I would highly recommend you read through the paper. Alongside these "advanced in individuality" comes reduced (internal) competition.
I agree that both are important but competition only seems to be important at the very edges of what selection is acting upon while cooperation is truly "fundamental"
I don't know of any cases of direct kidney v lung competition, but competition among body parts is common. Sometime that competition is adaptive, sometimes not. Examples of adaptive competition are things like when under extreme circumstances (particularly cold or hunger) your body will sacrifice parts of itself to keep other parts going. Examples of non-adaptive competition are things like autoimmune diseases. Also, sometimes individual cells go rogue and stop cooperating. That's called cancer.
> competition only seems to be important at the very edges of what selection is acting upon
I guess that depends on what you consider "the edges". In the case of humans, selection produces intuitions about "us vs them". Those intuitions range from very closely drawn boundaries ("us" includes only my immediate family or clan) to very broadly drawn boundaries ("us" is my entire species, or my entire phylum, or all living things). In between are things like "us" is all members of my species with my skin color. But the extremes of this range are non-adaptive. Draw the boundaries too narrowly and you end up without enough genetic diversity in your in-group to drive out maladaptive mutations. Draw them too broadly and you end up defenseless against parasites and with nothing to eat.
Your body prioritizing which parts to keep alive for the survival of the whole ship is not an example of competition. Competition would be if a body part actively attacked another body part. In this case, survival of the entire body will eventually benefit all body parts
> I guess that depends on what you consider "the edges"
The "edges" as thoroughly defined in the paper I linked. Major evolutionary transitions in individuality (METI). METI is a widely accepted framework in biology
I guess we'll just have to agree to disagree about this. I don't see a lot of daylight between "active attack" and starvation of resources. Just because your attacker chooses to lay siege to you rather than mount a full frontal assault doesn't make them any less of an attacker IMHO.
> The "edges" as thoroughly defined in the paper I linked.
Sorry, I don't see it. AFAICT the word "edges" only appears once in the paper:
"Evolution is a process of continuous change, and so we should expect blurry edges with a mosaic of features (1)."
[UPDATE] Oh, BTW, I think that paper is actually very good. Thanks for bringing it to my attention.