From the moment humanity developed agriculture, it allowed populations to expand but it wasn’t until the industrial evolution that our population saw an explosive growth. The extraction of energy was a turning point but it was only possible to sustain that population if humans managed to secure the equally explosive demand for food.

Obviously humans relied on all possible sources to accomplish this. Both increasing animal sourced food and plant sourced food. Animals are slow to grow and expensive while plants provide many more seeds for offspring and under optimal conditions can even yield multiple harvesting from the same land within the same year.
Protein yield from corn is about 720kg/ha. Yet plant protein is about 80% in bioavailability compared to animal protein. So let’s correct the 720kg to 576kg.
A cow yields a conservative 500 pounds of usable meat. About 227kg of which protein 59kg (~26%). This means we roughly need 10 cows per hectare while a general rule of thumb says about 1.37 cows per hectare (1.8 acre per cow). Thus +/- 81kg/ha.
You can argue about the correctness of those numbers but the discrepancy is so big, it is not worth getting to more precise values. It is obvious with those numbers that people tend to think we should let go of an animal based lifestyle and switch to a plant based one.
However, this would be a very one sighted look at the whole situation. We need to consider other factors. Although those other factors will not change the yield comparison, they may help us think different on the actions that should be taken.
Ruminants do not deplete the soil and create a sustainable land source. They do not require pesticides, gmo, herbicides etc. Generally they keep natural water flow in place, and are a net sink for CO2.
Whether you are a global warming denier or believer, fact is that humans increase CO2 and methane output into the atmosphere. Rice cultivation puts methane (1) into the air. Cultivation started around 5000 years ago and has seen an ever increasing volume. Needles to say, to continue increasing the volume, land has to be taken away continuously from wild life.

Our need for arable land increases. We are being inventive and reduce the need for land per person but our population keeps on growing. The following chart shows how much arable land there is available per person. It is decreasing.

Crops protection
Europe is aware of the issue that crops cultivation brings. Pesticides and other toxic products are sprayed on the plants to improve yields but they are a threat for the surrounding animals.
However, driven mainly by human activities, species are currently being lost 100 to 1,000 times faster than the natural rate; in the EU, only 17% of habitats and species and 11% of key ecosystems protected under EU legislation are in a favourable state.
Those products are not used for livestock.
If we move away from reliance on animals as our food, we will eventually cause them extinct. This is already happening now as we want to protect our food from wild animals and take up their space. By not relying on food from domesticated animals, we can and will get rid of them by taking up the land they are now occupying.
We try different things like creating urban agriculture but this is done in the most expensive housing places. This approach is just another proof that we are pressed for available land.
We already started experimenting with this for our astronauts and now we moved to creating plant-based burgers, imitating meat.
This is the future we are moving to if our population keeps expanding and there is no sign of this changing.
Do we have a choice really? Probably not. Is it an issue? That depends on our level of knowledge. We all want to live and we want to live healthily. Whatever diet or solution you prefer, we are not there yet. Our population is sicker than ever because we don’t know how to proactively generate health. We are good at keeping you alive but not in a healthy way, not by fixing the root cause and restoring good health.
But perhaps our population question gets resolved by itself? https://www.renalandurologynews.com/home/news/urology/reproductive-medicine/vegetarian-diet-lowers-sperm-quality/
Soil fertility
Another point to consider is how are we going to maintain soil fertility? We may be improving our techniques but at the same time face problems giving plants the necessary nutrients.

Without proper manure, the soils get more and more depleted loosing their yield.
Is it all bad?
Slowing population growth
Maybe not. If we can keep increasing the mean age, it seems we automatically cap our offspring. Looking at our world population there is a decline in the yearly percentage increase (3). Yet there is still a growing trend. This seems to be in line with the increase in mean age which is visualized in the following chart.

Yield improvement
We are also getting more efficient. At least in case of cereal we are able to increase the yield per square meter of land used and have been quite good at it as shown by the following graph. Note however that this cannot be stretched forever and more importantly, despite the higher efficiency this graph does not show us if we are using more land or not for cereal production.

Further improvements can be obtained in the way we cultivate rice. Reducing the flooding gives better yield, lowers water consumption and reduces methane output (2).
Indoor farming
Perhaps a very interesting development and certainly needed, is the indoor farming. If we get this right we can create arable land while not taking away land. But we’ll have to get this right in terms of nutritional quality, energy efficiency etc in order to succeed.
But in how far is this just delaying the inevitable? Where is that drive for efficiency coming from? Isn’t it because obtaining land becomes increasingly more difficult? We try to preserve nature but how good are we succeeding at this?
Animals under extinction
Have a look at the WWF list of animals under threat. These are all wild animals. We continue to take up their land to create new arable land, further supporting our expanding population, further requiring arable land.
The guardian reported on a study looking at exactly this topic.
Some 5,407 species (62%) were threatened by agriculture alone.
Lifestock
We are also taking up land for livestock so it is not just all about plants but there are more sustainable practices emerging such as regenerative agriculture. Thanks to the use of livestock we are actually able to prevent desertification. This means making useless land useful again. This is today not possible with our techniques, we need the livestock for that.
Finally
The point is, whatever makes our population more sustainable will cause further extinction of animals. So what I want to say is, if you think going vegan or vegetarian is going to save the animals, give it a bit more thought. You’ll be contributing to their extinction rather than protecting them. It’s an illusion.
The arguments back and forth on food yield, health, climate etc all don’t matter. The fact that this is being argued, shows we are getting squeezed on resources due to our population. No matter what diet we follow, we can’t solve the problem with a growing population.
Put your brain power into how we can sustain a smaller smarter population that prospers technological advances and spares what is left of nature and who knows even let nature blossom again. Maybe we should start with putting a fence around ourselves to protect nature from us rather than putting animals behind fences to protect us?
Whatever we do, however we solve it, it will have to be in a way that brings us excellent health. Health and longevity together with technological advances are the elements that reduce our population in a natural way. One thing is for sure, we need nature for our mental health. And wild animals are part of that nature and part of the effect on our mental health.
References
(1) “Methane Emissions from Rice Cultivation: Flooded Rice Fields” https://www.ipcc-nggip.iges.or.jp/public/gl/guidelin/ch4ref5.pdf
(2) “More Rice, Less Methane” https://www.wri.org/blog/2014/12/more-rice-less-methane
(3) https://www.worldometers.info/world-population/world-population-by-year/
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