Your comment on menstruation times are a little misleading.
A woman is LEAST likely to be fertile during menstruation.
Additionally, Ovulation & menstruation are INDEPENDENT, but related.
Ovulation may be triggered by a rush of hormones (frx - many "harbour wives" may get pregnant even when their calander and general physical condition might suggest otherwise, becuase their partner arrives in and this can trigger ovulation).
Menstruation is the outward face of a complex cyclical pattern that represents the progressive build-up of the receptive (and blood-rich) wall of the womb that typically cumulates at roughly "day 18" of the "average womans" biological cycle. After that point, the womb remains receptive to implantation (is maintained in that state) for a further 6-8 days before a change in hormone levels causes the lining of the womb to beging to slough-off and be lost. This typically continues for 2-3 days, at the end of which the cycle starts again and the lining starts to build up again.
For someone to "bleed" for a month at a time (as suggested above) would probably kill them if it was at comparable levels to a human.
Other Mammals organise things differently. When a Dog/wolf goes into "Heat", this represents that their womb is now at optimal condition for implatation. However, it is maintained in that state by allowing a very low, but continual loss of the old lining, that is continually replaced during oestrus. However, this fertile period is unlikely to last for very long or the animal would be come ill.
Either way - there is NO connection to the phases of the moon (the proximity in timing is co-incidental). However, the proximity of other women DOES have an effect. If several women live in close proximity, their biological cycles tend to slowly come into approximate synchronisation. Humans may not overtly notice the hormones ... but our bodies react to them anyway.
Make what you wish of that.
Cormac