I'm not seeing in this where he's given any kind of numbers that we should expect in these scenarios? He's given factual examples with their numbers but that's really not the same thing. Why would he give evidence to make a claim he isn't making? Do you think he is saying that the distribution of the heavenly bodies is the same as lobster territories,
I think he's actually talking about two separate things here that you are conflating, one being hierarchy and the other being how things are distributed, which can be applied to a lot of other kinds of things as well. I've seen it applied to how much people wear the different clothes they have relative to each other, for example, which isn't about social hierarchy at all.
It is Peterson who conflates outcomes in the world of the (male) lobster with the distribution of human wealth when he starts crossing over the line with this sentence:
It’s winner-take-all in the lobster world, just as it is in human societies, where the top 1 percent have as much loot as the bottom 50 percent [11] — and where the richest eighty-five people have as much as the bottom three and a half billion.
If Peterson makes a comparison and says outcomes observed in one system are 'just as it is' in another system then he needs to back that up with data. Otherwise a skeptical person might not believe what he says is true.
For everything except lobsters Peterson gives us a mathematical law which tells us how those other things are distributed:
This principle [of Unequal Distribution] is sometimes known as Price’s law, after Derek J. de Solla Price, [13] the researcher who discovered its application in science in 1963. It can be modelled using an approximately L-shaped graph, with number of people on the vertical axis, and productivity or resources on the horizontal.
To be precise Price created a mathematical model of networks of citation, in an attempt to explain how some papers are cited so much more than others. It assumes the mean out-degree (i.e. the number of citations) of nodes (each paper is a node) is fixed over time. Price's model predicted a power law distribution. Price compared his model to real citation network data and found a reasonable fit to a power law distribution.
en.wikipedia.org/wiki/Price%27s_model
In the examples Peterson cites researchers have done the work to fit the data sets to power law curves with various coefficients.
Power law distributions are highly skewed distributions with long tails which I suppose if you squint hard enough might be very, very roughly the L-shaped graph that Peterson describes. Statisticians would not model a power law as an L-shaped graph because they'd want sufficiently many data points to fit a power law curve. You can see the shape here en.wikipedia.org/wiki/Power_law
Peterson is trying to embed reasonable research about male lobster behaviour in a wider narrative of reasonable statistical research (and in the whole book fit them into a even wider narrative). The relationship between the two bodies of research is tenuous.
Peterson's narrative is not one in which he says 'hey look at the male lobster hierarchy', now 'look at the human wealth hierarchy', but this is merely an observation that these hierarchies exist, and these hierarchies are unrelated in any way whatsoever, except by the fact that they are hierarchies. Peterson says humans have primordial calculator at the very foundation of our brains that evaluates rank, part of a serotonin feedback loop where the production of more serotonin improves how others rank you, which feeds back into your primordial calulator, ranks you higher, produces more serotonin... Or it can opperate in the opposite negative direction. Peterson claims this mechanism is subject to Price's law:
Circumstances change, and so can you. Positive feedback loops, adding effect to effect, can spiral counterproductively in a negative direction, but can also work to get you ahead. That’s the other, far more optimistic lesson of Price’s law and the Pareto distribution: those who start to have will probably get more.
There is not enough evidence fro a scientific person to believe him.