On Time and Space

The long-term evolution experiment (LTEE) began in 1988, and the E. coli populations are approaching 60,000 generations.  That’s a long time for an experiment, and I hope it continues for much, much longer.

But when I give talks about the LTEE, I also try to remind people that 26 years is only a drop in the proverbial bucket of evolutionary time.  If you were to add these experimental populations to the tree of life—or even to a tree showing only other E. coli strains—they would not be visible to the eye because the branches they represent—tiny twigs, really—would be so short (in time) and so close (in genetic distance) to their ancestors.

On Time and the LTEE

Life has existed on Earth for roughly 3.5 to 4 billion years.  That’s about 140 million times longer than the LTEE has existed.  Expressed the other way around, this experiment has been running for about 0.0000007% of the time that life has been evolving on our planet.

As I said, a mere drop in the bucket of time …

That’s a somewhat mixed metaphor, though, with “a drop in the bucket” being a statement about space and relative volumes, not about time.  And that got me wondering about the spatial scale of the LTEE relative to the spatial scale of the biosphere.

If the LTEE is just 0.0000007% as old as life on Earth, what fraction of the space—of the total biovolume—of life on our planet exists in the confines of the LTEE?

On Space and the LTEE

That’s a harder a question to answer.  We know the volume of the LTEE:  there are 12 flasks, one for each of the evolving populations, and each flask contains 10 milliliters (mL) of liquid medium.  (In medicine, by the way, a drop has been defined as 1/20th of a mL, so each flask in the LTEE contains 200 drops.)  If we sum across the populations, then the LTEE occupies 120 mL.

Before you read further:  What’s your quick intuition?  Is the LTEE larger on this spatial scale than on the temporal scale?  Or is the LTEE smaller?

Volumes and Numbers

How should we estimate the volume of Earth’s biosphere?  Here are three back-of-the-envelope approaches to get a rough sense of the scale.

1)  Most of the Earth is covered by its oceans, which are full of life.  While life is not equally abundant throughout the oceans, none of that space is entirely devoid of life.  The total volume of Earth’s oceans is about 1.3 billion cubic km.  That’s a lot of mL!  A mL is a cubic centimeter, or cc, and that’s 1/(100^3) = 1 millionth of a cubic meter.  A cubic meter is 1/(1000^3) = 1 billionth of a cubic kilometer, and the oceans contain over a billion of those cubic kilometers.

So the 120 mL in the LTEE correspond to 120 / (1.3 x 10^9 x 10^9 x 10^6), or about 9 x 10^-22 of what  the oceans contain.  That’s just 0.000000000000000000009% of the volume of the oceans.

By this calculation, then, the temporal scale of the LTEE is ~75 trillion times greater than its spatial scale, when both are expressed relative to nature.  If the LTEE is “a drop in the bucket” with respect to time, then that drop has to be diluted by a factor of 75 trillion with respect to the oceans.

2)  Let’s try another quick-and-dirty calculation.  Most life, in the oceans and on land, is near the Earth’s surface.  The surface area of our planet is about 510 million square kilometers.  If we take just the top meter, that’s equivalent to 510/1000  = 0.51 million cubic kilometers.  That’s about 1/2600 of the volume of the ocean.  But even this conservative estimate of the volume of the biosphere makes the relative scaling of the LTEE with respect to time and space differ by a factor of 30 billion.

3)  Here’s one more approach—it’s based not on the volume of the physical environment but, instead, on the number of organisms in the LTEE and in the biosphere.  When grown to stationary-phase density in the LTEE environment (i.e., when the limiting resource, glucose, is depleted), the ancestral bacteria could achieve a maximum density of ~5 x 10^7 cells per mL.  Most populations have evolved so that they now produce slightly fewer, but larger, cells; and one population has evolved the ability to use the citrate that is also in the medium, and it now reaches a density that is several times greater than the other populations.  In any case, given 10 mL of medium for each population, and 12 populations, the total population size across the LTEE is on the order of 10^10 cells.

And how many cells exist in the Earth’s biosphere?  Whitman et al. (1998, PNAS) estimated that there are more than 10^30 prokaryotes—bacteria and archaea combined—in the biosphere, and they make up the great majority of all living things.

So by this approach, using the number of cells as a proxy for the spatial scale, the size of the biosphere is over 10^20 (a hundred-million-trillion) times larger than the LTEE.  We’re back into the trillions in terms of the relative scaling of the temporal and spatial scales of the LTEE.

On Time, Space, and the LTEE

By all three approaches, then, the LTEE is vastly older with respect to the history of life on Earth than it is large with respect to the size of Earth’s biosphere.

The LTEE really is a long-running experiment, as experiments go.

But the LTEE is a “drop in the bucket” with respect to how long life has been evolving on Earth.  And it is a vastly more miniscule “drop in the bucket” when compared to the spatial extent and number of living organisms on our planet.

Maybe I should give the LTEE a new name—the “incredibly tiny but relatively long-term evolution experiment.”

[Photo of a water drop on a leaf taken by tanakawho and shared on Wikipedia (en.wikipedia.org/wiki/File:Water_drop_on_a_leaf.jpg).]


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9 responses to “On Time and Space

  1. Do you also present comparable back of the envelope calculations for other famous ecology and evolution experiments? I’ve been known to do this for our protist microcosms when I give talks. For instance, one of our microcosms typically contains more protists than there are tropical trees in the famous 50 hectare plot on Barro Colorado Island. So in that sense, our microcosms are actually enormous. It’s funny, at some level I’m sure the audience must know that without me saying it–but yet whenever I point this out some people’s eyes always widen.

    • Besides this blog post, I haven’t generally made these sorts of comparisons. But I sometimes get asked by people in the audience and reporters, especially about the temporal aspect.

      The easy comparison to make, and the one I’m often prodded to make, is this: How long would the 50,000 generations of the LTEE represent in human generations? With a typical human generation time of roughly 20 years, that would be a million years.

      It’s a nice number, and it does get people thinking. Still, it’s really only 25 years — the experimental subjects are bacteria, not humans, and there are many differences between them besides generation times: asexual versus sexual reproduction, population sizes, genome sizes, standing variation, environmental heterogeneity, nature and nurture, etc.

  2. Sorry this is slightly off topic, but have y’all determined the number of mutations that resulted in the cit+ cells? The last paper I saw on it was Blount’s 2012 piece. I was just curious if there was an actual number of mutations that could be identified.


    • There is the tandem duplication that produced the first Cit+ cell, and then the further amplification that allowed decent growth on citrate, so that’s one or two depending on whether very weak growth on citrate counts. And there were one or (probably) more “potentiating” mutations that occurred before the tandem duplication. However, we have not yet definitely identified the potentiating mutation(s) among the several dozen mutations that arose in the lineage before the duplication.

  3. This isn’t surprising given that the experiment was designed to be (relatively) *long term*, but not designed to be large scale. So how would one design the LSSEE (Large Spatial Scale Evolution Experiment), and what questions would it answer? I would think that it would aim to answer the questions of how evolution occurs in heterogenous/interconnected environments. Perhaps it would consist of a large array of interconnected microcosms, or a mega-cosm where environmental properties (thermal layering?) vary continually.

    • I agree it’s not too surprising that the LTEE is relatively smaller than it is short, though I was surprised at how big the difference in scaling is.
      But more importantly, I like your idea for the LSSEE, and the proposed focus on questions of heterogeneity and interconnectedness.
      I hope you will do the experiment!

  4. Pingback: Morsels For The Mind – 04/04/2014 › Six Incredible Things Before Breakfast

  5. Nicholas Kortessis

    I happened to have this exact same conversation with some colleagues just two weeks ago and argued for space being relatively greater. Although I think there is an interesting assumption here that has not in fact been tested, which is that space and time are equivalent (i.e. ergodic to borrow a term from mathematics) with respect to evolutionary change. We have some good reasons to expect that they are in fact not the same. The species coexistence literature has some good theory on when space and time are not directly comparable for species growth rates. I imagine something similar happens with evolutionary change as well. Of course, we have a lot of information about how different spatial structure may affect gene flow and adaptation, especially in environments with variable selection. Great post!

    • Thanks, Nicholas. I agree that space and time are not equivalent with respect to rates and patterns of evolution, either in general or for the LTEE.

      It would be interesting to see a review article of empirical evidence (if any) and/or theoretical models (or discussion) concerning the similarities and differences between space and time with respect to evolutionary rates.

      One trivial case where there is, I think, an equivalence is the “supply” (number) of de novo mutations. Doubling space and time (all else equal, such as population densities) should be equivalent. But this is likely an exceptional case of equivalence, and one can readily imagine scenarios where space has different effects in terms of isolation, heterogeneity, etc, etc.