presents a genetic thinning algorithm

Known:

• Ramet number and breeding value for each clone

Result:

• Number of ramets to be rouged for each clone

The algorithm combines the two desires:

• High effective number of clones

and

• High genetic gain

Linear deployment is optimal for establishment!

• No other deployment combines higher gain with higher effective number

Linear Deployment at seed orchard establishment

0

50

100

150

200

100 110 120

Breeding value of clone

Ra

me

ts

At thinning ramets cannot be added, just withdrawn. The

algorithm has to be modified.

Linear deployment for genetic thinning

Linear Deployment at genetic thinning

0

50

100

150

200

100 110 120

Breeding value of clone

Ra

me

ts

The optimal line is the same for all clones

Bondesson, L. and Lindgren, D. 1993. Optimal utilization of clones and

genetic thinning of seed orchards. Silvae Genet. 42: 157-163 .

Mathgi = breeding value of clone i ri = ramets (grafts) of clone i after thinning Ri = ramets of clone i before thinning (higher border) g0 = intercept b = slope Ne = effective number of clones G = breeding value of seed orchard clones

ii

ii

e

r

rN

2

2

iii rgrG /

At given effective number, gain is maximized if ramet number is proportional to breeding value

More math…The linear deployment thinning algorithm maximizing G at Ne is as follows:

0

)(

0

000

0

ii

iiii

iiii

rgg

ggbrgggb

R

Rrggb

R

The algorithm results in an optimal combination of G, Ne and ramets remaining, but there are many optimal combinations. The specific solution is given by the choice of g0 and b. g0 and b are chosen to result in desired combination of values for

G, Ne and ramets remaining.

(Bondesson and Lindgren 1993).Note that linear deployment can be seen as a solution searching for a problem, and not as usual a problem asking for a solution.This presentation shows three practical applications

Genetic thinning characteristics

1. Remaining ramets

2. Genetic gain (breeding value)

3. Effective clone number

Linear deployment thinning is optimal

No other deployment can increase one of these three factors without decreasing another

This is first presentation of applications of the algorithm

published 1993!

Put into a worksheet…

Output: Gain, effective number, remaining ramets per clone

Input:

breed

ing v

alues

,

ram

et num

bers

Linear Deployment at www.genfys.slu.se/staff/dagl

Three objectsPlace Species Type BV from

Lagan,

Sweden

Norway spruce

Seed orchard,

Cuttings

Clonal test

Maglehem,

Sweden

Norway spruce

Seed orchard,

Grafts

Progeny test

Coimbatore,

India

Eucalyptus camaldulensis

Clonal test converted to seed orchard

The site itself

At a suitable thinning intensity

106

107

108

109

110

16 18 20 22 24 26 28

Effective clone number

Bre

ed

ing

Valu

e

The graph is generated by trying different lines

Result Lagan, linear deployment thinning

Before Thinned

Clones 32 32

Ramets 5351 3644

Gain (% ) 106.0 108.5

Effective number

20.0 22.0

Substantial improvement for both Gain and Effective number!

Truncation

24

3644

109.0

16.8

Marginally higher gain, but many clones lost, effective clone number substantially reduced!

Practical thinning resulted in almost full optimality!

Genetic thinning Maglehem

0102030405060708090

100

-2.50 -1.50 -0.50 0.50 1.50

Breeding value for height

Ra

me

ts p

er

clo

ne

Before thinning

After thinning

Intended Linear Deployment

Thinning at Maglehem

Before Thinned

Clones 36 32

Ramets 2006 1260

Gain -0.03 0.48

Effective number

34.9 26.8

Truncation

28

1565

0.36

27.´0

Truncation selection that preserves the effective number results in much lower gain!

Thinning at Maglehem

Before Thinned

Clones 36 32

Ramets 2006 1260

Gain -0.03 0.48

Effective number

34.9 26.8

Truncation with the same number of ramets results in a little higher gain, but much fewer clones and effective number

Truncation

23

1261

0.56

22.1

Thinning at Maglehem

Before Thinned

Clones 36 32

Ramets 2006 1260

Gain -0.03 0.48

Effective number

34.9 26.8

Linear

32

1260

0.49

26.8

The optimality remains!

Eucalyptus clone trial at Coimbatore

A clonal test of Eucalyptus camaldulensis established at Coimbatore in south India comprising 87 clones (selected from 7 seedling seed orchards and commercially available clones). There were 15 ramets of each clone arranged in 3 tree plots with 5 replications.

The test was to be converted to a clonal seed orchard based on height assessment in the trial at three years.

The Eucalyptus clone trial at measurement and the ramets at planting

0

4

8

12

16

4 5 6 7 8 9

Clone height (m)

Nu

mb

ero

f ra

me

ts

InitialSame ramet numberSame gainSame effective NumberTruncation

Thinning Coimbatore

Linear DeploymentSame ramet

Truncation selection

Clones 72 43

Eff number 57.3 42.4

Ramets 573 573

Height 7.49 7.56

At the same thinning intensity there are much higher retained number and effective number, but marginal loss in gain,

Linear DeploymentSame Gain

Truncation selection

Clones 70 43

Eff number

50.5 42.4

Ramets 429 573

Height 7.56 7.56

At the same genetic gain there are much higher retained number and effective number, but a more intensive thinning is requiered.

Linear Deployment Same Ne

Truncation selection

Clones 62 43

Eff number 42.4 42.4

Ramets 396 573

Height 7.65 7.56

At the same effective number of clones there are a higher retained number and more gain, but a more intensive thinning is required.

Conclusions• Linear deployment at thinning is theoretically

optimal!• The loss from optimality because of practical

difficulties is marginal and the added flexibility may offer advantages!

• The added practical difficulty is marginal.• The increase in gain and clones retained at the

same effective clone number are substantial!• It is sometimes possible to make significant

increases for both gain and effective clone number with a moderate genetic thinning. These entities have earlier been seen as incompatible!