A robust growth modelling

strategy for Prediction of genetic

gain

Sue Carson

Carson Associates Ltd, Rotorua, New Zealand January, 2006

Breeding results in economically

significant increases in growth

Large estate of genetic gain trials

Large-plot trials:

49 sites planted 1978-1994

60+ seedlots

Final crop stocking 200-1000 sph

~1390+ large plots

Annual measurements in PSP since

age 5-8, bi-annual starting age 15

Volume observed in genetic gain trials

Site: RO 2103/2 Actual data

0

200

400

600

800

8 10 12 14 16 18 20 22 Age

Vo

lum

e GF2

GF7

GF14

GFplus26

Percent gain in volume of GFPLUS26 at age 22 (Planted 1978, sawlog regime)

Forest Region % gain

Aupouri Northland 49.7

Kaingaroa CNI 15.1

Kaingaroab CNI 15.2

Mohaka Hawkes Bay 49.9

Golden Downs Nelson 44.8

Waimate Canterbury 38.2

Longwoodb Southland 12.4

Mean 32.2 b. pulpwood regime

Genetic gain in growth – Growth

modelers have to get it right!

Site and stand density have a much

larger effect on growth than genetics

The effects of site and silviculture

must be well predicted!

Site and stand density have a much

larger effect on growth than genetics

Data from 6 sites, 4 seedlots, 1/3 rotation (Carson, Kimberley, Hayes & Carson 1999)

0

5

10

15

20

25

Kaingaroa Otago

Coast

Woodhill Ditchlings Tahorakuri Glengarry Overall

Site

Ra

ng

e i

n b

as

al

are

a (

m2/h

a)

among sites among silvicultures among seedlots

Challenge: predict growth of

genetically improved forests

Usual situation:

1. Have existing growth models which predict

genetic gain based on stand density and

site quality

2. These growth models are most often based

on unimproved stands

3. May have large-plot genetic gain trials with

a few representative seedlots. Often only

one silviculture represented.

Challenge: predict growth of

genetically improved forests

Usual situation:

4. Better (ie. more highly improved) seedlots

will be constantly developed, that is, the

very best seedlots will not be represented in

genetic gain trials.

5. Breeding values can be used to quantify a

relative genetic value of any seedlot

Traditional strategy

Procedure:

1. Establish all seedlots of interest on all

site qualities of interest, and treat with all

stand densities of interest

2. establish and measure PSP over a

period of time

3. Refit model

Traditional strategy

Limitations:

Very extensive set of stands, plots and

assessments required

Long time frame required

Can’t extend model beyond seedlots

represented in PSP

More robust strategy: Genetic gain multipliers

(Growth rate multipliers)

Assumptions:

Genetic gain is expressed as an increase

in growth rate

Compression of the time scale: Improved

trees grow similarly to unimproved, but

get there faster

Increases in diameter and height growth

rates are independent

More robust strategy: Genetic gain multipliers

(Growth rate multipliers)

Procedure:

Insert growth rate multiplier into model function &

solve for growth rate multiplier

Plug in data from large-plot genetic gain trials to

estimate growth rate differences between seedlots

Correlate growth rate differences to genetic quality

(breeding values)

Insert estimate of multiplier into model function

based in input of genetic worth of planting stock

More robust strategy: Genetic gain multipliers

(Growth rate multipliers)

Advantages:

Are modeling genetic gain as a process

Can extrapolate to stand densities, and site

qualities not represented in genetic gain trials

Can extrapolate to newly-developed highest-

quality seedlots, and seedlots not represented

in genetic gain trials

Can examine the effects of stand density and

site quality on realization of genetic gain

Estimation of genetic gain multipliers

from genetic gain trial data

Step 1: - for Seedlot A (unimproved)

a) Insert multiplier term (m) into model:

y = a + bx y = a + m bx

or t2 = a + b t1 y = a + m b t1

b) Rearrange equation:

m = (t2 – a)/ t1x

c) Use plot data at time tA1 and tA2 to

estimate mA

Estimation of genetic gain multipliers

from genetic gain trial data

Step 2:

a)mA is a measure of how much faster or

slower seedlot A is growing than the model

predicts

b)Estimate mB for Seedlot B (improved)

c)Genetic gain multiplier = (mB – mA) + 1

Case Study:

New Zealand radiata pine

Good empirical growth models

already developed

Seven regional growth models:

Three equations: Height, basal area, stocking

Oscar Garcia’s State-Space Model - 13

coefficients fit simultaneously

Based on large amounts of PSP data

Models predict growth well

First estimation of genetic gain multipliers

from genetic gain trial data (10 large-plot trial sites, 4 seedlots, age 8-14)

(Carson, Garcia & Hayes 1999)

Growth rate multiplier

Seedlot Height Basal area

Unimproved 0.998 0.997

Climbing select 1.000 1.000

OP seed orchard 1.051 1.130

Control pollinated 1.045 1.264

Second estimation with more

extensive data

Growth rate multipliers estimated from 18

large-plot trials with 35 seedlots and 495

plots, ages 5-19 years, and

Breeding Values for diameter estimated

from 41 single-tree plot progeny trials,

1800 parents, approx age 8 years, BLUP

Relationship of Breeding values for

diameter and growth rate multiplier

Relationship of Breeding values for

diameter and growth rate multiplier

Growth Rate Multiplier using Breeding Values (BV)1978 - 1990 Genetic Gain & Silviculture/Breed Trial Series

All sites

1.06

1.12

1.22

1.00

1.05

1.10

1.15

1.20

1.25

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Diameter BV

Mu

ltip

lie

r (B

A)

Climbing select (GF7)

Open-pollinated (GF14)

Control-pollinated

(GFPLUS26)

Growth rate increases appear to

be constant over:

Stand age (unpublished data)

Growth modelling regions (unpublished data)

Tree stocking (Carson, Kimberley, Hayes & Carson 1999,

unpublished data)

How well do the multipliers predict

growth?

Completely independent validation:

Independent Models:

Implemented genetic gain multipliers in three

regional models not used for estimation of growth

rate multipliers

Independent Data:

Examined accuracy of predictions using data

from 3 large-plot genetic gain trials not used

for estimation of growth rate multipliers)

Growth Predictions with and without

genetic gain multipliers

Regional

Growth Model

Multiplier

Implementation

Mean %

error

NAPIRAD

2 sites

7 seedlots

30 plots

None (Base model) 8.2

BV multiplier 7.3

CLAYSF

1 site

4 seedlots

14 plots

None (Base model) 15.6

BV multiplier 10.0

SANDS

1 site

4 seedlots

16 plots

None (Base model) 9.3

BV multiplier 7.7

Concept of genetic gain

multiplier is robust

• Models a process rather than just fitting coefficients to data

• Can be extrapolated to seedlots, sites and silviculture not in genetic gain trials

• Can be utilized with models derived from different data

Can be utilized with models of different form

Example of the need to extrapolate to include

better planting stock

1200

1300

1400

1500

1600

1700

3.50 3.75 4.00 4.25 4.50 4.75

Height age 4 (m)

Ac

ou

sti

c v

elo

cit

y a

ge

4

(m

/se

c)

OP seedling (GF16) OP seedling (GF19) CP cutting (GF30)

Mean of Prod.Clones Production Clone

Seedlots can be rated for genetic quality

New Zealand Seed Certification Service

10

12

14

16

18

20

22

24

26

28

30

-10 -5 0 5 10 15

Breeding value

Seed

lot

rati

ng

(GF

PL

US

)