for breeding programs

This study had the following objectives: to investigate the sexual expression in seven watermelon populations; to evaluate some population parameters and the genetic potential of a population (PCS) obtained by crossing and segregating for sexual expression and other traits. For verifying the sexual expression, populations were evaluated with respect to type of flower, under controlled conditions. Maternal and selfed progenies were obtained from the PCS population for field evaluation, considering: fruit yield per plant, fruit weight, number of fruits per plant, flesh colour and sugar content. On the basis of molecular marker data (RAPD), the outcrossing rate v. and t,), aliei ic frequencies (p) and the coefficient of inbreeding (F) were estimated for the PCS population. Results indicated that populations 89 and P14 are andromonoecious in which natural selfing occurs, giving rise to normal fruits. The remaining populations are monoecious. Population PCS practices a mixed mating system (tm = 0.765) and, having shown sufficient genetic variation and relatively low inbreeding depression, has high potential for breeding purposes. The importance of obtaining accurate estimates ofthe outcrossing rate is pointed out, specially because sexual expression and the mating system are genetical1y conditioned in watermelon populations.

Adequate breeding programs depend on the knowledge ofthe mating systern of a population since methods are applied according to the specific and prevailing reproduction system of that population. Distinct genetic population structures occur under outcrossing and/or selfing, in natural conditions. In addition, inbreeding that takes place naturally when the aim is to evaluate components of genetic variance. Under outcrossing it is assumed that individuaIs within an open pollinated family are half-sibs. However, when some inbreeding takes place due to selfing, assuming panrn ixia will lead to biased estimates ofthe genetic parameters of a population. Also, inbreeding can increase the probability that different individuais have similar alleles, resulting in a reduction in genetic variability within farnilies and an increase in variability among families.
On the other hand, the ways plants reproduce are influenced by rnany factors and one ofthem is sexual expression. According to Robinson et al. (1976), there are records of different kinds of sexual expression in cucurbits. In spite of being genetically controlled, this expression is also affected by other factors such as ternperature, hurnidity, fertilization and growth regulators. Studies on watermelon, for instance, have shown monoecious and andromonoecious populations. In the former, there are male and fernale flowers and in the latter there are male and herrnaphrodic ones. These traits are controlled genetically by a single pair of genes, being andromonoecism (aa) recessive in relation to rnonoecism (A~ (Rhodes and Zhang, 1995 Breeding and Applied Biotechnology, v. 2, n. 1, p. 39-48, 2002 Among cucurbits of commercial importance, the cucumber is the one that shows greater variability for sexual expression. Their populations can be andromonoecious, androecious (plants with only male flowers), gynoecious (plants with only female flowers), hermaphrodites, monoecious and trimonoecious (plants with male, female and hermaphrodic flowers). ln the case ofthe melon, most of the American populations are andromonoecious, while the Asian and lndian ones are monoecious. There are also other populations that are androecious, gynoecious, gynomonoecious (plants with more female than hermaphrodic flowers), hermaphrodites and trimonoecious. A smaller variability is found in watermelon and pumpkin, and most pumpkin cultivars are monoecious (Robinson et aI., 1976). For the ridged luffa or vegetable sponge (Lujja acutangula), the d ifferent forms of sexual expression are similar to those ofthe cucumber, while the bottle gourd (Lageneria siceraria) is strictly monoecious, except for one andromonoecious variant found in a segregating population (Singh et aI., 1996).
There are other genes that affect the structure and fertility offlowers in cucurbits, like those controlling the male sterility in pumpkins, watermelon, melon and cucumber and the parthenocarpy in cucumber (Hexun et al., 1998;MalepszyandNiemirowicz-Szczytt, 1991;Robison et al., 1976;Zhang et al., 1996).
Cucurbits are considered allogamous despite their large variability in sexual expression and the great environmental influence over this trait. However, Robinson et a!. (1976) have reported that different types of sexual expression have influence on the natural outcrossing rate, since both natural outcrossing and selfing for the cucumber and melon can occur. Kohn and Biardi (1995) estimated a selfing rate of 73% in monoecious plants and 11.9% to 40.7% in gynoecious plants from two populations ofCucurbitajoetidissima, a perennial cucurbitaceae that is native of the United States and Northeast Mexico. These estimates indicate a mixed mating system, which is intermediate in relation to autogamy and allogamy.
A llard (1960) reports that cucurbits are closer to autogamy than to allogamy, since populations may derive from a few individuaIs during the domestication process, due to the botanical characteristics of the plants (they are creepers with many vines and the fruits have many seeds). This may have helped outcrossings among relatives and thus reducing the genetic load along generations. Mohr (1986) showed that in watermelon andromonoecious populations pollination takes place 2002, Brazilian Society of Plant Breeding with efficiency because insects visit the hermaphrodic flowers. As a consequence, there would be no advantage of andromonoecious populations over monoecious ones regarding the maintenance of pure inbred lines. Therefore, the author considers the watermelon as an allogamic species.
However, since both selfing ofhermaphrodic flowers and outcrossing, with pollen coming from another plant, may occur, it is believed that andromonoecious populations may show a mixed mating system, and that depending on the selfing rate, they could be closer to autogamy. Natural selfing is less probable but obviously possible to take place in monoecious populations through the fertilization offemale flowers by pollen of male flowers from the same plant. These populations may have a mixed mating system, even though closerto allogamy. For segregating populations for sexual expression, the mating system should vary from predominantly allogamous to predominantly autogamous, due to the variable frequency of monoecious and andromonoecious plants.
Andromonoecious populations in watermelon have probably evolved from monoecious ones, once the recessive allele that determines an andromonoecious individual (a) is kept in individuaIs within monoecious heterozygotes (Aa). While investigating the evolution dynamics of the watermelon in Northeast Brazil, a secondary centre of genetic diversity of this species, Romão (1995) found natural seed banks in the soi I, as a consequence of the action of a number of factors namely, genetical (genes that determine the dormancy ofthe seeds and explosive rind), ecological (spreading of seeds by the guará wolf) and cultural (when people eat fruits and leave seeds on the ground). The existence of these seed banks, along with the persistence of populations under adverse conditions, and the use of different farming systems in the region, have ali contributed to the development of subspontaneous populations formed by a few individuaIs. It is believed that mating among relatives must have occurred. This led to the fixation of alleles along generations, which were responsible for andromonoecious individuais (Vencovsky et a!., 2001).
Considering available informations, even under field conditions and with the presence ofpollinator insects, it is believed that natural selfing in andromonoecious and monoecious populations is perfectly possible. Depending on the natural selfing rate these populations may have a mixed mating system. Therefore, the main goals of this work were: a) to evaluate the sexual expression of some watermelon populations, to verify whether or not natural selfing takes place; b) to estimate the natural outcrossing rate in segregating populations for sexual expression; c) to discuss the implications of the sexual expression to breeding programs and d) to estimate quantitative parameters.
MATERIAL AND METHODS ln this study, materiaIs and methods are described as follows:

Sexual Expression
The traditional populations B9, B13, P14 and M7, collected in the Northeast of Brazil (Bahia, Pernambuco and Maranhão, respectively) (Queiróz 1993(Queiróz , 1998, as well as the American varieties Crimson Sweet, Charleston Gray and New Hampshire Midget, were evaluated in a greenhouse protected from pollinator insects. The greenhouse is located in the Horticultural and Medicinal Plants Department at the School of Agrarian and Veterinary Sciences (UNESP) in Jaboticabal -SP, from January to April 1995. The experiment was set in four randomized blocks, with four replications and eight plants per plot. At flowering time, besides observing the emergence of male flowers, 100 observations were made, at random, per population, counting the number of female and hermaphrodic flowers. The occurrence or not ofnatural selfing in the hermaphrodic flowers, as well as the formation offruits, were also observed.

Segregating population PCS
During 1996 and 1998, a base population was synthesized in order to com bine the characteristics of population PI4 (high yield, small fruits and resistance to powdery mildew) with the commercial variety Crimson Sweet (high soluble solid contents and flesh of intense red colour).
In addition, populations P 14 and Crimson Sweet are clearly andromonoecious and monoecious, as it could be observed in a previous greenhouse experiment.
Initially, 100 hand pollinations were carried out taking 100 individuaIs from each population, producing up to 100 FI fru its. Subseq uently, a population of 1000 individuaIs was established through a m ixture of 10 seeds from each FI fruit, which reproduced naturally in an isolated field. A single fruit was chosen, at random, from each plant ofthis population, and two seeds were taken from each fruit, randomly as well. This bulk of 2000 seeds formed the base population PCS.
Population PCS was installed in an isolated field and at flowering time plants were evaluated for their sexual expression. Sixty-four plants for seed parents were also sarnpled at randorn, each one giving rise to an open pollinated or maternal progeny (PL) and one selfed or SI (AF) progeny. The term family is used to indicate the group of offspring (PL and AF) of a given seed parent and the term progeny to indicate sibblings of a given type (PL or AF). From the 64 progenies, 12 were sampled at randorn for molecular analysis to determine the natural outcrossing rate. Th u s, molecular data were obtained through RAPO genotyping and the corresponding maternal progenies, with 23 individuaIs each. Primers B02, B 14, C04 and C 16 gave origin to 16 polymorphic loci; however, only nine were used in this study.
The natural outcrossing rate was estimated by maximum likelihood, considering the mixed mating system mcdel establ ished by the software MLOT (Multilocus Estimation ofOutcrossing with Dorninant Markers). The outcrossing rate was estirnated by ali loci simultaneously (til/ multilocus) and each individual loci (t, single locus), which corresponds to the average of the estimate of each locus individually (Ritland, 1990). The allelic frequency (p) and Wright's (F) inbreeding coefficient of the population were also estimated.
Maternal and selfed farnilies were evaluated at the Experimental Station of Bebedouro, Petrolina-PE (EMBRAPA Sem i-Árido Research Center), in two experiments, with three replications.
To evaluate the genetic potential of population PCS, the following traits were considered: fruit yield per plant (PP) (kg/plant); average fruit weight (PF) (kg); nurnber offruits per plant (NF); flesh colour (CP) (score 1 was given to intense red, 2 for the red colour, 3 for the light red, 4 for the pink colour and 5 for the white colour) and total soluble solid contents (TS) (OBrix).
As mentioned earlier, this population was derived frorn the crossing of contrasting parents in relation to sexual expression and other characteristics of commercial importance.

Sexual Expression
Results showed that ali assessed populations bore male flowers first and then the female and hermaphrodic ones. The percentages presented here refer to female and hermaphrodic flowers only. Populations B9 and P 14 bore 100% of hermaphrodic flowers, thus indicating that they are andromonoecious.
Crimson Sweet and New Hampshire Midget bore 92% to 97% of female flowers, respectively, indicating that these populations are mainly monoecious.
On the other hand, populations Charleston Gray, B 13 and M7, with 100% of female flowers, are typically monoecious ( Figure  I). Moreover, the occurrence of natural selfing, with the development of normal fruits, was verified in ali the hermaphrodic flowers found in populations B9 and P14, which is an evidence ofpollen viability.

Outcrossing Rate
Plants from the segregating population PCS bore 53.5% of female flowers, thus being monoecious, and 46.5% of andromonoecious flowers. Table 1 shows the estimates of the frequency of dominant alleles, the outcrossing rates f/ll and I" as well as the inbreeding coefficient. Three groups of estimations were obtained. The first considered ali progenies jointly and the others took only progenies stemming frorn andromonoecious or monoecious seed parents.
The outcrossing rate for ali progenies varied from 73.2% to 76.5%, showing that population PCS has a rnixed mating system. This rate tended to be larger in monoecious progenies than in andromonoecious ones. These results were expected, since under isolated greenhouse cond itions natural selfing in andrornonoecious plants from popu lation P 14 was verified. lnbreeding rates for these individuais were also expected to be greater than the rate for monoecious ones, and this was confirmed through the estimates ofthe inbreeding coefficient. lt should be pointed out that the use of dom inant markers is' perfectly adequate for estimating the outcrossing rate.
There are exarnples in the literature (Gaiotto et al., 1997) showing good agreement between estimates of I obtained through dominant (RAPO and AFLP) and codorn inant markers.
Estimates of the inbreeding coefficient (F = 0.091) also indicated a m ixed mating system for this population but tending to allogamy. Under inbreeding equilibrium. This is expected frorn an intervarietal hybrid, derived frorn very contrasting parents and highly heterozygotic such as population PCS. Another factor that may have contri buted to th is relative excess ofheterozygotes is a possible selection against homozygotes, as a consequence of inbreeding depression at the seedling stage. Since seedlings were grown in trays and later transplanted, non-intentional selection rnay have occurred during this phase.
Actually, a variation in the seeds germination percentages was verified. Some genninated laterthan others, conditioning more or less vigorous seedlings.  , 1986, in Ferreira 2000, it is concluded that one additional generation would be sufficient for this population to reach the expected 90% of hornozygous equilibrium condition. With this additional generation this study would be more suitable for quantitative genetics studies.
In addition, it would generate more transgressive and commercially desirable individuais, since one more generation of recombination would take place. Assuming that the progenies of open pollination taken from this segregating population have already reached 90% of homozygosity at equilibrium and that they were produced after two generations of open poli ination, it would be adequate to take a bulk of seeds from these progenies and generate a new base population for extraction of new progerues.
In conclusion, it was verified that the watermelon PCS population has a mixed mating system, and that its outcrossing rate had a tendency to alternate frorn monoecious to andrornoecious progenies. lt was also noted an excess ofheterozygotes in relation to what is expected from an inbreeding equilibrium.
Even though it did not reach the ideal equilibriurn condition. it showed a satisfactory 68.7% rate for a possible hornozygous condition. This population is genetically closer to allogamy than to autogamy despite having a mixed mating system.
Handling of a population with a mixed mating system is closer to allogamy, especially in relation to quantitative genetics. However, such a situation offers some advantages, as it will be discussed later in this paper.

Genetic variance
The evaluation of the maternal and selfed progenies showed that this population contains genetic variance for ali analyzed traits (significant P effects). PCS is therefore a very promising population to be exploited in plant breeding programs, The difference between PL and AF overall means was significant for the traits PF, CP and TS. This was detected through the sign ificance of types of progeny effects (T effect) as well as the farnily x types interaction. Results showed inbreeding depression, which varied among progenies (significance ofthe P x T interactions; Table 2).
Expressive progeny effects were detected for ali traits in both PL and AF progenies. This clearly dernonstrates that there are genetic differences among progenies within each type, and indicates the potential genetic variability ofthis population. This is especially true for traits related with fruit yield where a large range of variation was observed for both PL and AF progeny means. Variables PP, PF and NF showed a range of24.5 kg/plant; 3.4 kg/fruit and 15.3 fruits/plant for PL progenies and of 30.8 kg/plant; 4.6 kg/fruit and 12.4 fruit/plant for the AF progenies, respectively. However, the experiment coefficients of variation were high for these traits, implying low experimental precision. High values of the coefficient of variation for these traits are to a certain extent expected, once they tend to be more influenced by the environment than other characteristics (Table 2). On the other hand, to evaluate more precisely the real effect of inbreeding depression on watermelon, additional studies are needed which would take into accountdifferent levels of inbreeding as well as better environmental contraI.

Final Considerations
For populations with mixed mating system, the coancestry among individuais ofthe maternal families is higher than expected under allogarny. This implies that the estimates may be wrong if the F rate is considered zero. The genetic variance (dJ of such populations involves other cornponents besides additive (d) and the dorninance (dI) variances, and

is: o}j=(I+J.'P~+(I-FPb+4FDI+F/)i+F(I-F)H+~J.~._F2 X H 2 _H+ )-
The cornponent D J is a covariance between the additive effects and dominance effects of the homozygotes; D+ 2 is the variance of dominance effects of the hornozygotes, H* and H' are components of inbreeding depression and F, is the joint inbreeding coefficient for two loci. Al110ng these components, DI deserves the greatest attention, as it represents a covariance and it rnay be negative. In this case, it contributes to the reducction of the genetic pragress (Cockerham and Weir, 1984).
As more than one generation of randorn pollination is required to reach equilibrium, these populations show three types of genetic progress: (I) imrnediate progress (P GI)' which is the progress in the generation immediately after selection; (2) perrnanent progress (P GP)' which is the progress reached when the selected population returns to Table 2. Synthesis ofthe analysis ofvariance for fruit yield per plant (PP) in kg/ha; average fruit weight (PF) in kg; number of fruits per plant (NF); flesh color (CP) and sugar content (TS), with overall means and the range observed for alI traits.  (3) transient progress (P GT)' which is the genetic progress after P GI' generation after generation, until the population reaches its equilibrium. P GI depends on ali of the components of the genotypic variance, while P GP depends only on ()"~,DI and D~,since the dominance and inbreeding depression components are eliminated along the generations (Wright and Cockerham, 1985).
Therefore, determining the outcrossing rate of the populations under study is essential because it allows a better knowledge of the genetic structure of these populations and makes quantitative studies possible.
• The use of biochemical and molecular markers are preponderant tools as they make the quantification of some genetic parameters of the populations possible, such as the outcrossing rate and the inbreeding coefficient.
The importance of the quantification of these parameters for watermelon populations is even more essential since sexual expression and, consequently, the reproductive system are conditioned by genetic and environmental factors. Strictly andromonoecious populations may present a higher natural selfing rate and, in this case, be closer to autogamy than to allogamy. On the other hand, monoecious populations may present a greater outcrossing rate and be closer to the allogamous ones. These facts should be pointed out for the PCS population, which is segregating for sexual expression. ln relation to populations with a mixed mating system two major points should be taken into consideration. The first one concerns pollen contamination while doing selective processes on accession and cultivar multiplications.
The floral structure should be carefully isolated and emasculations should be done in the hermaphrodic flowers before pollen shed. The second refers to the occurrence of non-intentional selection during seedling development.
Studying ways ofbreaking seed dormancy is one possible way to avoid this problem.
On the other hand, an advantageous feature of populations such as PCS, which tends more to allogamy, is that they may the submitted to recurrent selection. This type of selection procedure not only increases the frequency of favorable alleles but also allows for the recombination to take place, increasing the probability of selecting superior genotypes with commercial value.
Another great advantage of species with a mixed mating system is the fact that with simultaneous outcrossings and selfings, recombination and the elimination of genetic load, occurs naturally. This also makes selection of segregating individuais with little or no inbreeding depression possible, as recorded by Ferreira (2000). For allogamic species there is natural recombination, however, high inbreeding depression is expected. With autogamic species, on the other hand, there is no depression, but recombination is only possible through artificial pollination.
Results obtainedby this study have shown that a PCS population is indicated for recurrent selection programs. The method of cryptic hybrids (Paterniani and Miranda Filho, 1978) is one interesting scheme to be used with one or more populations aimed at superior inbreed lines for synthesis of hybrids. In addition, the AF progenies performance indicated great potential for generating productive and prolific inbred lines with good fruit characteristics.

CONCLUSIONS
Considering sexual expression, populations B9 and PI4 are andromonoecious, and Crimson Sweet, New Hampshire Midget, Charleston Gray, B 13 and M7 materiais are monoecious.
Hermaphroditic flowers of B9 and P14 populations showed natural selfings and normal fruit development.
The segregating population PCS has a mixed mating system, closer to allogamy, but the outcrossing rate differs between andromonoecious and monoecious families. Thus this population may be improved through recurrent selection without the need for hand pollinations for recombination.

Population
PCS has not yet reached complete inbreeding equilibrium. but it got close, since 68.7% of the possible homozygous increase was reached.
Even without complete equilibrium, population PCS exhibited sufficient genetic variation in ali the investigated traits. lt shows high potential for a breeding program, as well as for generating inbred lines with good plant and fruit characteristics.
The appropriate determination ofthe outcrossing rate of watermelon populations is very important for breeding programs, once sexual expression and consequently the reproductive system are controlled by genetic factors.
Alberto de Oliveira and the other colleagues from the Cell and Molecular Biology Department at Escola Superior de Agricultura Luiz Queiroz (ESALQ/USP), for their technical support during this study. We'd like to also to thank Banco do Nordeste for its financial support and CNPq, CAPES and FACEPE for granting a scholarship for the first author.