Innovative behaviour achieved through exploration, learning and insight heavily depends on certain motivational, social and ecological conditions of short duration. We propose that more attention should be given to what these conditions are and where they are realized in natural groups of non-human primates. Only to the extent that such favourable conditions were frequently realized in a social structure or an extraspecific environment could selective pressures act on innovative abilities. There is hope that research into field conditions of innovative behaviour will help to identify its selectors in evolution.

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In this paper we prove some theorems about the n-representability problem for reduced density operators. The first theorem (Theorem 6) sharpens a theorem proved by Garrod and Percus. Let Tnp be the set of all n-representable p-density operators. Then a density operator Dp belongs to Tnp¯ (the bar indicates the closure with respect to a certain topology) if and only if Tr (DpBp) ≥ 0 for all bounded self-adjoint p-particle operators Bp, such that their n-expansion (pn)ΓpnBp≡ ∑ i1<…<ipBp(i1…ip)is a positive operator in n-particle space. Moreover, it is shown that Tnp¯ is the closed convex hull of the exposed points of Tnp of finite one-rank (Theorem 9). A more practical version of this theorem may be formulated in the following manner (cf. Theorem 8). Consider the set γp of subspaces of the n-particle space, occurring as an eigenspace to the deepest eigenvalue of a bounded n-particle operator which is the n expansion of some p-particle operator. Choose from every element of γp one (and only one) vector (function) and form the corresponding reduced p-particle operator. Tnp¯ is the closed convex hull of all these p-density operators (cf. Theorem 9). For p = 1, this theorem reduces to Coleman's theorem about the n representability of the 1 matrix.

Field observation and pilot field experiments suggested the hypothesis that a social inhibition prevents male hamadryas baboons from encroaching on each other's females. The hypothesis was tested in a set of enclosure experiments which led to the following results : 1. When two males were simultaneously confronted with an unfamiliar female, one would become her "owner", either by defeating his rival or by the latter's withdrawal. 2. No fights occurred, however, when one male was allowed to watch a troop mate interact with a new female before he was admitted to them. He then respected the pair bond even if he was dominant over the owner. This agreed with the inhibition hypothesis. The alternative dominance hypothesis was rejected at the 0.01 level. 3. When males from different troops were used, some rivals attacked the owners and took their females. Most attacks were directed by powerful rivals against the particularly inferior males of one troop, suggesting that dominance factors can, in extreme cases, override the rival's inhibition. 4. The inhibition appeared to be restricted to the context of owning females in that it did not significantly affect the male's performance in food dominance tests. 5. A few casual interactions between the pair sufficed to inhibit the rival. The owner's overt demonstrations of possession had no additional effect in these experiments. 6. The stabilizing functions of the inhibition in the hamadryas society are discussed. 7. The inhibited rivals performed a number of redirected and conflict activities. An analysis shows that the inhibition suppresses friendly as well as aggressive approaches in the rival, thus keeping him away from the pair. 8. The owner's interactions with the rival were also inhibited, but much less than the rival's interactions with the pair. In contrast, interactions between the pair were increased and intensified by the rival's presence. 9. In one exceptional test, the female appeared in the role of the excluded rival. The formation of triads thus seems to reduce two of the component dyadic relationships while furthering the third. The possible mechanisms of such "triadic differentiation" are mentioned and its probable function in the formation of groups and subgroups is outlined.

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