1. Two’s Company, Three’s a Crowd Ivan Chase, Sociology and Ecology & Evolution, SUNY Stony Brook Craig Tovey, Ind. & Systems Eng., Georgia Tech

2. Definition of “Analysis” Separation of anything into constituent parts or elements; also, an examination of anything to distinguish its component parts, separately, or in their relation to the whole. Webster’s Collegiate Dictionary, 5th Edition

3. The subject of our analysis: Dominance Hierarchies

4. Birds do it… (Schjelderup-Ebbe 1913, 1922)

5. Bumblebees do it (honey bees don’t); Fish do it

6. We do it (Strayer&Strayer 1976, Savin-Williams 1980, Weisfeld 1980, Bakeman&Brownlee 1982)

7. HOW? “Prior attribute” explanation not adequate Round robin tournaments have cycles ( Chase,Tovey, Manfredonia 2002) Mon beats SF 7-0 SF beats St.L.5-1 but St.L beat Mon 5-1 2003 Season 19 games among Mon,SF, St. L

8. A Cycle Based on Two Attributes RPRH RPLH LPRH LPLH

9. Winner and Loser Effects A Dominates B if A acts aggressively towards B but not vice-versa. Fish: nips, chases, displacement Birds: pecks, bites, jumps, displacement Primates: vocalization, all of the above LOSER EFFECT: if A beats B and then B meets C, B is very likely to lose to C. WINNER EFFECT: not as strong, long lasting, or even verified.

10. Winner/Loser theory of acyclicity Consider a group of three: A,B,C WLOG A beats B initially If the next meeting is B vs. C, B loses w.h.p.; If the next meeting is A vs. C, A wins w.h.p.  Either way, some individual has 2 wins or 2 losses hence the hierarchy is acyclic, w.h.p.

11. A Model of Hierarchy Formation Let P L =.9 and P W =.8 Let C be equally likely to meet B or A first Prob (cycle) ¼ (.5)(.1)(.1) + (.5)(.2)(.1) =.015 For groups of four or more, the predicted probability of a cycle is generally higher than the observed frequency, but the model accounts for a large portion of acyclicity. (Beacham 2003 ).

12. Experimental Test of Model BCD A

13. B CD A

14. B C D A Expected: B often at bottom of hierarchy; A often at top of hierarchy.

15. Experimental Test of Model Findings: B more likely than random to be low in hierarchy; A more likely than random to be high in hierarchy. HOWEVER: probabilities not as high as predicted by model. WORSE: B sometimes dominates A!

16. Experimental Tests of Our Mode of Analysis 1.Stability of Dominance Relationships 2.Repeatability of Dominance Relationships 3.Loser Effect 4.Winner Effect

17. STABILITY  The defining property of a dominance relationship  In pairs, once A delivers several (6-8) consecutive aggressive actions towards B, we rarely observe B being aggressive towards A ?Does this hold true in “crowds” of 3 or more?  Experiment: A establishes dominance over B; control: keep in tank; exp: add fish to tank. ?: Compare Stability

18. Stability of Relationships PairsTriads Stable100.0%78.9% Not Stable0.0%21.1% Fisher exact test, <.01

19. Stability of Relationships PairsTetrads Stable100.0%65.2% Not Stable0.0%34.8% Fisher exact test, <.001

20. REPLICABILITY Of two individuals, which will be dominant? We hypothesized that the identity of the dominant would be more random in crowds.  Experiment: Pair (group of 4) forms dominance relationships Separate for two weeks to forget Put pair (group) back together

21. Replication of Relationships Pair/Re-PairGroup/Re-Group Replicates93.5%75.8% Doesn’t Replicate6.5%24.2% Fisher exact test,.02 (all).02 (one per group)

22. LOSER AND WINNER EFFECTS Loser effect most well established dynamical property of dominance Crucial to many models of acyclic hierarchy formation Always established by pairwise experiments Does it hold up in groups?  Experiment: Control: classic winnner/loser experiment Experimental: after A dominates B, A(?) B(?) meets C with the other present Design issue: can not control meetings

23. Loser Effect PairsTriads Loser Loses87.5%61% Loser Wins12.5%39% Fisher exact test,.047

24. Loser Effect PairsQuads Loser Loses87.5%59% Loser Wins12.5%41% Fisher exact test,.04

25. Winner Effect PairsTriads Winner Wins62.5%61% Winner Loses37.5%39% Fisher exact test,.6

26. Winner Effect PairsQuads Winner Wins62.5%65% Winner Loses37.5%35% Fisher exact test,.7

27. Summary of Results Significant differences between dominance behavior of isolated pairs and dominance behavior of socially embedded pairs in three major aspects. No winner effect found in either context. Each of the three properties operating in isolated pairs was absent or significantly reduced in social contexts. Little difference between crowds of 3 and crowds of 4.

28. Implications  Isolated pairs are not the proper unit of analysis for understanding dominance in groups [Holekamp & Smale 91, Chapais 95]  Experimental design issue: control versus applicability  Multi-person games may be needed rather then 2- person games in evolutionary studies  Hierarchy formation not just an agglomeration of behaviors between pairs

29. Incorporating Social Context Observation, Eavesdropping Cognition of Relationships (Cheney & Seyfarth 90), transitive inference in monkeys, pigeons, rats (Fersen et al. 91, Roberts et al. 94, Wynne 97) Patterns of interactions among groups (Chase 82, Chapais 95)

30. Final Thoughts How do we analyze a system if its components have different properties in situ than in isolation? Understanding dominance hierarchies may require different observational data, not just different theories.