A Standardized Method for Determining Tillering Capacity of Wheat Cultivars

Genotype and agronomic management greatly influence crop growth and grain yield in wheat (Triticum aestivum L.). To ensure sustainable production, seeding rate selection is important to maximize efficiency of every plant. Tillering can allow wheat plants to adjust growth relative to plant density and quality of growing conditions. This research sought to determine a method for assessing tillering of wheat cultivars and develop a standardized approach for characterizing cultivar tillering capacity. Nine cultivars with diverse genetic and phenotypic characteristics were seeded in 2017-2018 at Prosper, ND using various seeding techniques at differing plant spacing arrangements to evaluate tillering habit and spikes plant −1 . Cultivars grown at population densities common in grower fields did not express full tillering potential. Spaced-plantings of cultivars promoted cultivar expression of tillering phenotype. The SOFATT (seed only a few, and then thin) method, where average spikes plant −1 was determined from multiple plants sampled from a cultivar grown at spaced-plantings (inter-row and intra-row spacing at 30 ± 12 cm), is rec-ommended to properly assess tillering habits of wheat cultivars. Breeders and researchers can use results from SOFATT evaluations to determine tillering capacity rating for each cultivar based on raw or transformed z-score values for

vum L.) cultivars [1] [2]. The actual yield attained by a wheat cultivar is greatly influenced by interactive effects from environment and agronomic management.
One way that these factors can affect yield is by influencing plant growth habit and composition of yield components. For wheat grown in irrigated, intensively-managed environments, production of uniculm plants is considered ideal for yield [3]. As the majority of hard red spring wheat (HRSW) in the Northern Plains region of the U.S. is seeded in dryland environments, crop management for economic production includes using cultivars with both main stem and tillers contributing to yield. Tillering can allow plants to adjust growth relative to density of neighboring plants or quality of growing conditions [4]. Diversity among modern HRSW cultivars includes a range of genotypes differing in plant growth habit and tillering capacity. Although an extensive record of publications document efforts employed to identify quantitative trait loci (QTL) associated with tillering in wheat, no findings have been published to date identifying a specific gene associated with tillering traits [5] [6].
Agronomic management for sustainable HRSW production includes selecting a seeding rate that will maximize efficiency of production for every plant. For example, a high tillering cultivar could be seeded at a lower rate compared to a cultivar with a lower number of tillers contributing to total grain yield. When determining the seeding rate optimal for cultivar yield, it is important to consider the tillering capacity of a cultivar to avoid economic losses due to unnecessary seed costs (overseeding) or uncaptured yield (underseeding). Underseeding to promote plant tillering is likely to negatively impact yield if the plant is not prolific at tillering, though differences in reportings for percent of total grain yield contributed by tillers (range 6.7% to 46.9%) make it difficult to determine a definitive percent [7] [8]. Additionally, underseeding a field with a low tillering cultivar can limit leaf area index, reducing the amount of radiative light intercepted ha −1 , and thereby lowering production efficiency and subsequent yield at harvest [9]. Richards and Townley-Smith [10] noted that greater leaf area index proved to be a disadvantage for high tillering cultivars subjected to early drought conditions occurring prior to anthesis. When drought conditions were only present after anthesis, pre-anthesis vegetative growth was estimated to contribute 60% of total grain yield.
Though it is apparent that differences among cultivars in tillering capacity and plant leaf area influence yield, spikes plant −1 generally has a greater influence on plant yield [11]. Applying this understanding on a field scale, Holliday [12] noted yield gains observed in high tillering stands could be attributed to contributions from spikes, based on the understanding of spike photosynthetic efficiency reported by Archbold and Mukerjee [13]. Elhani et al. [14] conducted tillering experiments and concluded that a high tillering capacity provided cultivars with advantages in plant growth habit and yield components over low tillering cultivars, but only in non-stressed, irrigated environments. Hucl and Baker [15] noted that though tillers m −2 is closely associated with spikes m −2 (r = 0.84), spikes m −2 is a poor determinant of yield (R 2 = 0.005). Considering diversity in American Journal of Plant Sciences tillering capacity among cultivars and production potential across environments, these findings reinforce the importance of considering cultivar tillering capacity when determining optimal seeding rates to maximize yield throughout the Northern Plains region.
Although environment can influence tillers plant −1 produced by a cultivar, it can be expected to observe similar relative responses in other cultivars across environments. Klepper et al. [16] indicated that the process of wheat plant development is unchanged across environment types, but noted that environment affects the rate at which development occurs. This can be used to explain the reporting from Friend [17] that reduced tiller numbers in mature wheat plants was not attributable to the plant's inability to form tiller buds, but rather the lack of tillers emerging from axillary buds. Though environment and agronomic factors can impact tillering, it can be expected that genotypes will not be differentially affected by these factors. Work completed by Richards [5] provides support for this statement as varying planting timing of spring-seeded wheat produced similar changes in spikes plant −1 among tillering cultivars. Evaluations of tiller numbers of cultivar seeded in various arrangements (adaptations in spacing and rectangularity) indicated arrangement had no interactive effect on cultivar tillering [18]. Carr et al. [19] found that no rank changes were observed among HRSW cultivars when evaluating tillage and seeding rate effects on tiller production. In general, these study all document cultivar responses to agronomic practices that are similar in scale across cultivars.
Numerous published findings have noted differences in tiller number in response to changes in agronomic management for row spacing, seeding rate, and planting method. However, documentation is minimal for current methods used by breeders and researchers to assess tillering characteristics of individual cultivars. Hucl and Baker [15] utilized various approaches for evaluating tillering characteristics of wheat genotypes based on spikes plant −1 . One approach included single row planting and subsequent thinning to 10 plants m −2 for sampling of 5 plants to represent each genotype. Additional approaches included solid-seeded (2.40 million seed ha −1 ) and space-planted (est. 0.12 million seeds ha −1 ) conditions to determine spikes plant −1 for relative comparisons among genotypes. The objective of the space-planted method was to provide growing conditions with minimal competition among plants to promote plant tillering for full evaluation of genotype tillering capacity. Of the 373 genotypes originally evaluated, the genotypes with the 10 lowest, and 10 highest values for spikes plant −1 were reported as low tillering and high tillering genotypes, respectively. This study demonstrated various experimental approaches used to identify high and low tillering genotypes, based on relative rank among genotypes for spikes plant −1 . However, not all HRSW cultivars available to growers are designated as having characteristics of high tillering or low tillering. This reinforces the importance of developing a standardize system for assessing cultivar tillering habit and determining a tillering capacity rating. Without a standardized system for assessing cultivars for tillering characteris-

Experimental Approach
Experiment 1 was conducted concurrently within a small plot seeding rate experiment. Experimental units were 5.5 m 2 plots in a randomized complete block design with a factorial arrangement of cultivar and seeding rate. Treatments included combinations of four seeding rates and nine HRSW cultivars (  only slightly correlated (r = 0.33), the focus was on relative cultivar response across the various methods.
Space-planted methods were used in Experiment 2 and Experiment 3 to promote cultivar expression of tillering phenotype by minimizing competition among plants [15]. Experiment 2 was a randomized complete block design with four replicates. Nine HRSW cultivars were assigned as treatments. Experimental units were 5.5 m 2 plots seeded with a 4-row Hege 1000 no-till planter (Hege Company, Waldenburg, Germany) with 30 cm spacing. A SOFATT (seed only a American Journal of Plant Sciences few, and then thin) method was applied by seeding at a fixed rate of 215,000 seeds ha −1 with the objective to establish wheat plants within each plot at an equidistant of 30 cm for both intra-row and inter-row spacing. Plots were thinned in early June to remove excess wheat plants, including any plants spaced < 18 cm from a neighboring plant ( Figure 1). Spikes plant −1 was measured at physiological maturity (Zadoks 89) to allow plants to reach full tillering potential [22]. Intra-row spacing of plants (in meters) and mean spikes plant −1 were recorded for each plot by averaging spike counts of 8 plants sampled from each plot ( Figure 2).

Statistical Analysis
Analysis of variance of Experiment 1 data was performed for 2017 and 2018 environments using PROC MIXED in SAS 9.4 (SAS Institute Inc., Cary, NC). Variance of environments was considered homogenous and data were combined for ANOVA. Following the approach outlined by Carmer et al. [23], environment was assigned a random effect, and fixed effects were cultivar and seeding rate. A one-way ANOVA was completed for Experiment 2 in PROC MIXED and for Experiment 3 in PROC GLIMMIX evaluating spikes plant −1 of cultivar treatments. Mean separations were completed according to F-protected LSD values (P ≤ 0.05) determined in PROC MIXED for Experiment 1 and Experiment 2, and PROC GLIMMIX for Experiment 3 as an unequal number of cultivar replicates were present.

Parameterization Methods
Three methods were evaluated as potential approaches for determining parameters for classifications of the tillering capacity rating system. These methods included the "Means Comparisons approach", the "Z-score approach", and the "Standardized Distribution approach". For the "Mean Comparisons approach", SAS output for LSD mean separations of spikes plant −1 were used to assign parameters as qualifiers associated with each classification of the tillering capacity rating system (low, moderate, high). As an objective was to develop a standardized system that could be applied in various environmental settings, this required a robust system with the capacity to assign tillering capacity ratings to cultivar from diverse genetic backgrounds that were assessed in differing growing conditions. To account for the effects of these experiment-specific variables in regards to cultivar tillering expression, it was determined that cultivar tillering capacity should be evaluated only after accounting for potential differences in spike densities across experiments. This was done by using Z-score transformations for spikes plant −1 observations in each experiment. This approach has been utilized by numerous agricultural and ecological studies to account for variability across environments [24] [25] [26]. The "Z-score approach" proposed that standardized z-scores calculated from spikes plant −1 observations could be used to determine cultivar tillering capacity based on relative tillering performance of the cultivar. The "Z-score approach" required a data transformation step in SAS (PROC STANDARD) to calculate standardized z-scores from observations for spikes plant −1 as: where x is observed spikes plant −1 , x is experimental mean, and s is experimental standard deviation [27]. This adjusted the scale of plant response for spikes plant −1 to have a mean of 0, and standard deviation of 1.
The "Standardized Distribution approach" was somewhat of a continuation of the "Z-score approach", as standardized z-scores were used to calculate spikes plant −1 estimates to represent data relative to the distribution of the population American Journal of Plant Sciences as: where, x is estimated spikes plant −1 , z-score is the z-score of the spikes plant −1 observation, σ is the population standard deviation, and μ is population mean.  (Table 4). An increase in seeding rate from 1.85 to 3.09 million seeds ha −1 , reduced the number of spikes plant −1 from 3.3 to 2.5 spikes plant −1 , respectively. At the highest seeding rates of 4.32 and 5.56 million seeds ha −1 , spikes plant −1 was the lowest at 1.9 and 1.8 spikes plant −1 , respectively. As a consistent decrease in spikes plant −1 was observed across cultivars seeded at increasing rates, agronomic management appeared to be a factor limiting cultivar tillering potential.  Though spikes plant −1 were influenced by seeding rate, changes in seeding rate did not differentially affect cultivar spikes plant −1 ( Table 5). This is likely because it is expected that plants established in densely-seeded conditions will have greater intraspecies competition compared to plants in space-planted conditions.

Assessing Cultivar
To further evaluate cultivar spikes plant −1 relative to seeding rate, cultivar spike counts from the 2018 environment were used for one-way ANOVA for each seeding rate factor level. The purpose of this was to evaluate each seeding rate level (seeding density) as a potential approach for assessing cultivar tillering capacity. Results in Table 5 indicate assessments to determine cultivar tillering capacity should not be completed in HRSW production fields, as spikes plant −1 was similar among cultivar at seeding rates greater than 1.85 million seeds ha −1 .

Experiment 2
Spaced-plantings using the SOFATT method in Experiment 2 promoted cultivar expression of tillering phenotype, as mean spikes plant −1 was 22.1 spikes plant −1 (   there was no interaction for cultivar by seeding rate in Experiment 1, and Shelly did not have an apparent advantage over other cultivars when different seeding density methods were used to assess tillering capacity of cultivars.

Experiment 3
Experiment 3 had poor emergence and uneven establishment across replicates, which was attributed to dry soil conditions at planting. Spikes plant −1 differed among cultivar at spaced-plantings used in Experiment 3, and the mean spikes plant −1 was 22.9 spikes plant −1 ( Table 6). The highest tillering cultivar was ND VitPro (

Parameterization Methods
Three parameterization methods were identified as potential approaches for differentiating the classes selected for the tillering capacity rating system (low, moderate, and high). Parameters determined by the "Mean Comparisons approach" (using letters from mean separations based on LSD values) were selected based on SAS output for mean separations (P ≤ 0.05) for cultivar spikes plant −1 in Experiment 2 ( Table 6). As four groupings of cultivars were indicated by mean comparisons based on Fisher's LSD, parameters for each rating class were relatively easy to distinguish (Table 7). Parameterization by the "Z-score approach" (data transformation to standardized z-score values) provided a quantitative method for determining cultivar  tillering capacity ratings. As spikes plant −1 responses in Experiment 2 followed a normal distribution, z-score values at the first quartile (Q1) and third quartile (Q3) were used as parameters for assigning tillering capacity ratings (Table 7).
Cultivar with an average z-score of <−0.6745 were considered to have a low til-  (Table 7). This method is most relevant for application in future tillering studies.
With the diversity of cultivars and n = 36 spikes plant −1 observations in Experiment 2, it was surmised that results from Experiment 2 were representative of most HRSW cultivars currently available to growers for production. Therefore, the spikes plant −1 parameters outlined in Table 7 can be readily used by researchers to determine tillering capacity of cultivar when using the tillering

Cultivar Tillering Profiles
The ranking for tillering capacity was similar across parameterization methods for each cultivar ( Tiller density, spikes plant −1 , and tillering capacity did not have an apparent influence on tiller mortality of cultivars. As tiller mortality differed among cultivars in Experiment 2, these results indicate tiller production and survival is likely influenced primarily by wheat genotype (Figure 5).  Though tiller mortality differed among cultivars, tiller production and survival were consistent for all cultivars as indicated by high correlation coefficients (r ≥ 0.93) between stem density and spikes plant −1 (Table 9). Lang-MN and Surpass appear to have produced a more variable number of yield-contributing spikes relative to the number of tillers formed. Overall, this reveals that wheat plants may self-regulate tiller formation to consistently produce a certain number of viable spikes relative to the number of tillers formed.

Method Validation
To validate the application of these approaches for determining cultivar tillering capacity, experimental means from eight similar space-planted tillering studies conducted at Prosper, ND and Crookston, MN in 2014 and 2015 were used to determine tillering capacity of 12 HRSW cultivars (Table 10). Observations for tiller density (stems plant −1 ) were used for this validation, as spikes plant −1 was not reported. Z-scores and standardized values for cultivar tiller density guided the selection of tillering capacity rating for each cultivar (Table 10). Results for the validation set were similar to Experiment 2 results as interactions between photoperiod gene Ppd-D1 and semi-dwarfing genes (Rht-B1 and Rht-D1) appear to be associated with plant tillering response. The most revealing finding is that the two cultivars that are photoperiod insensitive (Ppd-D1a) and express the Rht-B1b allele, have a high tillering capacity. This response is similar to what was revealed in Experiment 2, as Shelly and ND VitPro are both cultivars with high tillering capacity and share similar genetic traits (Table 8).
Cultivars with photoperiod sensitivity appeared to have variable tillering capacity profiles, as no apparent groupings were observed for sensitive cultivars with similar genetic background for traits affecting plant stature. As data were compiled over multiple environments, it is likely that these results represent a robust assessment of tillering habit of these cultivars, sufficient to determine the tillering capacity that accurately characterizes each cultivar.

Discussion
The observations that spikes plant −1 of cultivars were consistent across environments are in line with findings of Klepper et al. [16]. This offers support that seasonal differences in environmental conditions are not likely to influence results when assessing tillering of wheat cultivars to determine tillering capacity. It was apparent that plant spacing affected spike production, as incremental increases in seeding rate had an inverse effect on spikes plant −1 (Table 4). Similar responses to seeding rate were reported by Joseph et al. [28], where 3.7, 2.3, and  [30]. As a consistent decrease in spikes plant −1 was observed across cultivars seeded at increasing rates, it is apparent that seeding density can limit cultivar tillering potential.
Though spikes plant −1 was influenced by seeding rate, changes in seeding rate did not differentially affect cultivar spikes plant −1 ( Table 5). Simmons et al. [31] reported similar findings for barley genotypes that varied in tillering capacity.
Cultivar differences in tillering capacity and growth habit may explain why greater differences were not seen among cultivars seeded at different rates in  [33]. Though differences in spikes plant −1 were observed among cultivar seeded at 1.85 million seeds ha −1 , the differences were minimal and not likely to be readily detected in field evaluations. However, it is still important to note that spikes plant −1 of cultivars became more dissimilar as seeding rate decreased. This is supported by the increased cultivar expression of tillering habit with incremental decreases in seeding rate that was represented by a continual decrease in correlation coefficient (r) values when comparing treatments (Table 5). Experiment 1 confirmed the effects of plant density on HRSW tillering, primarily in relation to the level of competition among neighboring plants.
As a consistent decrease in spikes plant −1 was observed across cultivars as seeding rate increased, tillering assessments based on plants seeded at production-level densities (1.85 to 5.56 million seeds ha −1 ) will not represent the full tillering capacity of a cultivar. The high standard error observed in Experiment 3 could be attributed to the unfavorable environmental conditions at varying intensity throughout the site, and additional error within the experiment (CV = 21.5) that was unaccounted for (Table 6). Based on these results, the space-planted method used in Experiment 3 is not likely to provide an accurate assessment of tillering of wheat cultivars.
Results for the three experiments assessing cultivar tillering indicate spacedplantings provided for the most accurate assessment of cultivar tillering. As results for cultivar spikes plant −1 in Experiment 3 were correlated with Experiment 2 results (r = 0.79; P = 0.011), this indicates that both space-planted methods provided for similar tillering expression of cultivars. However, cultivar tillering habit was best represented by average spikes plant −1 of multiple plants sampled from a cultivar grown at spaced-plantings (inter-row and intra-row spacing at 30 ± 12 cm). In general, assessing cultivar tillering to determine tillering capacity was best represented by the SOFATT method used in Experiment 2. This is likely because the greater growing area of the experimental units helped minimize experimental error and maximize tillering potential of cultivars. Limited competition from neighboring plants promoted phenotypic expression of tillering, providing for an accurate assessment of cultivar tillering abilities. Based on these findings, spaced-plantings are needed to properly assess tillering of wheat cultivars.
Considering the three parameterization methods proposed in this study, the "Mean Comparisons approach" was the easiest as it readily provided four groupings of cultivars to be used as parameters for each rating class (Table 7). However, in experiments where the number of treatments or level of precision results in greater than four groupings of letters, defining parameters for each tillering capacity rating class would be a highly subjective process. Also, in experiments with unequal replication where alternative mean separations tests (such as Tukey procedure, or Tukey-Kramer test [34]) are most appropriate, results would not be readily comparable across experiments. As these factors are additional sources of error and uncertainty that are not easy to account for, this is likely the reasoning why there is currently no standardized method that is widely used to assign tillering capacity ratings to wheat cultivars.
Parameterization by the "Z-score approach" provided a quantitative method for readily determining cultivar tillering capacity ratings. This method is favorable for researchers and breeders as the parameterization was very easy to complete, and interpretation of results is not limited to the dataset evaluated. Researchers in other wheat production regions could utilize this approach to determine tillering capacity of cultivars that are adapted for their region. Assuming a sufficient number of diverse cultivars are included in initial tillering evaluation trials to ensure a dataset with a normal distribution, z-score values at the first quartile (Q1) and third quartile (Q3) could be used as parameters for assigning tillering capacity ratings (similar to Table 7). As region-specific data would be adjusted to a standardized scale (with a mean of zero and standard deviation of one), z-scores for cultivar spikes plant −1 could be readily compared across experiments to determine relative tillering of cultivars in differing environments (similar to the example in Figure 4). Though data from Experiment 1 data were not used to determine cultivar tillering capacity, Figure 4 demonstrates how z-scores can be used to standardize observations to a scale that is relative to the experimental mean. Therefore, relative response of a cultivar can be compared when more than one experimental dataset is used to determine cultivar tillering capacity.
The "Standardized Distribution approach" could be used by researchers and breeders to assign cultivar tillering capacity ratings once initial parameters are established using the "Z-score approach". This would eliminate the need for excessive evaluation trials that continuously include a sufficient diversity in cultivars to ensure a normal distribution required for establishing parameters if the "Z-score approach" was used alone. Once the population mean and standard deviation are determined from initial tillering studies, these values can be used with the "Standardized Distribution approach" to readily assign tillering capacity ratings based on observations for spikes plant −1 . As breeding programs are likely already documenting this information in spaced-plantings of their advanced wheat lines, this data could be readily utilized to assign a tillering capacity rating to further characterize cultivars when released.
Prior studies in barley indicated the importance of evaluating phenotypic characteristics such as tiller density (stems plant −1 ) relative to the number of spikes plant −1 , as tiller mortality differs with genotype and can negatively impact grain yield [35] [36]. As tiller mortality differed among cultivars in Experiment 2, these results offer additional support to the understanding that genotype greatly influences tiller mortality. These observations also revealed the importance of considering the plant structure used to assess and determine tillering capacity of wheat cultivars, as determining tillering capacity based on stems plant −1 could potentially lead to a different tillering capacity than when based on spikes plant −1 . Though this is an important consideration, this was not the case in Experiment 2 as cultivar tillering capacity based on stems plant −1 or spikes plant −1 arrived at the same tillering capacity rating (results not included). As spikes plant −1 is a primary component of wheat yield, cultivar tillering capacity based on spikes plant −1 is more relevant to growers making seeding and crop management decisions; especially as not all tillers formed will produce spikes that contribute to the final yield.
As there was inconsistency in tillering expression among cultivars relative to specific genetic traits, tillering habit was not attributable to a single genetic trait of the three evaluated. Contrasting responses among cultivar sharing similar genetic traits may represent the effects of Ppd-D1 interactions with other genes as discussed by Gonzalez et al. [37]. However, trends in tillering habit were apparent among cultivars sharing similar backgrounds for multiple genetic traits (Table 8). Interactions between photoperiod gene Ppd-D1 and semi-dwarfing genes (Rht-B1 and Rht-D1) appeared to influence plant tillering response. The most revealing finding was that the cultivars that are both photoperiod insensitive (Ppd-D1a) and express the Rht-B1b allele for semi-dwarf phenotype, all have a high tillering capacity rating (Table 8 and Table 10). This response could be influenced by QTL reported by Borras-Gelonch [38], who indicated QTLs at a similar locus were associated with tillering and phenology characteristics. Eagles et al. [39] suggested Ppd-D1 interactions with alternate gene(s) (that also have effect on tillering) as a possible explanation for contrasting yield responses observed in genotypes with similar genetic background for Ppd-D1. In comparison to these high tillering cultivars, the photoperiod insensitive cultivars with Rht-D1 gene have a moderate tillering capacity. As it has been noted by Addisu et al. [40] that Rht-D1 plants can have reduced biomass and greater harvest index in comparison to Rht-B1 plants, these differences in tillering capacity observed in photoperiod insensitive cultivars are understandable. Overall, as a potential interactive effect of Ppd-D1a × Rht-B1b on tillering habit has not been previously reported, this association would be important to consider exploring in future studies.

Conclusion
Plants grown at high population densities in grower production fields are not likely to represent full tillering potential of a cultivar, therefore it is necessary to utilize spaced-plantings to properly assess tillering habits of wheat cultivars. Assessing cultivar tillering to determine tillering capacity was best represented by the SOFATT method, where average spikes plant −1 was determined from multiple plants sampled from a cultivar grown at spaced-plantings (inter-row and intra-row spacing at 30 ± 12 cm). Researchers can use results for average spikes plant −1 to determine tillering capacity rating for each cultivar, based on raw or transformed z-score values for spikes plant −1 . The Z-score approach is most relevant for researchers evaluating a diverse selection of wheat genotypes (e.g. advanced breeding lines, variety trials). The Standardized Distribution approach is American Journal of Plant Sciences also useful, as researchers can establish values for spikes plant −1 that can be used as parameters in future studies to readily determine cultivar tillering capacity rating.

Conflicts of Interest
The authors declare no conflict of interest. Author J.D.S. was employed by Syn- The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.