Foraging coefficient

Figure 10.4. Numerical example of the joint effect of foraging (x-axis) and antipredation benefits (y-axis) favoring solitary versus social foraging. The panels represent situations in which the recruiter is assumed to have complete (D = 0, upper left panel) orvarying degrees of incomplete (D = 0.04, 0.1, and 0.2) control over the division of resources. If the recruiter has complete control over the division of resources, all groups are transactional (i.e., the recruiter provides a joining incentive). Under incomplete control (e.g., D = 0.2, lower right panel), as the benefits of group foraging increase, groups switch from being transactional to nontransactional (i.e., the recruiter provides no joining incentive). If the benefits of group foraging are sufficiently high, the recruiter and joiners may be in conflict over group size (i.e., group size may exceed the optimum from the recruiter's perspective). (After Hamilton 2000.)

likelihood of conflict. In nontransactional groups, group size is likely to be stable only ifjoiners accrue no antipredation benefits. Ifjoiners receive foraging benefits only, group size is likely to remain small (close to G*) and under the control of the recruiter. However, if joiners accrue both antipredation and foraging advantages, group size is likely to be unstable. Predicted group size may increase to the maximum stable group size G.

A compelling question remains: if models tell us that group size will equilibrate around some stable size, then why are observed group sizes so variable? A recent study used a dynamic model to address this question. Specifically, Martinez and Marschall (1999) asked why juvenile groups ofthe coral reef fish Dascyllus albisella vary in size (range: 1—15 individuals). They uncovered an explanation not only for why observed group size varies, but also for why it may often fall below the intake-maximizing group size G*. Consider the natural history of D. albisella. Following a pelagic larval stage, these fish return to a reef, where they settle into juvenile groups. Martinez and Marschall modeled the joining decision as a trade-off between body growth (faster in smaller groups) and survival (better in larger groups), assuming that individuals reaching maturity by a specified date joined the adult population. When larvae encounter a group into which they may potentially settle, they must decide whether to join or to continue searching. By assumption, a larva settles only if the fitness value of doing so (i.e., the product of size-specific fecundity and probability of recruitment) exceeds the fitness value of further searching.

Rather than groups of a set size, Martinez and Marschall found that a range of acceptable group sizes arose from the fitness-maximizing choices of individuals. Their analysis suggests that, on any given day, fitness is maximized by settling in any encountered group that falls within the acceptable range. The policy for a larva settling early in the season is to settle in large groups (G* = 9), which have high survival rates. By contrast, a small larva searching late in the season should settle as a solitary or join a very small group; otherwise, it will not grow fast enough to reach maturity. This dynamic joining policy creates persistent variation in group size, whereas conventional theory predicts that group size will equilibrate around a stable size.

The combination of this dynamic joining model with Ian Hamilton's recruiter-joiner model would allow new questions: Should current members provide a joining incentive to recruit new members? In the case of the coral reef fish D. albisella, would the size of this incentive depend on date, the recruit's body size, or current group size? Would increased foraging skew in large groups reduce the upper limit of acceptable group size earlier in the season? Would many more individuals choose to settle as singletons? Would the theory predict highly variable final group sizes? Under what conditions is group size stable? We expect Ian Hamilton's recruiter-joiner approach to play a key role in the development of group size theory, particularly in systems in which resource owners benefit from the presence of other individuals.

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