Structural equation modeling of the Canadian flax (Linum usitatissimum L.) core collection for multiple phenotypic traits

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Tao Zhang1, Eric G. Lamb1, Braulio Soto-Cerda2,5, Scott Duguid3, Sylvie Cloutier2,6, Gordon Rowland1, Axel Diederichsen4, and Helen M. Booker1 1

Department of Plant Science, University of Saskatchewan, 51 Campus Drive, Saskatoon, Saskatchewan, Canada S7N 5A8; 2Cereal Research Center, Agriculture and Agri-Food Canada, 195 Dafoe Road, Winnipeg, Manitoba, Canada R3T 2M9; 3Morden Research Station, Agriculture and Agri-Food Canada, 101 Route 100, Unit 100 Morden, Manitoba, Canada, R6M 1Y5; and 4Plant Gene Resources of Canada, Agriculture and Agri-Food Canada, 107 Science Place, Saskatoon, Saskatchewan, Canada, S7N 0X2. Received 29 April 2014, accepted 23 June 2014. Published on the web 26 June 2014. Zhang, T., Lamb, E. G., Soto-Cerda, B., Duguid, S., Cloutier, S., Rowland, G., Diederichsen, A. and Booker, H. M. 2014. Structural equation modeling of the Canadian flax (Linum usitatissimum L.) core collection for multiple phenotypic traits. Can. J. Plant Sci. 94: 13251332. Flax seed yield is a complex trait that results from the inter-relationship between many crop characteristics. Structural equation modeling (SEM) is a statistical method used to determine the relationship between measured variables such as crop characteristics. Crop phenology, canopy traits, yield, and its components were included in structural equation models to determine how these crop characteristics relate to seed yield in a phenotypically diverse collection of flax germplasm. Early season vigor (scored as greater plant stand) was positively associated with canopy light interception and higher seed yield. Plant height also had a significant positive effect on seed yield. Moreover, yield components such as 1000-seed weight, number of bolls per unit area, and boll weight were strongly and positively correlated with seed yield. Focusing on yield-related traits, canopy architecture and expansion, and seed weight may be advantageous over yield per se in breeding for yield improvement. Key words: Structural equation modeling, Linum usitatissimum, flax, yield, yield components, canopy traits, morphological traits, phenological traits Zhang, T., Lamb, E. G., Soto-Cerda, B., Duguid, S., Cloutier, S., Rowland, G., Diederichsen, A. et Booker, H. M. 2014. Mode´lisation par e´quation structurelle d’une importante collection canadienne de lin (Linum usitatissimum L.) en vue du de´pistage de caracte`res phe´notypiques multiples. Can. J. Plant Sci. 94: 13251332. Le rendement en grains du lin est un caracte`re complexe de´coulant des relations entre de nombreux parame`tres culturaux. La mode´lisation par e´quation structurelle (SEM) est une me´thode employe´e en statistique pour e´tablir les liens entre les variables quantifie´es, comme les parame`tres culturaux. La phe´nologie de la culture, les caracte´ristiques du feuillage, le rendement et leurs composantes ont e´te´ inte´gre´s a` des mode`les par e´quation structurelle dans le but d’e´tablir les relations unissant ces parame`tres au rendement en grains dans une collection de ge´notypes du lin au phe´notype varie´. La vigueur en de´but de saison (cote´e d’apre`s l’importance du peuplement) a e´te´ positivement associe´e a` la lumie`re capte´e par le feuillage et a` un rendement en grains supe´rieur. La hauteur du plant pre´sente elle aussi une incidence positive marque´e sur le rendement en grains. Par ailleurs, certaines composantes du rendement comme le poids de mille graines, le nombre de capsules par unite´ de surface et le poids des capsules illustrent une forte corre´lation positive avec le rendement grainier. Se concentrer sur les caracte`res associe´s au rendement, sur l’organisation et l’expansion du feuillage et sur le poids des graines plutoˆt que sur le rendement proprement dit lors de l’hybridation pourraient s’ave´rer avantageux. Mots cle´s: Mode´lisation par e´quation structurelle, Linum usitatissimum, lin, rendement, composantes du rendement, caracte´ristiques du feuillage, caracte`res morphologiques, caracte`res phe´nologiques

5 Current address: Agriaquaculture Nutritional Genomic Center, CGNA, Genomics and Bioinformatics Unit, Km 10 Camino Cajo’n-Vilcu’n, INIA, Temuco, Chile. 6 Current address: Eastern Cereal and Oilseed Research Centre, 960 Carling Avenue, Ottawa, Ontario, Canada K1A 0C6.

Can. J. Plant Sci. (2014) 94: 13251332 doi:10.4141/CJPS-2014-158

Abbreviations: BPA, bolls per area; BW, boll weight; DTF, days to flowering; DTM, days to maturity; GDD, growing degree days; GDDF, growing degree days to flowering; GDDM, growing degree days to maturity; Ia, irradiance absorption; MAD, modified augmented design; PAR, photosynthetically active radiation; SEM, structural equation modeling; TSW, thousand-seed weight 1325

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Flax (Linum usitatissimum L.) is grown in the Canadian prairies mainly for its seed. Yield improvement is a major goal of plant breeding programs; however, yield is a complex trait that results from the interrelationship between many crop characters (Li et al. 2011; Soto-Cerda et al. 2014a). Seed yield in flax has been correlated with plant density, number of capsules per plant, and weight of seed per capsule (Copur et al. 2006). Soto-Cerda et al. (2014a) report that seed yield and its components in flax are positively associated with each other but negatively correlated with time to flowering, plant branching, height, and lodging. Crop yield is a polygenic trait that is greatly affected by environment and gene-environment interactions. Yield-related genes are affected to a different degree by environment in any given year; therefore, selection based on yield per se is not always effective in the long term (Tadesse et al. 2009). Indirect selection through yield components is likely to be more effective than focusing on grain yield (a trait generally known to be highly influenced by the environment with low heritability) because the components of yield are less environmentally sensitive and have higher heritability (Ford 1964; Soto-Cerda et al. 2014a). The growth of a crop is determined by its ability to capture light and its efficiency of conversion of solar energy into biomass (Confalone et al. 2010). The dry matter accumulation of a crop can be estimated as the outcome of three terms: (1) the incident photosynthetically active radiation (PAR) per unit of soil surface, (2) the proportion of PAR intercepted by the crop (PAR interception efficiency), and (3) the production of dry matter per unit of PAR intercepted (PAR use efficiency). A method for analyzing crop growth based on these three terms has been used to develop some simple crop models (Monteith 1994). PAR interception efficiency is affected by leaf area of the plant population, leaf structure, and inclination of the canopy (Bergamaschi et al. 2010). As such, plant density, phenology, and architecture are connected to the yield potential of a crop. Kiniry et al. (1989) suggest a linear relationship between seasonal biomass accumulation and cumulative intercepted radiation in grain crops. This relationship was also reported in potato with respect to tuber yield and leaf area index values above three (Bremner and Radley 1966). Using manual defoliation of soybean, significant linear yield losses were reported for leaf area index below 3.54.0 (Malone et al. 2002). However, relationships between canopy traits and flax yield have not been well documented. In flax, positive relationships have been demonstrated (in descending order of strength) between seed yield and number of bolls, number of branches, thousand-seed weight (TSW), and plant height (Chandra 1977; Copur et al. 2006; Soto-Cerda et al. 2014a). As environmental factors exert a major role in determining yield potential, it is important to understand environmental effects on yield. Weather patterns and soil types affect seed yield in flax, but plant density has little effect because flax

compensates for reduced stand densities mainly through increasing the number of bolls per plant (Casa et al. 1999). Temperature affects the rate of crop development; however, excessively high temperatures during flowering limit flax seed production due to reduced seed set and boll numbers (Cross et al. 2003). Path analysis has been used to study the relationship between crop yield and yield components (Dewey and Lu 1959). Structural equation modelling is the modern version of path analysis that employs more robust methods to estimate path coefficients. The application of structural equation modeling (SEM) to crop science is a useful tool to understand the relationship between yield and yield components (Grace 2006; Lamb et al. 2011). In this study, SEM was used to examine how crop phenology, canopy traits, and yield components influence seed yield in flax. SEM was utilized because this analysis allows for evaluation of the relative importance of multiple factors influencing yield in a single comprehensive analysis. The overall objective of was to use SEM to determine the relationship between crop phenology, canopy traits, and yield components and to evaluate their effects on seed yield in flax. Moreover, SEM was used to identify factors that maximize yield response in flax to inform breeding strategies for this crop plant. MATERIAL AND METHODS Experimental Material, Design, and Analysis for Phenotypic Traits Genebank accessions (390) representing the Canadian flax core collection from Plant Gene Resources of Canada (PGRC) (Diederichsen et al. 2013) and an additional nine Canadian flax cultivars were planted in 2010, 2011, and 2012 at the Kernen Crop Research Farm (KCRF), Saskatoon, Saskatchewan, Canada (lat. 52809?N, long. 106833?W) on clay loamy, Dark Brown Chernozemic soils. The crop did not mature in 2010 due to delayed seeding and excessive moisture; this resulted in extremely poor seed quality of harvested plots. Thus, SEM was only conducted on the 2011 and 2012 field datasets. Accessions/cultivars were planted in 2011 and 2012 in six-row plots using a six-row Wintersteiger small-plot seeder. A modified augmented design (MAD) was used (May et al. 1989). MAD is widely used for testing large numbers of lines without replications (Schaalje et al. 1987). Main plots were arranged in grids of 10 rows and 10 columns. Each main plot was divided into five parallel subplots (2 m 2 m with 20-cm row spacing) with a plot control cultivar (CDC Bethune) located in the center. Additionally, cultivars Macbeth and Hanley were used as sub-plot controls and assigned to five randomly selected main plots. Control plots were used to adjust for heterogeneity and the final adjusted mean values were calculated using Agrobase Generation II software (Agronomix Software Inc.) for a MAD type-2 design (AAD) according to Lin and Poushinsky (1985). Each experiment (year) was analyzed separately with entry, row, column, control plot,

ZHANG ET AL. * STRUCTURAL EQUATION MODELING OF CANADIAN FLAX

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control sub-plot, and plot field numbers. The adjusted values were obtained using either Method 1, which assumes row and column effects, similar to a Latin square, or Method 3, which assumes no significant whole-plot or range gradients, but instead adjusts by regression of control plots on control sub-plots. Both methods were evaluated; if row and column effects were not significant, then adjustments were obtained using Method 3. Phenotypic Data Phenotypic data included in the models were plant height (measured from the uppermost plant part to ground, at capsule maturity), plant branching (1 1/1, 21/2, 3 1/3, 41/4, 5 1/5, 6 1/6 of total stem length branched) as described in Diederichsen and Richards (2003), days to flowering (DTF; from sowing to 5% flowering of the plot), days to maturity (DTM; from sowing to 80% capsule maturity, i.e., brown bolls of the plot), growing degree days to flowering (GDDF), growing degree days to maturity (GDDM), irradiance absorption (Ia), plot seed yield, and its component traits [TSW, bolls per area (BPA), and boll weight (BW)] (Table 1). Irradiance absorption equaled the proportion of PAR intercepted by the crop measured as (abovecanopy PAR  below-canopy PAR)/above-canopy PAR. For the PAR measurement, one above-canopy measurement of total PAR was recorded and three below-canopy measurements were taken in each plot using an AccuPAR probe (Decagon Devices). Yield components (TSW, BPA, and BW) were obtained by harvesting two 0.5-m sections of a row from the central part of each plot according to Soto-Cerda et al. (2014a). The boll weight from each 0.5-m row was measured to obtain BPA (Soto-Cerda et al. 2014a). Seed yield was the seed weight harvested from the whole plot. Plant stand, which reflects early season vigor, was also recorded. Flax normally takes about 5 d to emerge after seeding. Plant stand was assessed 1015 d after seeding using a scale of 1 to 10, where a score of 1 corresponded to 10% of the row having adequate stand to a maximum score of 10, where the entire plot had an adequate stand. To better understand the impact of environment,

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accumulated growing degree days (GDD) in the 2011 and 2012 growing seasons were compared. GDD was calculated by taking the average of the daily maximum and minimum temperatures compared with a base temperature using the formula GDD (maximum daily temp. minimum daily temp)/2 minus a base temperature, where the base temperature was 08C (Miller et al. 2001). Accumulated GDDF or GDDM were calculated by summing GDDs for each day during the growing season for each genotype to flowering and maturity, respectively. SEM Software Lavaan (latent variable analysis) is a free, open source algorithm for SEM implemented in the R package (R Development Core Team 2012). This statistical software is used to estimate many multivariate statistical models, including path analysis, confirmatory factor analysis, SEM, and growth curve models (Rosseel 2012). The main steps include: (1) model development and comparison, (2) writing code for SEM and R, (3) extracting model information in R, (4) graphically representing models in R, and (5) agronomic interpretation. The Initial Model Development An initial path model was developed for the Canadian flax core collection based on the 2011 and 2012 field datasets (Fig. 1). Adjusted values were calculated for 388 and 393 accessions/cultivars or genotypes in 2011 and 2012, respectively, for each trait studied and used in the SEM analysis. All exogenous variables were assumed to have a direct causal path to yield; a subset of those variables also had indirect links to yield through irradiance absorption. The 2 yr of data were analyzed together and growing season precipitation (PPT) in millimeters was introduced for each year. Plant height and plant branching were included in the initial model. Moreover, plant stand score, which indicated early season vigor of the accession/cultivar, was hypothesized to have a direct causal path to seed yield. Phenological traits, such as days to flowering and days to maturity, were added into the model based on the initial hypotheses. Irradiance absorption, identified as canopy absorption, was also indicated

Table 1. Phenotypic variable, mean values, standard deviations, and units Variable Plant stand Plant height Plant branching Days to flowering Days to maturity GDDFz GDDMz Bolls per weight Boll weight Thousand seed weight Irradiance absorption Final seed yield z

Mean

Sd. dev.

Units

7.7 61.1 3.7 46.8 98.8 788.1 1702.3 169.8 96.4 5.37 77.6 339.0

1.45 17.13 1.07 3.45 7.45 58.49 132.80 52.71 32.02 1.08 12.92 137.85

010 (110% of row had adequate plant stand) cm (measurement of uppermost plant part to ground at capsule maturity) 16 (11/1, 21/2, 31/3, 41/4, 5 1/5, 61/6 of total stem length branched) days (sowing to 5% flowering of the plot) days (sowing to 80% capsule maturity, i.e., brown bolls of the plot) aGDD(max. daily temp.min. daily temp)/2 aGDD(max. daily temp.min. daily temp)/2 Bolls g 1 g m 2 g % (above canopy PAR-below canopy PAR/above PAR) g m 2

GDDF, growing degree days to flowering; GDDM, growing degree days to maturity.

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Fig. 1. The initial path model. Rectangles are used to indicate observed variables; single-headed arrows indicate a causal relationship where a change in the variable at the tail is a direct cause of changes in the variable at the head (x26 15.609, P0.016).

to show a direct relationship to seed yield. Yield component traits TSW, BPA, and BW were assumed to have a direct effect on seed yield (Soto-Cerda et al. 2014a). Yield in this study was derived directly by measuring seed weight of the plot and adjusted according to Lin and Poushinsky (1985). Finally, days to flowering, days to maturity, and growing degree days to flowering and maturity were also assumed to have a direct causal path to seed yield. RESULTS AND DISCUSSION Models were fit using the lavaan library (Rosseel 2012) and the R statistical package (R Development Core Team 2012). A satisfactory model should have a nonsignificant x2 value (P 0.05). The initial model (Fig. 1) did not have an adequate fit to the data (x26 15.609, P 0.016). Modification indices suggested the addition of paths from DTM to Ia and GDDM to Ia; these paths were not considered in the initial model as no reports indicated such relationships. After the model evaluation and model modification, both of these paths were included; these paths were considered biologically reasonable and the modified model had an adequate fit (x24 6.760, P 0.149) (Fig. 2). Non-significant paths indicated by grey arrows in Fig. 2 were retained in the final model because they represent known biological mechanisms influencing yield that were relatively unimportant in this diverse collection of flax germplasm.

Unstandardized path coefficients, standardized path coefficients, and tests of coefficient significance are shown in Table 2. Unstandardized coefficients represent the effect of a change on other variables in absolute terms based on the data and evaluated as the slope of the relationship, i.e., the mean response. Standardized coefficients represent the response variable in standard deviation units and are calculated from the square root of the variance. The standardized path coefficient corresponds to the effect-size estimate. Standardized path coefficients with absolute values less than 0.1 are interpreted as having a ‘‘small’’ effect, values around 0.3 as having a ‘‘medium’’ effect, and values 0.5 having a ‘‘large’’ effect. A positive standardized path coefficient indicates a positive relationship between the measured traits, while a negative standardized path coefficient suggests a negative relationship. Both unstandardized and standardized coefficients are presented in Table 2 to accommodate their different applications and interpretations (Grace 2006). The Z-value obtained by the Wald test (Hoyle 1995) was used to test the hypothesis of the unstandardized coefficient being significantly different from zero. Early season vigor (scored as higher plant stand; Table 1) had a significant, large positive effect on canopy absorption and seed yield in flax (Table 2; Fig. 2). Yield and its components (TSW, BPA, and BW) were all significantly and positively associated (Table 2; Fig. 2).

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Fig. 2. The modified model rectangles are used to indicate observed variables; standardized path coefficients are displayed for significant (P 50.05) paths; non-significant paths (P 0.05) are in gray; path width is proportional to the magnitude of the standardized coefficients (x24 6.760, P0.149); and r2 values are shown for the two endogenous variables.

The linear relationships between DTF, DTM, and yield were non-significant in the SEM models (Table 2). Furthermore, bivariate plots between these variables did not indicate a dominant nonlinear or threshold response (data not shown).

The effect of GDDM on higher seed yield was the only large positive relationship (P 0.059) indicated for the phenological characters (Table 2; Fig. 2). The lack of a clear relationship between phenological traits and yield may be due to the moderate heritability of these

Table 2. Parameter estimates for the initial structure equation model including unstandardized (unstd.) estimate, the standard error (SE), Z value (based on the Wald test), P value for the test of the path coefficient significance, and standardized path coefficient (std. estimate) Paths PS 0 Yield TSW 0 Yield IA 0 Yield Branch 0 Yield Height 0 Yield BPA 0 Yield BW 0 Yield DTF 0 Yield DTM 0 Yield GDDF 0 Yield GDDM 0 Yield PPT 0 Yield PS 0 IA Branch 0 IA Height 0 IA DTF 0 IA DTM 0 IA GDDM 0 IA PPT 0 IA

Unstd. estimate

SE

Z value

P value

Std. estimate

43.712 9.931 0.946 6.570 1.123 0.453 1.244 4.017 8.028 0.349 0.632 1.312 4.186 0.187 0.029 0.223 1.452 0.096 0.063

3.194 4.677 0.279 5.749 0.378 0.104 0.173 19.243 5.562 1.053 0.334 1.105 0.363 0.734 0.048 0.235 0.655 0.039 0.037

13.685 2.123 3.391 1.143 2.974 4.347 7.183 0.209 1.443 0.332 1.892 1.187 11.545 0.255 0.606 0.947 2.217 2.437 1.713

B0.001 0.034 0.001 0.253 0.003 B0.001 B0.001 0.835 0.149 0.740 0.059 0.235 B0.001 0.798 0.544 0.344 0.027 0.015 0.087

0.448 0.077 0.087 0.051 0.140 0.169 0.283 0.073 0.382 0.130 0.541 0.482 0.466 0.016 0.039 0.044 0.750 0.889 0.249

traits reported for the Canadian flax core collection grown at KCRF (Soto-Cerda et al. 2014a). GDDM had a large negative effect on canopy light interception indicating that accessions/cultivars that showed greater GDDM had reduced canopy closure mid-season (Table 2; Fig. 2). Significant paths in the model are indicated by black arrows in Fig. 2. GDDF and GDDM did not have any direct causal relationship to yield. The non-significant paths indicated by grey arrows in Fig. 2 were retained because of their biological significance and contribution to the overall model fit. Agronomic Interpretation The structural equation model (Fig. 2) presented illustrates the relationships between crop phenology, canopy, yield components, and seed yield for the Canadian flax

core collection grown for 2 yr at KCRF near Saskatoon, Saskatchewan, Canada. To better understand the causal relationships between variables, the significant bivariate relationships from the SEM model (Table 2; Fig. 2) were plotted in Fig. 3. A clear direct significant positive relationship was observed between seed yield and scored plant stand as an indicator of early season vigor in flax (Tables 1 and 2; Figs. 2 and 3). Plant height also had a significant small positive effect on seed yield at this location (Table 2; Figs. 2 and 3). Soto-Cerda et al. (2014a) report that plant height is negatively correlated with seed yield in the Canadian flax core collection. The core collection consists of both shorter more branched linseed accession/cultivars and taller less branched fiber types (Diederichsen et al. 2013). Generally, fiber types

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Fig. 3. Bivariate scatter plots between variables with significant relationships with yield in the modified structural equation model.

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ZHANG ET AL. * STRUCTURAL EQUATION MODELING OF CANADIAN FLAX

flower and mature earlier than linseed accessions/cultivars and exhibit lower seed yield; this explains the negative relationship reported between plant height, plant branching, and yield in Soto-Cerda et al. (2014a). Taller plants at the Saskatoon location may be an indication of plant stand vigor and, consequently, were associated with seed yield in this environment (Table 2; Figs. 2 and 3). In this study, plant branching did not significantly affect seed yield (Table 2); however, this trait was included in the model as it relates to canopy absorption and seed yield (Fig. 2). A branched accession/cultivar (with a lower plant branching score) can produce a fuller canopy earlier in the growing season and intercept more PAR over the season. A direct positive relationship between canopy irradiance absorption and seed yield was also observed (Table 2; Figs. 2 and 3). Crop growth and yield are related to the ability to capture or intercept irradiance via canopy and transfer this energy through photosynthesis to a carbon source in yield (Hay and Walker 1989). The total amount of incident irradiance captured and translated into growth and yield within a field season sets the upper limit on yield. This study shows that early season vigor, canopy interception, and seed yield are strongly associated in flax. Historically, crop yields in the Canadian prairies have been improved by adapting the lifecycle length with balanced growth and yield (Bueckert and Clarke 2013). The results presented here illustrate the potential to improve early-season canopy growth in flax and the total amount of irradiance intercepted during the crop lifecycle. The use of SEM indicated that all three components of yield (BPA, BW, and TSW) had a significant positive effect on seed yield at P B0.05 (Table 2; Figs. 2 and 3). This finding was also reported in Soto-Cerda et al. (2014a), suggesting that these yield components consistently reflect yield potential of an accession/cultivar under multiple environments. Yield improvement through indirect selection on yield components in flax has been recommended as a strategy for yield improvement in flax rather than selecting for yield per se (Soto-Cerda et al. 2014a). However, evaluating yield components (with the exception of TSW) is not a common practice in flax breeding programs due to the laborious nature of measuring yield components on numerous breeding lines tested in replicated multi-location yield trials. Markertrait associations have been identified for five favorable alleles for TSW in the Canadian flax core collection using association mapping; none of the Canadian cultivars studied in the Canadian flax core collection exhibited all five alleles, suggesting that marker assisted selection for favorable alleles conditioning TSW in flax is feasible (Soto-Cerda et al. 2014a, b). Flax yield can also be improved by selecting for a fixed lifecycle length and a higher translation of growth going into yield. The proportion of yield to total seasonal biomass is known as harvest index, which measures the overall ability of a crop to translate growth to yield (Hay and Walker 1989).

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This study also demonstrates the feasibility of SEM analysis on a large diverse germplasm collection such as the Canadian flax core collection (Diederichsen et al. 2013). SEM is a useful method for understanding the processes or principles underlying the relationships among variables. In particular, SEM is well suited to data arising from observed (measured) variables such as in this study. SEM is an appropriate analysis tool when facing a challenging research problem that requires the modeling of numerous, complex, interrelated variables such as yield, its components, and other crop characteristics. The final model suggested in this study had a good fit to the analyzed dataset exhibited by the diverse phenotypes present in the Canadian flax core collection (Diederichsen et al. 2013). Understanding the underlying processes that limit yield in flax is useful with respect to enhancing the breeding of flax for yield improvement. ACKNOWLEDGEMENTS The authors are grateful for the technical assistance of S. Froese, K. Jackle, B. Boon, A. Gerein, and M. Holland. This work was conducted as part of the Total Utilization Flax GENomics (TUFGEN) project funded by Genome Canada and co-funded by the Saskatchewan, Ministry of Agriculture, Flax Council of Canada and the Saskatchewan Flax Development Commission. Bergamaschi, H., Dalmago, G. A., Bergonci, J. I., Bianchi, C. A. M., Heckler, B. M. M. and Comiran, F. 2010. Intercepted solar radiation by maize crops subjected to different tillage systems and water availability levels. Pesq. Agropec. Bras. Brasilia 45: 13311341. Bremner, P. M. and Radley, R. W. 1966. Studies in potato agronomy. II. The effects of variety and time of planting on growth, development and yield. J. Agric. Sci. (Camb.) 66: 253262. Bueckert, R. A. and Clarke, J. M. 2013. Review: Annual crop adaptation to abiotic stress on the Canadian prairies: Six case studies. Can. J. Plant Sci. 93: 375385. Casa, R., Russell, G., Lo Cascio, B. and Rossini, F. 1999. Environmental effects on linseed yield and growth of flax at different seed rates. Eur. J. Agron. 11: 267277. Chandra, S. 1977. Use of index selection method in improvement of yield linseed (Linum usitatissimum L.) Plant Breed. Abstr. 47: 994994. Confalone, A., Lizaso, J. I., Ruiz-Nogueira, B., Lopez-Cedron, F.-X. and Sau, F. 2010. Growth, PAR use efficiency and yield components of field-grown Vicia faba L. under different temperature and photoperiod regimes. Field Crops Res. 115: 140148. Copur, O., Gur, M. A., Karakus, M. and Demirel, U. 2006. Determination of correlation and path analysis among yield components and seed yield in oil flax varieties (Linum usitatissimum L.). J. Biol. Sci. 6: 738743. Cross, R. H., McKay, S. A. B., McHughen, A. G. and BonhamSmith, P. C. 2003. Heat stress effects on reproduction and seed set in Linum usitatissimum L. (flax). Plant Cell Environ. 26: 10131020. Dewey, D. R. and Lu, K. H. 1959. A correlation and pathcoefficient analysis of components of crested wheatgrass seed production. Agron. J. 51: 515518.

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