際際滷

際際滷Share a Scribd company logo

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

Naoki Masuda
Naoki Masuda

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).

1 of 23
Download to read offline
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
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 colonys benefit Thorleif Schjelderup-Ebbe (1894-1976) - 鏝 鏝 鏝 鏝 鏝 - 鏝 鏝 鏝 鏝 - 鏝 鏝 鏝 - 鏝 鏝 - 鏝 - self peer Icon and picture from Freepik.com and Wikipedia
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)
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
nest marked workers aggressive behaviour (bite and jerk) = directed link Photos by H. Shimoji
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
(almost) directed acyclic graph (DAG) dominant subordinate
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
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
Quantifications of DAGs (link weight ignored) 1. Reversibility (Corominas-Murtra, Rodr鱈guez-Caso, Go単i, Sol辿, 2010) Information necessary to reversely travel to the most dominant nodes 2. Hierarchy (their 2011) 僚 [-1, 1] 僚 = 0 lack of hierarchy in either direction
Quantifications of DAGs (cntd) 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
Null model networks Randomised DAGs (Go単i, Corominas-Murtra, Sol辿, Rodr鱈guez-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 袖null(GRC) null(GRC)
鏝 Similar results for link-reversed dominance networks colony Reversibility (H 0)Reversibility (H 0)Reversibility (H 0) Hierarchy (0 僚 1)Hierarchy (0 僚 1)Hierarchy (0 僚 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
鏝 Similar results for link-reversed dominance networks *: p<0.05; **: p<0.01
Lets look at the degree attacked by 2 workers (in-degree = 2) attacks 3 workers (out-degree = 3) Photo by H. Shimoji
Only the out-degree is heterogeneously distributed (CV = 1.9-3.5)
Global network structure of dominance hierarchy of ant workersAntnet slides-slideshare
Global network structure of dominance hierarchy of ant workersAntnet slides-slideshare
Out-strength out-strength = 8 1 4 3 5 3 link weight = # observed aggressive behaviour Photo by H. Shimoji
The top ranker is often not the most frequent attackers. Out-strength vs workers rank
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.
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)
Discussion (cntd) 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

More Related Content

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

  • 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. 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 colonys benefit Thorleif Schjelderup-Ebbe (1894-1976) - 鏝 鏝 鏝 鏝 鏝 - 鏝 鏝 鏝 鏝 - 鏝 鏝 鏝 - 鏝 鏝 - 鏝 - self peer Icon and picture from Freepik.com and Wikipedia
  • 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. 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. nest marked workers aggressive behaviour (bite and jerk) = directed link Photos by H. Shimoji
  • 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. (almost) directed acyclic graph (DAG) dominant subordinate
  • 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. 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. Quantifications of DAGs (link weight ignored) 1. Reversibility (Corominas-Murtra, Rodr鱈guez-Caso, Go単i, Sol辿, 2010) Information necessary to reversely travel to the most dominant nodes 2. Hierarchy (their 2011) 僚 [-1, 1] 僚 = 0 lack of hierarchy in either direction
  • 11. Quantifications of DAGs (cntd) 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. Null model networks Randomised DAGs (Go単i, Corominas-Murtra, Sol辿, Rodr鱈guez-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 袖null(GRC) null(GRC)
  • 13. 鏝 Similar results for link-reversed dominance networks colony Reversibility (H 0)Reversibility (H 0)Reversibility (H 0) Hierarchy (0 僚 1)Hierarchy (0 僚 1)Hierarchy (0 僚 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. 鏝 Similar results for link-reversed dominance networks *: p<0.05; **: p<0.01
  • 15. Lets look at the degree attacked by 2 workers (in-degree = 2) attacks 3 workers (out-degree = 3) Photo by H. Shimoji
  • 16. Only the out-degree is heterogeneously distributed (CV = 1.9-3.5)
  • 19. Out-strength out-strength = 8 1 4 3 5 3 link weight = # observed aggressive behaviour Photo by H. Shimoji
  • 20. The top ranker is often not the most frequent attackers. Out-strength vs workers rank
  • 21. 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.
  • 22. 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)
  • 23. Discussion (cntd) 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