Bugs, bunnies, bombs and branches 2
Wascally wabbits
Rabbits also have a reputation for reproducing at a high, but less fearsome rate. I’ve never kept rabbits, so I had to do a bit of crawling around the web to find out some basic facts. In rough terms, I found out that female rabbits (‘does’) take about six months or so to become fertile. Pregnancy is about a month long. Almost immediately after the birth of a litter (giving around three new does), a doe can become pregnant again. There is no particular breeding season, although temperature and such does affect propensities to breed. The breeding life of a doe is up to around six years old.
There are many possible models and parameter sets one could apply. This is also a very variable situation with undetermined outcomes. However, we will look at it as a deterministic branching process. One doe over 5.5 years (she takes six months to become fertile) gives birth every month to three does: 5.5×12×3=198. These 198 give rise to 198 each, resulting in 39204. The next generation goes on to produce 7762392. The exact values are of course nonsense, given all the variations.
Further, one might be tempted to associate the third generation value with 18 years after the initial bunny. In reality, the births are staggered over the period. In fact, after 18 years you will have around does who are part of the 36th generation, the ones resulting from six months after birth in all the first pregnancies in series. So the number of rabbits would be much more than 8 million, or 16 million, if we add on an equal number of males. At this stage we don’t want to get bogged down in perfecting the model. The main point is that the dynamics of branching leads to power law behaviour that is associated with “exponential growth”.