What's the connection? I thought the Ci would be Koppen climate classification but it's actually alternate carbon-fixing photosynthetic processes
As the temperature rises, so does the error rate. At a high-enough temperature, the plant loses energy overall, which it can't survive long term.
C4 plants separate this process into two steps spatially. They build a four-carbon molecule in a much less error-prone way, then move this to a part of the cell where it's broken down into CO2. RuBisCO is again used to build the three-carbon sugars, but because the relative concentration of CO2 to O2 is so high, the error rate is low. There's some additional overhead to this process, but it pays off in warm climates.
Incidentally, there's another warm-climate metabolism: CAM (crassulacean acid metabolism). CAM works by temporally separating parts of the process. At night, they open their stomata, and use CO2 to build an acid. During the day, they close their stomata, cleave CO2 off of the acid to increase the concentration, and let RuBisCO its thing.
I believe RuBisCO is the most common enzyme on Earth by weight. I find it striking that Mother Nature has had to find all these hacks to get around its shortcomings, but hasn't found a way to simply fix the enzyme so it doesn't make so many errors.
Now I see in the last paragraph it says C4 photosynthesis is more efficient in hot climates and C3 more efficient in cooler climates.
I don't see though what's the benefit of bioengineering C3 plants to operate with C4, rather than to utilise C4 plants where the climate is suitable for them?
(Note that maize, sugar cane, sorghum, and some millets are C4 crops already in use.)
It takes a lot of selective breeding to develop varieties that are palatable, productive, climate adapted, (remain) disease resistant, amenable to automation, etc etc. There are folks doing amazing work in their backyard to improve promising and interesting species (see "landrace gardening" community. It's super cool how one can leave a "genetic legacy" for future generations this way.) And of course university and extension office breeding programs too.
Many people believe that we need to shift towards a more management-intensive perennial-emphasized polyculture / "permaculture" type approach in order to create diverse and resilient systems tailored to the local conditions. But then the entire food consumption system needs to align on top of that. Lots of coordination problems.
So of course the big industrial ag systems are also doing things their way, which includes modern biotechnology. I'm not opposed to that - if I could wave a wand to improve some crops I certainly would. Hopefully we get lots of people exploring all types of solutions.
But I get your point. This was of course obvious to any subsistence farmer in history. Without long-distance trade and perfectly reliable preservation, you had better be harvesting food as close to year-round and possible, which means lots of different crops (in different microclimates if possible, to spread out their season.)
There were layers and layers of fallbacks, down to "famine foods" like wild roots or acorns. They also invested in social relationships by banqueting each other in productive times.