Post hoc experimental designs improve genetic trial analyses: A case study of cherrybark oak (Quercus pagoda Raf.) genetic evaluation in the western Gulf region, USA

Abstract

Oaks (Quercus spp.) are widespread hardwood trees in the Northern Hemisphere and of high ecological, economic, and social values. Optimal experimental design of genetic trials is essential for accurate estimates of genetic parameters and improving the genetic merit of breeding stock. Here, we evaluate the use of post hoc row-column factors combined with spatial adjustment to improve genetic analyses of parents and individual trees in field progeny tests of plantation hardwoods, using cherrybark oak (Quercus pagoda Raf.) as an example. For tree height, post hoc incomplete blocking reduced ~14% more of the within-block environmental variance compared to the randomized complete block design (RCBD) model. Incomplete blocking also improved the heritability estimates for height by 7% to 14% compared to the original RCBD model. No clinal trend for growth breeding values was identified due to provenances. Our approach warrants the initial selection for height as early as age ~10 based on its moderate narrow-sense heritability of 0.2; however, diameter and volume need longer evaluation times. The post hoc incomplete blocking is more efficient and promising to improve the genetic analysis of Q. pagoda to minimize the environmental heterogeneity influences. Adjusting competition and spatial effects, including the distance principal components and autoregressive residual structure notably improves the model fit based on the observed reductions in AICs and BICs. Employing our approach is promising for hardwood genetic improvement in the southern USA.

Fig 1. Map of the WGFTIP Q. pagoda Raf. progeny test sites and selection locations.

Note, The two series of Q. pagoda Raf. progeny tests were planted at the adjacent locations in Arkansas and Mississippi. The Texas sites were established at separated locations for two series. The grey points depict the 305 1^st-generation selections originating from 51 counties; the triangles represent the 52 2^nd-generation selections from parents originating in17 of those 51 counties. The x-axis is the longitude and y-axis is the latitude. Map data were obtained from urbnmapr R package and state boundaries were from the US Census Bureau (www.census.gov).

Fig 2. AIC differences of BLUP models of four traits using the complete blocking (BLK) AIC as the benchmark at four selected trials.

The negative values indicate more preferred models compared to the BLK model (zero). Note, RCBD, is original RCBD model; SUBB, incomplete blocking; SUBH, incomplete blocking with heterogeneous residual variance; SUBNN, incomplete blocking with neighboring effect; SUBNNH, incomplete blocking with neighboring effect and heterogeneous residual variance; SUBNNPCA1, incomplete blocking with neighboring distance PC model; SUBNNPCA2, incomplete blocking with neighboring effect and distance PC model; BLK, complete blocking; BLKH, complete blocking with heterogeneous residual variance; BLKNN, complete blocking with neighboring effect; BLKNNH, complete blocking with neighboring effect and heterogeneous residual variance; NNPCA1, complete blocking with distance PC model; NNPCA2, complete blocking with neighboring effect and distance PC model. The RCBD model of survival was not converged.

Fig 3. BIC differences of BLUP models of four traits using the complete blocking (BLK) BIC as the benchmark at four selected trials.

The negative values indicate more preferred models compared to the BLK model (zero). Note, RCBD, is original RCBD model; SUBB, incomplete blocking; SUBH, incomplete blocking with heterogeneous residual variance; SUBNN, incomplete blocking with neighboring effect; SUBNNH, incomplete blocking with neighboring effect and heterogeneous residual variance; SUBNNPCA1, incomplete blocking with neighboring distance PC model; SUBNNPCA2, incomplete blocking with neighboring effect and distance PC model; BLK, complete blocking; BLKH, complete blocking with heterogeneous residual variance; BLKNN, complete blocking with neighboring effect; BLKNNH, complete blocking with neighboring effect and heterogeneous residual variance; NNPCA1, complete blocking with distance PC model; NNPCA2, complete blocking with neighboring effect and distance PC model. The RCBD model of survival was not converged.

Fig 4. The variance components of height (HT) and the standard errors of several design factors.

Note, VE (residual variance), VROW(sub-blocking and complete row blocking), REP (blocking variance), and VCOL (sub-blocking and complete column blocking) for four selected trials. RCBD, is original RCBD model; SUBB, incomplete blocking; SUBH, incomplete blocking with heterogeneous residual variance; SUBNN, incomplete blocking with neighboring effect; SUBNNH, incomplete blocking with neighboring effect and heterogeneous residual variance; SUBNNPCA1, incomplete blocking with neighboring distance PC model; SUBNNPCA2, incomplete blocking with neighboring effect and distance PC model; BLK, complete blocking; BLKH, complete blocking with heterogeneous residual variance; BLKNN, complete blocking with neighboring effect; BLKNNH, complete blocking with neighboring effect and heterogeneous residual variance; NNPCA1, complete blocking with distance PC model; NNPCA2, complete blocking with neighboring effect and distance PC model. The incomplete blocking method reduced HT V_E ~14% compared to the original RCBD method (RCBD).

Fig 5. Correlation of provenance of 2^nd-generation selections (latitude (Lat) and longitude (Long)) versus the breeding values of DBH, HT, and volume, as well as the HT breeding value of 2^nd-generation parents over the landscape based on the provenance locations and six trials.

The green bar indicates the magnitude of volume breeding value, the average of the 12 post hoc methods. The six 2^nd-generation progeny tests were labeled as (AFC1&2, MFC1&2, and TFS 1&2). Pearson’s correlation coefficients are in the right upper diagonal, the scatter plots are in the lower left diagonal for the pairs of traits, while the diagonal are the histograms of each trait. The p-values are denoted as following ***<0.001, **<0.01, *<0.05. Map data were obtained from urbnmapr R package and state boundaries were from the US Census Bureau (www.census.gov).