Multiple mating by females (polyandry) is of interest to behavioral biologists because of its effect on the evolution of male traits and the maintenance of variation within populations.   American horseshoe crabs are a particularly interesting system in which to study polyandry because both monandrous (females that mate with only one male) and polyandrous females occur within one population and populations vary in the frequency of polyandry. Attached pairs of horseshoe crabs arrive on beaches to nest and spawn (eggs are fertilized externally) where they may be joined by roving, unpaired males that engage in sperm competition with the attached male. Some pairs attract satellite males and some do not: even at very high nesting densities and under strongly male-biased operational sex ratios, some females remain monandrous.  Experimental field manipulations demonstrate that polyandrous matings are costly for all females (reduced number of clutches laid per beach visit).  However, experimental in vitro matings reveal that polyandrous females benefit from multiple male paternity of their eggs through increased developmental success of their offspring whereas monandrous females do not.  An in vitro breeding experiment revealed that most of this variation in developmental success was due to maternal and incompatibility (MxF) effects.  Attached males of monandrous (AM) and polyandrous (AP) females differ: AM males have more concentrated sperm and they pair more quickly in mate choice experiments than AP males.  One explanation for these patterns is that females attract satellite males (i.e. become polyandrous) when they are attached to a low quality or incompatible male.  Taken together, these results suggest that monandrous and polyandrous females differ in the costs and benefits of multiple mating and that genetic incompatibility and/or differences in male quality may offset the costs of polyandry. Differences among populations in the frequency of polyandry may affect heterozygosity.