Euphytica 38: 247-260 (1988) © Kluwer Academic Publishers, Dordrecht - Printed in the Netherlands

Genetic strategies to determine the mode of 2n egg formation in diploid potatoes

D.S. Douches and C.F. Quiros Department of Vegetable Crops" University of California, Davis, CA 95616, USA

Received 28 April 1987; accepted in revised form 15 July 1987

Key words: Solanum, potato, half-tetrad analysis, isozymes, 2x-4x, megasporogenesis.

Summary

In this study, nineteen diploid potato clones (Solanum spp. 2n = 2x = 24) were identified as 2n egg producers on the basis of fruit set in 2x-4x crosses. The segregation of three genes mapped close to the centromere, Got-l (1.1 cM), Pgm-2 (2.0 cM), and Sdh-1 (8.3 cM), were analyzed in the tetraploid offspring in these 2x-4x crosses to discriminate between First Division Restitution (FDR) and Second Division Restitution (SDR) modes of 2n egg formation. The co-dominant nature of these markers lead to more precise estimates of the recombinational frequencies as a result of completely classifying the segregating progenies. 2x-4x data revealed a predominance of SDR mechanisms occurring in 20 of the 21 families analyzed. With a SDR mode established, half-tetrad analysis (HTA) of four distal loci, 6-Pgdh-3, Mdh-1, Pgi-l, and Aps-l, revealed two SDR segregation patterns in some of the families. One pattern fit the expectations for the distal arm position. The gene-centromere map distances based upon SDR modes in the families following this pattern, were generally close to 4x-2x (FDR) estimates suggesting similar recombina­tion rates between micro- and mega-sporogenesis. Heterozygosity transmission, on average, was 39.10/0. In the other segregation pattern, in which the diploid parents were derived from S. chacoense PI 230580, higher than expected homozygosity levels were found in the female 2n gametophyte populations. A post-meiotic doubling of the reduced megaspore, which generates homozygous 2n eggs, is suggested to operate in three families. The common genetic background of the diploid clones suggested a heritable nature of this mechanism. Pooled data from these three deviant families calculated that 1.80/0 of the heterozygosity was transmitted to the tetraploid progeny.

It is concluded that utilization of seven enzyme-coding loci, with previously established gene-centromere map distances, in 2x-4x crosses improved half-tetrad analysis (HTA) as a means to determine the mode of2n gamete formation in megasporogenesis and megagametogenesis of diploid Solanum species.

Introduction synthesize highly heterozygous clones and to pro­duce uniform true seed potato cultivars (Mendibu­

Nunlerically unreduced or 2n gametes offer a ru & Peloquin, 1977; Peloquin, 1982). It is impor­unique approach to maximizing heterozygosity in tant to identify the mechanisms of 2n gamete for­polyploid species. Their discovery in diploid potato mation occurring in the diploid parent since the species (Group Tuberosum 2n = 2x = 24) has led level of heterozygosity transmitted can be extreme­to the proposal of various breeding schemes to ly different. In general, 2n gametes formed by first

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division restitution (FDR) are considered superior to those formed by second division restitution (SDR) because, in the former, most of the hetero­zygosity that is present in the diploid parent is transmitted to the tetraploid progeny (Mok & Pe­loquin, 1975). This superiority of FDR 2n pollen has been well established in 4x-2x crosses (Quinn & Peloquin, 1973; Mok & Peloquin, 1975; Mendi­buru & Peloquin, 1977; Tai & Dejong, 1980; McHale & Lauer, 1981).

Cytological identification of the meiotic mecha­nisms which generate diplandroids, is routine and diagnostic, hence, most of the information con­cerning 2n gamete mechanisms has been derived from studies of microsporogenesis (Mok & Pelo­quin, 1975; Ramanna, 1979; Veilleux, et al., 1982). Direct information concerning the mechanisms of 2n egg formation has been limited because of the difficulties of cytologically studying megasporoge­nesis. However, recently improved cytological techniques have begun to examine megasporoge­nesis and megagametogenesis, and mechanisms in­volved in diplogynoid formation (Stelly & Pelo­quin, 1984; Jongedijk, 1985).

As an alternative, Mendiburu and Peloquin (1979) proposed that if a chromosome marker could be identified close to its centromere, the mode of 2n egg formation could be determined through half-tetrad analysis (HTA) of the segre­gating marker in the progeny. This approach re­sulted in varying degrees of success in the potato (Ross & Langton, 1974; Mok & Peloquin, 1975; Iwanaga & Peloquin, 1979; Mok, 1981; Stelly & Peloquin, 1986). In these cases, the limitations of HTA were strongly influenced by the chromosome arm position of the segregating marker in the 2x-4x crosses. To improve HTA as a means to study diplogynoid formation, new markers closer to the centromere need to be mapped. Douches & Quiros (1986b) recently determined gene-centromere map distances for ten co-dominant electrophoretic markers in the potato. These enzyme-coding loci offer a more precise testing of the theoretical ex­pectations for FDR and SDR segregations in 2x-4x crosses.

In this paper we report on the identification of a number of a 2n egg producing diploid clones that

were heterozygous for these markers. The segre­gation of three proximally positioned enzyme-cod­ing loci were used to discriminate between FDR and SDR modes of2n egg formation through 2x-4x crosses, while the segregation of the more distal loci were also exanlined to gain insight into these mechanisms. In addition, heterozygosity levels transmitted through SDR 2n eggs were compared to theoretical expectations.

Material and methods

2x-4x crosses: The diploid clones P129-4 (S. tuber­osum L. x S. berthaltii Hawkes) and P178-1 (S. tuberosum x S. tarijense Hawkes) kindly supplied by Dr. S. Jansky (North Dakota State University) and DM56-4 supplied by Dr. F.L. Haynes Jr. (North Carolina State University), were crossed to the tetraploid clones NDD277-2, Nooksack, and maintained by Dr. R.E. Voss (University of Cali­fornia, Davis). Additional diploid parents were species selections chosen for their ability to set seed in 2x-4x crosses. These included S. chacoense Bitt., S. kurtzianum Bitt. et Witt., S. phureja Juz. et Buk., and S. tarijense which were obtained from the Potato Introduction Station, Sturgeon Bay, Wisconsin. In 1985, ten diploid selections were identified as 2n egg producers. In 1986, three addi­tional 2n egg producing clones were selected fronl the cross 106-2-1 x DM56-4, while four others were selected from an open pollinated berry of 111-2-1. Table 1 lists these selections.

Seed from 2x-4x crosses were treated with 1000 ppm gibberellic acid to break dormancy. Germi­nated seedlings were transplanted into trays (50 plants per tray). Chromosomes of off-types were counted to rule out diploids and triploids (Raman­na, 1979). In four to six weeks, leaf samples from healthy and vigorously growing seedlings were sampled for starch gel electrophoretic analysis. To assay for Aps-l, a tuber specific locus, the seedlings were allowed to tuberize in the trays. Small mature tubers were harvested in three to four months for analysis.

We assayed the diploid and tetraploid parental clones in 11 enzyme systems which revealed 14

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enzyme-coding loci: Glutamate oxaloacetate trans­aminase (GOT), Phosphoglucomutase (PGM) , Peroxidase (PRX) , Triose phosphate isomerase (TPI), Diaphorase (DIA), Shikimic acid dehydro­genase (SDH) , 6-Phosphogluconic acid (6­PDGH) , Malate dehydrogenase (MDH) , Phos­phoglucose isomerase (PGl), Isocitrate dehydro­genase «(IDH) , and Acid phosphatase (APS) as described by Quiros & McHale (1985) and Douch­es & Quiros (1986a; 1986b). Gene-centromere map distances were previously estimated by Douches & Quiros (1986b), except for Tpi-l. Specific electro­phoretic and enzyme staining procedures are de­scribed by Quiros (1981) and Vallejos (1983) re­spectively. Table 1 lists the diploid clones and the heterozygous loci identified for each individual.

Half-tetrad analysis: HTA is ideally ascertained by a locus tightly linked to its centromere (00/0 recom­bination frequency). The expectations ofFDR and SDR segregations in diploids are the inverse of

each other, under this model. If FDR occurs, all tetraploid progeny would be simplex heterozy­gotes. When SDR occurs, the progeny would be equally divided between the nulliplex and duplex classes. A mixture of the three genotypes for this locus would be found if both FDRand SDR 2n eggs were operating.

Three loci, Got-l, Pgm-2, and Sdh-l, were iden­tified by 4x-2x (FDR) crosses to be proximal to their centromeres (Douches & Quiros, 1986b) (Ta­ble 2) hence, approaching the ideal HTA case. Observed multinomial data for these three loci re­sulting from 4x-2x (FDR) crosses, were used to establish probabilities for the genotypic classes, shown in Table 2. The validity of these probabil­ities rests upon the assumption that the gene-cen­tromere map distances were well-estimated and that reconlbination levels are similar in both sexes. From pooled family sizes of 624, 1122, and 396 we estimated the centromeric linkages for Got-l, Pgm-2, and Sdh-l, respectively, and considered

Table 1. 2n egg producing diploid Solanum selections with genotypes for eight isozyme loci.

Diploid clone Parentagea Heterozygous isozyme loci

Got-1 Pgm-2 Sdh-1 6-Pgdh-3 Mdh-l Tpi-1 Pgi-1 Aps-1

106-1 chc, PI 230580 + + + + 106-1-9 chc, PI 230580 + 106-2-1 chc, PI 230580 + + + + + 106-2-6 chc, PI 230580 + + + 106-3-4 chc, PI 230580 + + + + 108-1-5 chc, PI 265576 + + 111-2-1 chc, PI 320283 + + 111-3-1 chc, PI 320283 + + 113-1-1 chc, PI 320294 + 113-2-5 chc, PI 320294 + P129-4 hap x tar + + + + P178-1 hap x ber + + 86SD34-2 106-2-1 x DM56-4 + + + + + 86SD34-6 106-2-1 x DM56-4 + + + + 86SD34-8 106-2-1 x DM56-4 + + + + 86SD43-1 111-2-1 OP + + 86SD43-3 111-2-1 OP + + + 86SD43-5 111-2-10P + + + 86SD43-6 111-2-1 OP + + +

a Species abbreviation in Huaman & Ross (1985). + = heterozygous. - = honlozygoUs.

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these to be unbiased estimates (Douches & Quiros, 1986b, 1988). Chi-square tests were performed to test the segregation ratios observed at these loci in 2x-4x crosses under FDR and SDR modes. For small family sizes(n~8), Baye's Rule was used as an alternative to calculate posterior probabilities for the SDR and FDR segregations from the ob­served data (Mendenhall, 1986).

To calculate gene-centromere map distances with an SDR mode operating, the following formu­la was used: Gene-centromere map distance =

.50-freq(nulliplex + duplex)/2 x 100 eM (adapted from Mendiburu and Peloquin, 1979.)

Transmission of heterozygosity: Estimates were based upon the segregation patterns of the larger families, which were divided into two subpopula­tions: 1) expected SDR segregation, and 2) deviant SDR segregation. The percent heterozygosity was calculated for each locus within these subpopula­tions. To obtain a value of average amount of het­erozygosity transmitted through SDR 2n eggs, we combined the data over all loci as follows: average heterozygosity = Simplex genotype/(Nulliplex + Duplex + 8in1­plex).

Results

Selection of 2n egg producing diploid clones: Ap­

proximately 100 seedlings from 20 diploid potato species accessions (S. chacoense, S. kurtzianum, S. phureja, S. tarijense) and other selected clones de­scribed in materials and methods were sampled for 2n egg production using fruit set in 2x-4x crosses as a criteria for selection. Fruit set ranged from 65 to zero berries; however, fruit set was not a good indicator of seed yield (r = 0.264). In general, seed yield on a seed per fruit basis was low with a range of 5.1 to 0.1 seeds per fruit and a mean of 1.6 (Table 3).

Assays for 14 enzyme-coding loci revealed nine polymorphic loci in the selected diploid parents: Aps-l, Got-I, Idh-I, Mdh-l, 6-Pgdh-3, Pgi-I, Pgm-2, Sdh-I, and Tpi-l. When heterozygosity was ascertained for these loci, most of the respective clones were used directly for 2x-4x crosses. Of the diploid clones tested, 95% were heterozygous for at least one of the three proximally positioned loci. Got-I, Pgm-2, and Sdh-l were heterozygous, on an individual basis, in 43% , 140/0 and 520/0 of the clones, respectively. The 6-Pgdh-3 and Tpi-l loci were the most polymorphic with 67% of the diploid clones being heterozygous, while 53% were heter­ozygous for Mdh-l. The Pgi-I locus was hetero­zygous in only 140/0 of the plants, while the tuber specific locus, Aps-l, was heterozygous in two of 13 (15%) parents assayed. The Idh-llocus was heter­ozygous in 140/0 of the plants, but all the tetraploid parents were also heterozygotes, thus, the segre­gation of this locus was not amenable to HTA in the 2x-4x crosses.

Table 2. Expectations of genotypic frequencies for FDR and SDR modes of2n ganlete formation in 2x-4x crosses for three loci located close to the centromere.

Locus Gene-centromere map distancea Mode Genotypes

Nullipex Duplex Simplex

Got-1 1.10 FDR .005 .005 .99 SDR .495 .495 .010

Pgm-2 2.00 FDR .010 .010 .980 SDR .490 .490 .020

Sdh-1 8.30 FDR .041 .041 .918 SDR .459 .459 .082

a Based upon 4x-2x (FDR) crosses (Douches & Quiros, 1987b, 1987c).

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Segregation ofproximal loci in large families: Eight 2x-4x families were analyzed (Table 4). The Got-I, Pgm-2, and Sdh-Iloci were segregating in 4,1, and 5 of the families respectively. In addition, two fam­ilies (86SD35 and 87SD4) segregated simultane­ously for two of these loci. Specific triallelic condi­tions were found for each of these three segregating loci and are described below.

For the Pgm-2 locus (Fig. 1), a monomeric en­zyme, the triallelic condition resulting after the 2x-4x cross was more ideal than the typical diallelic model. that is referenced for HTA (Mendiburu & Peloquin, 1979; Mok, 1981). Unlike HTA utilizing a dominantly controlled marker, the use of the Pgm-2 locus insured complete classification of the segregating progeny. In family 86SD35, the diploid parent was heterozygous for alleles Pgm-21 and Pgm-23, while NDD277-2 was homozygous for the Pgm-22 allele. Considering the proximity of this locus to the centromere (2.0 cM), a preponderance of three-banded phenotypes would indicate FDR, while a 1: 1 ratio of the duplex genotypes

(Pgm_21212222 and Pgm-22222323) recognized as two­banded phenotypes would manifest SDR (Fig. 1B). A comparison of chi-square probabilities for the FDR and SDR expectations demonstrated by the high frequency of homozygous gametes that 2n eggs generated by the diploid clone 106-3-4 orig­inate via SDR (Table 4).

The Got-I locus (Fig. 2), which has the tightest linkage to a centromere (1.1 cM) of all the proximal loci tested, segregated in four 2x-4x families: 86SD35, 86SD40, 86SD41, and 87SD4 (Table 4). A triallelic segregation was found in the resulting 4x progenies. The tetraploid parent of all these cross­es, NDD277-2, was heterozygous for this locus (Got-1313J414), while all four diploid parents had a heterozygous genotype Got-J4J5. The three expect­ed genotype classes for the gametes of the diploid parents were Got-14J4, Got-J5J5, and Got-J4J5. With a common allele between the two parents, discrimi­nation between the progeny classes was based upon the presence, absence, or dosage of the Got-15 al­lele. The genotype 00t-1415 would be expected if an

Table 3. Fruit set and seed yield of 2n egg producing diploids in 2x-4x crosses.

Family Cross

86SD74 P178-1 x NDD 86SD73 P129-4 x NDD 86SD77 P129-4 x Nooksack 86SD70 106-1-3 x NDD 86SD36 106-1-9 x NDD 86SD40 106-2-1 x NDD 86SD41 108-1-1 x NDD 86SD71 106-2-6 x NDD 86SD35 106-3-4 x NDD 86SD75 111-2-1 x NDD 86SD72 111-3-1 x NDD 86SD22 113-2-5 x NDD 86SD42 113-1-1 x NDD 87SDI 106-1 x NDD 87SD2 86SD34-2 x NDD 87SD3 86SD34-6 x NDD 87SD4 86SD34-8 x NDD 87SD5 86SD43-1 x NDD 87SD6 86SD43-3 x NDD 87SD8 86SD43-5 x NDD 87SD9 86SD43-6 x NDD

Fruit Seed SeedlFruit

20 9 0.45 20 8 0.40 3 2 0.67

33 3 0.09 12 4 0.33 55 195 3.55 4 12 3.00 4 14 3.50

18 46 2.56 65 14 0.22 15 7 0.47 NA 13+ NA NA 76+ NA 6 7 1.17 5 6 1.20

17 17 1.00 23 60 2.61 5 6 1.20

16 13 0.81 9 18 2.00

16 81 5.06

NDD = NDD277-2; NA = Not available; mean = 1.6 SeedslFruit; Standard error = 0.32; r = 0.514a•

a Correlation between fruit set and seed set.

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FDR mode of 2n egg formation was occurring, while a SDR segregation would give in an equal proportion of Got-J4J4- and Got-J5J5_genotypes. Chi-square tests for fit to FDR expectations have highly significant deviations (P~.OOOl). Mean­while, chi-square tests for fit to SDR expectations did not deviate significantly in three of the four families. The lack of fit for the family 86SD40 was due to an excess of the Got-J5J5_genotype in com­parison to the Got-J4J4_genotype (Fig. 2B). Hence, SDR was concluded to occur in these clones. Het­erogeneity between these four families precluded pooling segregation data for the Got-Jlocus, how­

ever, the lack of the Got-J4J5_genotype (none in 254 offspring) also reaffirmed a tight centromeric link­age for the Got-Jlocus.

Five 2x-4x families (86SD22, 86SD42, 86SD42, 87SD4, 87SD8, and 87SD9) segregated for the Sdh-J locus (8.3cM) (Fig. 3). In all crosses, NDD277-2 was used as the pollen parent. The het­erozygous nature of the Sdh-Jlocus (Sdh-J2J2]5J5) in the tester parent did not hinder out ability to discriminate between the homozygous and hetero­zygous gametes produced by the diploid parents. Each family ratio fit SDR expectations while at the same time deviating significantly from FDR expec-

Table 4. Segregation of various isozyme markers in 2x-4x crosses in large families and its applications to determine the mode of 2n egg formation and gene-centromere map distances.

Family Diploid Genotype 4x-2x Genotypesb Prob Prob Mode of Map parent (FDR) Map _ SORc FOR 2n egg distance

distancea Nulliplex Duplex Simplex formation

86SD22 113-2-5 Sdh-1113 8.3 19 23 o 0.91 0.00 SDR 0.00 6-pgdh-3132 30.1 16 13 49 30.9

86SD41 108-1-5 Got-1315 1.1 3 6 o 0.82 0.00 SOR 0.00 6-pgdh-3132 30.1 2 o 7 38.9

86SD42 113-1-1 Sdh-1113 8.3 7 6 o 1.00 0.00 SDR 0.00 6-pgdh-3132 30.1 2 1 13 40.6

87SD8 86SD43-5 Sdh-1113 8.3 9 3 o 0.40 0.00 SDR 0.00 6-pgdh-3132 30.1 7 8 22 29.7 Mdh-1316 33.5 5 8 23 31.9

87SD9 86SD43-6 Sdh-1131 8.3 21 15 o 0.73 0.00 SDR 0.00 6-pgdh-3132 30.1 7 8 22 29.7 Mdh-1316 33.5 5 8 23 31.9

86SD40 106-2-1 Got-1315 1.1 65 118 o 0.002 0.00 SDR 0.00 6-pgdh-3132 30.1 109 58 4 1.2 Mdh-1315 33.5 86 85 3 0.9 Tpi-1113 98 81 4 1.1 Aps-1112 13.4 65 51 2 1.1

86SD35 106-3-4 Pgm-2123 2.0 19 12 o 0.60 0.00 SDR 0.00 Got-1315 1.1 12 14 o 0.99 0.00 SDR 0.00 6-pgdh-3132 30.1 17 11 2 3.3 Mdh-1315 33.5 9 6 1 1.9 Tpi-1112 7 17 2 3.8

87SD4 86SD34-8 Got_1315 1.1 12 24 o 0.20 0.00 SDR 0.00 Sdh-1113 8.3 15 21 o 0.73 0.00 SDR 0.00 Pgi-1213 26.0 13 23 o 0.00 Mdh-1315 33.5 23 13d 0.00 Tpi-1112 19 14 3 4.17

a Obtained from Douches & Quiros (1986b; 1988c); b Nulliplex and duplex refer to genotypes fornled from homozygous 2n eggs; simplex refer to genotypes formed from heterozygous 2n eggs; c Probabilities based upon chi-square tests; d Simplex and duplex classes were pooled.

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p

Fig. 1. Segregation of Pgm-2locus (2.0 cM). Anodal direction is above. A. FDR segregation is family 86SD30. P = tetraploid parent (NDD277-2) (Pgm_2~22222), while the rest are simplex genotypes. B. First five lanes showing SDR segregation with 1: 1 ratio of the duplex genotypes Pgm_2~22323 (D1) and Pgm_21212222(D2) in the family 86SD37. In Figs 1-3 the upper photograph represents a 4x-2x (FDR) segregation for each enzyme-coding locus (Douches, 1987). The origins of the 2x-4x families are found in Table 3.

Fig. 2. Segregation of Got-1 locus (1.1 cM). Anodal direction is above. A. FDR segregation in 86SD19. The tetraploid (Got_13131414 NDD277-2) and diploid parents (Got-1415 84SD22) are in the lanes to the far right respectively. The rest are simplex genotypes. B. SDR segregation in 86SD40 for the Got-15 allele. In Figs. 1-3 the upper photograph represents a 4x-2x (FDR) segregation for each enzyme-coding locus (Douches, 1987). The origins of the 2x-4x families are found in Table 3.

tations (Table 4) (Fig. 3B). Segregation of more distally positioned loci in large The five families that segregated for the Sdh-l families: The 6-Pgdh-310cus, 30.1 cM from its cen­

locus were pooled to estimate its centromeric link­ tromere, segregated in seven of the eight families. age (Table 6). A comparison to SDR expectations These tetraploid progenies were classified into deviated significantly (X2 = 7.5 P<.005), indicat­ three genotypic classes: nulliplex, duplex, and sim­ing a tighter centromeric linkage than expected. plex, based upon the diallelic segregation pattern.

254

.: ."~F:. l'

. '~ '. .. .••.

~

-..'

" ..

Fig. 3. Segregation of Sdh-l locus (8.3 cM). Anodal direction is above. A. FDR segregation in 85SD41. R denotes recombinant offspring. B. SDR segregation in 87SD8. Note the 1: 1segregationofSdh-13 allozyme band (slowest migrating). Tdenotes a Sdh-13131215

genotype, while D is an example of Sdh-1215-phenotype. In Figs. 1-3 the upper photograph represents a 4x-2x (FDR) segregation for each enzyme-coding locus (Douches, 1987). The origins of the 2x-4x families are found in Table 3.

Two types of segregation patterns were observed for this locus: 1) a SDR segregation typical for its distal arm position, and 2) SDR segregation as if it was proximally positioned. The first segregation pattern was observed in families 86SD22, 86SD41, 86SD42, 87SD8, and 87SD9, which are known to produce 2n eggs by SDR as suggested by the segre­gation of the proximal loci (Table 4). A pooled estimate of 152 progeny allowed us to detect a 30.9 cM gene-centromere distance for 6-Pgdh-3, based on SDR expectations (Table 6). This value was not significant from the distance determined by 4x-2x (FDR) crosses (X2 = 0.177 P = .90). When using the 6-Pgdh-3 locus to attempt to predict the mode of 2n egg formation, the segregation data also marginally fit FDR (X2 = 5.08 P = .08). In the families 86SD35 and 86SD40, this locus segregated in a SDR pattern typical of proximal position. Hence, the data fit poorly FDR and SDR expecta­tions assuming normal recombination levels. A gene-centromere recombination frequency, based upon SDR, was calculated to be 1.5% in the two deviant families (Table 6).

The Mdh-llocus, which is 33.5 cM from its cen­tromere, segregated in five 2x-4x families (Table 4). Two new Mdh-l alleles were identified in the diploid parents of these crosses. The clones 106-2-1 and 106-3-4 carried the Mdh-P allele, while 86SD43-5 and 86SD43-6 carried the Mdh-1 6 allele

(Fig. 4). The upper band of the two-banded Mdh-P allele migrated more slowly than the upper band of Mdh-J3, while the upper band of the two-banded Mdh-1 6 allele migrated further than the upper band of the Mdh-13 allele. NDD277-2 was homozygous for the Mdh-F allele, which overlaps with the slow­er-migrating band of Mdh-13 , thus a triallelic segre­gation pattern was observed in the tetraploid pro­genies. Analysis of the progenies for this locus was similar to the reasoning used for the Pgm-2 locus. The gametic types were completely classified on the presence and absence of Mdh-l alleles in the four families generated from these parents.

The segregation patterns of Mdh-l for these fam­ilies were separated into two groups in the same manner as that for 6-Pgdh-3. The Mdh-l locus in the pooled data from the two families, 87SD8 and 87SD9, segregated according to SDR expectations. A 29.2 cM centromeric distance was estimated from a total progeny size of 48 (Table 6). This estimate was not significantly different from those obtained by 4x-2x (FDR) crosses. The segregation of the Mdh-l locus (33.5 cM) could not discrimi­nate between the two modes since expectations are practically the same for both FDR and SDR (X2 =

2.5 P = .33). In contrast, from the pooled segre­gation data of progenies 86SD40 and 86SD35, a 1.1% recombination rate was observed for the Mdh-l-centromere chromosome segment on the basis of SDR (Table 6).

255

Two other loci that are loosely linked to their through 4x-2x (FDR) crosses. The Pgi-l locus, respective centromere were segregating in these expected to be 26.0 cM from its centromere, segre­families and had a similar behavior as 6-Pgdh-3 and gated in a SDR manner in the family 87SD4, how­Mdh-l. The Aps-l locus segregated in the family ever, no simplex genotypes were recovered in 36 86SD40. A 1.1010 recombination frequency was ob­ offspring. served for this locus, despite having previously esti­mated a 13.4cM gene-centromere map distance

Table 5. Segregation of various isozyme markers in 2x-4x crosses in small families and its application to determine the mode of 2n egg formation.

Family Diploid Genotype 4x-2x (FDR) Genotypesb Prob Prob Mode of2n parent Map distancea SDRc FDR egg formation

Nulliplex Duplex Simplex

87SD1 106-1 Got-1315 1.1 0 2 0 0.9999 0.0001 SDR 87SD2 86SD34-2 Sdh-1113 8.3 1 2 0 0.9993 0.0007 SDR

Pgi-1213 26.0 1 2 0 87SD3 86SD34-6 Got-1315 1.1 3 0 0 0.9997 0.0003 SDR

Sdh-1113 8.3 2 1 0 Pgi-1213 26.0 1 2 0 Mdh-1315 33.5 2 1 0

87SD5 86SD43-1 Sdh-1113 8.3 4 2 0 0.9999 0.0001 SDR Tpi-1112 3 0 3 Mdh-1316 33.6 4 2d

87SD6 86SD43-3 Sdh-1113 8.3 3 2 0 0.9993 0.0007 SDR Mdh-1316 33.5 1 0 4 Tpi-1112 1 3 1 6-Pgdh-3132 30.1 2 0 3

86SD37 106-3-4 Pgm-2123 2.0 3 2 0 0.9999 0.0001 SDR 86SD74 P178-1 Pgm-2122 2.0 2 3 0 0.9999 0.0001 SDR

Tpi-1112 1 1 3 6-Pgdh-3132 30.1 1 2 2

86SD36 106-1-9 Pgm-2122 2.0 1 1 0 0.9997 0.0003 SDR Got-1315 1.1 1 1 0

86SD75 111-2-1 Sdh-1113 8.3 2 4 0 0.9999 0.0001 SDR 6-Pgdh-3233 30.1 2 0 3 Tpi-1112 2 0 3

86SD72 111-3-1 Sdh-1113 8.3 2 3 0 0.9993 0.0007 SDR Tpi-1112 3 8 0

86SD38 106-2-6 6-Pgdh-JI.32 30.1 7 3 0 0.4999 0.5001 SDR? Mdh-1315 33.5 6 5 0 Tpi-1112 3 8 0

86SD39 106-2-6 6-Pgdh-3132 30.1 1 3 2 0.4244 0.5756 SDR? Mdh-1315 33.5 5 2 0 Tpi-1112 5 0 2

86SD73 P129-4 6-Pgdh-3132 30.1 2 0 2 0.6666 0.3334 Mixture? Tpi-1112 3 0 1 Mdh-1214 33.5 2 2d

a Obtained from Douches & Quiros (1986b; 1988c); b Nulliplex and duplex refer to genotypes formed from homozygous 2n eggs; simplex refer to genotypes formed from heterozygous 2n eggs; C Probabilities based upon chi-square tests; d Simplex and duplex classes were pooled.

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HTA ofsparse family data: Thirteen 2x-4x families gations based upon these two loci could not dis­of small size were analyzed using Bayes' Rule (Ta­ criminate between a SDR and FDR TIl0de in the ble 5). Three families each segregated for the families 86SD38 and 86SD39 (P = .4999 and .4244 Pgm-2 and Got-l loci respectively, one of these respectively) . families segregating for both (86SD36). The Sdh-l Pooled family data for the 6-Pgdh-3, Pgi-l, and locus segregated in six of the families while one Mdh-lloci revealed a progeny distribution through segregating for both Got-l and Sdh-l (87SD3). the three genotypic classes (Table 5). The progeny

In ten of the 13 families, the discrimination be­ sizes were too small to calculate accurate gene­tween SDR and FDR modes was straightforward centromere values, howeve~, two families, 87SD2 and sinlple. All these probability values were based and 87SD3, were unique in that they lacked sim­upon the segregation of at least one of the three plex genotypes for the 2x-4x segregations of the proximally positioned loci. A SDR mode was con­ Pgi-l and Mdh-lloci. cluded for these ten families with the data summa­rized in Table 5. Gene-centromere relationship ofTpi-llocus: Segre­

The diploid parent, 106-2-6, involved in families gation of the Tpi-llocus in six 2x-4x families gave 86SD38 and 86SD39, was homozygous for the some insight into the centromeric relationship of three proximal loci, but was heterozygous for the this previously unreported enzyme-coding locus distal loci 6-Pgdh-3 and Mdh-l. The 2x-4x segre- (Fig. 5). The pooled data from 86SD72, 86SD75,

Table 6. Heterozygosity transmission through 2x-4x crosses and comparison of gene-centromere distances estimated by 4x-2x and 2x-4x crosses.

a) Normal2x-4x families

Locus Number of Nulliplex Duplex Sinlplex Percent (SDR) 2x-4x 4x-2x (FDR) families heterozygosity Map distance Map distancea

Got-1 1 3 6 0 0.0 0.0 1.1 Sdh-1 4 56 47 0 0.0 0.0 8.3 6-Pgdh-3 5 30 28 92 61.3 30.9 30.1 Mdh-1 2 8 12 28 58.3 29.2 33.5 Tpi-1 1 4 2 6 50.0 25.0 NA

Total 101 95 126 39.1

b) Deviant 2x-4x families (86SD40, 86SD35, 87SD4)

Locus Number of Nulliplex Duplex Simplex Percent (SDR) 2x-4x 4x-2x (FDR) families heterozygosity Map distance Map distancea

Got-1 3 89 156 0 0.0 0.0 1.1 ,,­Pgm-2 1 19 12 0 0.0 0.0 2.0 Sdh-1 1 15 21 0 0.0 0.0 8.3 Aps-1 1 65 51 2 1.1 0.6 13.4 Pgi-1 1 13 23 0 0.0 0.0 26.0 6-Pgdh-3 2 126 69 6 3.0 1.5 30.1 Mdh-1 2 118 114 4 1.7 0.9 33.5 Tpi-1 3 124 112 9 3.7 1.9 NA

Total 569 558 21 1.83

a Obtained from Douches & Quiros (1986b, 1988c). NA = not available.

257

Fig. 4. SDR segregation for Mdh-l locus (33.5 cM). Anodal direction is above. A. Progeny from 86SD40 segregating 1: 1 for Mdh_12121515 (M) and Mdh_12121313 (M2 genotypes). B. Progeny from 87SD9 segregating in a SDR manner. S, T, and F denote Mdh_12121313, Mdh_12121316, and Mdh_12121616 genotypes respectively.

N 0"

Fig. 5. SDR segregation for Tpi-llocus in 87SD4. D and N denote the Tpi_11111212 and Tpi_12121212 genotypes respectively.

86SD74, 87SD5, 87SD6, and 87SD8 suggests a more distal chromosome arm position based upon a SDR mode of 2n egg formation, however, the small total progeny size of 33 precluded any precise chromosome arm location. Tpi-l also segregated in the three deviant families 86SD35, 86SD40, and 87SD4. Pooled data for the Tpi-llocus had a segre­gation pattern that was similar to the other distal loci in these deviant families. Few simplex geno­types were observed. Pooled data of 255 offspring estimated a 1.8% recombination frequency on the basis of SDR.

Heterozygosity transmission through 2x-4x crosses: Estimates of gene-centromere map distances are simply another way of expressing the recombina­tion frequency for that chromosome segment. The 2x-4x segregation data from this study offered an opportunity to examine the ability of the female 2n gametophyte to transmit its heterozygosity through an SDR mechanism. This analysis was limited to

the large 2x-4x families. The isozyme data were subdivided into two gametic populations for this analysis: normal recombination vs. deviant SDR segregations (Table 6).

The gametic population in which the large fam­ilies showed normal recombination levels was be­lieved to be the least biased population since most centromeric linkages were within expectations. The SDR gametes transmitted on average 39.1% of their heterozygosity (Table 6). The other large families (86SD35, 86SD40, and 87SD4) which showed abnormal SDR segregations had a much different gametic population structure. For the eight chromosome segments sampled, only 1.83% of the heterozygosity was transmitted on average, indicating an almost completely inbred population of 2n gametes. Almost all the heterozygosity was found between rather than within the gametes.

258

Discussion

We conclude from the segregation of these isozyme loci that SDR is more prevalent than FDR in 2n egg formation. Similar conclusions were drawn by Stel­ly & Peloquin (1986) when a different population of diplogynoid producing parents was analyzed in 2x-4x crosses. Prevalence of SDR mechanisms is predicted as a result of sequential type of embryo sac development that the female gametophyte fol­lows in Solanum (Jongedijk, 1985). In alfalfa, which has a sinlilar embryo sac development, SDR 2n eggs also have been identified cytologically (Pfeiffer & Bingham, 1983). FDR 2n eggs have been previously identified through HTA in potato (Ross & Langton, 1974; Mok & Peloquin, 1976; Iwanaga & Peloquin, 1979; Mok, 1981), however in these instances, the frequency was very low or in combination with a SDR nlechanism. A FDR mechanism comparable to the parallel/fused spin­dles during nletaphase II in meiosis during micros­porogenesis is not feasible in megasporogenesis because of successive divisions associated with its development. Hence, a reduction in chromosome pairing is a prerequisite for FDR 2n egg formation through abnormal megasporogenesis (Jongedijk, 1985). Under normal synaptic conditons as seen in this study, SDR 2n eggs should prevail.

Five of the eight large 2x-4x families segregated in an expected manner. A SDR mechanism such as second division omission or premature cytokinesis could account for the observed results. In these families, recombination levels were generally close to expectations extrapolated from 4x-2x (FDR) data, suggesting similar recombination levels in mi­cro- and megasporogenesis. Gene-centromere map distance estimates were within expectations for Pgm-2, Got-l, 6-Pgdh-3, and Mdh-l, while the Sdh-llocus in megasporogenesis showed a slightly tighter linkage than expected (0.0 vs. 8.3 eM).

HTA of the more distal loci estimated severely reduced recombination rates in the families 86SD35, 86SD40, and 87SD4. These discordant results indicate that a different SDR mechanism other than second division omission was occurring. It is unlikely that a low frequency of simplex geno­types would result from a reduction in recombina­

tion. For instance, a strong expression of a desy­naptic gene would lead to univalents at metaphase I and an unbalanced first division (Jongedijk, 1985; Hermsen, 1984). Sterility would be extremely high if a SDR mechanism was exclusively operating in this synaptic genotype, while, only FDR-type ga­metes would be expected to be fertile under these desynaptic conditions. The segregation data for the proximal loci in this study did not support an FDR mode of 2n egg formation. Under less extreme desynaptic conditions, a mixture of SDR and FDR gametes could be possible, however" the data did not support this contention either.

Jongedijk (1985) has suggested that a post­meiotic doubling of reduced megaspores taking place during gametogenesis could lead to the for­mation of homozygous 2n eggs. Stelly & Peloquin (1986) also noted this mechanism as a potential source of excess homozygous genotypes in certain 2x-4x crosses. To account for this heterogeneous population of almost completely homozygous 2n eggs in our study, it is likely that two separate mechanisms of 2n egg formation occur in these diploid parents: 1) a high frequency of post meiotic doubling of the reduced megaspore generating completely homozygous 2n eggs and, 2) an omis­sion of the second division generating SDR-type gametes with normal meiosis occurring at a low frequency in the gametophytic population.

Transmission ofheterozygosity through SDR mech­anisms: The SDR gametes, produced in non-de­viant families, transmitted on the average 39.1% of their heterozygosity (Table 6). In comparison, the­oretical expectations, based upon a number of cyt­ological assumptions, estimated SDR gametes can transmit 35-40% of their heterozygosity (Peloquin, 1981; Hermsen, 1984). Our observed value, based upon six chromosome segments, supports theoret­ical expectations that SDR mechanisms are unable to transmit heterozygosity at high levels.

A SDR mechanism which promotes homozy­gous 2n gametes is less desirable for transmitting heterozygosity in 2x-4x crosses than SDR gametes formed through second division ommission of the megaspore. A mechanism such as post-meiotic doubling of the reduced megaspore, prevents any

259

heterozygosity from being transferred through the female 2n gametophyte (Jongedijk, 1985). SDR gametes of this type appear undesirable, consid­ering the importance of heterozygosity when breeding a tetrasomic autoploid crop like the pota­to. FDR gametes transmit a large percentage of the parental genome intact (81.5-98.00/0), which tends toward homogeneous populations of highly hetero­zygous 2n gametes (Douches & Quiros, 1988). SDR eggs generated through a post-meiotic dou­bling mechanism produce a population inbred 2n ganletophytes.

The feasibility of producing inbred lines through SDR mechanisms has been studied in several orga­nisms. Matromorphoric embryos generated through SDR mechanisms have been identified in Brassica spp. (Eenick, 1974a, 1974b) and in S. an­digena (Taylor, 1978), however, heterozygosity has been found in them. In rainbow trout, diploid gy­nogenesis, a potential method to produce inbred lines, has been suggested through retention of the second polar body (Allendorf et aI., 1986), or by suppression of the first mitotic cell division (Pur­dom, 1983). A system to generate completely in­bred potato clones would be established if these 2n gametes produced through post-meiotic doubling, cou~d be induced to develop parthenogenetically. Parthenogenetic seed development has been rou­tine in generating potato haploids (2n = 2x = 24) from tetraploid clones (Hougas & Peloquin, 1957; Montelongo-Escobedo & Rowe, 1969) and has al­so been extended to generating monoploids (n =

x = 12) (Van Breukelen et aI., 1975). The gener­ation of inbred diploid clones could have important genetic and breeding implications; i.e. inheritance studies and the use of F1 hybrid and double-cross breeding methodologies. The testing of the efficacy of generating inbred diploid clones through ha­ploid pollinator and tissue culture techniques would be of interest.

Value ofHTA: The limitations of HTA, in the past, were mainly influenced by the markers available. For example, the dominant nature of chromosome position of the yellow tuber flesh locus (y) limited its value to determine the composition of the 2n gametophyte populations (Stelly & Peloquin,

1986). The enzyme-coding loci used in this study expand HTA as a means to study megasporogene­sis and megagametogenesis. Their co-dominant na­ture allowed the segregating progeny to be com­pletely classified to obtain more precise estimates of segregation patterns through 2n gamete mecha­nisms. In addition, the identification of markers with tighter centromeric linkage has improved our ability to discriminate between SDR and FDR modes even in small progenies. The analytic pow­ers of HTA were greatly improved by following the segregation of both proximal and distal loci in a 2x-4x family. Initially, the segregation of proximal markers was used to determine the mode of 2n egg­formation. Secondly, the segregation of a distal locus provided information concerning recombina­tion levels within the 2n gametic pool, which has been extremely difficult to assess cytologically. In this study, a post-meiotic doubling of the reduced megaspore was suggested to be operating in at least three of the 19 clones, leading to homozygous SDR gametes. Hence, caution should be exercised when SDR mechanisms are utilized in 2x-4x and 2x-2x breeding schemes, since heterozygosity transmis­sion can vary greatly (39.1% vs. 1.8°/0).

An analytic system as described above would be useful in: 1) discriminating between FDR/SDR and exclusive FDR populations of female 2n game­tophytes, and 2) quantifying the asynapsis associ­ated with FDR 2n gametophytes, if sufficient prog­eny sizes can be generated.

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