Table 1.

Examples from vertebrates that form multi-level societies and engage in tasks with individuals in different social units. Social units are termed as is in the original studies.

		definition of social units and tasks performed within...
species	number of social levels	...social level 1:	...social level 2:	...social level 3:	... social level 4:
hunter–gatherer societies [17,27] (Homo sapiens)	3 or 4	household: male–female complementarity and sex division of labour.	cluster: social units formed by extended family. Assistance from kin and intergenerational division of labour.	camp: cooperation with both related and unrelated individuals. Selection of foraging partners.	between-camp visits: information sharing and cultural innovations.
hamadryas baboons [28,29] (Papio hamadryas)	4	OMU: one male unit which hosts multiple females. Breeding unit.	clan: two to three OMUs led by kin males, observable during resource scarcity. Foraging as OMUs or clans.	band: multiple clans together, like troops in olive baboons. Communal sleeping, movement coordination, some affiliative interactions.	troop: two bands sharing sleeping sites. Predator detection and defence, but no other group tasks.
geladas [30] (Theropithecus gelada)	4	OMU: one male unit which hosts multiple females and potentially also a few follower males. Breeding unit. AMG: all-young-male units are an alternative first-level structure.	team: aggregation of two or more first-level units that associate with each other at least 90% of the time. Tasks not specified.	band: collection of first-level units that spend between 50 and 90% of their time together. Communal sleeping and foraging, not more specific tasks. Like band in hamadryas baboons.	community: the set of units with overlapping home ranges that are found together < 50% of the time. Tasks not specified.
guinea baboons [31–33] (Papio papio)	3	reproductive unit: one male, one to several females, young and many secondary males.	party: three to five reproductive units. Foraging, socializing, collective movement.	gang: several parties together. Predator detection and defence in communal sleeping sites.
golden snub-nosed monkeys [34,35] (Rhinopithecus roxellana)	3	OMU: one male unit which hosts multiple females. Breeding unit.	band: social units formed by different OMUs. Males within bands likely defend females from bachelor males.	troop: several bands together. Females disperse between troops to breed.
African elephants [36,37] (Loxodonta africana)	up to 6	breeding females with calves are listed as the first level. We kept the paper’s definition for the first level here, but we would not characterize mothers with calves as a distinct social level.	family: small size compared to third and fourth levels. Not affected by seasonality. Raising offspring and coordinating movement.	bond/kinship social units: affected by seasonality. Predator defence, territoriality, knowledge sharing and rearing of young.	clans: broader compared to third but functional differences have not been identified.
Indo-Pacific bottlenose dolphins of Shark Bay [24–26] (Tursiops aduncus)	3	first-order alliance: duos or trios of males consorting females in a cooperative manner.	second-order alliance: pool for forming first-order alliances. Socializing and supporting second-order allies to defend females. Stable membership.	third-order alliance: individuals from two or more second-order alliances come together and fight against rival males from neighbouring third-order alliances.
pacific sperm whales [38,39] (Physeter macrocephalus)	3 to multiple	permanent social units: contain around 11 females and immatures from unrelated matrilines. Caring for offspring.	temporary intermediate social units of multiple first-level units of the same cultural clan: defence from killer whales.	clans: can contain up to 20 000 individuals. They have culturally determined vocalizations and distinct movement patterns.	there is a big difference in size from the second- to the third-level units and the literature suggests that intermediate levels might be missing.
superb fairy-wren [10,11,40] (Malurus cyaneus)	3	cooperatively breeding unit: individuals that assist a breeding pair to raise a brood of young.	supergroup: two neighbouring breeding units that merge stably. Tasks not specified.	community: emerges from repeated interactions between three to four breeding units and supergroups. Likely cooperative defence against predators, and communal defence against competitors.
bell miner [41,42] (Manorina melanophrys)	3	cooperatively breeding unit: individuals that assist a breeding pair to raise a brood of young.	coterie or clan: occupying a discrete area within the colony. May contain one or more breeding pairs and nonbreeders. Members associate preferentially with each other, and helpers may assist more than a single pair within a coterie.	colony: a geographically discrete aggregation of between 20 and 200 individuals that together inhabit and communally defend an area against avian intruders and predators.
vulturine guineafowl [15,43–46] (Acryllium vulturinum)	3	cooperatively breeding units and stable clusters of males: breeding pairs can be stable from one breeding season to the next and raise young cooperatively with specific non-parents. Clusters of males (potentially highly related) remain stable across years.	groups: can contain from 13 to 65 individuals that forage, decide collectively and move as single entities.	stable between-group associations: driven by social preferences as well as by resource abundance and distribution. They share communal roosts and information. They also form supergroups and travel together to rarely visited areas.
cooperatively breeding cichlid fish [47–49] (Neolamprologus pulcher)	3	cooperatively breeding group: individuals assist a breeding pair to raise a brood of young.	colony: neighbouring breeding groups jointly defend against predators.	aggregation: feeding assemblies of members from different breeding groups exchanging social information by sporadic interactions.