Recent Advances in the Theory of Group Membership

Recent theoretical studies have provided insights into the flexibility of group membership decisions. One such study used optimal skew theory to predict

Figure 10.3. Relationship between pack size and average daily per capita net rate of intake assuming either negligible or minor scavenging pressure by ravens (see also fig. 6 in Vucetich et al. 2004). To assess how raven scavenging might affect the predicted relationship between pack size and intake rate, we first considered how pack size and rate of loss to scavengers (kg/d) affect the number of days required to consume the carcass of an adult moose (295 kg). For a given pack size and rate of loss, we calculated carcass longevity assuming a consumption rate of 9 kg/d/wolf. Then, to obtain kg/wolf/day as a function of pack size and number of ravens, we multiplied the kg/wolf/kill (a function of pack size and loss to scavengers) by the kills/day (a function of pack size).

Figure 10.3. Relationship between pack size and average daily per capita net rate of intake assuming either negligible or minor scavenging pressure by ravens (see also fig. 6 in Vucetich et al. 2004). To assess how raven scavenging might affect the predicted relationship between pack size and intake rate, we first considered how pack size and rate of loss to scavengers (kg/d) affect the number of days required to consume the carcass of an adult moose (295 kg). For a given pack size and rate of loss, we calculated carcass longevity assuming a consumption rate of 9 kg/d/wolf. Then, to obtain kg/wolf/day as a function of pack size and number of ravens, we multiplied the kg/wolf/kill (a function of pack size and loss to scavengers) by the kills/day (a function of pack size).

group size (Hamilton 2000). This study modeled the division of resources as a game between an individual (recruiter) that controls access to resources and a potential recruit. If another individual's presence benefits the recruiter (fig. 10.4), the recruiter may provide an incentive to join or stay. The incentive may increase the recruit's foraging payoff, reduce its predation risk, or both. We restrict our attention to the simple case in which the incentive provides a foraging payoff. For joining to be profitable, this incentive must cause the recruit's payoff to equal or exceed the payoff it would obtain by remaining solitary.

This model predicts that the stable group size will fall between G* (equal division of resources and group-controlled entry) and a maximum stable group size G (equal division of resources and free entry). Stable group size increases as the recruiter's control over resource division decreases (fig. 2 in Hamilton 2000). As this control decreases and the benefits of group membership increase, predicted group size G shifts from being transactional (i.e., where the recruiter provides an incentive) to nontransactional (i.e., where the joiner obtains a sufficient payoff without using any of the recruiter's resources) (see fig. 10.4). In transactional groups, the recruiter and joiners agree about group size because the stable size is the same for all parties. However, in nontransactional groups, there may be conflict over group size. Factors that reduce the recruiter's control (e.g., minimal dominance) or increase the benefits of group membership (e.g., large food rewards) will also increase the

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