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Results were listed in Table 2 and Fig. Based on the information in Table 2, the chromosome loci numbers of E. Representative pictures of 5S gene chromosomal location were displayed in Fig. There were fewer fluorescence loci in E. More fluorescence loci numbers were detected in triploid hybrids than that in diploid hybrids and E. Strong signals in the white frames of Fig. The strong signals were in the middle of chromosome in diploid hybrids, Huang et al.

BMC Genetics Fig. Discussion Karyotype analysis is a useful method to trace chromosome filiations in polyploid hybrid progenies. Karyotype analyses by Qin et al. In this paper, triploid hybrid groupers were produced from E. Natural polyploids were more and more commonly detected in many fish species in recent years.

Tsuda et al. Bai et al. Control: embryo sections of E. Triploidization: triploidizition processes of the hybrid embryos. Triploid hybrids were generated from the interspecies hybridization of female Ctenopharyngodon idellus and male Megalobrama amblycephala [10]. However, the cellular formation processes of the polyploids were still unclear. In this study, embryo images and sections were conducted to investigate the triploidization processes. Results showed that the hybrid embryo images were not substantially different from the related of E.

The hybrid female pronucleus might retain two sets of chromosomes and Huang et al. Class I and Class II were pointed out by arrows, the two bands were nearly bp and bp respectively extrude a pseudo polar body without genome. To our knowledge, this was the first report of cellular polyploidization processes in interspecies hybridization. Our results suggested that the extra sets of chromosomes in triploids might be caused by failure formation of the second polarized genome.

Analysis of genetic organization and variation may be helpful in evaluating the role of hybridization. The NTS of 5S rDNA gene is neutral and freely mutative, and it has been widely employed as a molecular marker to assess the organization of genomes and to trace recent evolutionary events [13, 18].

Analysis of different ploidy hybrids of Carassius auratus red var. In the present study, the 5S rDNA genes were cloned and analyzed, Class II sequences bp, bp in diploid and triploid hybrids were composed of two monomer structures Class I which were originated from their parent species. The results indicated that the new sequences in the hybrids were recombined by the parental sequences. In this paper, the NTS sequences in diploid and triploid hybrids were slightly different, but not blocks of variant sequences, the results were similar to that of He et al.

The number of fluorescent loci in the triploid hybrids was less than that in mother species, which indicated that the recombination of 5S gene might enfeeble the efficiency of M probe in triploid hybrid chromosomes.

However, despite this comprehensive investigation, a general and basic understanding of heterosis remains elusive. Single loci have a relatively small contribution to hybrid traits [2]. Heterosis or hybrid vigor may be shaped by different traits that are affected by multiple gene loci [19].

In our study, the new 5S gene sequences in diploid and triploid hybrids were composed of different parental monomer structures. Dots indicated the identical nucleotides, hyphens represented the insertions or deletions. In bold letters were shown the nucleotide substitutions. The TATA sequences were framed in boxes that genome loci of parental species might be exchanged or recombined during the hybridization. Our results would provide the basic molecular evidence for explaining the heterosis phenomenon in hybrids.

Conclusions In conclusion, triploidization processes and genetic patterns of 5S rDNA in hybrid groupers had been investigated in this paper. The extra sets of chromosomes in triploid hybrids had been demonstrated to come from the mother species. The failure exclusion of sister chromosomes might be occurred during the second meiosis stage, a pseudo polar body without genome might be excluded instead.

Hybrid heterosis might be induced by interspecies genome re-fusion and gene exchanging. More evidence and further research are still needed to reveal the molecular mechanisms of natural polyploidization and hybrid vigor.

Karyotype slides were prepared from cultured peripheral blood cells. Detailed processes were conducted as described by Huang et al. The cells were then treated with 0. Blood cells were dropped on the cold slides and air-dried at room temperature. Chromosomes were stained by Giemsa solution pH 6. Good-quality metaphase spreads images were obtained by a Nikon 50i microscope Nikon, Japan for karyotype analyzing.

Fine karyotype analysis was carried out as Qin et al. Long-arm to short-arm ratios of 1. Methods Embryo development Karyotype analysis Breeding of E. The methods were conducted as described in Huang et al. Good-quality eggs were hatched in seawater nearly Karyotype analyses of each five individuals of E. Sequences were analyzed with ClustalW 2. Fluorescence in situ hybridization was performed as described by He et al.

For each type of grouper, metaphase spreads 20 metaphase spreads per sample of chromosomes were analyzed. The white arrows indicated the fluorescent signals green loci. The strong signals were framed and partial enlarged in the white boxes. The embryo development processes were imaged by a Nikon 50i microscope camera. The fry were reared to fingerlings in the same environment. The eggs were dehydrated in alcohol, embedded in paraffin wax, sectioned, and stained with hematoxylin and eosin.

Photomicrographs were taken with a Nikon 50i microscope camera. PCR conditions were the same as described by Qin et al. Monoclonal bacteria were obtained from Additional files Additional file 1: Figure S1. Alignment results of coding region of 5S gene. M, coding region of and bp 5S sequences from mother species E. Dots indicated the identical nucleotides.

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Ascend Y6 II Compact. Merida-L09C Merida-L29C Merida-L29D Merida-L49C Y7 The current generation is labeled 0. Let r denote the probability of intra-locus recombination at an autosomal locus per meiotic generation.

Thus, we only trace the lines of descent for the autosomal locus up to its minimal topological enclosure by diploid karyons within individual zygotes.

These parent-offspring choices occur independently among individuals of the same generation due to panmixia. In the absence of recombination, i. When recombination is certain, i. Note that the karyotic ancestral graph in Fig.

We can choose to track backwards in time various aspects of the ancestry of a sample of Ancestries of a recombining diploid population individuals from current generation 0 that is embedded within the karyotic ancestral graph, a subgraph of the karyotic population pedigree.

Here, we simply track the number of lineages that are ancestral to our sample, perhaps the most foundational aspect of the ancestry. The forward-time offspring distribution of Eq. Otherwise, we need to embed the sub-karyotic ancestral graph of our locus within the karyotic ancestral graph by a particular r -thinning as described in Remark 1.

This is shown in Fig. Section 6. Some classical examples of such finer genealogical resolutions include: 1 the ARG of Hudson that describes sampled loci as unit intervals of infinitely many sites and only tracks the recombining ancestry of the parts of the intervals that have genetic material in the sample, 2 the two-locus ARG of Griffiths that allows recombination to occur between the loci but can track the complete ancestry of the two-locus samples including the gene genealogies, and 3 the ARG of Griffiths and Marjoram that tracks the complete ancestry of the sampled unit intervals of infinitely many sites and generalizes the previous two models.

It is also of importance in situations where very small population sizes would tend to keep genetic diversity very low in the absence of recombination. Indeed, the number of pedigree ancestors of the whole population is a good indication of how efficiently recombination is able to foster or restore diversity.

We establish this in Theorem 4 by showing the convergence of the transition probabilities in Theorem 1 to those of the standard continuous-time ARG model. Indeed, let us fix a realization of the latter.

Coalescences are not modified. When studying large populations, it will be convenient to use the following slight modification of our model: when a lineage recombines, two parents are chosen independently and uniformly at random within the previous generation instead of a pair of distinct individuals. For large values of n, we use the following approach of Chang to study the ancestral process. For any i, let the set of descendants in generation t of individual I0,i be denoted by Gti , and the cardinality of Gti by G it.

We drop the superscript i when there is no confusion. In particular, once we identify an individual, say I , who is unlikely to go extinct over generations, we follow the set of its descendants in each generation, and denote the sizes of these sets as G t. For the purposes of the proofs, we shall also consider another process: the individuals who are not descendants of i. In generation t, there are Bti such individuals. In particular, we refer to the number of individuals in generation t that are not descendants of a chosen individual I in generation 0 by Bt.

In other words, the standard continuous-time ARG model can be recovered from the recombining Wright—Fisher model in the regime of parameters where recombination is weak and population size is large. In this case, we need to consider the population ancestry over time intervals of length O n as in the coalescent approximation of the non-recombining Wright—Fisher model. Remark 3 In our models when two lineages share a common ancestral karyon we consider them to have physically coalesced in terms of being enclosed within a single Ancestries of a recombining diploid population diploid karyon.

From these exact computations of the stationary distributions depicted in Fig. The thickness of the CDF increases with n. The mass at the most likely state is shown by a stem plot for each distribution R. Table 1 gives a tabular summary of 25 simulations of the fraction of CAs at Un for a range of r and n values. In Table 2 the approximation for Tn is working well uniformly over r as n increases, albeit slower for smaller r. In Table 3 the approximation for Un is also improving as n increases.

One needs much larger n due to the log log terms that have been dropped in the limits in Theorems 2 and 3. Table 3 The median minimum, maximum based on 25 simulations of Un for different values of r and n r Population size n in simulation 0.

Since the parents are chosen uniformly at random, we have B J0 I, K k 4. Therefore, combining Eqs. We can count B j i, k by the inclusion-exclusion formula , given by the next lemma. Let A be the set of parents of vertices in I.

Moreover, the probability that the family of I eventually goes extinct is negligible. We shall give more details about the proofs concerning Stages B2 and B3 , although most of the arguments are similar to those used in the other stages.

We shall use it in the regime where G or B is large, to show that the behaviour of these processes is very close to their expectations. Therefore, if every m n generations we test whether the individual labelled by 1 at that time has at least ln n 2 descendants another m n generations later, we obtain a geometric trial that ends with a success in a finite number of steps with probability 1.

This gives us the desired upper bound on Tn. Let us thus show Eq. The proof of the lower bound is thus complete. Let us give the outline of the proof. The main distinction between Theorems 2 and 3 is that at the end of Stage G1 of Theorem 2, we only require that at least one individual should have ln n 2 descendants.

At the end of the first stage of Theorem 3, we require each individual in generation 0 to have become successful or extinct, which is why we expect this stage to take longer than Stage G1 of Theorem 2. Similarly, we expect Stage 3 of Theorem 3 to take longer than Stage B3 of Theorem 2 since all the families of successful individuals have to reach n and not just one. Stage 2 of Theorem 3 is already detailed in Stages G2 to B2 of Theorem 2 and so we do not analyze it here.

This corresponds to the following lemma. This completes the proof of the lower bound. Now we turn to the upper bound. Stages G2 to B2 of Theorem 2 and Stage 3 above. The upper bound is proved. Recalling the notation I0,i for the individual labelled by i at the generation that we call 0, Fn is formally defined as R.

Let us start with the expectation of Fn. Finally, using the same reasoning as in the study of the third term in the r. Then the same reasoning as above shows that conditionally on the two families surviving the first stage, they both reach size n with probability tending to one. A simple use of the Markov inequality then ends the proof of Corollary 1. Equation 8.