## Legume Research

**Chief Editor**J. S. Sandhu**Print ISSN**0250-5371**Online ISSN**0976-0571**NAAS Rating**6.80**SJR**0.391**Impact Factor**0.8 (2023)

**Chief Editor**J. S. Sandhu**Print ISSN**0250-5371**Online ISSN**0976-0571**NAAS Rating**6.80**SJR**0.391**Impact Factor**0.8 (2023)

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BIOSIS Preview, ISI Citation Index, Biological Abstracts, Elsevier (Scopus and Embase), AGRICOLA, Google Scholar, CrossRef, CAB Abstracting Journals, Chemical Abstracts, Indian Science Abstracts, EBSCO Indexing Services, Index CopernicusPredicting the Frequency of Transgressive RILs and Minimum Population Size Required to Recover Them in Dolichos Bean [*Lablab purpureus* (L.) Sweet]

G. Basanagouda^{1,*}, S. Ramesh^{1}, B.R. Chandana^{1}, H. Sathish^{1}, C.B. Siddu^{1}, M.P. Kalpana^{1}, R. Kirankumar^{1}

**Submitted**03-09-2022|**Accepted**22-12-2022|**First Online**26-12-2022|**doi**10.18805/LR-5035

Dolichos bean is one of the ancient legume crops grown in dry and semi-arid regions of Asia and Africa. It is a versatile crop grown for vegetable, pulse, fodder and green manure purposes (Ramesh and Byregowda, 2016). As is true with other predominantly self-pollinated legume crops, pure-lines are the only cultivar types used for commercial dolichos bean production by farmers. Pedigree selection of desirable recombinant inbred lines (RILs) for use as pure-line cultivars from bi-parental crosses-derived segregating populations is the most widely used breeding method in dolichos bean (Ramesh and Byregowda, 2016). The breeders routinely develop a large number of bi-parental crosses-derived segregating populations to implement pedigree selection to identify superior RILs. Handling of a large number of segregating populations is not only prohibitively resource demanding, but also reduces the efficiency of breeding process in terms of less than satisfactory genetic gain. The crosses made between parental combinations that fail to produce useful cultivars consume over 99% of the resources (Witcombe *et al*., 2013). Allocation of resources only to large-sized segregating populations derived from a few promising crosses selected based on an objective criterion is expected to enhance the chance of identifying desirable RILs for use as pure-line cultivarsand thus helps enhance breeding efficiency (Chahota *et al*., 2007; Witcombe *et al*., 2013; Bernardo, 2020). Given that resources are most often limited, determination of the minimum population size required to be raised to ensure(by say 95%) that at least one of the predicted RILs is recovered is equally important. Jinks and Perkins (1972) conceptualized the theory and out-lined the analytical procedure to predict the frequency of RILs that transgress pre-determined standards.The quantitative genetic parameters such as additive gene effect [a] and additive genetic variance [s^{2}A] reliably estimable from parental and early segregating generations (F_{2} and F_{3}) are sufficient to predict the frequency of transgressive RILs (Jinks and Pooni, 1976). Thomas, (1987) demonstrated that even random sample of a few F_{3} families provide a reliable estimate of [a] and [s^{2}A]. Kearsey and Pooni (1996) have described the method of predicting the minimum population size (n) required to recover at least one such predicted transgressive RIL. The objective of the present study is to predict the frequency of transgressive RILs and minimum population size required for their recovery from reciprocal crosses derived from two elite parents that complement the desirable traits in dolichos bean.

The basic material consisted of two elite parents, namely HA 4 and HA 5 (Table 1). Both HA 4 and HA 5 are high yielding pure-lines cultivars released for commercial production of dolichos bean in eastern dry zone of Karnataka, India. While HA 4 produce relatively fewer branches, racemes and large-sizedcurved pods bearing large-sized grains, HA 5 produce relatively many branches, racemes and small-sized pods bearing small-sized grains (Table 1). The objective was to develop new pure-lines that producea large number of branches, racemes and large-sized pods and grains. Reciprocal crosses, namely HA 4 × HA 5 and HA 5 × HA 4 were synthesized during 2020 rainy season at the experimental plots of the Department of Genetics and Plant breeding (GPB), University of Agricultural Sciences, (UAS), Bangalore, India. A total of 20 and 15 well-filled F_{1} seeds could be obtained from HA 4 × HA 5 and HA 5 × HA 4 crosses, respectively. The F_{1 }seeds were planted in 2020 post rainy season. All the F_{1} seeds germinated and survived to maturity. The F_{1 }plants of the two reciprocal crosses were carefully inspected for the traits specific to male parents to confirm their true hybridity. Indeterminate growth habit of all the 20 candidate F_{1} plants of HA 4 × HA 5 cross confirmed their true hybridity considering that indeterminacy is dominant over determinacy (Modha *et al*., 2019; Basanagouda *et al*., 2022). Production of curved pods (typical pod shape of HA 4) by all the 15 candidate F_{1} plants of HA 5 × HA 4 confirmed their true hybridity considering that curved pod shape is dominant (Girish and Byregowda, 2009) over straight pods (typical pod shape of HA 5). The selfed pods from F×’s of the reciprocal crosses were harvested, hand-threshed and sun-dried to obtain F_{2} seeds. F_{2} plants from these two crosses were raised in 2021summer season. A spacing of 0.3m was maintained between F_{2} plants of the reciprocal crosses. A total of 236 and 225 F_{2} plants from HA 4 × HA 5 and HA 5 × HA 4 crosses, respectively survived to maturity. Selfed pods from each F_{2} plants were manually harvested, hand-threshed and seeds were sun-dried for use in raising F_{2:3 }populations during 2021 rainy season. The seeds ofthe two parents and randomly selected 144 F_{2:3} families derived from each of the HA 4 × HA 5 and HA 5 × HA 4 crosses were planted in asingle row of 3 m length in alpha-lattice design using two replications during 2021 post rainy season. Fifteen-days after planting, seedlings of two parents and 144 F_{2:3} families were thinned to maintain a spacing of 0.3m between the plants and 0.6m between the rows. The recommended production package was practiced to raise two parents, F_{1}, F_{2 }and F_{2:3 }generations. A total 12 plants in each of the two parents and within each F_{2:3 }families in each replication survived to maturity.

**Sampling of plants and data recording **

Data were recorded on 10 randomly selected plants (avoiding border ones) fromtwo parents, their reciprocal F_{1}’s and from each of the 144 F_{2:3} progenies in each of the two replications and all the individual F_{2} plants (236 and 225) derived from HA 4 × HA 5 and HA 5 × HA 4 crosses, respectively for four traits, namely, number of primary branches and pods and weights of sun-dried pods and grains. The average of these traits across ten sample plants in each replication was computed and expressed as primary branches plant^{-1}, pods plant^{-1}, pod weight plant^{-1} (g) and grain weight plant^{-1} (g).

**Estimation of quantitative genetic parameters **

Data recorded on 10 randomly selected individual plants in two parents and their two reciprocal F_{1}’s and F_{2} plants (236 and 225) and replication-wise mean data of 10 randomly selected plants from each of the 144 F_{2:3} progenies were used for estimation of three quantitative genetic parameters, namely mid-parental value [m], additive gene effect [a] and additive genetic variance [s^{2}A] for use in prediction of the frequency of transgressive RILs that could be derived from HA 4 × HA 5 and HA 5 × HA 4 crosses. Assuming additive-dominance (A-D) model, the parameters, [m] and [a] were estimated using the multiple regression model (Kearsey and Pooni, 1996) implemented in SPSS software version, 16.0. Adequacy of A-D model was examined by joint scaling test (Kearsey and Pooni, 1996) implemented in SPSS software version 16.0. The [s^{2}A] was estimated by equating observed and expected mean squares (MS) attributable to ‘between F2:3 families’ from analysis of variance (ANOVA) of F_{2:3} families and solving for s^{2}A using the formula; (van Ooijen, 1989).

The analysis was implemented suing Microsoft Excel software.

**Predictingthe frequency and minimum population size required for the recovery of transgressive RILs**

Assuming that the data follow normal distribution, the probability (frequency) of recovering RILs that are likely to transgress the better parent (HA 5) was estimated as standard normal distribution integrals corresponding to quotient, (mean of HA 5-m)/sA for each trait considered in the present study; where, [m] is mid parental value and s_{A} is square-root of s^{2}_{A} (Jinks and Pooni, 1976). The minimum population size required to guarantee (say 95%) that RILs transgress HA 5 was predicted as the number (n) of RILs need to be raised such that probability of RILs that do not surpass HA 5 is less than 5% (Kearsey and Pooni, 1996). This probability was translated in to the equation,

(1-P)^{n} £0.05,

where,

P= Probability of RILs that transgress HA 5.

(1-P) = Probability of RILs that do not transgress HA 5.

The equation was solved for ‘n’ by applying logarithm to both the sides and rearranging the terms as n ³ log 0.05/log (1-P). If say 1% of RILs are predicted to surpass the HA 5, then ‘n’ was predicted as the ratio of log 0.05 to log 0.99, which is ³298.

Data were recorded on 10 randomly selected plants (avoiding border ones) fromtwo parents, their reciprocal F

Data recorded on 10 randomly selected individual plants in two parents and their two reciprocal F

The analysis was implemented suing Microsoft Excel software.

Assuming that the data follow normal distribution, the probability (frequency) of recovering RILs that are likely to transgress the better parent (HA 5) was estimated as standard normal distribution integrals corresponding to quotient, (mean of HA 5-m)/sA for each trait considered in the present study; where, [m] is mid parental value and s

(1-P)

where,

P= Probability of RILs that transgress HA 5.

(1-P) = Probability of RILs that do not transgress HA 5.

The equation was solved for ‘n’ by applying logarithm to both the sides and rearranging the terms as n ³ log 0.05/log (1-P). If say 1% of RILs are predicted to surpass the HA 5, then ‘n’ was predicted as the ratio of log 0.05 to log 0.99, which is ³298.

ANOVA is a diagnostic step to detect and estimate variation attributable to target source (s

Pure-line cultivars in most naturally self-pollinating crops including dolichos bean are developed by crossing parents, which are often cultivated varieties (as is true in the present study) and selecting RIL (s) with desired combination of traits. If no RIL was ever found which were betterthan their parents (or ancestors), referred to as transgressive segregants, plant breeding would notwork (Mackay, 2021). Though transgressive segregation (TS) occurs frequently enough that plant breeding works as amatter of routine, not all crosses display it and only a small proportion ofprogeny in any particular crossdisplay TS. It is therefore relevant to identify the potential crosses that uncover high frequency of TS. Predicting the frequency of transgressive RILs that could be derived from advanced generationsis an objective method of identifying potential cross (es). In the present study, the predicted frequency of RILs that are expected to transgress the better parent (HA 5) varied with the cross (Table 3). The predicted frequencies of RILs that transgressed HA 5 were higher from HA 5 × HA 4 than those from HA 4 × HA 5 for primary branches plant

As expected, the minimum population size required to recover the transgressive RILs predicted from HA 5 × HA 4 was relatively smaller than those predicted from HA 4 × HA 5 (Table 3). These results also suggest the importance of the direction of the crosses to be developed for generating breeding populations to maximize the recovery of transgressive RILs for use as pure-line cultivars. Our results augur well with theoretical results of Bernardo, (2022), who demonstrated that breeding populations generated from good × good crosses as is the case in our study, would tend to uncover higher frequency of transgressive RILs in a predictable manner. Both quantitative genetic theory and empirical results indicate that TS mostly results from the combinations of complementary ‘plus’ and ‘minus’ alleles that are dispersed between parents (Rieseberg

It is possible to accelerate the process of identification of new crop varieties with a desired combination of both farmer and end-user preferred traits in breeding populations that are predicted to result in high frequency of transgressive RILs (Kochetov

We believe that the method of identifying a few promising crosses at early segregating generations based on the frequency and minimum population size required for the recovery of transgressive RILs sounds practical as breeders develop F_{2}/F_{2:3} populations from a large number of crosses on a routine basis. Based on our results and those reported, we opine that there is no reason why crop breeders ever need to go beyond F_{2:3 }generation of cross if the predicted frequency of transgressive RILs is low.

The senior author gratefully acknowledges Council of Scientific and Industrial Research (CSIR), New Delhi, India for providing Junior Research Fellowship (JRF) vide No. 09/0271(11202)/2021-EMR-1 dated 01-07-2020 for pursuing PhD degree program at University of Agricultural Sciences, Bangalore.

None.

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