Introduction

Sexual polyploidisation has been widely exploited in several plant-breeding programmes (Ramanna and Jacobsen, 2003). Diploidy is the general rule in Citrus and related genera, with a basic chromosome number x=9. However, sexual polyploidisation is currently a central approach used in triploid citrus-breeding programmes, aiming to develop new seedless ‘mandarin-type’ cultivars (Ollitrault et al., 2008); very large triploid progenies have been obtained from 2x × 2x crosses and several cultivars patented (Aleza et al., 2010). The recovery of triploid citrus hybrids arising from 2n megagametophytes produced by diploid plants was described in the 1970s (Esen and Soost, 1971, 1973). Cytogenetic studies (Esen and Soost, 1971) showed that triploid embryos are associated with pentaploid endosperm, indicating that triploid hybrids result from the fertilisation of unreduced ovules by normal haploid pollen. According to the genotype, the frequency of duplication in the female gametes can range from below 1% to over 20%. Esen et al., 1979 proposed that 2n eggs result from the abortion of the second meiotic division in the megaspore (SDR) in citrus. This hypothesis has been corroborated for Clementine (Citrus clementina Hort. ex Tan.) by molecular marker analysis (Luro et al., 2000). However, Chen et al. (2008) proposed that 2n eggs of sweet orange (C. sinensis (L.) Osb.) resulted from first meiotic division restitution (FDR). The genetic configuration of 2n gametes depends on the mechanism of their formation (Figure 1), and the rate of parental heterozygosity restitution is directly linked with the rate of effective chiasma between the centromere and the considered locus (Mendiburu and Peloquin, 1976; Park et al., 2007). It is, total and null until the first chiasma for FDR and SDR, respectively. It is, thus, essential to gain a better understanding of the mechanisms underlying 2n gamete formation to optimise sexual polyploidy breeding schemes and to carry out trait-association studies of breeding populations. The objective of the present work was to shed light on the mechanism underlying 2n gamete formation in ‘Fortune’ mandarin (C. clementina Hort. ex Tan. x C. tangerina Hort. ex Tan.) by simple sequence repeat (SSR) marker analysis. ‘Fortune’ mandarin is widely used in triploid breeding because of its fruit qualities, late maturing period and relatively high percentage of 2n eggs. This diploid cultivar is highly fertile, producing an average of 18.5 seeds per fruit, including 6.5% of seeds arising from 2n gametes (our unpublished data). Without the previous knowledge of centromere position, and to avoid the risk of misinterpreting data due to an insufficient or biased set of markers, we selected 35 SSR markers according to their position on the Clementine (C. clementina Hort. ex Tan.) map (Ollitrault et al., 2011). A general approach is proposed to estimate the centromere position by best-fit value between observed data and theoretical functions of heterozygosity restitution for no interference and partial interference models. For this purpose, we used the functions developed by Zhao and Speed (1998a) for ordered tetrads, based on the random spindle–centromere attachment hypothesis (Griffiths et al., 1996), and extended by the same authors to half-tetrad analysis (HTA; Zhao and Speed, 1998b). The results obtained were compared with the method proposed by Tavoletti et al. (1996) using the multilocus structure of half-tetrads. Finally, we discuss the implications of the 2n gamete restitution mechanisms for citrus triploid breeding.

Figure 1
figure 1

SDR and FDR 2n gametes resulting from: (a) no crossover; (b) one crossover; (c) two crossovers involving two chromatids; (d) two crossovers involving three chromatids and (e) two crossovers involving four chromatids.

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Materials and methods

Plant material

The mechanism underlying 2n gamete formation in ‘Fortune’ mandarin was investigated in 171 triploid hybrids, derived from four crosses between ‘Fortune’ mandarin (C. clementina Hort. ex Tan. × C. tangerina Hort. ex Tan.) as female diploid genitor and ‘Ellendale’ (C. reticulata Blanco × C. sinensis (L.) Osb.), ‘Common Mandarin’ (C. deliciosa Ten.), ‘Minneola’ (C. paradisi Macf. × C. tangerina Hort. ex Tan.) or ‘Murcott’ (C. reticulata Blanco × C. sinensis (L.) Osb.) as male diploid genitors. Parental accessions and hybrids were grown at the ‘Instituto Valenciano de Investigaciones Agrarias’ orchards in Moncada, Valencia, Spain. Practical details on how the triploid populations were established from diploid × diploid crosses by embryo rescue and triploid selection by flow cytometry, can be found in Aleza et al. (2010). Genomic DNA of triploid hybrids and their parents was isolated using the Plant DNAeasy kit from Qiagen Inc. (Valencia, CA, USA), following the manufacturer’s protocol.

Triploid progeny genotyping

SSR markers that proved heterozygous for ‘Fortune’ were selected to genotype each triploid progeny, depending on the polymorphism existing between ‘Fortune’ and the male genitor. Thirty-five microsatellite loci were used to analyse the triploid progenies: CAC15, TAA41 (Kijas et al., 1997), CX6F03, CX6F23 (Chen et al., 2007), mest121 (Luro et al., 2008), mest56, mest192, mest123 (Aleza et al., 2011), mest104, mest110, mest247, mest488 (François Luro, personal communication; mail to luro@corse.inra.fr for further information), mCrCIR07F11 (Kamiri et al., 2011), Ci01C07, Ci02B07, Ci08C05, mCrCIR01E02, mCrCIR01F04a, mCrCIR06A12, mCrCIR06B05, mCrCIR06B07, mCrCIR07E12 (Froelicher et al., 2008) and thirteen new designed primers (mCrCIR01C06, mCrCIR02A09, mCrCIR02D09, mCrCIR02F12, mCrCIR02G01, mCrCIR02G02, mCrCIR03B07, mCrCIR03C08, mCrCIR03G05, mCrCIR04H06, mCrCIR05A05, mCrCIR07D05, mCrCIR07D06; Table 1). The polymerase chain reactions (PCRs) were performed with wellRED oligonucleotides (Sigma-Aldrich, St Louis, MO, USA) with the following protocol: Mastercycler epgradient S (Eppendorf Scientific Inc., Westbury, NY, USA); reaction volume 15 μl: 0.8 U Taq polymerase (Fermentas, Burlington, VT, USA), reaction buffer 750 mM Tris-HCl (pH 9), 50 mM KCl, 200 mM (NH4)2SO4, 0.001% bovine serum albumin, 0.1 mM of each dNTP, 5 mM MgCl2, 3 μM of each primer, 30 ng DNA; PCR programme: 94 °C for 5 min; 40 cycles of 30 s at 94 °C, 1 min at 50–55 °C and 30 s at 72 °C; final elongation 10 min at 72 °C). Separation was carried out by Capillary Gel Electrophoresis (CEQ 8000 Genetic Analysis System; Beckman Coulter Inc., Fullerton, CA, USA). Data collection and analysis were carried out with GenomeLab GeXP (Beckman Coulter Inc.) version 10.0 software.

Table 1 New primers designed to amplify the markers used in this study
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2n gamete allelic structure inference from triploid hybrid genotypes

For a locus bearing totally different parental allelic configurations (A1A2 × A3A4), the genotype of the 2n gamete was directly read from the triploid hybrid structure. When the male and female genitor shared one allele (A1A2 × A2A2 and A1A2 × A2A3), the inference of the 2n female gamete structure was carried out from the measured allele dosage by the microsatellite DNA allele counting-peak ratio method (MAC-PR; Esselink et al., 2004), for the triploid hybrids that have inherited the common allele from the male genitor. The validation of the MAC-PR method for the analysed loci and populations is given as Supplementary Information.

Identification of 2n gamete origin by single-locus analysis

Once female gamete structures were inferred, the percentages of heterozygosity were calculated for each locus in the whole population and for each genotype over all analysed loci. Without previous knowledge about relative markers/centromere position, the observation of heterozygosity restitution over 50% for a single locus is not informative because it could have come from either FDR or SDR; however, theoretical heterozygosity restitutions lower than 50% are only found for SDR (Park et al., 2007). When such low values of heterozygosity restitution were observed for a marker, we compared the highest probability of such a population structure under the SDR and FDR hypothesis. Under SDR, the highest probability for such an observation is obtained for a centromere position, leading to a theoretical proportion of h heterozygous gametes, whereas the best theoretical proportion of heterozygous gametes to fit with such observed data is 0.5 in the case of FDR. Thus, logarithm of the odds ratios (LODs) were estimated as:

with h being the heterozygosity transmission observed for the marker and n, the number of genotypes analysed with this marker.

Comparison of observed heterozygosity restitution within a linkage group with theoretical functions to infer the 2n gamete formation mechanism and centromere position

To integrate the information on all loci of the same linkage group coming from different populations, we propose a method based on the comparison between observed heterozygosity restitution among a linkage group with theoretical restitution functions under different models. We have tested FDR and SDR mechanisms, for no-interference and partial chiasma interference on a chromosome arm (and no between-arm interference), assuming several centromere positions (interval of 0.5 cM between two theoretical adjacent positions of the centromere). Discrepancies between the different models and the observed data were estimated by the sum of the squared differences between observed and theoretical values at the marker map positions. Under one model of restitution (FDR or SDR), let Fit(c) be the value of the sum of the squared distance for each position of the centromere; the best theoretical centromere position under this model is deduced by searching c, which minimises Fit(c). The confidence interval (95%) for the centromere position was estimated by bootstrap on the loci (500 bootstraps). For this analysis, we have used the marker position of the Clementine genetic map (Ollitrault et al., 2011), which should be very similar to the ‘Fortune’ map, because ‘Fortune’ is a hybrid between Clementine and ‘Dancy’ mandarin.

No interference model

According to Zhao and Speed (1998a), assuming that the number of chiasmata in an interval follows a Poisson process (no interference model corresponding to Haldane's map function), the probabilities of a tetrad displaying a first-division segregation (FDS; Griffiths et al., 1996) pattern and a second-division segregation (SDS; Griffiths et al., 1996) pattern are as follows: p(FDS)=(1/3)(1+2e−3d) and p(SDS)=(2/3)(1−e−3d), where d is the genetic distance in Morgan units (Haldane’s map function) between a given locus and the centromere. Under the FDR mechanism for 2n gamete formation, the FDS tetrads and half of the SDS tetrads transfer the parental heterozygosity, whereas under the SDR mechanism, the restitution of parental heterozygosity will result from SDS tetrads (Zhao and Speed, 1998b). We can, thus, derive the rates of heterozygosity transmission (H) as function of the distance to the centromere (d):

H(d)=(1/3)(1+2e−3d)+(1/3)(1−e−3d)=(1/3)(2+e−3d) for FDR and H(d)=(2/3)(1−e−3d) for SDR. According to this model, from the centromere to the telomere, H varies between 1 and 2/3 for FDR and from 0 to 2/3 for SDR (Figure 2).

Figure 2
figure 2

Theoretical curves of heterozygosity restitution as function of genetic distance to the centromere for FDR and SDR without chiasma interference and two χ2-(Cx(Co)m) models of partial interference.

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Let p and c, respectively, be the positions of a locus and of the centromere in a linkage group. As Haldane's map function is additive, the distance between the considered locus and the centromere is d=∣p−c∣. The heterozygosity restitution H(d) as a function of the distance to the centromere (d) can thus be applied to any locus position (p) on the Clementine's genetic map after transposition according to each theoretical position of the centromere (c) on the linkage group:

H(p)=(1/3)(2+e−3∣(p−c)∣) for FDR and H(p)=(2/3)(1−e−3∣(p−c)∣) for SDR. Theoretical curves of H(p) are presented in Figure 2 for FDR and SDR models.

Partial interference models

There are several proposals in the literature to incorporate chiasma interference in relating the map distance and SDS-ordered tetrad proportion. Zhao and Speed (1998a) developed functions for ordered tetrad frequencies derived from the χ2-chiasma interference models, which provide good fits to data from different organisms (Zhao et al, 1995). Moreover, most map functions could be approximated by one of the χ2-models (Zhao and Speed, 1996). The model is represented in the form Cx(Co)m, where m is a parameter positively related to the interference level. For m>0, the SDS proportion rises above 2/3 and as m increases, the maximal frequency of SDS increases (Zhao and Speed, 1998a). Likewise for the no interference model, the restitution of heterozygosity under FDR and SDR can be directly derived from the SDS-tetrad frequency for different χ2-models; as examples, Figure 2 shows the pattern of heterozygosity restitution along a linkage group for the Cx(Co) and Cx(Co)4 models. The heterozygosity restitution at any position (p) on the Clementine's genetic map can, therefore, be inferred for each theoretical position of the centromere (c) on the linkage group and thus, Fit(c) evaluated. The genetic map is established according to the map function corresponding to each considered χ2-model (Foss et al., 1993).

Identification of the mode of 2n gamete formation and localisation of the centromere by half-tetrad multilocus structure analysis

Multilocus analyses were performed on 87 genotypes and five loci mapped in the linkage group whose order was obtained from the current map of Clementine (Ollitrault et al., 2011). The analysis was made according to Tavoletti et al. (1996), assuming that multiple crossovers do not occur between contiguous markers. Under this hypothesis, each crossover between two markers, i and i+1, leads to a change from homozygosity to heterozygosity in the case of SDR and a half change from heterozygosity to homozygosity in the case of FDR. Thus, the distance between two adjacent markers (dMiMi+1) can be estimated by the proportion of 2n gametes with changes (homozygosity versus heterozygosity; CMiMi+1) between the two markers. For FDR, dMiMi+1=CMiMi+1 and for SDR, dMiMi+1=½CMiMi+1.

The probability of the observed multilocus progeny under the different models (FDR or SDR with different centromere positions) was calculated according to Tavoletti et al. (1996). Detailed formulas can be found in Supplementary Information. Both under FDR and SDR models, the centromere position was virtually moved from before the first considered locus along the linkage group to after the last considered locus (intervals of 0.5 cM), and the relative probability was estimated for each position. The LOD between best position under SDR and FDR was calculated in order to determine the mode of 2n gamete restitution, and the position of the centromere was considered as the one producing the highest relative probability under the identified mode of restitution. The confidence interval was estimated following the LOD drop-off method (Lander and Botstein, 1989). After determining the centromere position, chiasma interference can be estimated for each chromosome arm with three-point linkage mapping as follows:

Let rM1M2 denote the observed recombination rate (heterozygous to homozygous and vice versa) between the locus 1 and 2; rM1M2 the observed one between locus 2 and 3; and rd the observed rate of double recombination between the three loci. Thus, chromosome interference (I) is:

Results

Genotyping of triploid progenies

Thirty-five heterozygous SSR markers in ‘Fortune’ were selected and used for genotyping the different triploid families, according to their polymorphism between ‘Fortune’ and the male genitors. Overall, 22, 18, 21 and 26 of these markers were polymorphic between the two parents for the families with ‘Minneola’, ‘Common Mandarin’, ‘Ellendale’ and ‘Murcott’, respectively, (Table 2) as male parent. The unambiguous differentiation of allele dosage in heterozygous triploids has been confirmed by the very clear bimodal distribution of the peaks area ratio of the different triploid hybrids for all markers (Supplementary Information). The loci with total allelic differentiation between female and male genitors enabled (based on heterozygosity transmission or allele dosage estimation) the genitor producing the 2n gametes for each triploid hybrid to be identified unequivocally. Maternal origin of the 2n gamete has been observed for all the analysed triploids; therefore, on the basis of the maternal origin of the 2n gamete and allele dosage, it was possible to infer the 2n gamete structure from the triploid hybrid genotypes. Potential allelic segregation distortion in the 2n gamete population was tested for each marker by χ12-analysis (Table 3); only one of them (Ci02B07) showed significant distortion.

Table 2 Polymorphism observed among ‘Fortune’ mandarin and the male genitors for the 35 heterozygous loci in ‘Fortune’
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Table 3 Heterozygosity restitution (% HR) for each analysed locus, χ2-test for allelic segregation, and LOD SDR/FDR for markers with <50% of heterozygosity restitution, linkage group (LG), number of individuals (NI) and populations (NP) analysed
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Maternal heterozygosity restitution in the 2n eggs

Restitution of maternal heterozygosity in each 2n gamete (based on all analysed loci) varied between 15.38 and 100%, with 54.98% as mean value.

The unimodal distribution of heterozygosity restitution in the 2n megaspores among the analysed genotypes suggests that all these 2n gametes arise from the same mechanism (Figure 3).

Figure 3
figure 3

Distribution and density trace of the heterozygosity restitution rates estimated for each 2n megaspore (estimation of restitution rates based on all markers).

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Global heterozygosity restitution for each marker

Rate of maternal heterozygosity restitution was calculated for 35 loci, covering eight out of nine linkage groups from the current map for Clementine (Table 3); the average rate was 55.23% and values varied from 10.34% (mCrCIR02G02 marker) up to 82.46% (mCrCIR02D09 marker). Twelve of the analysed markers displayed <50% maternal heterozygosity restitution. For these markers, LODs of SDR/FDR probabilities were calculated and varied between 0.77 and 19.05. These observations could only fulfil the SDR hypothesis, with markers that are close to the centromere, and rule out the FDR scenario.

Pattern of heterozygosity restitution within linkage group II and centromere mapping

Twelve of the analysed markers in linkage group II of the Clementine genetic map (Ollitrault et al., 2011) were used to perform this analysis. Taking into account marker order and the distances between them (Haldane’s map function), the pattern of heterozygosity is represented in Figure 4 (dots). From one side of the linkage group to the other, the heterozygosity decreases from 82.46% for mCrCIR02D09 marker to 14.29% for CX6F23 marker and increases again up to 80% as the position rises on the map. Such a pattern within a linkage group is totally incompatible with the FDR model, in which the opposite variation is expected and the lowest theoretical restitution value would be 50%. Therefore, the search for the centromere position producing the best fit between the theoretical function of heterozygosity restitution and the observed data was only conducted under the SDR hypothesis. Under the SDR hypothesis with no interference, the best estimation of centromere position is 10.1±6.4 cM from CX6F23 marker (Figure 4). Without chiasma interference, the maximum theoretical heterozygosity restitution is 2/3, whereas we have observed values over 75% for five telomeric markers (two of them with very low P-value: mCrCIR02D09, P=10−5 and mCrCIR05A05, P=0.006), suggesting the existence of chiasma interference. On the other hand, the maximum restitution found over all analysed markers was 82.5%, whereas 100% should be expected for telomeric markers in case of total interference. Therefore, among the χ2-models proposed by Zhao and Speed (1998a) for partial interference, we have tested the Cx(Co)4 model, allowing a maximum restitution of heterozygosity close to 75%. Under this model of chiasma interference and SDR hypothesis, the best estimation of centromere position is 11.8±7.1 cM from CX6F23 marker (Figure 5). This model fits better with the observed data than the no interference model (Fit(c)=0.08 and Fit(c)=0.24, respectively).

Figure 4
figure 4

Observed heterozygosity restitution values for markers in linkage group II (dots) and theoretical heterozygosity restitutions (line) for the best-fitting centromere position under SDR model without chiasma interference (markers in x axis are positioned according to Clementine genetic map using Haldane’s map function).

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Figure 5
figure 5

Observed heterozygosity restitution values for markers in linkage group II (dots) and theoretical heterozygosity restitutions (line) for the best-fitting centromere position under SDR and the Cx(Co)4 model of partial interference (markers in x axis are positioned according to Clementine genetic map using the corresponding Cx(Co)4 map function).

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Multilocus half-tetrad structure analysis in linkage group II

Considering homozygosity and heterozygosity at each locus, 15 different multilocus profiles have been observed. These profiles and the number of corresponding 2n gametes are given in Table 4. Probabilities of the observed 2n gamete population under the FDR and SDR hypotheses for moving centromere positions have been calculated from this table. The LOD value of the SDR highest probability/FDR highest probability was 6.8, confirming that SDR is the most probable model. Under the SDR hypothesis, the probability variation as a function of the centromere position suggests that the most probable position is between 2.25 and 7.00 cM (Morgan’s map function; which is between 2.30 and 7.54 cM with Haldane’s map function) close to the CX6F23 marker, between the former and the mCrCIR05A05 marker. This confidence interval overlaps the ones of the estimations carried out by the best-fit method. If up to two crossovers per chromosome occur, it is possible to observe phase-changing between two markers when complementary crossovers take place (that is, two crossovers involving all four chromatids) via the SDR restitution mechanism (Figure 1). The HTA analysis detected 16 complementary crossovers, by revealing allelic phase changes between markers in homozygosity, as shown in Table 5; only two double crossovers affecting a chromatid pair have been identified.

Table 4 Heterozygous (HE) and homozygous (HO) profiles for 87 genotypes and five simple-sequence repeat markers within linkage group II
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Table 5 Number of observed crossing over events on each arm in chromosome II for 87 genotypes and five markers
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Interference analysis

Considering centromere position between CX6F23 and mCrCIR07D05 markers, the interference coefficient was estimated for each arm of chromosome II with three markers per side. For arm 1, analysing 87 genotypes for mCrCIR02D09, mCrCIR04H06 and CX6F23 markers, the interference coefficient was found to be 0.73. For the other arm, the interference estimation was 0.53, analysing 66 2n gametes for mCrCIR03C08, mCrCIR05A05 and TAA41 markers.

Discussion

MAC-PR is an efficient method to determine allelic configurations in triploid citrus-segregating progenies

In this work, the HTA is based on gamete allelic configuration inferred from triploid progeny genotyping. MAC-PR has been proposed to deal with differential amplification intensities among alleles in polyploid plant species (Esselink et al., 2004) for allele dosage estimation. Under the PCR conditions used for citrus SSR analysis, we have successfully verified the correlation between allele dosage and PCR product ratio. Finally, the very clear bimodal distribution of estimated doses for the 35 analysed SSR markers among triploid hybrids ruled out the occurrence of random PCR drift in our amplifications and validated the MAC-PR approaches for triploid citrus progenies genotyping. A basic assumption of the MAC-PR method is the repeatability of relative allelic amplification intensities among individuals and, thus, the total homology of primer sites for DNA fragments producing the same allele (same PCR product size). Homoplasy of SSR markers was found at interspecific levels in citrus (Barkley et al., 2009), and could limit general application of MAC-PR. ‘Fortune’ mandarin and most of the male genitors used in our study are closely related, which should explain why we have not encountered this difficulty because of the by-descent homology of alleles.

Origin of 2n gamete-producing triploids in citrus

We observed that all the 171 analysed triploid hybrids show maternal heterozygosity restitution for at least one marker. This confirms that all triploid hybrids found in the progenies of 2x × 2x crosses with ‘Fortune’ mandarin as female genitor arose from 2n megaspores. This result is in agreement with the cytogenetic observations of Esen and Soost (1971), and with previous molecular observations (Luro et al., 2000; Chen et al., 2008; Ferrante et al., 2010). In the present work, the restitution heterozygosity rates significantly lower than 50% for several markers (distributed in six of the eight represented linkage groups) and the pattern of heterozygosity inside linkage group II, definitively ruled out the FDR hypothesis. Multilocus 2n gamete allelic configuration in the same linkage group also revealed that SDR was much more likely to be the mechanism underlying the unreduced gamete formation than FDR (LOD=6.8). Moreover, this analysis enabled us to detect four-strand (complementary) double crossovers by phase changes of several homozygous markers. Such phase changes between homozygous positions are only possible under the SDR hypothesis if up to two crossovers per arm are considered. This conclusion for SDR is in agreement with that proposed by Luro et al., 2000, who observed low heterozygosity restitution in C. clementina 2n megagametophyte. The conclusion of FDR given for sweet orange (Chen et al., 2008) is questionable because of the low number of analysed markers. Indeed, the unambiguous identification of FDR without previous location of the centromere must be based on a large set of markers with good genome coverage. In the same way, the results of Ferrante et al. (2010), based on a very low number of individuals and markers for each parental genotype are not sufficient to prove the authors’s conclusions of SDR for ‘Fortune’ and ‘Wilking’ mandarin and FDR for lemon. Systematic analysis of 2n gamete allelic configuration with the same set of loci, close and far from the centromere, will shed light on whether SDR is the only mechanism underlying 2n egg formation in citrus, or whether there is a different mechanism depending on genotype or environmental conditions.

Analysis of the pattern of heterozygosity restitution within a linkage group is an alternative way to map the centromere compared with half-tetrad multilocus allelic configuration analysis

Centromere mapping has been carried out in several crops (Douches and Quiros, 1988; Okagaki et al., 2008) and animals (Kauffman et al., 1995; Lindner et al., 2000), using HTA. In the present work, HTA has been carried out in two ways: by multilocus allelic conformation analysis, as described in Tavoletti et al. (1996) and by comparison of observed and theoretical pattern of heterozygosity restitution rate within the linkage group under several models. Both methods estimated the centromere position to be between CX6F23 and mCrCIR07D05 markers. Confidence intervals of the positions obtained with the two methods overlapped, validating the best-fit method. The fitting curve adjustment has the advantage of potential application to a set of loci analysed in different progenies (between a same parent producing the 2n eggs but different male parents), potentially enlarging the usable set of markers to all those heterozygous for the female 2n gamete producer. It could potentially be used to compare a large range of interference model functions. Furthermore, this method should be easily applied to dominant markers by estimating the heterozygous restitution as 1−2f (with f being the frequency of homozygous progeny for the recessive allele). However, it requires the use of an existing genetic map and assumes that crossover distribution is similar during normal meiosis and 2n gamete formation. Multilocus allelic HTA is advantageous in that it can be used without a previous genetic map of the markers and can be applied with a predefined order of markers (Tavoletti et al., 1996) as we have performed, or without any previous information about marker position (Da et al., 1995). An excel template has been developed for easy identification of restitution model (FDR or SDR) and positioning of centromere within a linkage group, from heterozygosity restitution data for a set of mapped loci. It includes an estimation of confidence interval for the centromere position by bootstrap on the loci. It is available upon request to the authors.

Evidence for positive chiasma interference in citrus cv ‘Fortune’

Many models of HTA are based on the hypothesis of complete interference. In the present work, the analysis of multilocus configuration in linkage group II revealed the occurrence of up to four crossovers in the same chromosome arm and thus, incomplete interference. It is confirmed by the maximum restitution values between 75 and 82% observed for five of the markers, whereas for SDR, the maximum restitution should be 66.6% under the no interference hypothesis and should reach 100% for total interference. A better adjustment was found between observed data and theoretical curve with the Cx(Co)4 χ2-model for partial interference than the no interference one. Interference values were estimated by three-point analysis for each arm of linkage group II, with results suggesting that it was higher for one arm (0.73) than for the other (0.53). Such variation of interference level between different parts of the genome has also been observed in Arabidopsis (Drouaud et al., 2007), in human (Lian et al., 2008) and in mouse (Broman et al., 2002).

Implications for citrus breeding

Seedlessness is one of the most important characteristics for the citrus fresh-fruit market. An efficient way to achieve this aim is to obtain triploid mandarin varieties. Sexual triploidisation is a classical method to obtain triploid citrus hybrids (Ollitrault et al., 2008). Indeed, some genotypes such as ‘Temple’, ‘Wilking’ and ‘Fortune’ mandarin (Esen and Soost, 1973; Aleza et al., 2010) are well known for their production of diploid megagametophytes. The other classical method to create triploid citrus progenies is inter-ploidy hybridisation with doubled-diploid. Assuming an SDR origin of 2n gametes in ‘Fortune mandarin’, sexual polyploidisation may lead to lower average of heterozygosity restitution than interploid hybridisation, whatever the segregation model considered for the doubled diploid (Marsden et al., 1987). As heterozygosity and epistatic interactions are maintained for a great number of individuals in the progeny from interploid crosses with doubled-diploid, this triploid breeding strategy should be more efficient than 2x × 2x hybridisation for developing new cultivars that are phenotypically close to ‘Fortune mandarin’ genitor. Conversely, 2x × 2x hybridisation should produce more polymorphic progenies, by creating larger number of new multilocus allelic combinations (David et al., 1995), providing the opportunity to select innovative products within the perspective of market segmentation as a commercial strategy.