My question is, if photosynthetic carbon capture is nutrient limited, what happens when we are adding both CO2 and phosphorus to the environment? Does everything grow better? And what's the next limiting nutrient?
Nitrogen limitation is one common one, which can apply either on land or in the oceans in different areas. We're adding quite a lot of that to the environment too though, up to a 200% increase in reactive nitrogen availability over pre-Haber-Bosch times [1]; accordingly about half the nitrogen in your body may come from the Haber-Bosch process [2].
In the ocean, there are already a good number of places that are Fe limited (Fe is needed to make chlorophyll, among other things [3]), so they'll stay that way unless we go with Fe-fertilization or increase dust input [4].
Si limitation is another possibility in the oceans -- particularly for phytoplankton that make silica tests like diatoms [5] (though as an interesting aside, a surprising number of plants need silica to make their phytoliths [6])
On land, there's plenty of Fe and Si (from soil), so if we're supplying P, N, and CO2 then we're mostly left with water or light (photon) limitation.
If all nutrients are superabundant (particularly in aqueous settings), then we end up with runaway growth and eutrophication, which is dangerous in its own way [7]
[1] https://en.wikipedia.org/wiki/Human_impact_on_the_nitrogen_c... [2] https://en.wikipedia.org/wiki/Haber_process#Economic_and_env... [3] https://www.tandfonline.com/doi/abs/10.1080/0190416840936323... [4] https://en.wikipedia.org/wiki/Iron_fertilization [5] https://www.sciencedirect.com/science/article/pii/S096706370... [6] https://en.wikipedia.org/wiki/Phytolith [7] https://en.wikipedia.org/wiki/Eutrophication
Anyone who studies the biology and evolution of plants, as well as the actual constraints of their growth processes, will understand why this gigantic transformation has been happening. There are similar measurements of major increases in ocean plankton over the last decades.
[1] https://www.nasa.gov/feature/goddard/2016/carbon-dioxide-fer...
My apologies if that isn't what you were doing.
And that apparent silver lining's actually got a downside, too. Plants working hard to draw up water is a Good Thing, because that water is the only source of nitrogen and other elements needed to make proteins and vitamins.
CO2 just gets turned into carbs; it makes plants grow big and tall but less nutritious. This won't be a problem for us overfed gluttons in the West, but it is going to exacerbate malnutrition issues in poorer regions of the world.
See e.g.:
https://www.nature.com/scitable/knowledge/library/effects-of...
All scientific, controlled experiments with plants demonstrate conclusively that they thrive (faster growth, larger leaves, increased biomass, larger fruits, less need for water, etc.) at higher CO2 levels than what we have today and than we had before the Industrial Revolution. I encourage people who are intellectually curious and honest to look up the scientific papers on the topic and read them for themselves (you don't have to be a biologist or a geologist to understand the experiments, the parameters, or the outcomes).
Yes, CO2 is what plants eat, but it doesn't tend to be the limiting nutrient very often on Earth today. For the ocean (where 50-85% of photosynthetic oxygen production, and equivalently carbon burial, happens [1]) there are actually maps of this [2], and you may note that CO2 does not appear. On land, it's usually water, nitrogen, or phosphorus [e.g., 3].
Accordingly, there have been many studies on CO2 fertilization, but since it's not the limiting nutrient it doesn't tend to have much of an effect [e.g. 4]. At best there are benefits for some plant species in areas where water is the limiting nutrient, since higher CO2 means plants can keep their stomata closed more [e.g. 5], but even this is a bit of a mixed bag since dry places tend to get hotter and drier under global warming.
[1]https://en.wikipedia.org/wiki/Phytoplankton#Oxygen_productio... [2] https://media.springernature.com/m685/nature-static/assets/v... [3] https://nph.onlinelibrary.wiley.com/doi/full/10.1111/j.1469-... [4] http://www.pnas.org/content/early/2016/12/07/1610156113.shor... [5] https://nph.onlinelibrary.wiley.com/doi/full/10.1111/nph.124...