If you have a large, diverse population of individuals, you can look at the average observed heterozygosity of the SNP markers from your sequencing data. Make a histogram of heterozygosity by individual. If your individuals are all the same ploidy, it will form a nice bell curve. Using GBS data on a large population of diploids, the one known triploid had a heterozygosity five standard deviations above the mean. A sample that was an accidental mixture of two individuals was even higher.

From my point of view there is not way to infer if a species is a polyploid based in the SNP from a transcriptomic data because the expression of different alleles/homoeologs probably will be different, so if you find a polymorphic position AAAB or ABBB it could means a heterozygogus gene where one allele is expressed 3 times and the other 1. Also it could be interesting to do a transcriptome assembly and compare the number of genes with a diploid species, but generally the majority of the homoeologous genes will colapse in the same contig (http://www.biomedcentral.com/1471-2164/13/406/) so it is not a good method.

Nevertheless I also have been using GBS data for diploids and allotetraploids species. In this case when I compare the polymorphic positions with some confidence (for example with a read coverage > 10X), the diploid species show that almost all the heterozygous SNP positions are present in a 0.5 proportion (AB). For the polyploids samples I found a variable distribution of 0.25, 0.5, 0.75 variation proportions, that could be interpreted as AAAB, AABB (or AB) and ABBB. I think this analysis can give you an idea if the species is a polyploid, but still there are a lot of variables to consider, for example, you need to have a diploid reference to map the reads before call the SNPs.

If you have any question, please let me know,

The distribution of synonymous substitutions (Ks) along the coding regions of duplicated gene pairs (paralogues if any) can be used to uncover polyploidy events and their frequency. EST datasets generated by assembling NGS transcriptome data can be used in such analysis.

I think the best way to infer ploidy if you do not have karyotype data is to estimate genome size through flow cytometry and compare with genome size of related known diploid species. Otherwise, if you look at microsatellite data, you will normally see some loci more than two alleles.

If available, the simplest way to infer polypoïdy would be to use short tandem repeat markers (STRs).

If informative (alleles with different sizes after fluorescent PCR and capillary electrophoresis), STRs allow you to count the number of haploïd sets of chromosomes in a given species. For exemple, profiles in the triallelic range (1.1.1 or 2.1.) are consistents with a tripoïde genome.

If you have a large, diverse population of individuals, you can look at the average observed heterozygosity of the SNP markers from your sequencing data. Make a histogram of heterozygosity by individual. If your individuals are all the same ploidy, it will form a nice bell curve. Using GBS data on a large population of diploids, the one known triploid had a heterozygosity five standard deviations above the mean. A sample that was an accidental mixture of two individuals was even higher.

I agree with France; I am working with polyploids following interspecific-interploidy crosses and I'm using flow cytometric analyses to identify the polyploid hybrids, comparing the 2C-DNA content of the progeny with the diploid and tetraploid specie. Of course, the diploids and tetraploids i'm using were identified in previous works by karyotypic analyses. But, in your case, just you need to compare between them the DNA content measured against an internal standard. After that, I think you can apply some NGS in order to find some marker or with fluorescent SSR you can analyse the electropherograms to identify the dosage effect through the allele copy number.

You might also look at the method used in this paper: http://elife.elifesciences.org/content/2/e00731

Yoshida et al. The rise and fall of the Phytophthora infestans lineage that triggered the Irish potato famine. Elife. 2013 May 28;2:e00731. doi:10.7554/eLife.00731.

Look at Figure 8 in particular.

They write: "To estimate ploidy level in our specimens, we investigated the distribution of read counts at biallelic SNPs for high-coverage genomes. In a diploid species, the mean of read counts at heterozygous positions should have a single mode at 0.5, while there should be two modes, 0.33 and 0.67, for triploid genomes, and three modes, 0.25, 0.5 and 0.75 for tetraploid genomes"

Of course, they are using genomic NGS data, not transcriptomic -- and they have a reference genome against which to align the NGS data.

Perhaps GenomeStudio?

Transcriptome data could be affected by the expression of a specific allele and introduce biases in inferring polyploidy. Dependind on the dimension of the genome you can sequence it and de novo assembly it with some de novo assembler (like Velvet). Once you have an assembled draft genome you can map the reads used for the assembly to this new reference to estimates copy number variation with SNP calling. In this way you will infer only ploidy for the scaffold assembled.

Thank you everybody! Your answers were all very helpful! Specially thanks to David for the paper. Indeed we did something similar to what you propose Andrea, but we wanted to know if this has been done before. We are trying it with the transcriptome, though. Apparently there are ways around the noise introduced by differential expression. Thank you all! Suggestions of other papers are highly appreciated!

You might check out this too:

Article: A hybrid next generation transcript sequencing-based approach to identify allelic and homeolog-specific single nucleotide polymorphisms in allotetraploid white clover.

(Available on ResearchGate:

https://www.researchgate.net/profile/Istvan_Nagy6/?ev=prf_highl

One way is to look at the polymorphic sites and assess the level of polymorphism from the sequence data. You might find this article useful.

HANDS: a tool for genome-wide discovery of subgenome-specific base-identity in polyploids

http://www.biomedcentral.com/1471-2164/14/653

Although, HANDS is not designed for the detection of polyploidy but rather to use on a polyploid genome whose ploidy is known. However, it might be possible to use the principle underlying HANDS (similarity with diploid) to detect if a species is polyploid. If you have sequence data containing polymorphic sites (homozygous as well as heterozygous) in a species then by comparing the percentage identify of the polymorphic bases with other species it might be possible to see if more than one relative can be found.

This is a tricky problem and one would have to approach the problem differently for allo- , auto-polyploids and organisms with labile ploidy, such as some fungi . I'm not aware of any "one-fits all" approach and each situation is likely to require slightly different analysis. I was involved in the analysis of Batrachochytrium dendrobatidis (Bd) genomes, which presented a challlenge as we were dealing with variation in ploidy both between as well as within strains (aneuploidy). Our analyses can be found in the following paper.

http://www.plosgenetics.org/article/info%3Adoi%2F10.1371%2Fjournal.pgen.1003703

I would be reluctant to do anything similar on expression data.

This might help: http://biorxiv.org/content/early/2016/11/08/086488

Thank you everyone, very interesting! In the end we sort of figured it out, very similar to the approach in the paper you suggest Diego! Plus, we took advantage of the fact that our species it's a hybrid. We used RNA-seq data, so even with all the transcriptomic "noise" it was possible to detect a triploid. Here is the paper, if anybody it's interested.

http://onlinelibrary.wiley.com/doi/10.1111/mec.13717/abstract