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I'm curious about how much is known about this topic: how much has the total amount of life on Earth changed over the 4 billion years or so that it has existed on this planet?

Are there estimates of global Gross Primary Productivity (GPP), or biomass, or both, for previous geological epochs? If so, how certain are these estimates, and what assumptions are they based on?

If the total figures are thought to have changed much in the past, what are the main factors thought to cause these changes? Conversely, if the totals are thought to have been relatively stable, what are the main feedbacks that are thought to have ensured this?

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To answer your question to the point: we don't know at all.

For most of living organisms, the fossil record is either inexistent or very fragmentary. Even estimating the number of species (which is somewhat less difficult since you need only one specimen of each species to have access to that information) is very difficult and affected by many, many biases (see the works of Jack Sepkoski, David Raup and John Alroy for instance, to see the difficulty of estimating past biodiversity). Attempts at reconstructing marine "invertebrates" diversity (Sepkoski 1978; Alroy et al. 2001, 2008) showed an increase during the Phanerozoic (so, give or take, the last half-billion years), with five main mass extinction events (End Ordovician, Late Devonian, Permian/Triassic boundary, Triassic/Jurassic boundary and Cretaceous/Paleogene boundary).

The general assumption is that biomass increases when diversity increase. There is frankly not very strong basis for this assumption but that's basically all we can work with.

Some living organisms however have a much better fossil record: diatoms, radiolarians, foraminifera and calcareous nannofossils (mainly from the algae group of the Haptophyta) constitutes the bulk of marine sediments and are therefore recorded consistently and abundantly. Their Cenozoic record (i. e. the last 66 Myr) in particular is remarkably complete, but still in some cases biased enough to prevent us for estimating reasonably changes in their abundance.

As a matter of fact, my current research revolves around the changes in diatom abundance in sediments during the last 50 Myrs (Renaudie 2016). Without going too much into the details, it seems, in that case, that their abundance (in sediments at least) and their diversity are more or loss synced. The interest of diatoms, in regard to your specific question, is that, today, there are one of the two main oceanic primary producers (along with Haptophyta), oceanic production itself being more or less half of the global production (see this previous answer of mine). Their abundance increased significantly at the Eocene/Oligocene boundary and then during the Mid-Miocene. Of course it is possible that in the mean time other phytoplankton (Haptophyta, Dinoflagellates, or others) abundance might have dropped but what makes us think that this is not the case is that changes in diatom abundances during the Cenozoic match changes in atmospheric $p\mathrm{CO}_2$ (Beerling & Royer 2011), implying a global increase in the net primary production.

References:
Alroy, J. et al., 2001. Effects of sampling standardization on estimates of Phanerozoic marine diversification. PNAS, 98(11): 6261-6266.
Alroy, J. et al., 2008. Phanerozoic Trends in the Global Diversity of Marine Invertebrates. Science, 321: 97-100.
Beerling, D. J. & Royer, D. L. 2011. Convergent Cenozoic CO2 history. Nature Geosciences, 4: 418-420.
Renaudie, J. 2016. Quantifying the Cenozoic marine diatom deposition history: links to the C and Si cycles. Biogeosciences, 13: 6003-6014. [Disclaimer: I am the author of this article]
Sepkoski J. J. Jr, 1978. A kinetic model of Phanerozoic taxonomic diversity I. Analysis of marine orders. Paleobiology, 4: 223-251.

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