Some do – apes, old-world monkeys, elephant shrews (above), many bats and a single rodent: the spiny mouse. Many others have menstrual cycles, but reabsorb the old womb-lining rather than bleed it out.
The reasons behind the two strategies are unclear. Intriguingly, menstruating species, unlike those that reabsorb, tend to copulate throughout their reproductive cycles, rather than only around ovulation, when they are receptive.
This means that fertilisation might involve eggs or sperm that are past their best, increasing the risk of producing genetically defective embryos. One theory goes that menstruation is a way of getting rid of embryos conceived outside of an optimal time window.