Minecraft server ran out of memory

Minecraft ran out of memory while increasing the population of a friends chicken farm which had a population of less than 360 chickens when Minecraft ran out of memory. I was the only one on the server when this happened.

Its happened about 4 times now with a population of 360 chickens and its completely random when it happens. I could run the server for hours before this happens and it only occurs when I am in the farm. Just before it happens all of the icons of things in my inventory disappear.

I have an image of what the server screen looks like after it happens.