Addressing huge spatial heterogeneity induced by virus infections in lentil breeding trials
 Anastasia Kargiotidou^{1},
 Dimitrios N. Vlachostergios^{2},
 Constantinos Tzantarmas^{1},
 Ioannis Mylonas^{2},
 Chrysanthi Foti^{2},
 George Menexes^{3},
 Alexios Polidoros^{3} and
 Ioannis S. Tokatlidis^{1}Email author
DOI: 10.1186/s4070901600396
© Kargiotidou et al. 2016
Received: 29 October 2015
Accepted: 10 February 2016
Published: 1 March 2016
Abstract
Background
Spatial heterogeneity can have serious effects on the precision of field experimentation in plant breeding. In the present study the capacity of the honeycomb design (HD) to sample huge spatial heterogeneity was appraised. For this purpose, four trials were conducted each comprising a lentil landrace being screened for response to viruses.
Results
Huge spatial heterogeneity was reflected by the abnormally high values for coefficient of variation (CV) of singleplant yields, ranging 123–162 %. At a given field area, increasing the number of simulated entries was followed by declined effectiveness of the method, on account of the larger circular block implying greater intrablock heterogeneity; a hyperbolic increasing pattern of the top to bottom entry mean gap (TBG) indicated that a number of more than 100 replicates (number of plants per entry) is the crucial threshold to avoid significant deterioration of the sampling degree. Nevertheless, the honeycomb model kept dealing with variation better than the randomized complete block (RCB) pattern, thanks to the circular shape and standardized type of block that ensure the less possible extra heterogeneity with expanding the area of the block.
Conclusions
Owing to the even and systematic entry allocation, breeders do not need to be concerned with the extra spatial heterogeneity that might induce the extra surface needed to expand the size of the block when many entries are considered. Instead, they could improve accuracy of comparisons with increasing the number of replicates (circular blocks) despite the concomitant greater overall spatial heterogeneity.
Keywords
Honeycomb method Randomized complete block Selection effectivenessBackground
Total phenotypic variation, the outcome of planttoplant phenotypic differences, comprises two main parts of variability, the genetic part and the acquired one. Soil heterogeneity is the main source of acquired variability inflated by uneven seed emergence, effects of clods and capping in wet soils, uneven application of applied inputs, differential effects of biotic and abiotic stresses, and interactions among these factors [1]. Spatial heterogeneity, reflecting the acquired part of the planttoplant variability, is a major concern in conventional breeding associated with low heritability and obstructing recognition of the outstanding genotypes [2–5]. Nevertheless, spatial heterogeneity cannot be eliminated entirely, being thus a ubiquitous feature of breeding trials. Avoidance of heterogeneous soils as well as measures to limit other operative events (e.g. even application of applied inputs) constitute a common practice. Further, different experimental configurations have been invented to tackle the problem, with the classical randomized complete block (RCB) being the most popular among breeders [6, 7]. In addition, application of modified experimental designs combined with suitable analysis models have been suggested with promising results under certain premises [8, 9].
Even though oxymoron, in case of breeding for tolerance to any biotic or abiotic stress the spatial heterogeneity induced by that stress might be desirable. Such kind of acquired variability might allow recognition of the susceptible genotypes and selection of the potentially tolerant ones. It has been reported that spaced plants intensify phenotypic expression of susceptibility with regard to biotic stresses in general [10] or insecttransmitted viruses in particular [11, 12]. In a lentil landrace, ultralow density resulted in huge spatial heterogeneity due to insecttransmitted and seedborne viruses [13, 14]. Under such adverse circumstances the pattern of experimental field configuration to perform progeny testing of the selected individuals is of paramount importance to sample the extraordinary spatial heterogeneity and accomplish precise evaluation.
From breeding perspective, growing individual plants widely apart to preclude any planttoplant interference for resources and ensure nilcompetition has been asserted fundamental condition, leading to invention of the honeycomb breeding designs (HD) [15–18]. Nilcompetition maximizes phenotypic expression and differentiation to facilitate genotype screening; it also copes with the suspending role of competition in the evaluation and selection of individual genotypes [1, 17]. Another main principle that distinguishes the honeycomb breeding model from the common conventional breeding schemes is that the individual plant rather than the classical plot (PL) is considered as experimental unit [18]. In a recent work, the honeycomb field experimental arrangement was found more efficient compared to the classical models of RCB, nearest neighbor adjustment and the lattice design to counteract the confounding effects of acquired variability on the singleplant performance of maize and wheat trials [19]. It was documented that essential principles of blocking, replication, and nearestneighbor adjustment on the same baseline are its main characteristics. In honeycomb breeding, breeders do not need to be concerned with the pattern and orientation of soil variability in order to decide on the layout of the field plan, the shape, size and orientation of the PLs, and grouping of the PLs into blocks. Standardized configuration on account of even and systematic instead of random entry allocation makes the honeycomb model unique in sampling the acquired variability [13, 18, 19]. The objective of this study was to appraise the systematic entry allocation of the honeycomb configuration as a tool to effectively sample huge acquired variability mainly induced by virus infection. Intended situation of huge spatial heterogeneity for specific breeding purpose raises extra concern about objectiveness of entries’ comparative evaluation.
Results
The landrace tested, year and location, soil properties, and details of the two sets of trials of the study
Landrace  Year/Location  Soil properties  Trial details^{†} 

1st set  
Evros  2006–07/41^{o}29′Ν, 26^{ο}32′Ε, 25 m a.s.l. (Orestiada)  Silty clay with pH 7.6, organic matter 21.5 g kg^{1}, NNO_{3} 10.1 mg kg^{1}, POlsen 13.5 mg kg^{1} and K 171 mg kg^{1}  30 × 32 m/100 cm/34 rows × 32 plants/1088–584 plants 
Elassona  As above  As above  30 × 32 m/100 cm/34 rows × 32 plants/1088–622 plants 
2nd set  
Lefkada  2011–12/39^{o}36′Ν, 22^{ο}25′Ε, 74 m a.s.l. (Larissa)  Clay loam with pH 7.8, organic matter 12.7 g kg^{1}, NNO_{3} 39 mg kg^{1}, POlsen 10 mg kg^{1} and K 150 mg kg^{1}  18 × 32 m/80 cm/25 rows × 40 plants/1000–848 plants 
Lefkada  As above  As above  11 × 20 m/50 cm/25 rows × 40 plants/1000–894 plants 
Number of harvested plants (n), mean yield per plant, the respective standard deviation (s) and coefficient of variation (CV)
Landrace  n  Yield per plant (g)  s (g)  CV (%) 

Evros  584  3.35  4.31  129 
Elassona  622  3.35  4.10  123 
Lefkada80  848  3.61  5.84  162 
Lefkada50  894  4.71  6.61  140 
Top to bottom gap for various number of entries (in parenthesis the k constant to construct the honeycomb design) allocated according to the design for each set of trials (the first comprising landraces Evros and Elassona and their united trial, while the second landrace Lefkada at interplant distance of 0.50 and 0.80 m and their united trial). The coefficient of linear correlation (r) between TBG and the corresponding entry size (n, number of plants) is also given
1st set  2nd set  

Number of entries  Evros  Elassona  Pooled  Lefkada_50  Lefkada_80  Pooled  
n  TBG  n  TBG  n  TBG  n  TBG  n  TBG  n  TBG  
3  195  9  207  13  402  14  298  22  283  30  581  13 
4  146  24  156  27  302  16  224  19  212  26  436  21 
7 (2)^{†}  83  26  89  39  172  27  128  61^{†}  121  29  249  23 
7 (4)  83  31  89  48^{†}  172  23  128  23  121  33  249  20 
9  65  27  69  71^{‡}  134  30  99  51  94  61^{‡}  193  32 
12  49  77^{‡}  52  78^{‡}  101  45  75  56^{‡}  71  78^{‡}  146  40 
13 (3)  45  64^{‡}  48  44  93  51^{‡}  69  69^{‡}  65  55  134  47 
13 (9)  45  50  48  80^{‡}  93  46  69  46  65  64  134  39 
16  37  77^{‡}  39  53  76  52^{‡}  56  54  53  74  109  43 
19 (7)  31  74  33  84^{‡}  64  55^{‡}  47  86^{‡}  45  65  92  53^{‡} 
19 (11)  31  75  33  108^{‡}  64  56^{‡}  47  47  45  61  92  43 
21 (4)  28  62  30  122^{‡}  58  55  43  72  40  110^{‡}  83  76^{‡} 
21 (16)  28  96^{‡}  30  98^{‡}  58  61^{‡}  43  110^{‡}  40  93^{‡}  83  80^{‡} 
25  23  64  25  150^{‡}  48  71^{‡}  36  130^{‡}  34  107^{‡}  70  86^{‡} 
27  22  105^{‡}  23  85  45  64  33  86  31  85  64  77^{‡} 
28  21  109^{‡}  22  78  43  75^{‡}  32  114^{‡}  30  104^{‡}  62  80^{‡} 
31 (5)  19  161^{‡}  20  109^{‡}  39  94^{‡}  29  103^{‡}  27  149^{‡}  56  63 
31 (25)  19  149^{‡}  20  105^{‡}  39  69  29  96^{‡}  27  121^{‡}  56  80^{‡} 
r  −0.72***  −0.77***  −0.84***  −0.73***  −0.73***  −0.77*** 
Discussion
Grain legumes are fraught with uncertainty as they are sensitive to biotic and abiotic stresses increasing the spatial variability of yield [20]. Spatial heterogeneity due to stresses maximizes when plants are grown widely apart [10–14]. On the overall mean yields per plant and the respective CV values (Table 2), as well as the significant residuals of simulated entries (Table 3), it is obvious that huge spatial heterogeneity prevailed in the four trials of the three lentil landraces. Landrace ‘Lefkada’ was the most heterogeneous as further depicted in Fig. 3, and particularly at 0.80 m. Higher mean yield per plant by 30 % and lower CV by 14 % at the interplant distance of 0.50 compared to 0.80 m is an extra evidence that ‘Lefkada’ suffered the greatest spatial heterogeneity at 0.80 m. The three landraces of the study naturally evolving during farming in the past presumably comprised genetic variability; however, apparently the overwhelming majority of the variability recorded in this study was due to acquired planttoplant differences. The anomaly of acquired variability was a situation intended for specific breeding purposes since experimentation aimed to intensify virus infections seeking tolerant genotypes [13, 14], thus huge spatial heterogeneity was a reasonable consequence. Ultralow densities favour insect landing [11], thus aphidtransmitted viruses lead to increased planttoplant variability [21].
The honeycomb pattern of experimentation is distinguishing for even and systematic entry allocation, thus one of the most appropriate tools to sample the spatial heterogeneity in field trials. It was found more effective compared to the classical models of random allocation (the RCB and the ‘nearest neighbour’ models), as well as that of the latice design [19]. Results of the current study were also supporting the honeycomb model against the RCB (Fig. 4). Nevertheless, it was hard to deal with such an extreme spatial heterogeneity exhibited by the lentil landraces, and the difficulties were pronounced with increased number of entries. In comparison with the previous study including a maize hybrid [19], honeycomb analysis resulted in much higher TBG values (e.g. 71 vs 7.5 % for nine entries) not fully attributable to the intralandrace genetic variability. In addition, significant residuals appeared even in quite few entries, i.e. seven entries in ‘Elassona’ and ‘Lefkada’ at 0.50 m or nine entries in ‘Elassona’ and ‘Lefkada’ at 0.80 m or 12 entries in all the four trials. Moreover, under the atypical circumstances of this study k constant affected substantially the outcome of honeycomb analysis, contrary to the previous work where the k did not play any essential role [19].
Increasing the level of entries resulted in increased TBGs and significant residuals (Table 3). Larger area of the moving circular complete block to involve more entries reasonably inflates the mean differences because of greater intrablock variation. For instance, the interior circle in Fig. 1b (of both HD7 and HD19), that corresponds to the moving circular complete block involving seven entries, falls within a seemingly homogeneous area; however, the middle circle comprising 19 entries is obviously more heterogeneous, while even more heterogeneous is the exterior one including 31 entries. The size of the moving circular complete block was also the reason for the reduced success in ‘Lefkada’ at 0.80 compared with 0.50 m. At interplant distance of 0.50 m the area of the moving circular complete block of 7, 19 and 31 entries is 1.6, 4.3 and 7.1 m^{2}, respectively; the respective areas at 0.80 m are 3.8, 10.5 and 17.2 m^{2} [18].
The number of entries is determined by the genotype and treatment, and limiting them is not always realistic. From the honeycomb experimentation perspective, considering unification of the two trials looks as though the number of replicates is crucial to remedy the spatial heterogeneity. Despite the extra experimental area that might reflect additional spatial heterogeneity, duplication of replicates inflated considerably the TBG values (Table 3). Figure 3 reveals that a number of replicates approaching 100 is the optimum threshold to smooth the extreme spatial heterogeneity prevailed in the four trials. Pooled data are further indicative (Table 3). From the point of statistics, spatial heterogeneity was counteracted up to 12 and 16 entries for the first and the second set of trials, respectively. The corresponding number of replicates was 101 for the former and 109 for the latter, while significant residuals appeared with replicate decline.
In the first set of trials, unification to increase replication improved effectiveness of either RCB or HD models for both four and eight entries; nevertheless, this was true only for HD in the second set (Fig. 4). In RCB trials, increasing the area of a block (usually of oblong square shape) very likely increases intrablock spatial heterogeneity. The statistical validity of the RCB and accurate estimates depend primarily on the assumption that treatments are evaluated with respect to similar environmental and operational conditions within a block [3–5, 22, 23]. Additionally, randomization is a crude technique given the complex patterns of spatial variability that exist, and there is no way to lay out blocks that will successfully account for spatial yield variability [19, 24]. On the other side, circular shape and standardized block type of the honeycomb model are two features that ensure the less possible extra heterogeneity with expanding the area of the block. The systematic entry arrangement vindicates the hypothesis that replication is in itself an attempt to account for the existence of spatial heterogeneity. Therefore, increased replicates per entry improve precision of evaluation and promote objectiveness of comparison, in agreement with the previous finding in maize and wheat trials [19]. Moreover, increased number of replicates bridged the gap between the outcome of different k constants (see Table 3 for 7, 13, 19, and 21 entries of pooled data vs component trials). Consequently, in the honeycomb breeding procedure when many entries are included the remedy against the heterogeneity of the higher block is the increase of the replicates per entry despite the concomitant greater overall spatial heterogeneity.
Inability to combat spatial variation could cause biased estimates of heritability [7, 25, 26], decreased response to selection and reduced precision of testing statistics [5]. In general, breeders are reluctant to use elaborating statistical designs particularly for characteristics other than yield [5], and prefer classical fieldplot designs sustaining lower breeding efficiency [2, 7]. The necessity of elaborating statistical designs is imperative when huge spatial heterogeneity is avoidable and the honeycomb field layout seems appropriate to tackle such an adversity. Instead of the randomization in the classical models that bring about restrictions concerning the block size, the honeycomb model deals with the spatial heterogeneity in an exceptionally systematic way to cope with it effectively. Thanks to this attribute, breeders do not need to be concerned with the extra spatial heterogeneity that might induce the extra surface needed to expand the size of the block when many entries are considered. Instead, they could improve accuracy of comparisons with increasing the number of replicates per entry. The honeycomb breeding procedure in ‘Evros’ succeeded in potentially tolerant singleplant sister lines [13] and improved the sanitary status of seed stock in terms of seedborne viruses [14], particularly concerning the most destructive Pea seedborne mosaic virus (PSbMV); such an accomplishment has been realized in ‘Elassona’ and ‘Lefkada’ as well (data under consideration).
Conclusions
Extremely high spatial heterogeneity occurred in the three lentil landraces mainly induced by virus infections. Under such adverse conditions the option of the elaborating honeycomb breeding model might be imperative, instead of the commonly used RCB, thanks to the systematic way of entry allocation. Despite the extra field surface, increasing the number of replicates per entry improved accuracy of comparisons. A number of 100 plants per progeny line was found optimum to mitigate the biased estimates and enhance breeding efficiency.
Methods
Data from two sets of field trials (Table 1) were used pertaining to grain yield of individual plants of three lentil (Lens culinaris Medik.) landraces, named ‘Evros’, ‘Elassona’ and ‘Lefkada’. These trials are part of an ongoing project concerning breeding for tolerance to virus diseases, and extreme spatial variability due to severe infections [13, 14] rendered them appropriate from the perspective of this research effort. Spatial heterogeneity was approached by the TBG among the means of a number of simulated entries dispersed across the whole experimental area. The TBG was computed as a percentage of the overall trial mean. For example, the entry mean range of 70–125 % in relevance to the overall mean corresponds to 55 % TBG.
Two adjacent and similar trials were established according to the zigzag arrangement of the honeycomb pattern, one for landrace ‘Evros’ and the other for landrace ‘Elassona’, with interplant distance of 1 m. Each trial comprised 34 rows of 32 singleplant hills, i.e., 1088 hills in total, corresponding to 30 m width (i.e. 34 × 1 × 0.87 m) and 32 m length, thus a total area of 960 m^{2}.
The landrace ‘Lefkada’ was grown in two adjacent trials with interplant distance being 0.50 m in the first and 0.80 m in the second (i.e. ‘Lefkada_50’ and ‘Lefkada_80’). Each trial included 25 rows and 40 singleplant hills per row, approximating thus an experimental area of 220 and 576 m^{2}. For this landrace in particular, the uniformity map on singleplant yields was constructed (Fig. 1). A considerable number of plants failed to give any seed because of intensified virus infection; thus to ensure representative values just for the construction of the uniformity map, the yield of each hill was corrected to the average yield of the respective moving circle of size 19 (i.e. the yield of code 7 was replaced by the average yield of the 19 plants included within the exterior circle). Thereafter the procedure of Petersen [27] described in Tokatlidis [19] was applied, smoothed in two directions. The trial was divided into units of four (2 × 2) plants and their average corrected yield was recorded: it comprised 20 rows of 13 means on each row, i.e. 260 yield PLs. The running median of three PLs was used whereby the yield of a PL was replaced by the median of the three adjacent PLs on the same row or the same column. Finally, areas of equal yield were delineated.
Each trial was divided subsequently into 4, 8, 16, and 32 equal PLs, defined as PL4, PL8, PL16, and PL32, respectively. As depicted in Fig. 1a that was accomplished via the three vertical continuous lines for PL4, plus the horizontal continuous line for PL8; further trial split through the two horizontal discontinuous lines resulted in PL16 and the extra four vertical discontinuous lines led to PL32. The PL16 was also considered as four horizontal randomized complete blocks of four entries (RCB4), while the PL32 as four horizontal randomized complete blocks of eight entries (RCB8). For RCB analysis, the TBG was computed in two conditions; in case (a) of the best randomization resulting in the lowest TBG and (b) of the worst randomization (on the premise that all the highest yielding PLs within blocks belonged to the same entry, all the PLs that gave the second highest yield belonged to the same entry, etc.).
On the honeycomb procedure, data were analyzed for possible configurations with regard to the 3–31 entries (HD331) constructed on the alternative k values (k is used so as to define the starting codes of each row) [18]. Those HDs including 4, 9, 12, 16, 25, 27, and 28 entries (that is, HD4, HD9, …, HD28) are classified “grouped” (the set of entries is split into more than one row), while HDs for 3, 7, 13, 19, 21, and 31 entries are “ungrouped” (entire set of entries is set on each row). In any “grouped” design potential k constant did not affect the outcome of honeycomb analysis (e.g. entry mean and standard deviation) as it was found in Tokatlidis [19] and this study as well. Therefore, different k constant was considered only for the “ungrouped” designs, excepted HD3 for which a single k applies (Table 3).
Data from the two trials of each set were united as if they were obtained from a single trial, i.e. 68 rows of 32 plants each for the first set and 50 rows of 40 plants each for the second set. Pooled data were analyzed as above for the honeycomb method, and as eight horizontal randomized complete blocks of four (RCB4) and eight (RCB8) entries.
Statistical analysis
A computer program tailored to honeycomb designs was used for analysis of means (ANOM) [28]. Singleplant observations were subjected to the t test to appraise the significance of residual of each entry mean from the grand mean, i.e. \(t = (\bar{x}  \bar{x}_{1} )/\sqrt {s^{2} /n}_{1}\) [29] where \(\bar{x}\), and s, are mean and standard deviation of the overall population, while \(\bar{x}_{1}\) is the entry mean and n _{1} its size (number of singleplant replicates). To approach the acrossindividuals phenotypic heterogeneity, CV on the singleplant basis was measured, e.g. for the overall population \(CV = s/\bar{x}\). The relationship between the entry size and the magnitude of TBG was searched via the Pearson simple correlation and the data were adjusted to best fit excessive (hyperbolic) pattern (Fig. 3).
Abbreviations
 CV:

coefficient of variation
 HD:

honeycomb design
 PL:

plot
 RCB:

randomized complete block
 TBG:

top to bottom gap
Declarations
Authors’ contributions
AK and CT dealt with experimentation, and data collection and analysis of landraces ‘Evros’ and ‘Elassona’. DV, IM and CF dealt with experimentation, and data collection and analysis of landrace ‘Lefkada’. GM contributed to overall statistical analysis. AP participated in virus infection’ assessment. IT designed the study and edit the paper. All authors read and approved the final manuscript.
Acknowledgements
This research was cofinanced by the European Union (European Social Fund) and Greek national funds in the framework of the project “THALIS—Democritus University of Thrace—Selection for enhanced yield and tolerance to viral and vascular diseases within lentil landraces” through the Operational Program of the NSRF (National Strategic Reference Framework) “Education and lifelong learning investing in knowledge society.”
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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