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Global network structure of dominance hierarchy of ant workersAntnet slides-slideshare

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Presentation slides for the following paper:

Hiroyuki Shimoji, Masato S. Abe, Kazuki Tsuji, Naoki Masuda.
Global network structure of dominance hierarchy of ant workers.
Journal of the Royal Society Interface, in press (2014).

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Global network structure of dominance hierarchy of ant workersAntnet slides-slideshare

  1. 1. Dominance hierarchy of worker ants as directed networks Hiroyuki Shimoji (Univ. Ryukyus, Japan & Univ. Tokyo, Japan) Masato S. Abe (Univ. Tokyo) Kazuki Tsuji (Univ. Ryukyus) Naoki Masuda (University of Bristol, UK) Ref: Shimoji, Abe, Tsuji & Masuda, J. R. Soc. Interface, in press (2014); arXiv:1407.4277; data available online
  2. 2. Dominance hierarchy • Pecking order of hens (Schjelderup-Ebbe, 1922) • Automise the access to food/mates/space/shelter • Reduce aggregation • Keep workers to work for the colony’s benefit Thorleif Schjelderup-Ebbe (1894-1976) - ✔︎ ✔︎ ✔︎ ✔︎ ✔︎ - ✔︎ ✔︎ ✔︎ ✔︎ - ✔︎ ✔︎ ✔︎ - ✔︎ ✔︎ - ✔︎ - self peer Icon and picture from Freepik.com and Wikipedia
  3. 3. Dominance hierarchy as network • Most studies have focused on • How close data are to “linear” hierarchy • How to rank individuals in a group • Small groups • Network analysis of dominance hierarchy has been surprisingly rare. • Some recent work as undirected networks • Triad census (Shizuka & McDonald, 2012)
  4. 4. Diacamma sp. • Monogynous • A colony contains at most one (functional, not morphological) queen. • 20-300 workers, i.e., “large” groups • Suitable for observing behaviour: • Large body size • Many previous studies
  5. 5. nest marked workers aggressive behaviour (bite and jerk) = directed link Photos by H. Shimoji
  6. 6. • 4 days of observation (5 h/day) colony # nodes avg deg # bidir links C1 20 2.9 0/29 C2 32 3.4 0/55 C3 48 5.6 0/134 C4 70 4.5 0/158 C5 56 4.8 2/133 C6 64 4.3 0/137 “large” network (almost) acyclic?sparse
  7. 7. (almost) directed acyclic graph (DAG) dominant subordinate
  8. 8. A B C D E F G A B C D E F G 6 1 4 6 8 5 5 5 2 1 2 2 1 1 15 1 11 1 4 2 DAG hierarchy is not trivial 1. In large groups, linear hierarchy is often violated. data from Appleby, Animal Behaviour, 1983 winner dominant dominant red deer stags A B C D E F G A B C D E F G ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ A F G E B D C A F G E B D C ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ subordinatesubordinateloser
  9. 9. DAG hierarchy is not trivial 2. There are various DAGs. • Variation in link density • Even for a fixed link density, various DAGs linear tournament arborescence
  10. 10. Quantifications of DAGs (link weight ignored) 1. Reversibility (Corominas-Murtra, Rodríguez-Caso, Goñi, Solé, 2010) • Information necessary to reversely travel to the most dominant nodes 2. Hierarchy (their 2011) ν ∈ [-1, 1] • ν = 0 ⟺ lack of hierarchy in either direction
  11. 11. Quantifications of DAGs (cnt’d) 3. Global reaching centrality (Mones, Vicsek, Vicsek, 2012): • Large GRC ⟺ directed paths starting from a small fraction of nodes reach a majority of nodes • Directed star: GRC = 1 • 0 ≤ GRC ≤ 1 4. Network motif (Milo et al. 2002) GRC = 1 N 1 NX i=1 [Cmax R CR(i)] , where Cmax R = max i CR(i) CR(i) : local reaching centrality of node i
  12. 12. Null model networks • Randomised DAGs (Goñi, Corominas-Murtra, Solé, Rodríguez-Caso, 2010) • In-degree and out-degree of each node are fixed. • Thinned linear tournament (= cascade model by J. E. Cohen & C. M. Newman, 1985) • Number of links matched • Does not conserve in/out- degree of each node • Then, calculate the Z score: e.g., p=0.6 Z = GRCobserved µnull(GRC) null(GRC)
  13. 13. ✔︎ Similar results for link-reversed dominance networks colony Reversibility (H ≥ 0)Reversibility (H ≥ 0)Reversibility (H ≥ 0) Hierarchy (0 ≤ ν ≤ 1)Hierarchy (0 ≤ ν ≤ 1)Hierarchy (0 ≤ ν ≤ 1) GRC (0 ≤ GRC ≤ 1)GRC (0 ≤ GRC ≤ 1)GRC (0 ≤ GRC ≤ 1) colony Value Thinned tournament Random DAG Value Thinned tournament Random DAG Value Thinned tournament Random DAG C1 0.28 -2.36* - 0.59 3.68** -0.33 0.94 4.45** 1.01 C2 1.41 1.86 1.76 0.14 1.05 -1.70 0.71 2.72** -2.11* C3 1.73 0.24 2.33* 0.31 3.32** 0.05 0.88 4.93** -1.40 C4 1.33 -0.36 -1.33 0.32 3.90** -1.08 0.96 6.60** 1.66 C5 2.37 4.98** 0.20 0.28 3.15** 0.74 0.86 4.82** -0.89 C6 2.02 4.09** 1.69 0.14 1.72 0.66 0.82 4.54** -0.64 *: p<0.05; **: p<0.01
  14. 14. ✔︎ Similar results for link-reversed dominance networks *: p<0.05; **: p<0.01
  15. 15. Let’s look at the degree attacked by 2 workers (in-degree = 2) attacks 3 workers (out-degree = 3) Photo by H. Shimoji
  16. 16. Only the out-degree is heterogeneously distributed (CV = 1.9-3.5)
  17. 17. Out-strength out-strength = 8 1 4 3 5 3 link weight = # observed aggressive behaviour Photo by H. Shimoji
  18. 18. The top ranker is often not the most frequent attackers. Out-strength vs worker’s rank
  19. 19. Summary of the observations • Empirical dominance networks are close to random DAGs. • Similar to citation networks (Karrer & Newman, PRL, PRE 2009) • Not close to the thinned linear tournament • Sparse • Out-degree: heterogeneous, in-degree: not so much • Most aggressive workers are near the top (but not necessarily the very top) of the hierarchy.
  20. 20. Discussion • How is the link density regulated? • Cost of attacking • Benefit of keeping hierarchy: workers work for the colony (so-called indirect fitness) • Why (evolutionarily) does the DAG-like dominance hierarchy form? • For high rankers, more chances to reproduce (direct fitness) • For low rankers in the bottom of hierarchy, why? • Why does the top ranker limit the number of direct subordinates? • Generative models? Ref: Shimoji, Abe, Tsuji & Masuda, J. R. Soc. Interface, in press (2014)
  21. 21. Discussion (cnt’d) • Linearity is not detected by previous methods due to sparseness. colony h’ P(h’) ’) ttri P(ttri) C1 0.21 0.18 1 0.39 C2 0.12 0.23 1 0.23 C3 0.13 0.0003 1 0.001 C4 0.08 0.0005 1 0.029 C5 0.07 0.09 0.96 0.024 C6 0.07 0.05 1 0.053 h = 12 N3 N NX i=1 ✓ dout i N 1 2 ◆2 ttri =4 ✓ Ntransitive Ntransitive + Ncycle 0.75 ◆ (Landau, 1951; Appleby 1983; De Vries, 1995) (Shizuka & McDonald, 2012) cycle transitive

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