Finitely valued commutator sequences

If x and y are elements in the group G, then we denote their commutator by x o y = x-1y-1 = x-1xy; and x o G is the set of all commutators x o g with g G. A G-commutator sequence is a series of elements ci G with c1 + 1 ci O G. Slightly generalizing well known results one proves that the hypercenter of the group G is exacly the set of all elements h G with the property: every G-commutator sequence, containing h, contains 1 [Proposition 1.1

Male Mating Rate Is Constrained by Seminal Fluid Availability in Bedbugs, Cimex lectularius

Sexual selection, differences in reproductive success between individuals, continues beyond acquiring a mating partner and affects ejaculate size and composition (sperm competition). Sperm and seminal fluid have very different roles in sperm competition but both components encompass production costs for the male. Theoretical models predict that males should spend ejaculate components prudently and differently for sperm and seminal fluid but empirical evidence for independent variation of sperm number and seminal fluid volume is scarce. It is also largely unknown how sperm and seminal fluid variation affect future mating rate. In bedbugs we developed a protocol to examine the role of seminal fluids in ejaculate allocation and its effect on future male mating rate. Using age-related changes in sperm and seminal fluid volume we estimated the lowest capacity at which mating activity started. We then showed that sexually active males allocate 12% of their sperm and 19% of their seminal fluid volume per mating and predicted that males would be depleted of seminal fluid but not of sperm. We tested (and confirmed) this prediction empirically. Finally, the slightly faster replenishment of seminal fluid compared to sperm did not outweigh the faster decrease during mating. Our results suggest that male mating rate can be constrained by the availability of seminal fluids. Our protocol might be applicable to a range of other organisms. We discuss the idea that economic considerations in sexual conflict research might benefit from distinguishing between costs and benefits that are ejaculate dose-dependent and those that are frequency-dependent on the mating rate per se