Contribution
A short review, with some new counts, of one captive group of pigtailed macaques at Yerkes (1998). It sets out three stacked networks (fight outcomes, subordination signals, and the power distribution computed from the signals) and argues that each higher one changes more slowly than the one below it, predicts the system better, and is what the animals use. It names these predictive coarse-grained variables “slow variables” and proposes that building them is the first step towards a new level of organization.
Key insight
A higher level appears when components start conditioning their behaviour on a coarse-grained summary of their own interaction history, and the summary is useful because it changes slowly. A fight outcome is noisy; a subordination signal integrates many fights and flips only after several reversals; power integrates many signals. The slow variable reduces uncertainty, and the residual fast fighting keeps it revisable, so the two timescales trade predictability against lock-in.
Assumptions
- One captive group: 84 animals, 48 socially mature ones analysed, 156 hours of all-occurrence sampling over 20 weeks, June to October 1998, with “a 4 month period during which the group was stable”.
- The peaceful silent bared-teeth display is a subordination signal that communicates a contract to yield, as argued in Flack & de Waal (2007).
- Power is operationalized as signals received times number of signallers (Figure 1 caption, §6c), a simplification of the entropy-based measure of Flack & Krakauer (2006).
- Stationarity of the group over the study period, which is how the period was chosen (“no reversals in status-signalling interactions resulting in a change to an individual’s power score”).
Key results
- Fight network. 761 of 2256 ordered dyads fought; directional consistency 90.16%; outcome direction changed 292 times; 0.384 changes per dyad (s.d. 0.9285), 0.003 per dyad per hour.
- Signal network. 704 dyads exchanged the peaceful signal; direction reversed twice in the four months; 0.003 changes per dyad (s.d. 0.053), 0.00002 per dyad per hour; directional consistency 99.7% (peaceful), 96.6% (agonistic).
- The ratio. “Edges in the signalling network change approximately 165 times (roughly two orders of magnitude) more slowly than edges in the aggression network.”
- Power. The distribution is not significantly different from log-normal (Lilliefors), heavy-tailed; individuals in the tail police at negligible cost, and a knockout of policing (from Flack et al. 2006, not this paper) destabilized the group’s networks.
- Power’s timescale is not measured. “We do not have enough data in the present case study to estimate the precise time-scales on which properties of the power distribution change.”
- Use by the animals. “The data suggest that individuals can perceive and use these representations”; individuals “appear to reference the signal exchange, rather than fight outcomes”; for relative power, “We are presently exploring the heuristics the animals could be using”.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Subordination signals change direction far more rarely than fight outcomes | strong | counts in §3a–b, one group, four months |
| C2 | A single signal predicts future fight outcomes better than a single fight outcome | weak | asserted from C1; no prediction test is reported here |
| C3 | Individuals use the signal network, and their own and others’ power, to choose strategies | weak | inferred from earlier studies [21,24,32]; the paper’s own wording is “suggest” and “appear” |
| C4 | Power changes more slowly than any single contract | moderate | an argument from aggregation (§3c); not measured |
| C5 | Multiple timescales balance predictability against adaptability and found new levels | weak | interpretive (§§4–5) |
Concepts
- Slow variable: a coarse-grained, predictive variable that changes slowly because it integrates over fast microscopic dynamics; it reduces uncertainty only when components can detect it.
- Subordination contract: the peaceful silent bared-teeth display, by which the signaller agrees for a time to the subordinate role.
- Power: “the degree of consensus among group members that an individual can use force successfully”.
- Social niche construction: collective construction, by edge-building, of aggregate social properties that feed back on the constructors.
Connections
It builds on Flack & Krakauer (2006) on encoding power in signalling networks, Flack, de Waal & Krakauer (2005) on policing cost, and Flack et al. (2006) on the policing knockout, none of which the record holds. The slow-variable notion is Flack & Krakauer (2011, Chaos). The record’s nearly decomposable systems (LIT-905) give a structural reason for slow aggregates; this paper gives an informational one: slowness is useful to the members, not only a consequence of weak coupling.
Bearing on the record
- CLAIM-327 takes its member-accessible slow variable from this paper, as A9 read it: “The animals themselves appear to use information encoded in these more stable relationships”. The paper’s own words match A9’s “appear”: that the animals read and condition on the variable is what “the data suggest”, argued from earlier studies, and for relative power not yet worked out. Stage 1 of the claim (statistical regularity) is shown here for the signal network. Stage 2 (member accessibility) is asserted, not shown. Stage 3 (regeneration) is the paper’s §4 argument that fighting lowers after signals and so consolidates the relation; no measurement supports it here.
- CLAIM-331 (slowness a mark, not a definition, of a level). The paper supports the mark and adds a condition the claim does not state: a slow variable founds a level only when the components can detect and use it (§5a). It also states the converse limit, that a slow variable must not change too slowly or it stops tracking fighting ability.
- No instruction for machine-learning practice; nothing for the anthology.
Limitations
- One group, one season, captive. No replication, no second group.
- The 165× ratio does not follow from the counts given. Per dyad, 0.384 / 0.003 ≈ 128; from the raw counts, (292/761) / (2/704) ≈ 135; per hour, 0.003 / 0.00002 = 150. Each is “roughly two orders of magnitude”, but none is 165, and the paper does not show its computation.
- Inconsistent descriptive figures. “The mean number of agonistic interactions per individual … was 2.11 (s.d. = 0.713)” cannot be a count per individual over the study: 761 dyads that fought at least once give each of 48 individuals at least 31 participations on average. It is probably a rate, unstated. “The maximum number of outcome changes observed per dyad was 11 and the minimum was 1” must refer only to dyads that changed, since the mean over all is 0.384.
- Dyad counting. “(48 × 48)–48 or 2256” counts ordered pairs; the text calls them dyads.
- The stability criterion is circular for C1. The study period was chosen as one with no signal reversals that changed a power score, so the low reversal rate of signals is partly a selection effect.
- Use is not tested here. No analysis in this paper conditions behaviour on the signal network or on power.
Open questions
- Do the animals’ choices depend on the slow variable once the fast one is controlled for? A test that conditions strategy use on power with recent fight outcomes held fixed would settle C3.
- What is the timescale of the power distribution itself, and how does it depend on the algorithm that computes power?