3.4: Program results

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Here is what the program produces, shortened to fit on a page of this book.

6.64614 × 10³⁵

1.32923 × 10³⁶

If you run this program in R or another suitable language, you should see something essentially identical to the above. Between Monday and Friday, 120 bacterial doublings would produce over 10³⁶ bacteria—that’s 1 followed by 36 zeros. That is the computational result. The scientific question is how many individuals this amounts to. Worked out exactly, it is this number: 2¹²⁰ = 1,329,227,995,784,915,872,903,807,060,280,344,576. To understand the size of this number, suppose the bacteria are roughly cubical 1 µm on a side—one millionth of a meter, or about four hundred-thousandths of an inch (a suitable order-of-magnitude for a bacterium). What volume will the colony occupy in cubic meters at the end of the work week, after five full days of growing unchecked? You might want to speculate: will it fill the culture plate, overflow onto the lab bench, fill the lab, or what?

Work it out and you will see that the answer is 2¹²⁰ bacteria times 10^-18 cubic meters per bacterium equals about 1.3 × 10¹⁸ cubic meters total. How large is that? Estimate the ocean to be a film averaging 3.7 kilometers deep and coating two-thirds of a sphere with a 6400 kilometer radius (this approximates the amount of the earth’s surface that is covered by ocean). This is about 1.3 × 10¹⁸cubic meters! At the end of five days, the colony unchecked would thus fill all oceans of the earth with a dense microbial mass, from the greatest depths up to the surface!

This result has deep-reaching implications. First, even though this bacterial model can be quite accurate for a day or so, it fails completely over the course of a week. All models are approximations to reality, at best applicable over a suitable range. Second, there are lessons in its failure. It illustrates one of the inviolable laws of biology—that no population growth can remain unlimited for long. And third, in a mind like Charles Darwin’s, and coupled with other biological principles, it leads to the conclusion that organisms must evolve. That is the story of Darwin’s elephants.