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 800
600 Volume
GF2
GF7
400
GF14 GFplus26
200
0 8
10
12
14
Age
16
18
20
22
Percent gain in volume of GFPLUS26 at age 22 (Planted 1978, sawlog regime)
Forest
Region
Aupouri
Northland
Kaingaroa
CNI
Kaingaroab
CNI
Mohaka
Hawkes Bay
Golden Downs
Nelson
Waimate
Canterbury
Longwoodb
Southland
Mean b. pulpwood regime
% gain 49.7 15.1 15.2 49.9 44.8 38.2 12.4 32.2
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 Range in basal area (m 2/ha)
(Carson, Kimberley, Hayes & Carson 1999) 25
20
15
10
5
0 Kaingaroa
Otago Coast
Woodhill
Ditchlings Tahorakuri
Glengarry
Overall
Site 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 highestquality 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:
or
y = a + bx t2 = a + b t1
y = a + m bx 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 1.25
1.22
Multiplier (BA)
1.20
Control-pollinated (GFPLUS26)
1.15
1.12
1.10
Open-pollinated (GF14) 1.06
1.05
Climbing select (GF7)
1.00 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
Diameter BV
6
7
8
9
10 11 12 13 14 15 16
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 1700
Acoustic velocity age 4 (m/sec)
1600
1500
1400
1300
1200 3.50
3.75
4.00
4.25
4.50
4.75
Height age 4 (m)
OP seedling (GF16)
OP seedling (GF19)
Mean of Prod.Clones
Production Clone
CP cutting (GF30)
Seedlots can be rated for genetic quality
Seedlot rating (GFPLUS)
New Zealand Seed Certification Service 30 28 26 24 22 20 18 16 14 12 10 -10
-5
0
5
Breeding value
10
15