Genetic architecture of apple fruit quality traits following storage and implications for genetic improvement

Abstract

Accurate prediction of genetic potential and response to selection in breeding requires knowledge of genetic parameters for important selection traits. Data from breeding trials can be used to obtain estimates of these parameters so that predictions are directly relevant to the improvement program. Here, a factor allocation diagram was developed to describe the sampling design used to assess the quality of fresh and post-storage (2 months) fruit from advanced selection trial in an apple breeding program from which models for analyses were developed. Genetic variation was the largest source of variation for the fruit size, red colour type, proportion of red skin colour and lenticels, and instrumentally assessed fruit diameter, mass, puncture force and titratable acidity. In contrast, residual variation was the largest for fruit shape, juiciness, sweetness, aromatic flavour, eating and overall quality, and instrumental crispness. Genetic effects for traits were generally stable over fixed effects, except for a significant interaction with storage duration for firmness. Genetic correlations among traits were generally weak except between fruit mass (and diameter) and sensory size (0.98), titratable acidity and sensory acidity (0.97), puncture force and sensory firmness (0.96–0.90), crispness and juiciness (0.87), sweetness and aromatic flavour (0.84) and instrumental and sensory crispness (0.75). Predictions of the performance for seven commercial cultivars are presented. This study suggests that the Washington State apple production area can be treated as a single target environment and sufficient diversity exists to generate new elite cultivars. In addition, options for evaluating the efficiency of apple breeding are discussed.

Appendix

Experimental design

A factor allocation diagram (following Brien and Bailey 2006, Brien and Demetrio 2009 and Brien et al. 2011) was developed to describe the experimental design from which the data was generated and aid in the development of the linear mixed model for the analysis of individual and multiple fruit quality traits. In these diagrams, both the treatment factors and experimental units of the experimental design were displayed as belonging to objects. Panels were used to group factors associated with objects into the tiers and display the nesting and crossing structures of factors within a tier. Tiers are defined (Brien 1983) as a set of factors for which all levels of these factors are observable. Panels were connected by lines to display the allocation of the factors in a tier to experimental units in a second tier. Following Brien et al. (2011), solid lines indicate random allocation and dashed lines were used to represent systematic allocation. In the following description, the names of stages are capitalised and italicised, the names of the factors are italicised, the letter in the factor name used as the abbreviation in the development of the linear model is capitalised and the first mention of a factor is bold.

The experiment design is a four-stage design that requires five tiers for description (Fig. 3). The first tier (PLANTS) was composed of bgt trees described by t Trees of g entries (G) in b sEries.

Fig. 3

Factor allocation diagram for the evaluation of apple fruit quality traits assessed from the phase 2 trials in the Washington State University Apple Breeding Program

The second tier (FIELD SAMPLE) involved the allocation of the factors describing trees to those describing apples. It contained fbgns3z apples described by n positioNs in g Plots in b Blocks in f Farms. The sEries in tier 1 were systematically allocated to the b Blocks within each of the f Farms in tier 2. The g entries within sEries in tier 1 were randomly allocated to the g Plots within Blocks in tier 2. Thus, there was no replication of entries across Plots within a Block. In addition, there was little replication of entries across sEries as there was practically no replication of entries across Blocks within a Farm. To fully describe the randomisation of Trees in tier 1 to positioNs in tier 2, two pseudo-factors (Yates 1936; Brien and Bailey 2006) were created. Pseudo-factors define random grouping of subsets of objects to support randomisation to other objects. The pseudo-factor T ₁ indexed the random allocation of Trees within entry to Farms, and the pseudo-factor T ₂ indexed the random allocation of Trees within entry to positioNs within Plots.

A number (z _n ) of appLes were collected from each of the Trees at the n positioNs within a Plot for 3 Harvests (early, middle, late) over s Seasons (Fig. 3). Timing of first Harvest of all positioNs within a Plot in each Season was determined by weekly visual assessment of maturity, and all apples considered mature at the time of each Harvest were collected. Hence, Harvest has the same meaning across Seasons.

The third tier (STORAGE) involved the allocation of the factors describing apples to those describing fruit. It is based on s6fbg5 fruit described by four factors, fruIt within C ases within storage Room within Seasons. All appLes collected in each s Seasons in tier 2 were systematically allocated to each of the s Seasons in the third tier. Within each Season, appLes were bulked across the n Trees at the n positioNs within each Plot by Block by Farm in tier 2 and randomly allocated to the 3fbg Cases in the third tier. To describe the allocation of appLes in tier 2 to the 2 storage Rooms and 5 fruIt within each Case in the third tier, two pseudo-factors were created; A ₁ that indexes the random allocation of appLes to the Rooms, and A ₂ that indexes the random allocation of appLes to the 5 fruIt within Cases. At each Season in the third tier, the treatment storage Duration from the DURATIONS (fourth) tier was applied to the storage Rooms.

The fifth tier (EVALUATION) describes the structure of assessment of the Cases from the third tier to the units in the fifth tier. All Cases within each Season in the third tier were systematically allocated to the s assessMents in tier 5 and all the 3fbg Cases within each storage Room in a Season in tier 3 were systematically allocated to an eVent within an assessMent in tier 5. Within each eVent, the Cases were randomly allocated to the 3fbg Unit for evaluation. Thus, individual apples were not evaluated.

Linear model for individual trait analysis

The modified version of the method outlined by Brien and Bailey (2006) and Brien and Demetrio (2009) for the development of a mixed linear model form of a factor allocation diagram was followed for the analysis of this multi-tiered experiment. The initial activity was to include all identified sources of variation in the model, then reduce the model to an estimable model of convenience by removing confounded terms.

• 1. Determine intra-tier model composed of intra-tier random (IR) and intra-tier fixed models (IF).

The factor allocation diagram presented and described above identifies the objects (treatments and observational unit) and tiers of the experiment (see 1a and 1b in Brien and Demetrio 2009). The observational unit is the collective 5 fruit within each of the f*s*e*y*3*2 Units. The intra-tier formulas were formed by collecting all terms in the tiers to which no factor was randomised in the intra-tier fixed model (IF) and all terms in the other tiers in the intra-tier random model (IR):

$$ \begin{array}{l}\mathrm{I}\mathrm{R}:\ \left[\left(F/B/P/N\right)*{S}_2*H\right]/L + {S}_3/O/C/I + M/V/U\hfill \\ {}\mathrm{I}\mathrm{F}:E/G/T + D\hfill \end{array} $$

where the letters are the abbreviations defined in the description of the experimental design and Fig. 1.

• 2. Convert the intra-tier models to homogenous (HR) random and fixed (F) models.

Preliminary HR and F models were defined by setting the IR model to the HR model and the IF model to the F model. These were expanded by adding inter-tier interactions (2a in Brien and Demetrio 2009) E/G with F, S ₂ and H, and E/G with D, and [(F/B/P/N)*S ₂*H] with D.

$$ \begin{array}{l}\mathrm{H}{\mathrm{R}}^{\prime }:\left[\left(F/B/P/N\right)\ast {S}_2\ast H\right]/L+{S}_3/O/C/I+M/V/U+\widehat{\left[\left(F/B/P/N\right)\ast {S}_2\ast H\right]}D\kern1em \\ {}{\mathrm{F}}^{\prime }:E/G/T+\widehat{\left(E/G//T\right)}\left[\left(F\ast {S}_2\ast H\right)\right]+\widehat{\left(E/G/T\right)}D\kern1em \end{array} $$

Next, the HR and F models were augmented with the additional factor Age that was not taken into account in the initial factor allocation diagram (2b in Brien and Demetrio 2009). For a single series, Age is completely confounded with Season; however, as different sEries were planted at different years, the effect of Age and Season can be separated for some terms. Only Age and the interactions with F, D and H were added as S ₂^A and S ₃^A were confounded with E, and F^B^A is confounded with F^B:

$$ \begin{array}{l}\mathrm{H}\mathrm{R}^{\prime \prime }:\left[\left(F/B/P/N\right)*{S}_2*H\right]/L+{S}_3/O/C/I+M/V/U+\left[\left(F/B/P/N\right)*{S}_2*H\right]\hat{\mkern6mu} D\hfill \\ {}\mathrm{F}^{\prime \prime }:E/G/T + D + \left(E/G/T\right)\hat{\mkern6mu} \left[\left(F*{S}_2*H\right)\right] + \left(E/G/T\right)\hat{\mkern6mu} D + A/\left(F*H*D\right)\hfill \end{array} $$

Finally, the factors in the model were then designated as fixed or random and the terms swapped between the HR and F models so that only fixed terms appear in the F model and random terms appeared in the HR model (2c and 2d, in Brien and Demetrio 2009). The factors F, H, S ₂, A, S ₃, M and D were taken to be fixed and the remaining terms random. After interchanging the appropriate terms, the full model becomes:

$$ \begin{array}{l}\mathrm{H}\mathrm{R}:\left[\left(F\hat{\mkern6mu} B/P/N\right)/\left({S}_2*H\right)\right]/L+{S}_3\hat{\mkern6mu} O/C/I+M\hat{\mkern6mu} V/U + E/G/T + \left(E/G/T\right)\hat{\mkern6mu} \left[\left(F*{S}_2*H\right)\right] + \left(E/G/T\right)\hat{\mkern6mu} D + \left[\left(F\hat{\mkern6mu} B/P/N\right)\hat{\mkern6mu} \left({S}_2*H\right)\right]\hat{\mkern6mu} D\hfill \\ {}\mathrm{F}:D*F*{S}_2*H + {S}_3 + M + A/\left(F*H*D\right)\hfill \end{array} $$

• 3. Construct random and fixed models of convenience (CR and CF) by removing terms that were confounded (3c in Brien and Demetrio 2009).

The HR and F model presented above are over-parameterised for the available data. Here we focus on achieving an estimable model. Firstly, preliminary CR and CF models were set to the HR and F model derived above. The models were then fully expanded. The terms E^G^T, F^B^P^N, [(F^B^P^N)^(S ₂^H)]/L and S ₃^O^C^I and interactions with these terms were removed as there is no data to estimate these. The term S ₃^O/C was removed as it is confounded with M^V/U. The terms S ₃ and M were removed from the fixed model as they are confounded with S ₂. The term F^B^P^S ₂^H^D was removed as it is confounded with M^V^U. The term M^V was removed as it is confounded with Y ₂^D. All terms involving E^F and E^G^F were removed as they are confounded with F^B^P. Finally, to simplify the model, E and F^B were removed from the model recognising that if differences exist among these terms, removing E will inflate the variance among entries (G) and removing F^B will inflate the variance among F^B^P. The final models of convenience were thus:

$$ \begin{array}{l}\mathrm{C}\mathrm{R}:G/\left(D*S*H\right) + F\hat{\mkern6mu} P/\left(S*H\right) + F\hat{\mkern6mu} P\hat{\mkern6mu} D/\left(S + H\right) + M\hat{\mkern6mu} V\hat{\mkern6mu} U\hfill \\ {}\mathrm{C}\mathrm{F}:F*\left(S + A\right)*H*D\hfill \end{array} $$