Plant materials. This study utilized 130 genotypes currently used for population improvement in Uganda for various breeding purposes and were screened for CSRFAB traits ( Table 2). The 130 genotypes included two distinct sweetpotato gene pool populations (Uganda A and Uganda B) that were formed to reflect similarity within and divergence between the populations based on 31 simple sequence repeat (SSR) markers ( David et al., 2018). The genotypes are maintained by the International Potato Center (CIP) at the National Crops Resources Research Institute (NaCRRI) at Namulonge in Uganda.

Experimental sites and duration of the study. Grüneberg et al. (2005) identified Uganda as environmentally diverse and suitable for sweetpotato selection for East African countries, and a breeding platform where crossings and selection in early and later breeding stages were conducted. The results from such environments are extended to all East African countries with one or two more season evaluations for confirmation. Two locations, NaCRRI-Namulonge and National Semi-Arid Resources Research Institute (NaSARRI-Serere) were therefore selected to host the trials for screening potential CSRFAB genotypes adapted to the East African agroecologies. The trials were planted on September 22, 2016 and September 29, 2016, respectively at Namulonge and Serere and harvested from January through April 2017 for the first season (2016B). In the second season (2017A), trials were planted on March 10, 2017 and March 29, 2017, respectively, at Namulonge and Serere and harvested from June to September 2017. The altitude of the sites was around 1,150 meters above sea level with an average day temperature of 22.2°C. Crops were not irrigated and often suffered from low rainfall 4 months after planting. Namulonge is characterized by a tropical rain forest zone with a bimodal rainfall average of 1,270 mm annually and high sweetpotato virus disease (SPVD) pressure, while Serere is in the tall grassland savanna zone with low rainfall and high weevil population ( Table 3).

Vine cuttings of approximately 30 cm of 3 to 4 nodes each were planted; 20 cuttings of each of the 130 sweetpotato genotypes were planted in a randomized complete block design in 2 locations (Namulonge and Serere) for 2 seasons, 2016B and 2017A (A and B are first and second season, respectively). Each genotype in a plot of five plants had four replications, but for ease of data collection and analysis, the samples were collected as two replications. Plant density was 1 m between rows and 0.3 m between plants within the row. The genotypes were sequentially and destructively harvested at 3, 4, 5 and 6 months after planting (MAP) to allow identification of storage root formation and bulking patterns following the repeated measures design ( Causton, 1994; Hesser, 2015). During each harvest period, four plants were uprooted for above and below ground part data collection. Each row was bordered by two sweetpotato plants at the extreme ends. The plots were kept weed free and no fertilizer or other agro-chemicals were applied.

Growth and development measurements. Traits that are known to characterize growth in sweetpotato storage roots were selected. These included: (i) number of harvested plants (NPH), allowing calculation of average values, (ii) total storage root number (SRN), (iii) Total root weight (TRW) measured with a round spring balance scale (Hanson, 8 in x 8 in x 3 in), was used to calculate yield as tons per hectare, (iv) commercial and noncommercial storage root number (CRN & NCRN, respectively) and commercial and noncommercial storage root weights (CRW & NCRW, respectively), allowing the estimation of storage root formation, bulking rate, (v) vine weight (VW), (vi) root system weight (RSW) used to calculate biomass yield (BMY), and (vii) harvest index (HI). Senescence (SEN) was estimated using a scale of 1 to 9, where 1 = no senescence, 9 = severe senescence marked by death/drying ( CIP/AVRDC/IPGR, 1991).

Development of a scale for continuous storage root formation and bulking (CSRFAB). To capture the possible overtime initiation and bulking in sweetpotato, we developed a rating scale of 1 to 9. The scale rates the expression of CSRFAB trait for an individual genotype. CSRFAB scores were therefore developed throughout the 2016B growing season. Detailed observation of storage root formation and bulking over 6 months provided comprehensive knowledge of the development of a scale for measuring changes in the CSRFAB trait. The scale was set to measure the changes in root formation and bulking of a given individual genotype. The change in scores would reflect the potential of roots to bulk into storage roots (fleshy or lignified), newly initiated storage roots, their status of bulking and their maturity levels (see Figure 1, scoring scale).

Growth model analysis. Growth models were estimated using a multilevel, mixed model framework described by Payne (2009) in GenStat 18 ^th Edition. Each of the 130 genotypes was maximally compared (4160 times) with the other genotypes in a model with two replications, four harvest times, two seasons and two locations.

To better understand the details in the storage root development patterns across the four harvest times, we analyzed piecewise, storage root growth patterns in different phases of the trial and selected individual plants to represent different growth pattern characteristics. Means were plotted to visualize the growth patterns using Genstat 18 ^th edition.

Restricted maximum likelihood (REML) variance components analysis of the phenotypic data was performed using the following general linear mixed model;

Y ijklcqm = μ+S i + L j + SL ij + SLR ijk + H l 1 + H q 2 + H c 3 + SH il + LH jl + SLH il + E m + E H l m 1 + E H q m 2 + E H c m 3 + SE im + LE jm + SLE ijm + € iml + LEH jml + SLEH ijml + ε ijklcqm

Where

Y _ijklm is the observed overtime response of genotypes across location and season.

μ, is the overall mean, S _i is the effect of the ith season, L _j is the effect of the jth location, SLR _ijk is the effect of the interaction between the ith season in the jth location and the kth replication, H T l 1 is the effect of linear term l in polynomial model, H T q 2 is the effect of the quadratic term q in polynomial model, H T c 3 is the random effect of the cubic term in the polynomial model, SH _il is the interaction between season and harvest time, LH _il is the random effect of interaction between jth location and h ^th harvest time, SLH _iil is the effect of the interaction between the ith season and the jth location at the mth harvest time, E _m is the effect of the m ^th genotype, E H l m 1 is the effect of interaction between mth genotype and lth linear term, E H q m 2 is the effect of the interaction between ith genotype and qth quadratic term in the polynomial model, E H c m 3 is the effect of interaction between ith genotype and cth cubic term in the polynomial model, SE _im is the effect of interaction between season and genotype, LE _jm is the effect of interaction between location and genotype, SLE _ijm is the random effect of the interaction between season, location and genotype. €SEH _iml, is the effect of the interaction between season, harvest time and genotypes, LEH _jml is the random effect of the interaction between location, harvest time and harvest time, SLEH _ijml is the interaction season, location and harvest time, Ɛ _ijklcqm is the error associated with all factors involved in the polynomial model.

The F-test denominator for genotypes tested in different locations and seasons ( Bararyenya et al., 2018b) was calculated following Satterthwaite’s formula for the “composite” F-test denominator for genotypes:

Satterthwaite’s formula for the “composite” F-test denominator for genotypes is as shown:

D e n M S = M S ( G L ) + M S ( G S ) + M S ( G S L ) D e n d f = [ M S ( G L ) + M S ( G S ) + M S ( G S L ) ] 2 M S ( G L ) 2 d f ( G L ) + M S ( G S ) 2 d f ( G S ) + M S ( G S L ) 2 d f ( G S L )

giving Satterthwaite-type approximation of mean squares (MS) and degrees of freedom (df),

where MS = mean square, G = genotype, S = season, L = location, df = degree of freedom, Den df = denominator degrees of freedom ( Satterthwaite, 1946; Snedecor & Cochran, 1967).

Variance component analysis and heritability estimates of selected sweetpotato growth traits in a nonlinear model structure. The genotypic variance among the nine traits associated with CSRFAB varied from 0.9 (CRW) to 7.7 (SRNO). Genotypic variance was high for SRNO (7.7), CRN (5.0) and CRW (5.0) ( Table 5). The phenotypic variance was high for VY (449.8), SRL (378.5) and SRY (84.6) and varied from 2.4 (CSRFAB) to 449.8 (VY). The residual variance was extremely high for VY (412.5) and SRL (339.6). These two particular traits are influenced by continuous growth. While some genotypes continue to increase in biomass weight, others die by senescence, likewise for vine length. The error and the GxE variances for CSRFAB are not big compared to its genetic variance. This implies that the scale used to measure the trait is precise and the trait is not influenced much by the environment. Heritability was relatively high for SRNO (67.2%) and CSRFAB (50.5%). The low residual variance and high heritability observed for CSRFAB confirmed the precision of the method used to study the CSRFAB trait in sweetpotato.

We performed a harvest basis analysis and calculated the corresponding heritability for each trait to understand the dynamics of breeding values across harvest times. We targeted the traits that can affect the final yield. Thus, the genotypic variances among seven main traits associated with CSRFAB varied from 0 to 72.46 ( Table 6). Genotypic variance was high for HI at 120 DAP (72.46) and VY at 180 DAP (59.91) ( Table 6). Zero variance was recorded for VY (120 DAP), HI (150 DAP), SEN (180 DAP) and weevils (180 DAP). The zero (or negative) variance components could be due to an artifact of the optimization algorithm that includes a non-negative constraint; a negative variance component could also represent competition effects between adjacent plots. These results imply that there is no significant change in VY, HI, SEN and weevil damage within the population for the respective growth periods. Since heritability is influenced by genetic variance, it was directly affected at the same traits and harvest periods, (ranging from 0 to 67%). The 0% heritability implies that the effect of the traits is moving to fixation, that is, its frequency in the population is very high. This is because polyploidy crops are dominated by large mutations with small effects and the genetic fixation pattern is affected by interactions between cosegregating alleles ( Kopp & Hermisson, 2009). If we score the effect of the allele(s) regulating the trait having no heritability in the population, the result would mean in genetic terms, that the allele frequency in the population is 100%, therefore the genetic variance at the loci of these genes is zero, so any variance in the corresponding phenotypic traits cannot be attributed to the non-existent genetic variance. These results need further investigation especially in the case of weevil resistance mechanisms as no significant increase in weevil infestation was observed in late harvest ( Bararyenya et al., 2018b). The rate in storage root bulking resulting in the available high green biomass may compete with weevil infestation. Broad sense heritability was relatively high for CSFRAB (50.5%) compared to other yield component traits indicating a better yield prediction using the scale.

We found temporal dynamics of genotypic influence on overall trait development ( Table 6). In the early growth phase, genotypic variance was mostly low. As plants grew, genotypic factors became in general more important. The increasing genetic effect was observed up to about 120 DAP and decreased thereafter. After 120 DAP, the genetic effect became relatively less important. This can be partly explained by the drought stress which became more important 4 months after planting (MAP). Although less obvious, the opposite pattern was seen in the growth recovery phase (after 5 MAP), likely due to growth resumption resulting in the decline in overall phenotypic differences between CSRFAB and DCSRFAB plants. The investigated highly correlated traits with CSRFAB showed dynamic changes in heritability during the entire plant growth stage ( Table 6). SRNO and CSRFAB showed similar patterns of heritability over time. We found that heritability of SRNO and CSRFAB increased in early growth stages and then decreased during drought stress, occurring between two consecutive rainy seasons and then increased thereafter during the growth recovery period occurring with the onset of the rainy season. These results are supported by Tuberosa (2012); quantitative traits reflecting the performance of crops under drought conditions tend to have low to modest heritability ( Table 6).

We have proposed in this study a method that can be used to estimate changes ( Figure 2 to Figure 5) in the CSRFAB trait and therefore estimate the potential maximum yield of a sweetpotato genotype. The scoring method developed in this study effectively measured changes in the CSRFAB trait. This is supported by its low residual variance (1.4) compared to SRN (16.3) and SRY (51.1) ( Table 4) and its high broad sense heritability of 50.5% compared with heritability of SRN (67.2%) and yield (11.1%) ( Table 5). Two types of growth patterns were identified according to the lifetime of sweetpotato genotypes. The first type which has determinate storage root formation and bulking is characterized by a rapid and short vegetative growth period, followed by a senescence period until the leaves die off. This period is also characterized by a quick maximum yield obtained about 90 to 120 DAP ( Figure 2) for most DCSRFAB genotypes. Respective CSRFAB scores for the same genotypes declined overtime due to lack of new root formation and similar level of bulking for mature storage roots ( Figure 3). Changes between successive harvest times were generally negative for DSRFAB genotypes. The cumulative yield changes, as were the cumulative score changes of DCSRFAB genotypes were therefore lower than the respective maximum single harvest yields and the rate of CSRFAB decreases in late stages. The second type of growth is characterized by a prolonged vegetative growth and a late switch-over time to reproductive phase ( Figure 3 and Figure 5). The cumulative yield changes over time, as were the cumulative score changes, of CSRFAB genotypes displayed similar results with the last harvest (180 DAP) confirming the accuracy of the scale to predict yield changes over time. The change responses were positive for CSRFAB genotypes and the cumulative responses increased overtime ( Figure 4) for yield and the increase was not significant ( Figure 5) for the CSRFAB scores suggesting a possibility of predicting CSRFAB genotypes responses from early growth stages. During this period the yield increase starts later and increases drastically after 150 DAP ( Figure 4) for most CSRFAB genotypes. Respective CSRFAB scores of the same genotypes did not change overtime due to continuous root formation and bulking ( Figure 5) suggesting the ability of the scoring scale to predict CSRFAB genotypes at early growth stages. This period increased drastically yields of CSRFAB genotypes, however, the maximum yields were not observed in this trial due to continued vegetative growth. According to Paltridge & Denholm (1974) the variation in yield observed may be due to the variation in their actual rates of dry matter production and the individual switchover time of the genotype to raise its maximum yield, referred to as the optimum growth pattern. The optimum growth pattern for determinate sweetpotato genotypes is of a two-phase plant growth, with the switchover occurring at the instant the plant becomes limited by restriction of its access to light (senescence). Subsequent values of the growing cycle which give maximum yield per unit time of harvest occur after these periods for indeterminate growth which are functions of above ground vegetative (leaves) lifetime. Each successive maximum is larger than the last, so one might expect the plants to evolve longer lifetimes and correspondingly longer periods of indeterminate (CSRFAB) growth. The intensity of senescence strongly varied (P<0.001) among genotypes and was negatively correlated with CSRFAB ( Table 7). The yield rate of change between the 120 DAP and the 150 DAP was always negative. For the CSRFAB ( Figure 3 & Figure 5), all the mean predictions and changes were positive. Yield increased up to more than 20-fold and the increase was genotype dependent.

These results are in agreement with the basic growth curves in many crop plants ( Schurr et al., 2006; Yanfu et al., 1989). The rapid growth in the first stage for determinate or DSRFAB genotypes could be attributed to early maturing genotype properties in which there is more energy invested in biomass production for early remobilization for storage root bulking and this plant growth expression is also reported in other annual crops ( Wenk & Falster, 2015). However, the maximum yield in this period was low and was limited by the available amount of green biomass which affected the bulking rate. Paltridge et al. (1984) reported similar common characteristics in which many plants have a rather sharp transition between the vegetative and the reproductive stages of growth. If the time of switch over is small, the amount of green leaf would be small and the subsequent rate of production and final yield would be also low. In this phase, the time of switchover was before 90 DAP. Sweetpotato continues to grow and branch if environmental conditions are favorable, due to its perennial habit, but the leaves formed earlier in the growing season start to fall and the total number of leaves and leaf area decrease toward the end of the growing season ( Somda & Kays, 1990). Determinate or DSRFAB genotypes lost their ability to initiate new shoots at around 120 DAP and the VW decreased drastically. These results agree with findings of Paltridge & Denholm (1974) and Bhagsari (1990) in which most annuals exhibit a single reproductive phase, often with a sudden onset.

The senescence phenotype was less observed in indeterminate types, although greenness intensity was reduced at 120 DAP which resumed and drastically increased (high positive quadratic slope) from 150 DAP when rains came back. Bhagsari (1990) reported similar results that sweetpotato cultivars maintained leaf area index to intercept a major portion of sunlight until harvest, and leaf area growth significantly differed depending on cultivar.

The slow increase in most of the yield component parameters in CSRFAB genotypes resulted in low storage root yield in the first growth phases ( Figure 3 & Figure 5). This can be explained by the fact that indeterminate genotypes invest resources for maintenance at earlier stages including root elongation for nutrition purposes and biomass production to maintain vegetative growth. This resulted in strong vegetative biomass increase for CSRFAB genotypes. For these genotypes the time of switchover to reproduction was very late (around 150 DAP). This was the last growth phase where yield increased drastically in CSRFAB corresponding to the switch to reproduction (onset of flower and seed) and storage root remobilization in sweetpotato in which the plant invests its vegetative resources in increasing the sink capacity. Because of high availability of resource/energy in upper biomass, sink strength is increased leading to increased productivity.

For sweetpotato breeders and practitioners, harvest index (HI) is difficult to estimate due to the problem of measuring its components. For instance, the time of harvest influences greatly the value of HI because storage root bulking is likely to vary progressively from the onset of storage bulking and increases with the biomass translocation into storage roots. However, the senescence reduces the above-ground biomass progressively leading to high and unrealistic values of harvesting index. Therefore, HI of sweetpotato varies greatly with the time of harvest ( Bararyenya et al., 2018b). This variation is also influenced by other environmental factors including wet or dry conditions during harvest which increase or decrease weight due to high or less moisture. Similar results in other root and tuber crops are reviewed by Hay (1995).

Overall, the starting yield was low at 90 DAP (overall mean) and increased progressively as growth time increased ( Table 7). This relationship is well explained by the variation in the data (R ² varied from 38% to 65%). High yielding genotypes showed consistently maximum yields in the population ( Bararyenya et al., 2018b) while low yielding genotypes showed inconsistent relationship. The maximum yield recorded across locations and seasons was 16.7 t/ha and 28.6 t/ha at the first harvest and the last harvest, respectively ( Table 7). This implies that the frequency of genotypes that increase yield overtime is high. In this trial, some genotypes reached maximum growth earlier, others late, leading to high variability in growth related parameters.

On average, there was a two-fold increase in yield from the 90 DAP to 180 DAP. The 10 most distinct DSRFAB genotypes were, MPG1146 (A26), Dimbuka-Bukulula (A34), NASPOT 1 (A24), Otada (A40), MPG1128 (A11), MSK1040 (A33), RAK786 (A10), KMI88 (A42), KBL648 (A14) and the 10 most distinct CSRFAB were, SPK004 (A19), Kala (A13), BSH740 (A16), KML872(A32), NASPOT 10 O (A22), Mayai (A3), Ukerewe (A41), NASPOT 7 (A30), APA352 (A27) and RAK819 (A18). These contrasting genotypes for CSRFAB can be used in breeding programs to study and improve sweetpotato yield in CSRFAB genotypes. The average yield at two locations in two seasons shows that you can more than double sweetpotato production by choosing high yielding genotypes ( Table 7 with maximum yield of 13.17 t/ha for DSRFAB versus maximum of 28.64 t/ha for CSRFAB). Similar results have been reported ( Çalişkan et al., 2007) in which there were significant differences among the locations, 60 to 70 t/ha of storage root yield being obtained by choosing high-yielding varieties.

For SRY and VY the first two box plots are comparatively equally shorter than the third and fourth box plots ( Figure 6). This suggests that, overall, genotypes have little variation over the first two harvest times. It also suggests low variation between time of harvest during this phase. The third and fourth box plots are higher than the first two box plots for SRY and VY. This suggests that genotypes have quite different growth patterns from the two first harvest times and the two last ones. It also suggests high variation among the genotypes. The last two box plots in each sub-figure show obvious differences within each box plot and the two first box plots. This suggests an area of difference that could be explored further. The four sections of the box plots are uneven in size. This shows that many genotypes have a similar growth pattern during the early growth phase, but in a later phase genotypes are more variable in their growth pattern. The long upper whisker shows that genotype growth varied amongst the most positive quartile group, and very similar for the least positive quartile group. This suggests a need for further exploration. The medians of the two first harvest time plots (which generally will be close to the average) are at the same level. However, the box plot of the last two harvest times shows very different distribution means. Variation and distribution of CSRFAB scores across location and seasons consistently remained almost the same ( Figure 6 and Figure 7), suggesting an effective response prediction of the scores from the beginning.

CSRFAB scores were highly and positively correlated with most of the yield component traits ( Table 8). This implies that CSRFAB is also a component of yield. In other words, the higher the CSRFAB scores of a sweetpotato genotype, the higher the yield of the genotype. CSRFAB scores were negatively correlated with SEN which confirms our hypothesis in which a CSRFAB genotype should maintain vegetative growth to continuously provide source/inputs for sink storage roots. The negative correlation with VW needs further investigation, however, the competition of source and sink activities in the plant, effects of pests and diseases such as nematodes and Alternaria stem blight ( Alternaria bataticola) and SPVD could be among the causal factors. It is possible to cease vegetative growth and continue survival for an extended period, but most varieties reduce their vegetative weight following the storage root bulking peak ( Venus & Causton, 1979). The comparison of a classic method of evaluating growth change (analyzing yield mean change between two consecutive harvests) and the developed scale for measuring CSRFAB traits produced consistent results with CSRFAB scores. This is supported by high heritability and low residual variance observed for CSRFAB versus yield and other component parameters. Using the developed scale, 48 genotypes were clustered among CSRFAB genotypes, whereas 62 genotypes clustered among DSRFAB ( Figure 5). These results were reproduced in the following season, and 41% were common to the two methods in 2016B versus 46% in 2017A ( Figure 8).

We characterized in this study growth patterns associated with CSRFAB in sweetpotato and compared the accuracy of CSRFAB scores and the classic method used to measure growth change overtime (compared yield change overtime) ( Figure 8). It was hypothesized that CSRFAB genotypes potentially increase yield over time, therefore, the trait can be screened for by measuring yield change overtime. This method, holding other factors constant, shall produce the same results of scoring for the trait using the developed 1 to 9 scale. We investigated this relationship in our data. Overall, the yield change analysis over four harvest times grouped the 110 genotypes (without missing data) into 39 CSRFAB and 71 DSRFAB genotypes. Using the developed scale, 48 genotypes clustered among the CSRFAB genotypes, whereas 62 genotypes clustered together as DSRFAB ( Figure 8).