In his book 12 rules for life Jordan Peterson claims that:
Consider serotonin, the chemical that governs posture and escape in the lobster. Low- ranking lobsters produce comparatively low levels of serotonin. This is also true of low- ranking human beings (and those low levels decrease more with each defeat). Low serotonin means decreased confidence. Low serotonin means more response to stress and costlier physical preparedness for emergency—as anything whatsoever may happen, at any time, at the bottom of the dominance hierarchy (and rarely something good). Low serotonin means less happiness, more pain and anxiety, more illness, and a shorter lifespan—among humans, just as among crustaceans. Higher spots in the dominance hierarchy, and the higher serotonin levels typical of those who inhabit them, are characterized by less illness, misery and death, even when factors such as absolute income —or number of decaying food scraps—are held constant. The importance of this can hardly be overstated.
at another passage he claims that:
A lobster with high levels of serotonin and low levels of octopamine is a cocky, strutting sort of shellfish, much less likely to back down when challenged. This is because serotonin helps regulate postural flexion. A flexed lobster extends its appendages so that it can look tall and dangerous, like Clint Eastwood in a spaghetti Western. When a lobster that has just lost a battle is exposed to serotonin, it will stretch itself out, advance even on former victors, and fight longer and harder.
For the second passage he cites the following paper
While there are many papers linking position in the social hierarchy in primates and humans I could not find a paper supporting the first passage.
The best I could find to support the first passage is an interview with Bret Weinstein where they mention that Peterson is indeed correct claiming that social hierarchy of lobsters in linked to serotonin levels. Interview with Bret Weinstein
A review paper claims that:
Is the marine environment less conducive to the establishment of dominance hierarchy structures, or does this just underline the lack of detailed behavioral information about most marine invertebrates?
Which suggests that not much is known about the relationship between serotonin levels in lobsters and the position in the social hierarchy.
Peterson basically argues that since the injection of serotonin leads to aggressive behavior in invertebrates, which is dominant trait in the animal kingdom this is proof that serotonin is indicated by the status in the social hierarchy. However It could just as well be that serotonin just leads to aggressive behavior in lobsters without being an indicator of the position in the hierarchy.
Are there any studies which specifically investigate whether the position of lobsters in a hierarchy is reflected in their serotonin levels?