Estimation and Application of Genetic- Gain Multipliers for Douglas-Fir Height and Diameter Growth Peter J. Gould 1, David D. Marshall 2, Randy Johnson 1 and Greg Johnson 2 1 USDA Forest Service Pacific Northwest Research Station 2 Weyerhaeuser Co.

Outline Issues, concepts, objectives Data and modeling approach Results Applications for projecting yield

Why Model Genetic Gain? Improved Douglas-fir is a reality in the PNW. Insight into stand development and return on investment (without waiting 20+ yrs). Genetics studies have not focused on stand- level growth and yield.

Genetic-Gain Multipliers Example: ΔD G = M∙ ΔD WR Extrapolates information from genetics studies to existing growth models. Other approaches include refitting equations and SI adjustments. Predicted growth from woods-run model Predicted growth with genetic-gain

Genetics Studies: Questions Asked Geneticist: What is the total height and diameter of a genotype at a given age relative to woods-run? Single-tree plots Families tested on multiple sites; interested in mean across sites. Select best parents for seed orchards / breeding

Genetics Studies: Questions Asked Modeler: What is the rate of height and diameter growth of an individual tree for a given period based on its pedigree and site, stand, and tree characteristics? Interested in growth within a stand. Genetics is one of many factors controlling growth.

Concepts from Genetics Breeding value: the value of a parent for passing some trait to its progeny (estimated from progeny tests). Genetic worth: the expected level of gain for some trait of an improved seedlot. GW = f(BV orchard, outside pollen) Both expressed as percentage difference from population (woods-run) mean in traits such as total height and diameter at a given age.

NWTIC 1 st Generation Progeny Tests Seed collected from wild, woods-run parents to test half-sib families. BV calculated for mother trees at age 10 yrs (genetics perspective). We used same data (up to age 20 yrs). Half-sib families treated as individual seedlots where:

Study Objectives Estimate genetic-gain multipliers for height and diameter growth for improved DF seedlots when GW is known. M = f (GW, stand age) Evaluate multiplier effects in growth models (ORGANON and FVS).

Modeling Strategy 1. Estimate growth of individual trees (e.g., ΔD WR ) in progeny tests using woods-run models. 2. Calculate seedlot-level multipliers (M) from observed growth and expected growth under the woods-run model. ΔD G = M∙ ΔD WR M = ΔD G / ΔD WR 3. Estimate M from seedlot’s GW.

NWTIC 1 st Generation Progeny Tests Breeding zone: area of relatively uniform environment (≈ 50,000 ha) Site: Geographical location within breeding zone. Set: Group of families tested together. A more-or- less random sample of woods-run population. Rep 1Rep 2 Rep 3Rep 4 Rep 1Rep 2 Rep 3Rep 4 Rep 1Rep 2 Rep 3Rep 4 SET 1SET 2SET 3

DBH Data: Variation Between Breeding Zones 10-yr DBH (cm) 10 to 15 yr DBH Increment (cm)

DBH Data: Variation Between Sites 10-yr DBH (cm) 10 to 15 yr DBH Increment (cm)

DBH Data: Variation Between Sets 10-yr DBH (cm) 10 to 15 yr DBH Increment (cm)

Challenges of Progeny Test Data Limited individual-tree measurements – No crown ratios or crown class Single-tree plots – No stand density (e.g., basal area) – No site index Mixed genotypes –Superior trees may perform better – Inferior trees may perform worse

Modeling Strategy Could not use an existing model – Unmeasured variables – Precision needed to estimate small effects Created “custom” woods-run models: Ex: ∆HT = b1∙HT b2 ∙b3 HT random effects on b1,b2,b3 at set level Separate models fit for , and 15-yr periods.

Mixed Genotypes GW = 10 GW = -10 GW = 0 Probably not very important: – much overlap between seedlots in size / competitive position. – Woods-run models account for differences in initial size.

NWTIC 1 st Generation Progeny Tests Period (yr) Height GrowthDiameter Growth BZSeedlotsNBZSeedlotsN , , , , , ,396

Woods-run Model: Height Growth

1.8% 3.3%

Woods-run Model: Height Growth

Estimating Height-Growth Multipliers M = α 0 + α 1 ∙ GW OLS, WLS and method-of-moments regression fits (error in GW). WLS fits: Period Equation ∙GW ∙GW ∙GW

Estimating Diameter-Growth Multipliers WLS fits: Period Equation ∙GW ∙GW ∙GW

We Have Multipliers; Now What? ORGANON (Mark Hanus and David Hann). FVS PN and WC (FIXHTG and FIXDG keywords). Tested “virtual” seedlot with 10% GW for height and diameter at 10 yrs.

We Have Multipliers; Now What? Tree list for 10-yr-old stands generated with FGROW (Flewelling and Marshall). Adjusted 10-yr height and diameters by multiplying by Tested adjusted tree list with and without genetic- gain multipliers.

Projections Woods-Run Volume (cuft) Gain with Multipliers (cuft) Gain with Treelist (cuft)

Woods-Run Volume (cuft) Gain with Multipliers (cuft) Gain with Treelist (cuft) 1.1%5.7% 6.6% 12.7% Projections: 40-yr Rotation

Woods-Run Volume (cuft) Gain with Multipliers (cuft) Gain with Treelist (cuft) 0.2% 2.2% 4.3% 7.0% Projections: 60-yr Rotation

Conclusions Multipliers can put genetic information in models right now, though many questions remain. Genetic effects are relatively small, but significant. Modelers need more information and more precise estimates than tree breeding programs. Operational and controlled experiments are needed.