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

Transactional models of social evolution emphasize that dominant breeders m ay donate parcels of reproduction to subordinates in return for peaceful co operation. We develop a general transactional model of reproductive partiti oning 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, an d (2) the subordinates may receive fractions of total group reproduction (" staying incentives") just sufficient to induce them to stay and help the do minant instead of breeding solitarily. We focus especially on "saturated" g roups, that is, groups that have grown in size just up to the point where s ubsequent joining by subordinates is no longer beneficial either to them ti n parent-offspring groups) or to the dominant tin symmetric-relatedness gro ups). Decreased expected output for solitary breeding increases the saturat ed group size and decreases the staying incentives. Increased relatedness d ecreases 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 related ness, where N* is the size of a saturated group, provided that the g[N] fun ction near the saturated group size NY is approximately linear. Thus, stayi ng incentives can be insensitive to relatedness in saturated groups, althou gh 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. Striki ngly, 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 manipulati on by the dominant. Finally, symmetrical relatedness groups should tend to break up by threatened ejections of subordinates by dominants, whereas pare nt-offspring groups should tend to breakup via unforced departures by subor dinates.