Skip to main content
Biology LibreTexts

3.4: Program results

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    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 × 1018 cubic 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.

    This page titled 3.4: Program results is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Clarence Lehman, Shelby Loberg, & Adam Clark (University of Minnesota Libraries Publishing) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.