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I have single cell RNA-seq data on about 2000 cells in 9 time point. I have clustered my cells in each time point by Seurat. I am seeing in some time points I have 3 clusters while in another time points I have 2 clusters of cells (please look at the plot).

One hypothesis would be that, a new cell type is being emerged at last time point. But maybe if we had another further time point this third cluster being disappeared because that has been arose just because of undifferentiated cells from the later time point (second hypothesis).
Another hypothesis would be this new third cluster is a new cells type that only temporarily expresses a set of genes but if we had cells for another further time point, we would not see the expression of these genes anymore and we had again 2 clusters. I am really struggling with this how I could test my hypothesises.
The final hypothesis would be that the third cluster is really a new cell type born from old cell types during the differentiation.

Like UAD algorithm addresses my question. I just tried FateID algorithm on my data but got stopped by

> pr <- prcurve(y,fb,dr,k=2,m="tsne",trthr=0.4,start=2)
Error in svd(xstar) : a dimension is zero

Any suggestion would be highly appreciated.

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This is what packages like FateID and Monocle are for, namely taking single-cell RNAseq data and inferring differentiation trajectories from it. Don't try to reinvent the wheel on this, there are a number of packages out there to do this sort of thing and they're going to have pretty complicated methods that you're really not going to want to reinvent unless you absolutely have to.

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The answer is behind these papers:
The dynamics of gene expression in vertebrate embryogenesis at single-cell resolution
Single-cell mapping of gene expression landscapes and lineage in the zebrafish embryo

Also this.

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    $\begingroup$ Please avoid link only answers, provide summary text from the links. $\endgroup$
    – zx8754
    Sep 6, 2018 at 5:51
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    $\begingroup$ The papers are too difficult to follow but I just resealized that finding parent child clusters likely would work. $\endgroup$
    – Angel
    Sep 7, 2018 at 10:38

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