Mortality Risk of Spatial Positions in Animal Groups: the Danger of Being in the Front

Abstract

We modified Hamilton's (1971) selfish herd model by introducing directional movement to the prey groups and the predators. The consequences of this modification with regards to differential predation risks are compared to Hamilton's original model (using stationary prey groups) and tested against empirical data. In model 1, we replicated Hamilton's original predator-prey system. In models 2 and 3, prey groups were mobile and predators were mobile (model 2) or stationary (model 3). Our results indicate that additional to the positive risk gradient from centre to periphery predicted by Hamilton's model for stationary groups, there might be another positive risk gradient from the rear to the front part in moving groups. Furthermore, models 2 and 3 suggest that moving groups should generally exhibit an elongated shape (longer than wide along the axis of locomotion) if risk minimisation is the only factor concerned. Also smaller inter-individual distances are predicted for front individuals than individuals elsewhere in the group. Empirical data based on the three-dimensional structure of fish shoals (using roach, Rutilus rutilus) were consistent with the above two predictions. A second experiment which involved lake chub, Semotilus atromaculatus, as prey and rock bass, Ambloplites rupestris, as predators, provided direct support for the hypothesis that individuals in front positions of groups incurred a significantly higher predation risk than fish in rear positions. Finally, we discuss the differential risks of different group positions in the context of potential foraging gains which provides the basis for a dynamic model of position preferences in group-living animals.

Spatio-temporal vigilance architecture of an Australian flying-fox colony

“…This distance was then divided by three, and the individual was, by means of its exact position, assigned to a category accordingly. Bumann et al (1997; in an extension of Hamilton 1971) predicted an elevated predation risk only for individuals on the very edge of a group, so because our study colony covered a large area, we adjusted the classic categories of positions (peripheral vs. central only) by inserting an intermediate category, and we assigned all individuals in the inner half of the peripheral category to the intermediate category to highlight a potential edge effect. We also recorded the height above ground at which individuals hung in the vegetation (in 4 m increment categories, 0-4, 5-8 m etc.)…”

“…Furthermore, flying-foxes offer an opportunity to test multiple predictions made in the context of vigilance theory. The "edge effect" (Hamilton 1971;Colagross and Cockburn 1993;Bumann et al 1997) predicts individuals at the periphery of groups to be more vigilant than more centrally located animals. According to the "group size effect", individual vigilance is also expected to decline as group size increases (Elgar 1989;Roberts 1996;Blumstein et al 2001; for exceptions in primates see Treves 2000).…”

The effect of progressive hypoxia on school structure and dynamics in Atlantic herringClupea harengus

“…Previous work shows that the leading fishes of a school may be exposed to a higher predation risk (Bumann et al 1997) but will have first access to any resources encountered by the group (Krause et al 1992). Conversely, particularly in large schools in field conditions, fishes in the rear may experience reduced oxygenation due to oxygen consumption of the fishes ahead of them ( (2002) 1994).…”

Leadership, consensus decision making and collective behaviour in humans

“…Evidence of leadership behaviour has been found in a number of vertebrate species across a range of taxa, including ungulates (Leicester sheep, Ovis aries; Squires & Daws 1975; sable antelope, Hippotragus niger: Stine et al 1982; Charolais heifers, Bos taurus; Dumont et al 2005; zebras, Equus burchellii: Fischhoff et al 2007), primates (gorillas, Gorilla gorilla beringei : Fossey 1972; chimpanzees Pan troglodytes : Wilson 1980), canids (bush dogs Speothos venaticus : Macdonald 1996; wolves Canis lupus: Peterson et al 2002), birds (bar headed geese Anser indicus: Lamprecht 1992; zebra finches Taeniopygia guttata: Beauchamp 2000; homing pigeons Columba livia domestica: Biro et al 2006) and fishes (roach Rutilus rutilus: Bumann et al 1997; golden shiners Notemigonus crysoleucas : Reebs 2000: Reebs , 2001. In some species, it has been shown that groups tend to be led by dominant individuals (gorillas G. g. beringei : Fossey 1972;Leicester sheep, Squires & Daws 1975; chimpanzees P. troglodytes : Wilson 1980; sable antelope H. niger: Stine et al 1982;bush dogs S. venaticus: Macdonald 1996; wolves C. lupus: Peterson et al 2002).…”

“…Krause et al (1998) found that front positions tended to be occupied by larger fish and food-deprived fish. Bumann et al (1997) showed that individuals in front positions in shoals of roach R. rutilus led the group, finding that just a single individual in a front position could have a strong influence on an entire shoal of 16 fish. Couzin et al (2005) used a simple individual-based model to look at the mechanisms of leadership and decision making in moving animal groups, in the absence of complex signalling and in situations where it is not possible for individuals to establish which other individuals, if any, have information.…”