Ducks eating their own eggs??

Hi everyone - not been on here for ages but hope someone can clear this up for me.  When I let the ducks out this morning there was part of a broken egg shell on the ground and one less egg than usual in the nest.  Do ducks eat their own eggs sometimes?  Just wondered whether may be this one got broken and one of them has eaten it.  Had my ducks for a couple of years now and not ever come across this before!!

Thanks for your help 

Webby x