Social network analysis and valid Markov chain Monte Carlo tests of null models

Analyses of animal social networks derived from group-based associations often rely on randomisation methods developed in ecology (Manly, Ecology 76:1109–1115, 1995) and made available to the animal behaviour community through implementation of a pair-wise swapping algorithm by Bejder et al. (Anim Behav 56:719–725, 1998). We report a correctable flaw in this method and point the reader to a wider literature on the subject of null models in the ecology literature. We illustrate the importance of correcting the method using a toy network and use it to make a preliminary analysis of a network of associations among eagle rays.

[1]  J. Krause,et al.  Exploring Animal Social Networks , 2008 .

[2]  J. Krause,et al.  Social network theory in the behavioural sciences: potential applications , 2007, Behavioral Ecology and Sociobiology.

[3]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[4]  H. Ryser Combinatorial Properties of Matrices of Zeros and Ones , 1957, Canadian Journal of Mathematics.

[5]  T. Pitcher Behaviour of Teleost Fishes , 1986 .

[6]  D. Lusseau,et al.  Animal social networks: an introduction , 2009, Behavioral Ecology and Sociobiology.

[7]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[8]  Bryan F. J. Manly,et al.  A Note on the Analysis of Species Co‐Occurrences , 1995 .

[9]  Hal Whitehead,et al.  Techniques for Analyzing Vertebrate Social Structure Using Identified Individuals: Review and Recommendations , 1999 .

[10]  Barnes Discussion of the Paper , 1961, Public health papers and reports.

[11]  J. Besag,et al.  Generalized Monte Carlo significance tests , 1989 .

[12]  M. Dwass Modified Randomization Tests for Nonparametric Hypotheses , 1957 .

[13]  B. Manly,et al.  A NOTE ON NULL MODELS: JUSTIFYING THE METHODOLOGY , 2002 .

[14]  B. Nordstrom FINITE MARKOV CHAINS , 2005 .

[15]  K. N. Laland,et al.  Social structure and co-operative interactions in a wild population of guppies (Poecilia reticulata) , 2006, Behavioral Ecology and Sociobiology.

[16]  V. Lehsten,et al.  Null models for species co-occurrence patterns: assessing bias and minimum iteration number for the sequential swap , 2006 .

[17]  T. Pitcher Functions of Shoaling Behaviour in Teleosts , 1986 .

[18]  Sean F. Hanser,et al.  Social network theory: new insights and issues for behavioral ecologists , 2009, Behavioral Ecology and Sociobiology.

[19]  Nicholas J. Gotelli,et al.  SWAP ALGORITHMS IN NULL MODEL ANALYSIS , 2003 .

[20]  Karl-Heinz Jockel,et al.  Finite Sample Properties and Asymptotic Efficiency of Monte Carlo Tests , 1986 .

[21]  L. Bejder,et al.  A method for testing association patterns of social animals , 1998, Animal Behaviour.

[22]  János Podani,et al.  RANDOMIZATION OF PRESENCE–ABSENCE MATRICES: COMMENTS AND NEW ALGORITHMS , 2004 .

[23]  Richard James,et al.  Social structure in a colonial mammal: unravelling hidden structural layers and their foundations by network analysis , 2007, Animal Behaviour.

[24]  B. Manly Randomization, Bootstrap and Monte Carlo Methods in Biology , 2018 .