Spatial analysis methods for forest genetic trials

Abstract

Spatial analysis, using separable autoregressive processes of residuals, is increasingly used in agricultural variety yield trial analysis. Interpretation of the sample variogram has become a tool for the detection of global trend and "extraneous" variation aligned with trial rows and columns. We applied this methodology to five selected forest genetic trials using an individual tree additive genetic model. We compared the base design model with post-blocking, a first-order autoregressive model of residuals (AR1), that model with an independent error term (AR1η), a combined base and autoregressive model, an autoregressive model only within replicates and an autoregressive model applied at the plot level. Post-blocking gave substantial improvements in log-likelihood over the base model, but the AR1η model was even better. The independent error term was necessary with the individual tree additive genetic model to avoid substantial positive bias in estimates of additive genetic variance in the AR1 model and blurred patterns of variation. With the combined model, the design effects were eliminated, or their significance was greatly reduced. Applying the AR1η model to individual trees was better than applying it at the plot level or applying it on a replicate-by-replicate basis. The relative improvements achieved in genetic response to selection did not exceed 6%. Examination of the spatial distribution of the residuals and the variogram of the residuals allowed the identification of the spatial patterns present. While additional significant terms could be fitted to model some of the spatial patterns and stationary variograms were attained in some instances, this resulted in only marginal increases in genetic gain. Use of a combined model is recommended to enable improved analysis of experimental data.

Efficiency of using spatial analysis for Norway spruce progeny tests in Sweden

“…(2) A spatial model using an autoregressive spatial component and an independent error instead of just an independent error in base model (Costa e Silva et al 2001;Dutkowski et al 2002) as…”

“…Spatial analysis using first-order autocorrelation has been used as a common method to analyze forest genetic trials (Costa e Silva et al 2001; Costa e Silva and Kerr 2013; Dutkowski et al 2006Dutkowski et al , 2002Ye and Jayawickrama 2008). In Norway spruce, we have used spatial analyses as a first-stage analyses for individual sites, and adjusted data have been used for genotype-bysite (G×E) interaction study to dissect the patterns and causes of significant G×E (Chen et al 2017).…”

“…In forestry, there are several spatial analysis methods used, such as post-blocking (Dutkowski et al 2002;Ericsson 1997), nearest-neighbor adjustment (Anekonda and Libby 1996;Joyce et al 2002;Wright 1978), and kriging (Hamann et al 2002;Zas 2006). However, the most common method used in crop and forestry trials seems to be a combination of experimental design with a spatial component, in the form of separable first-order twodimensional autoregressive residual variation as recommended by Gilmour et al (1997).…”

“…Also, many of these trials have used completely randomized design (CRD) without designed pre-block in northern Sweden. Such a design was traditionally analyzed using post-blocking adjustment (PBA) with varying effectiveness (Dutkowski et al 2002;Ericsson 1997). Spatial analysis may improve breeding value prediction considerably by reducing environmental variation in the CRD field trials.…”

“…Recently, the competition effect between neighboring trees has been described in several papers (Cappa and Cantet 2008;Cappa et al 2015Cappa et al , 2016Dutkowski et al 2002;Dutkowski et al 2006;Ye and Jayawickrama 2008). Dutkowski et al (2006) reported that 10% of diameter variables showed competition effects, represented by negative first-order autocorrelation coefficients in both column and row directions at a residual level.…”