Additional Multiplication, TOS: S2E15 “Trouble with Tribbles”

Kirk has had it up to here with these things!

In 1788, the first European settlers in Australia brought rabbits as a source of food.  With no native predators in their new home, the rabbit population exploded, and became one of the country’s most devastating invasive pests.  Thus is the inspiration for this Star Trek story.  Perhaps one of the most iconic episodes of the original series, “Trouble with Tribbles” recounts the Enterprise’s epic space puff infestation.  Brought onboard a space station by the trader Cyrano Jones, the tribbles were meant to be sold as pets.  Jones didn’t know about their excessive reproductive capacity when he gave one to Uhura, who then took it aboard the Enterprise.  In only a matter of days the ship, and the station, were overrun.  To add insult to invasion, Kirk was responsible for safeguarding a supply of grain meant for export.  Kirk was only minimally invested in the assignment to begin with and abandoned all importance upon discovering the tribbles ate the grain.

The storage compartment was filled to the brim with the creatures.  As excess fuzzballs fall on Kirk’s head, Spock calculates exactly how many tribbles are on the station.  He’s not wrong, assuming the population began with one tribble given adequate food and space.  This seemingly innocent starter puff would have been able to produce ten tribblets every twelve hours.  The final population was given as 1,771,561 according to Spock, with each generation compounding:

0 Hours1 Tribble0 Babies
12 Hours1 Tribble10 Babies
24 Hours11 Tribbles110 Babies
36 Hours121 Tribbles1210 Babies
48 Hours1331 Tribbles13310 Babies
60 Hours14641 Tribbles146410 Babies
72 Hours161051 Tribbles1610510 Babies
1771561 Total Tribbles

This assumes perfect population growth.  If the tribbles have access to unlimited food and space, they could continue to multiply exponentially.  Unfortunately, we find out that the grain was poisoned, having already killed off many of the tribbles.  This might put the real number of tribbles far below Spock’s estimate, because the chart above assumes every tribble is reproducing at full capacity every twelve hours.  Tribble number one most likely would have died days ago.  Information on how fast the poison acts, and lethal tribble dosage, would be necessary to calculate how many of the earlier generations are no longer contributing toward population growth.  If one wants to further complicate the population dynamics, the average litter size was an oversimplified estimate.  Some tribbles may give birth to more or less than ten triblets on average, but Spock may also be assuming perfect reproductive conditions in this aspect.  Dr. McCoy discovers that tribbles don’t reproduce when they don’t have access to food, so we should ask, did every single tribble have equal access to food at all times?  Does the amount of food affect litter size?  Did the poison have any affect, and did all the tribbles eat the poisoned grain?  Many organisms reproduce at below capacity for a variety of reasons, and this could be the norm for tribbles given their population potential.

Regardless of whether Spock’s estimate was accurate down to the last tribble, it is clear that these fuzzies are able to overrun a new environment in short order.  It begs the question, what kind of environment could support tribbles?  Just like the non-native Australian rabbits, tribbles need predation to control the population.  An environment where predators are so prolific that tribbles would be eaten like popcorn as soon as they are born, though horrifying, would keep the numbers down.  Predator-prey dynamics would have the predator population increase to match the prey population, until the prey population declines and reduces the predator population along with it.  The fact that the tribbles cannot reproduce without food further complicates the delicate balance.  Either the tribble homeworld has an endless supply of food, or tribbles risk going extinct during cycles of scarcity.  Whatever the equilibrium may be, tribbles apparently found a niche, and no matter how cute, fuzzy, or useful an animal may be, it’s important that we keep them there.


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