Introduction

Rice (Oryza sativa L.) is one of the most staple foods and a good source for all generations, and more than one half of the world’s population is dependent on it (Bouman 2007). It is also a good source of calories, which provides all humans with about 50–80% of the daily calorific consumption (Seck et al. 2012; Futakuchi et al. 2013). Biotic and abiotic factors adversely limit the productivity of the rice growing areas of the world. It has been estimated that more than 200 million tonns of rice are lost every year due to environmental stresses (Moonmoon and Islam 2017). Increasing rice production is controlled by different factors, for instance, water deficit, which is an important factor due to the lack of water in many countries of the world (Nirubana et al. 2019). Water deficit affects plant growth, and it is a major constraint for about 50% of the world production area of rice (Khush 2005). Therefore, producing new varieties of rice which are high yielding and tolerant to water deficit through traditional breeding are considered the economical way to avoid the deficit of water, especially at the end of canals. Genetic variability is necessary for successful selection of superior breeds from segregating generations for further selection (Priyanka et al. 2019). The success of any crop improvement programme depends not only on the amount of genetic variation present in a crop, but also on the extent of variation that is heritable from the parent to its line (Bello et al. 2012). Trait genes can be better understood by using third- and fourth-degree statistics, kurtosis and skewness in segregation of generations. There is a necessity to beget information on genetic variance, coefficiency of genetic variation, heritability, and genetic advance (GA) to estimate the progress of their breeding programme in the future (Savitha and Ushakumara 2015). Heritability is considered to be a character which is important for plant breeders because it provides information on the range to which a particular trait can pass from parent to line. GA is also important because it clarifies the degree of the gain gotten in a character from one selection cycle. High GA combined with high heritability estimates the most favourable conditions for deciding the selection criteria (Syukur and Rosidah 2014). High GA connected with high heritability rating provides the best conditions of selection. It also displays the presence of additive genes in the trait, and furthermore submits reliable crop improvement during the selection of these traits (Nwangburuka and Denton 2012). Frequency distribution pattern based on skewness and kurtosis in F2 generation and genetic variability parameters is suitable to identify useful segregates with high yield coupled with desirable agronomic traits (Rani et al. 2016). Assessment of heritability with GA is more credible and significant than individual sights of the parameters (Nwangburuka and Denton 2012).

The aims of the present study were: (1) to analyse the statistics and quantify the extent of genetic variation available for grain yield and yield components in the F2 (segregating) generation of rice under normal and water deficit conditions; (2) to select superior segregants that have water deficit tolerance and high yield; and (3) to assess the genetic gain that can be made by selection when lines are involved in the hybridization.

Materials and methods

The present investigation was conducted at the experimental farm of the Rice Research and Training Centre (RRTC), Sakha, Kafr el Sheikh, Egypt, during three seasons in 2017, 2018, and 2019. The genetic materials used in this investigation involved four genotypes: the water deficit tolerant IR 78,936-B-B-B-B, the moderately water deficit tolerant Giza 178 and FL-496, and the water deficit sensitive Giza 177 varieties (Table 1).

Table 1 Origin and main characters of the four genotypes used as parents in the studied pair crosses
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In the growing season of 2017, the four studied parental varieties were sown on three sowing dates in the summer season with 15-day-intervals to overcome the difference of the heading date among the parental varieties. After 30 days from sowing, seedlings of the parents were transplanted to the experimental field in three rows, 5 m long and 0.2 × 0.2 m apart between the plants and rows.

The crossing was conducted among the parents in 2017 to produce four crosses. However, the crossing method of Jodon (1938) modified by Butany (1961), the hot water method of gelding, was used. The parental varieties and the F1 generations of IR 78,936-B-B-B-B (tolerant) x Giza 177 (sensitive), FL-496 (moderate) x Giza 177 (sensitive), IR 78,936-B-B-B-B (tolerant) x Giza 178 (moderate) and FL-496 (moderate) x Giza 178 (moderate) were evaluated and arranged in a randomized complete block design experiment with three replications in 2018. Each replication contained 25 individual plants under normal water supply (NWS) and deficit water supply (DWS). NWS represented normal irrigation as recommended for flooding rice in Egypt with 3–4 days intervals between the irrigation events. DWS represented water deficit stress, in that case, the intervals of irrigation were 12 days starting after transplanting.

In 2019, the parent F1 and F2 populations were planted and evaluated under NWS and DWS. Each F2 population consisted of more than 200 individual plants. All cultural practices such as field preparation, sowing, and fertilizers were applied as recommended in all seasons of the study. The studied characters (quantitative parameters) were recorded for the parents, F1 and F2 generations for plant height (cm), number of panicles per plant, panicle length, panicle weight (g), number of filled grains per panicle, sterility %, 100-grain weight (g) and grain yield per plant (g) according to IRRI (1996).

Phenotypic and genotypic coefficient of variation (PCV and GCV) for all the studied characters were calculated by the formula reported by Burton and DeVane (1953). The genetic advance as a percentage of mean (GAM) and broad sense heritability for all the traits as the ratio of GCV to the total PCV were calculated as reported by Johnson et al. (1955). Skewness and kurtosis statistics were estimated according to Snedecor and Cochran (1989) for understanding the nature of distribution of the F2 population for yield and its related traits to identify a superior segregant in the F2 generation of all crosses under study. Skewness and kurtosis mean values as well as correlation analysis were computed using the ‘SPSS’ software programme. The test of normality of the F2 populations was carried out by performing ‘Shapiro-Wilks’ W test (Shapiro et al. 1968) using STATISTICA statistical package R.

Results

Morphological and agronomic characteristics

Mean performance

The mean performance of the parents, F1 hybrids and F2 populations was significantly different between the two parents for all crosses under study (Table 2). The results showed that all the mean values of studied characters under DWS were lower than the means in NWS. For Cross 1, all the characters of P1 showed higher values than those of P2 under both water supply conditions, even for sterility % (Table 2). On the other hand, for Cross 2, the data showed that the means of P1 were also higher than those of P2 for most of the studied characters except for the number of panicles per plant and 1000-grain weight under NWS and plant height under DWS.

Table 2 Mean values of parents, F1 plants and F2 populations of the studied characters in rice Crosses 1 and 2
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For Cross 3, the results reflected that all studied characters for P2 were lower than for P1 except for panicle weight under NWS, plant height and 1000-grain weight under DWS, and the number of filled grains per panicles, sterility % under both water supply conditions (Table 3). In Cross 4, the data indicated that all characters of P1 were higher than those of P2 except for the number of panicles under NWS, plant height, 1000-grain weight under DWS, panicle weight and number of filled grains per panicle under both water supply conditions (Table 3). The averages of the measured traits of the F1 plants and the F2 populations in all crosses were similar to those of the parents. The F2 population for Cross 1 gave the highest yield under water deficit stress, while Cross 2 gave the highest yield under NWS condition (Tables 2, 3, 4).

Table 3 Mean values of parents, F1 plants and F2 populations of the studied characters in rice Crosses 3 and 4
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Table 4 Range and standard deviation for the studied characters in the F2 populations of rice crosses under normal (NWS) and deficit (DWS) water supply conditions
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Range and standard deviation

A range from 60 to 155 g was observed among the studied characters for grain yield per plant under NWS and from 35 to 90 g under DWS in all crosses (Table 4). In Cross 1, the number of filled grains per panicle under DWS and the grain yield per plant under NWS showed the maximum standard deviation of 6.98 and 6.39, respectively, followed by the number of panicles per plant under DWS with its range variation of 29 and standard deviation of 6.32 (Table 4).

In Cross 2, the highest standard deviation (38.8) was observed for the number of filled grains per panicle under DWS, then for the grain yield per plant character under DWS (17.1) subsequently with the ranges of 167 and 90, respectively. In Cross 3, the highest standard deviation was observed for the number of filled grains (47.3), then for the grain yield under NWS (33.7) subsequently with the ranges of 158 and 105, respectively. In Cross 4, the highest standard deviation was observed for the number of panicles per plant under DWS, then for the number of filled grains per panicle under NWS (31.9 and 22.9), subsequently with the ranges of 74.0 and 105, respectively (Table 4).

Plant height

In the F2 population, Cross 4 (FL-496 × Giza 178) under NWS showed the highest mean (134.96) and range (65.0) for plant height. The negative skewness (−0.126) with a positive kurtosis (0.574) under NWS states that a higher frequency of individuals had values at or near to the mean value (Table 4).

Number of panicles per plant

For the number of panicles per plant, Cross 4 (FL-496 × Giza 178) segregant gave the highest mean under both water supply conditions. The negative skewness with a positive kurtosis under NWS states that a higher frequency of individuals had values at or near to the mean value (Table 4).

Panicle length

In the F2 population, the highest mean value for panicle length was recorded for Cross 1 (IR 78,936-B-B-B-B x Giza 177) segregant under both of the water supply conditions under study. The frequency distribution graph showed highly negative skewness under DWS suggesting the presence of more individuals with plant height higher than the mean value (Table 4).

Panicle weight

The highest mean for the panicle weight was recorded for Cross 2 (FL-496 × Giza 178) segregant under NWS, while the highest mean of this character was recorded for Cross 1 (IR 78,936-B-B-B-B x Giza 177) under DWS. The frequency distribution under DWS conditions was fairly negatively skewed (Table 4).

Number of filled grains per panicle

Cross 1 (IR 78,936-B-B-B-B x Giza 177) gave the highest number of filled grains per panicle under both water supply conditions. The results indicated moderate positive skewness under water deficit stress with a negative kurtosis (Table 4).

Sterility %

Cross 3 (IR 78,936-B-B-B-B x Giza 178) gave the lowest sterility % under both water supply conditions. A graph shows negative skewness where most of the values are falling on the right side and the tail is longer towards the left (Table 4).

1000-grain weight

For Cross 1 (IR 78,936-B-B-B-B x Giza 177), it was recorded that the highest value of 1000-grain weight was in both water supply cases. The graphs representing DWS were approximately symmetrical with negative kurtosis (Table 4). This indicates a normal distribution for the population.

Grain yield per plant

Cross 1 (IR 78,936-B-B-B-B x Giza 177) gave the highest grain yield under water deficit and Cross 2 gave the highest value for the same characters. The graph representing the water deficit stress conditions was positively skewed with a negative kurtosis (Table 4). The distribution of the phenotypic variation for the grain yield per plant, which is the main trait, for the four F2 populations are presented in Figs. 1, 2, 3, 4. The phenotypic variation of this trait displayed a continuous distribution. It also illustrated that the frequency distribution varied widely and transgressive segregations indicating polygenic inheritance existed.

Fig. 1
figure 1

Frequency distribution of grain yield per plant trait in the F2 populations of Cross 1 (IR 78,936-B-B-B-B x Giza 177) under NWS (a) and DWS (b). The positions of the parental trait values are indicated by the arrows

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Fig. 2
figure 2

Frequency distribution of grain yield per plant trait in the F2 populations of Cross 2 combinations (FL-496 × Giza 177 under NWS (a) and DWS (b). The positions of the parental trait values are indicated by the arrows

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Fig. 3
figure 3

Frequency distribution of grain yield per plant trait in the F2 populations of Cross 3 combinations (IR 78,936-B-B-B-B x Giza 178) under NWS (a) and DWS (b). The positions of the parental trait values are indicated by the arrows

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Fig. 4
figure 4

Frequency distribution of grain yield per plant trait in the F2 populations of Cross 4 combinations (FL-496 × Giza 178) under NWS (a) and DWS (b). The positions of the parental trait values are indicated by the arrows

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Genetic traits

Estimation of variance components and GAM

Data in Table 5 show that PCV of the characters under study was slightly higher than the corresponding GCV in all crosses. The maximum of GCV was found for grain yield in Cross 1 under DWS, while in Cross 3 under NWS. GAM was also calculated and it ranged from 3.70 for panicle length under DWS to 89.33 of panicle weight and grain yield per plant under water deficit for Cross 1.

Table 5 Genetic traits for the studied characters in the F2 populations of rice crosses under normal (NWS) and deficit (DWS) water supply conditions
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Heritability

Heritability (h2b%) of the characters under stress conditions ranged from 42.69 to 92.36, while the range was between 48.49 and 96.57 under NWS in Cross 1 (Table 5). In Cross 2 under DWS, heritability ranged from 42.69 to 87.03, whereas the range was from 48.49 to 95.72 for NSW. The ranges in Cross 3 and Cross 4 were from 43.95 to 98.01 and from 48.44 to 97.37 under DWS, while from 51.98 to 96.18 and from 39.07 to 99.43 under NWS, respectively (Table 5). Heritability values were slightly lower under water deficit stress than in the non-stressed trial for all the characters under study except the number of filled grains per panicle in Cross 1, grain yield per plant in Crosses 1 and 4, number of panicles per plant in Crosses 2, 3 and 4, 1000-grain weight in Crosses 2 and 4, panicle length in Crosses 3, and sterility % in Cross 3 (Table 5). High heritability in a broad sense coupled with high GA was observed for grain yield in Cross 1 under the two studied conditions and hence offered good scope for selection.

W-test results

The results of the Shapiro-Wilks test (W-test) indicate that the F2 population did not show a normal distribution for all the traits except plant height in Crosses 1, 2 and 4 under NWS, in Cross 2 under DWS, number of panicles per plant in Crosses 2, 3, 4 under NWS, number of filled grains per panicle in Crosses 3 and 4 under DWS, and 1000-grain weight in Cross 1 under DWS (Table 6).

Table 6 Test of normality of the distribution curve for the studied characters in the F2 populations of rice crosses under normal (NWS) and deficit (DWS) water supply conditions
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Correlation analysis results

The estimates of the correlation coefficient among all the studied characters are presented in Table 7. Concerning plant height, data showed that no significant correlation, except for 1000-gain weight under DWS. Regarding the correlation between the number of panicles and all the other studied traits, the number of panicles significantly and positively correlated with panicle weight and the number of filled grains per panicle under NWS. Panicle length showed highly significant positive correlation with panicle weight, the number of filled grains and grain yield under DWS. Furthermore, the results showed a highly significant positive correlation between panicle weight and sterility % under both water supply conditions as well as between panicle weight and grain yield under DWS. Positive significant and highly significant correlations were found between the number of filled grains per panicle and grain yield under both the conditions under study. Positive significant correlation was found between the sterility % and 1000-grain yield under NWS. 1000-grain weight showed a significant positive correlation with grain yield weight under both water supply conditions.

Table 7 Estimates of the phenotypic correlation coefficients for the studied characters in the F2 populations of rice crosses under normal (NWS) and deficit (DWS) water supply conditions
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Discussion

The mean performance of the parents, F1 hybrids and F2 populations was significantly different between the two parents for all crosses. These differences between genotypes might be due to their genetic background. The mean values of studied characters under DWS were lower than the means in NWS stating that drought causes serious slowdown of growth (Bassuony et al. 2015). However, the grain yield per plant trait was varying greatly among the parents under water deficit. When drought occurred during panicle development, it was delayed and the number of spikelets per panicle was reduced (Bassuony et al. 2015). Estimating the means of F1 and F2 populations, the grain yield character under NWS was higher than the yield under DWS showing that this trait is influenced by the environment. Water deficit stress influences plant growth, and ultimately, it reduced the grain yield of rice as the percentage of spikelet sterility increased under water deficit stress, especially at the panicle initiation stage (Venuprasad et al. 2007).

Selecting the characters (number of filled grains) contributing to the yield together will improve the grain yield in the next segregating population (Ibrahim et al. 2018). The expected response to selection can be measured by determining the parameters like standard deviation (Scossiroli 1977).

Information about the nature of gene action is provided by the study of distribution using skewness and kurtosis (Fisher et al. 1932) and the number of genes controlling the traits (Robson 1956). The sign of skewness assists us to draw the inference about the gene action for a certain trait. The positive skewness showed the existence of epistatic gene action for that trait. The gain is slower with the mild selection and faster with intensive selection for that particular trait. The negative skewness showed the existence of duplicate epistatic gene action and therefore the obtained is faster with moderate selection and slower with strong selection (Snape and Riggs 1975).

The skewed distribution indicated both duplicate and non-additive gene interactions, while the negatively skewed one was connected with additive x additive duplicate gene interactions. Also, positive skewness indicated the non-additive integral gene interactions. The skewness of the distribution for the F2 population was found to be platykurtic with a kurtosis coefficient of less than 3, which means they are controlled by a large number of genes. The decrease in the mean of the number of the filled grains under DWS for this population was the lowest compared to others, which shows that water deficit stress had no considerable effect on this character (Rajan and Rani 2019). These transgressive segregants might have been a result of the accumulation of favourable genes derived from the parents. Transgressive segregation was usually noted in segregating populations for quantitative traits (Tanksley 1993; Xiao et al. 1996). There are many potential reasons of transgression including unmasking of recessive deleterious alleles due to inbreeding. However, it was also supposed that accumulation of complementary alleles of the parents at multiple loci is the basic factor for appearance of such transgressive segregants (Tanksley 1993; Mohammadi et al. 2013).

The PCV of the characters under study was slightly higher than the corresponding GCV in all crosses, but the small difference indicates an environmental effect on the phenotypic. GCV provides information on the genetic variability of the characters in the base population, but it is not possible to determine the heritable amount of the variation only from GCV.

Heritability values were slightly lower under water deficit stress than in the non-stressed trial for all the characters under study except some characters in crosses under study. In those cases, no consistent reduction in heritability appeared under water deficit stress relative to the non-stress conditions. These results confirm with (Lanceras et al. 2004) and support the hypothesis that the assessment of yield under drought stress in rice can be performed with an accuracy equivalent to that obtained for non-stress trials. It indicates that direct phenotypic selection for grain yield under stress will lead to gains if screening trials are well managed (Venuprasad et al. 2007).

The study of the relationships among the morphological characters under study is of great importance. Panicle length showed highly significant positive correlation with panicle weight, the number of filled grains and grain yield under DWS. Similar results were observed in a previous study (Zou et al. 2005). 1000-grain weight showed a significant positive correlation with grain yield weight under both water supply conditions (Bassuony et al. 2015).

The screening of the F2 populations of the four investigated crosses (IR 78,936-B-B-B-B x Giza 177, FL-496 × Giza 177, IR 78,936-B-B-B-B x Giza 178 and FL-496 × Giza 178) for water deficit tolerance indicates the complex nature of inheritance and higher heritability estimates. The results indicated high heritability in a broad sense coupled with high GA, which was observed for grain yield in Cross 1 under the two studied water supply conditions and hence offered good scope for selection. We believe that our results have scientific as well as practical significance and can motivate rice breeders to do crosses of various rice varieties with different water deficit tolerance in accordance with the demand of accommodation to the increasing frequency of weather extremes caused by climate change.