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I have been reading:

William B. Whitman, David C. Coleman, and William J. Wiebe, "Prokaryotes: The unseen majority", Proc. Natl. Acad. Sci. USA 95, pp. 6578–6583, June 1998. [Full Text] [PDF]

wherein they estimate the number of prokaryote cells on Earth to be of the order of $10^{31}$.

I can't seem to find any equivalent data for eukaryote one-celled life. Are there any estimates for the number of one-celled eukaryotic living things on Earth? Do any other estimates confirm or tell against the reference I have cited above?

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Could not fit in a comment....

To make sure we all understand your question...

Is your question how many (eukaryote) species are currently living? or How many (eukaryote) cells are currently living??

Just a hint to answer the question

Micheal Lynch, in his book (On the Origin of Genome Architecture) at page 3, Box 1.1 tries to answer the question How much DNA is there on earth?. He ends up with an estimation of a total length of DNA on earth of $10^{24}$ km for procaryotes, $10^{25}$ km for eukaryote (of which $\frac{1}{1000}$% is accounted to humans). This sums up to a total DNA length of $10^{12}$ light-years, or 10 times the diameter of the known universe!

In his calculations, he estimates that the total number of procaryote cells at $10^{30}$ (citing Whitman et al. 1998 as you did). He estimates the total number of eukaryote species to $10^7$, i.e. 6 times the number of known eukaryote species. However, he doesn't directly give any reference for this estimate but he refers to different chapters in the book that contain lots of references.

...I hope that helps...

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  • $\begingroup$ "How many eukaryotes cells are currently living?? or How many eukaryotes cells are currently living??" It's how many cells are currently living, so your reference is indeed helpful, thanks. $\endgroup$ – Selene Routley Dec 30 '14 at 4:12

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