We play on an 8 player survival realm where we decided to capture 4-5 turtles and breed them on a beach, near by to our village.

Whilst a player is loading these turtles (and their eggs), every 10 seconds or so, a large lag spike occurs (for every player) where all mobs temporarily freeze and the game in general becomes unplayable.

The more players that are on the realm, the longer these spikes last.

We tried restarting the realm, downloading the world and replacing the realm's world etc.... but still the lag spikes continued.

As soon as the turtles were killed and their eggs broken, the terrible lag was eliminated and we could enjoy Minecraft once again.

Extra notes:
The turtles were all enclosed in wooden fences on a small island of sand.
A pregnant turtle may have been trying to reach its home beach, but couldn't because of the fences.
The turtles were on the edge of an ocean, thousands of blocks away from spawn.