Density distribution and size sorting in fish schools: an individual-based model

In fish schools the density varies per location and often individuals are sorted according to familiarity and/or body size. High density is considered advantageous for protection against predators and this sorting is believed to be advantageous not only to avoid predators but also for finding food. In this paper, we list a number of mechanisms and we study, with the help of an individual-based model of schooling agents, which spatial patterns may result from them. In our model, schooling is regulated by the following rules: avoiding those that are close by, aligning to those at intermediate distances, and moving towards others further off. Regarding kinship/familiarity, we study patterns that come about when agents actively choose to be close to related agents (i.e., 'active sorting'). Regarding body size, we study what happens when agents merely differ in size but behave according to the usual schooling rules ('size difference model'), when agents choose to be close to those of similar size, and when small agents avoid larger ones ('risk avoidance'). Several spatial configurations result: during 'active sorting' familiar agents group together anywhere in the shoal, but agents of different size group concentrically, whereby the small agents occupy the center and the large ones the periphery ('size difference model' and 'active sorting'). If small agents avoid the risk of being close to large ones, however, small agents end up at the periphery and large ones occupy the center ('risk avoidance'). Spatial configurations are also influenced by the composition of the group, namely the percentage of agents of each type. Furthermore, schools are usually oblong and their density is always greatest near the front. We explain the way in which these patterns emerge and indicate how results of our model may guide the study of spatial patterns in real animals. Copyright 2005.

[1]  On the Manner of Swimming of Sardines in a Confined Space , 1934 .

[2]  C. Breder Equations Descriptive of Fish Schools and Other Animal Aggregations , 1954 .

[3]  V. M. Brawn Reproductive Behaviour of the Cod (Gad Us Callarias L.) , 1961 .

[4]  G. Thinés,et al.  The effect of submissive experiences on dominance and aggressive behaviour of Xiphophorus (Pisces, Poeciliidae). , 2010, Zeitschrift fur Tierpsychologie.

[5]  T. Schelling Models of Segregation , 1969 .

[6]  J. Hunter,et al.  Some Aspects of the Organization of Fish Schools , 1970 .

[7]  Thomas C. Schelling,et al.  Dynamic models of segregation , 1971 .

[8]  R. Trivers The Evolution of Reciprocal Altruism , 1971, The Quarterly Review of Biology.

[9]  Arthur A. Myrberg,et al.  Ethology of the Bicolor Damselfish, Eupomacentrus partitus (Pisces: Pomacentridae): A Comparative Analysis of Laboratory and Field Behaviour , 1972 .

[10]  T. Pitcher Some ecological consequences of fish school volumes , 1980 .

[11]  A Sih,et al.  Optimal behavior: can foragers balance two conflicting demands? , 1980, Science.

[12]  I. Aoki A simulation study on the schooling mechanism in fish. , 1982 .

[13]  V. Braitenberg Vehicles, Experiments in Synthetic Psychology , 1984 .

[14]  A. Peter Klimley,et al.  Schooling in Sphyrna lewini, a Species with Low Risk of Predation: a Non‐egalitarian State , 1985 .

[15]  Anne E. Magurran,et al.  Schooling mackerel and herring choose neighbours of similar size , 1985 .

[16]  Anne E. Magurran,et al.  Size-segregative behaviour in minnow shoals , 1986 .

[17]  H. Bleckmann,et al.  Role of lateral line in fish behaviour , 1986 .

[18]  J. Terborgh,et al.  Oddity and the ‘confusion effect’ in predation , 1986, Animal Behaviour.

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

[20]  C. Theodorakis Size segregation and the effects of oddity on predation risk in minnow schools , 1989, Animal Behaviour.

[21]  K. Warburton,et al.  Tendency-distance models of social cohesion in animal groups. , 1991, Journal of Theoretical Biology.

[22]  Further evidence for size‐assortative schooling in sticklebacks , 1992 .

[23]  K. Lindström,et al.  Size matters when three-spined sticklebacks go to school , 1992, Animal Behaviour.

[24]  J. Krause The effect of 'Schreckstoff' on the shoaling behaviour of the minnow: a test of Hamilton's selfish herd theory , 1993, Animal Behaviour.

[25]  Andreas Huth,et al.  THE SIMULATION OF FISH SCHOOLS IN COMPARISON WITH EXPERIMENTAL DATA , 1994 .

[26]  Hiro-Sato Niwa Self-organizing Dynamic Model of Fish Schooling , 1994 .

[27]  Jens Krause DIFFERENTIAL FITNESS RETURNS IN RELATION TO SPATIAL POSITION IN GROUPS , 1994, Biological reviews of the Cambridge Philosophical Society.

[28]  E. Ranta,et al.  A theoretical exploration of antipredatory and foraging factors promoting phenotype-assorted fish schools , 1994 .

[29]  Jens Krause,et al.  The mechanism of aggregation behaviour in fish shoals: individuals minimize approach time to neighbours , 1994, Animal Behaviour.

[30]  Hauke Reuter,et al.  SELFORGANIZATION OF FISH SCHOOLS : AN OBJECT-ORIENTED MODEL , 1994 .

[31]  D. Chivers,et al.  Familiarity and shoal cohesion in fathead minnows (Pimephales promelas): implications for antipredator behaviour , 1995 .

[32]  N. Franks,et al.  Spatial relationships within nests of the ant Leptothorax unifasciatus (Latr.) and their implications for the division of labour , 1995, Animal Behaviour.

[33]  W. L. Romey Individual differences make a difference in the trajectories of simulated schools of fish , 1996 .

[34]  J. Godin,et al.  Phenotypic Variability within and between Fish Shoals , 1996 .

[35]  Charlotte K. Hemelrijk,et al.  Great Ape Societies: Reciprocation in apes: from complex cognition to self-structuring , 1996 .

[36]  Animal Groups in Three Dimensions: Inside or outside? Testing evolutionary predictions of positional effects , 1997 .

[37]  Jens Krause,et al.  Mortality risk of spatial positions in animal groups: The danger of being in the front , 1997 .

[38]  J. Sivinski,et al.  The Evolution of Mating Systems in Insects and Arachnids: Mate choice and species isolation in swarming insects , 1997 .

[39]  Charlotte K. Hemelrijk,et al.  Spatial Centrality of Dominants Without Positional Preference , 1998 .

[40]  M. Ebbert The Evolution of Mating Systems in Insects and Arachnids , 1998 .

[41]  A. Magurran,et al.  Schooling decisions in guppies (Poecilia reticulata) are based on familiarity rather than kin recognition by phenotype matching , 1999, Behavioral Ecology and Sociobiology.

[42]  Rolf Pfeifer,et al.  Understanding intelligence , 2020, Inequality by Design.

[43]  G. Ruxton,et al.  The importance of stable schooling: do familiar sticklebacks stick together? , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[44]  Charlotte K. Hemelrijk,et al.  Towards the integration of social dominance and spatial structure , 2000, Animal Behaviour.

[45]  G D Ruxton,et al.  Fish shoal composition: mechanisms and constraints , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[46]  J. Godin,et al.  The social organization of free‐ranging fish shoals , 2000 .

[47]  E. Forsgren,et al.  Shoaling behaviour of the two-spotted goby , 2000 .

[48]  J. Krause,et al.  Body length assortative shoaling in the European minnow, Phoxinus phoxinus , 2001, Animal Behaviour.

[49]  Neha Bhooshan,et al.  The Simulation of the Movement of Fish Schools , 2001 .

[50]  I. Couzin,et al.  Collective memory and spatial sorting in animal groups. , 2002, Journal of theoretical biology.

[51]  K. Ruckstuhl,et al.  Sexual segregation in ungulates: a comparative test of three hypotheses , 2002, Biological reviews of the Cambridge Philosophical Society.

[52]  C. Hemelrijk Understanding Social Behaviour with the Help of Complexity Science (Invited Article) , 2002 .

[53]  I. Couzin,et al.  Self-Organization and Collective Behavior in Vertebrates , 2003 .

[54]  Charlotte K. Hemelrijk,et al.  Artificial Fish Schools: Collective Effects of School Size, Body Size, and Body Form , 2003, Artificial Life.

[55]  T. Pitcher,et al.  The sensory basis of fish schools: Relative roles of lateral line and vision , 1980, Journal of comparative physiology.

[56]  Jens Krause,et al.  The relationship between foraging and shoal position in a mixed shoal of roach (Rutilus rutilus) and chub (Leuciscus cephalus): a field study , 1993, Oecologia.

[57]  J. Deneubourg,et al.  The blind leading the blind: Modeling chemically mediated army ant raid patterns , 1989, Journal of Insect Behavior.