All animals are bound to certain types of land, in certain types of tile sets. You forgot to edit the Kingdom when you created your scenario. Set this to a higher number and this problem will not occur. Every part of your city must have constant access to the kingdom road. This is so that new immigrants can move in and emigrants can move out.
Access can be in the form of land, ferry, or bridge.
To avoid this problem, make sure that there are no areas of your city that can only be accessed by crossing the flood plain. To further ensure that this will not happen, place your People entry and exit points on one contiguous landmass. Finally, remember that immigrants and emigrants will not cross flood plain unless there is road allowing them to cross the edge of it. You probably forgot to flag that city as a trade city. In the Mission Editor, click on the Kingdom button and the find the city that you are hoping to trade with.