Reproductive skew and group size:: an N-person staying incentive model

Transactional models of social evolution emphasize that dominant breeders may donate parcels of reproduction to subordinates in return for peaceful cooperation. We develop a general transactional model of reproductive partitioning and group size for N-person groups when (1) expected group output is a concave (decelerating) function g[N] of the number N of group members, and (2) the subordinates may receive fractions of total group reproduction (staying incentives) just sufficient to induce them to stay and help the dominant instead of breeding solitarily. We focus especially on saturated groups, that is, groups that have grown in size just up to the point where subsequent joining by subordinates is no longer beneficial either to them tin parent-offspring groups) or to the dominant tin symmetric-relatedness groups). Decreased expected output for solitary breeding increases the saturated group size and decreases the staying incentives. Increased relatedness decreases both the saturated group size and the staying incentives. However, in saturated groups with symmetric relatedness, an individual subordinate's staying incentive converges to 1 - g[N* - 1]/g[N*]) regardless of relatedness, where N* is the size of a saturated group, provided that the g[N] function near the saturated group size NY is approximately linear. Thus, staying incentives can be insensitive to relatedness in saturated groups, although the dominant's total fraction of reproduction (total skew) will be more sensitive. The predicted ordering for saturated group size is: Parent-full sibling offspring = non-relatives > symmetrically related relatives. Strikingly, stable groups of non-relatives can form for concave g[N] functions in our model but not in previous models of group size lacking skew manipulation by the dominant. Finally, symmetrical relatedness groups should tend to break up by threatened ejections of subordinates by dominants, whereas parent-offspring groups should tend to breakup via unforced departures by subordinates.