Tag Archives: theory and experiments

Optimizing the product of the wow factor and the beneficial mutation supply rate

This post follows up on my post from yesterday, which was about choosing a dilution factor in a microbial evolution experiment that avoids the loss of too many beneficial mutations during the transfer bottleneck.

If we only want to maximize the cumulative supply of beneficial mutations that survive dilution, then following the reasoning in yesterday’s post, we would chose the dilution factor (D) to maximize g Ne = (g2) Nmin = (g2) Nmax / (2g), where Nmax is a constant (the final population size) and D = 1 / (2g). Thus, we want to maximize (g2) / (2g) for g > 0, which gives g = ~2.885 and D = ~0.1354, which is in agreement with the result of Wahl et al. (2002, Genetics), as noted in a tweet by Danna Gifford.

The populations would therefore be diluted and regrow by ~7.4-fold each transfer cycle. But as discussed in my previous post, this approach does not account for the effects of clonal interference, diminishing-returns epistasis, and perhaps other important factors. And if I had maximized this quantity, the LTEE would only now be approaching a measly 29,000 generations!

So let’s not be purists about maximizing the supply of beneficial mutations that survive bottlenecks. There’s clearly also a “wow” factor associated with having lots and lots of generations.  This wow factor should naturally and powerfully reflect the increasing pleasure associated with more and more generations.  So let’s define wow = ge, which is both natural and powerful.  Therefore, we should maximize wow (g2) / (2g), which provides the perfect balance between the pleasure of having lots of generations and the pain of losing beneficial mutations during the transfer bottlenecks.

It turns out that the 100-fold dilution regime for the LTEE is almost perfect!  It gives a value for wow (g2) / (2g) of 75.93.  You can do a tiny bit better, though, with the optimal ~112-fold dilution regime, which gives a value of 76.03.

3 Comments

Filed under Humor, Science

Questions from Jeremy Fox about the LTEE, part 2

EDIT (23 June 2015): PLOS Biology has published a condensed version of this blog-conversation.

~~~~~

This is part 2, I guess, of my response to Jeremy Fox from his questions about the LTEE over at the Dynamic Ecology blog.

It’s not an answer to his 2nd question, but it’s a partial answer to the first part of his 3rd question? (Have I got you confused already? Me, too.) Well anyhow, Jeremy asked:

~~~~~

  • Did the LTEE have any hypotheses initially, and if so, how were you going to test them? This question probably just reflects laziness on my part, not having gone back and read the first publications arising from the LTEE, sorry. 🙂 I ask because, with just one treatment and no quantitative a priori model of how the experiment should turn out, it’s not clear to me how it initially could’ve been framed as a hypothesis test. For instance, I don’t see how to frame it as a test of any hypothesis about the interplay of chance and determinism in evolution. It’s hard to imagine getting any result besides some mixture of the two, and there’s no “control” or a priori theoretical expectation to compare that mixture to. Am I being dense here? (in addition to being lazy…)

 ~~~~~

Short answer: Yes, the LTEE had many hypotheses, some pretty clear and explicit, some less so. (What, did you think I was swimming completely naked?)

Medium answer that will be fleshed out in later responses: Before we get to specific hypotheses—those formal, testable suppositions and predictions—I like to begin with general questions about how and why things are they way they are. So, what were the questions the LTEE originally set out to answer? (I emphasize “originally” because new or substantially refined questions have arisen over the course of the project, as we’ve answered some questions, made new observations, framed new questions, etc.)

What follows below are three overarching sets of questions that I hoped, long ago, the LTEE could answer, at least in the context of the simple flask-world that it encompassed. I present all three sets of questions  in some of my talks about the LTEE. However, in my talks to broad public audiences – like my Darwin Day talk at the University of Calgary next week – I focus especially on the third set of questions – about the repeatability of evolution – because I think it is the most interesting to people who are not necessarily evolutionary biologists or even scientists, but who are curious about the world in which we live.

Motivating questions for the LTEE

A few more thoughts: The first set of questions, about the dynamics of adaptation, include ones where I had clear  expectations that were testable in a fairly standard hypothesis-driven framework. For example, I was pretty sure we would see the rate of fitness improvement decelerate over time (and it has), and I was also pretty sure we’d see a quasi-step-like dynamic to the early fitness increases (and we did). Nonetheless, these analyses have yielded surprises as well, including evidence (and my new strong conviction) that fitness can increase indefinitely, and essentially without limit, even in a constant environment. In regards to the second set of questions, about the dynamics of genome evolution and their coupling to phenotypic changes–I’m sure these were part of my original thinking, but I will readily admit that I had almost no idea how I would answer them. Hope sprung eternal, I guess; fortunately, wonderful collaborators—like the molecular microbiologist Dom Schneider—and brand new technologies—wow, sequencing entire genomes—saved the LTEE.

 

4 Comments

Filed under Science

What We’ve Learned about Evolution from the LTEE: Number 5

This is the fifth in a series of ~10 posts in which I summarize what I think are the most important findings and interesting discoveries from the LTEE.  The previous entry, number 4, also has links to the earlier entries.

Number 5.  We have seen large changes in the spontaneous mutation rate in some of the LTEE populations.  These changes reflect an interesting tradeoff between short-term fitness and long-term evolvability.

Proximate causes.  Six of the 12 LTEE populations evolved to be so-called “hypermutators” by 50,000 generations.  The proximate (i.e., biochemical) causes of these changes are mutations in genes whose products are involved in DNA repair or the degradation of molecules that cause damage to DNA.

These mutations typically cause the rate of point mutations throughout the genome to increase by roughly 100-fold (Sniegowski et al., 1997, Wielgoss et al., 2013), so their effects are not at all subtle.  They also change the spectrum of mutations:  mutations in the mutS gene, which encodes a protein involved in mismatch repair, cause increased A·T–>G·C and G·C–>A·T transitions (Lenski et al., 2003); while mutations in mutT, which encodes an enzyme that degrades an oxidized nucleotide, cause A·T–>C·G transversions (Barrick et al., 2009).

Evolutionary effects.  The evolutionary effects of these hypermutators are subtle and interesting.  In essence, one can think of mutations that produce hypermutators as affecting the tradeoff between short-term fitness and long-term evolvability.

Short-term cost.  Of all the possible mutations that might occur, many more are deleterious than are beneficial. Therefore, hypermutators produce more maladapted progeny than otherwise identical cells with a lower mutation rate.  Hence, hypermutators suffer a fitness cost caused by the increased production of progeny with deleterious mutations.

However, the E. coli strain that was the ancestor to the LTEE has a low point mutation rate, which we’ve estimated as ~10-10 per base-pair per generation (Wielgoss et al., 2011).  Given the genome contains ~5 x 106 base-pairs, this rate translates to only ~0.0005 point mutations per genome per generation.  Therefore, even a 100-fold increase means that most hypermutator progeny are mutation-free.  Considering that only a fraction of genomic sites are subject to mutations that would be deleterious in the LTEE environment, we infer that the short-term cost to a 100-fold hypermutator is ~1% (Wielgoss et al., 2013).

Evolvability benefit.  Even a 1% cost is not trivial, so how can a hypermutator survive and spread through a population?  In fact, most hypermutators do not survive; the vast majority of mutations that cause hypermutators will die out as a consequence of that short-term cost.  However, hypermutators result from loss-of-function mutations, and a dozen or so large genes are targets for these mutations.  Hence, new hypermutators will continually be regenerated in large populations.  Absent other forces, an equilibrium frequency of hypermutators would be reached that reflects the balance between the rate of appearance of hypermutators by new mutations in the relevant genes and the rate at which they are removed by selection against the deleterious mutations they cause—in other words, the familiar mutation-selection balance of population-genetics theory.

But another force is at play: the populations in the LTEE are not sitting on a fitness peak, so there are on-going opportunities for beneficial mutations to appear.  And a hypermutator cell has a much higher probability of generating a beneficial mutation than does a “normal” cell.  In essence, there’s a race to produce the next winner.  If a hypermutable cell generates the next beneficial mutation that sweeps through the population, then the hypermutator will “hitchhike” along with it because, without sex, the two mutations are linked.

Combining forces.  So how do the short-term cost and the evolvability benefit play out together?  Mutations that knock out any one of the genes involved in DNA repair probably occur at a rate between 10-5 and 10-6 per generation, and the resulting hypermutable cells have a fitness disadvantage of ~1% owing to the production of deleterious mutations.  At mutation-selection balance, the frequency of hypermutators is between 0.01% (10-4) and 0.1% (10-3).  Let’s use 0.05% to illustrate.

Although the hypermutators are a small minority, on a per capita basis each of them has a 100-times higher probability than a normal cell of generating the next winner.  So 5% of the time, a hypermutator will be swept to fixation, but most of the time the winner will be produced by a normal cell.  Now consider the fact that each of the LTEE populations has had many beneficial mutations go to fixation over its history.  After 14 selective sweeps, the odds are better than 50:50 that at least one of those beneficial mutations was generated by a hypermutator.

King of the mountain.  After a hypermutator becomes common, it becomes very hard to dislodge it from the population.  This difficulty follows from the same logic as above.  Once the hypermutator reaches 1% of the population, it has a 50% chance of generating the next winner; by the time it gets to a 50% frequency, the odds are 100:1 in its favor.  Thus, a hypermutator only needs to get lucky once, and then it becomes extremely difficult to displace it … at least so long as the population is far from the fitness peak.

Nothing lasts forever.  Even before a population reaches a fitness peak, its rate of fitness improvement typically decelerates, at least in a constant environment like that of the LTEE (Wiser et al., 2013).  At some point, the magnitude of the benefit that would result from reducing the mutation rate and its associated fitness cost may become commensurate with the fitness advantages that are available from other mutations.  When that happens, selection to reduce the mutation rate becomes effective, and the hypermutable “king of the mountain” can be displaced by a genotype with a lower mutation rate.

Indeed, we have observed this displacement occurring in one of the LTEE populations (Wielgoss et al., 2013).  In that population, not one but two lineages independently arose (see Figure below) that reduced the mutation rate by about half, while reducing the fitness cost from ~1% to ~0.5%.  The population thus remains hypermutable, but less so than before.

What the future may hold.  In that paper, we hinted that it is probably easier to reduce the mutation rate in stages rather than to revert to the ancestral rate in a single step.  That’s because the population is continuing to adapt, albeit at a slower rate.  A genotype with a 50% reduction in the mutation rate will save half of the fitness cost of the full-blown hypermutator, yet it will continue to produce 50 times as many other beneficial mutations as would a genotype that reverted to the ancestral mutation rate.  In essence, the fitness costs and the evolvability benefits are on very different scales.

The figure below shows the decelerating fitness trajectory (dark green curve, left axis) and the number of mutations (right axis) as the lineage with the ancestral mutation rate (blue) is replaced by a hypermutator lineage (red), which in turn is displaced by two independent lineages with somewhat lower mutation rates (light green and purple).  The figure comes from Wielgoss et al., 2013, Proc. Natl. Acad. Sci. USA; it is shown here under the doctrine of fair use.

Mutation trajectory, PNAS 2013

8 Comments

Filed under Science

What We’ve Learned about Evolution from the LTEE: Number 2

This is the second in a series of posts where I summarize what I think are the most important findings and discoveries from the LTEE.

Number 2.  An exciting new twist on the dynamics of adaptation by natural selection is the discovery that fitness can increase “forever” – or at least for a very long time – even in a constant environment.

A power-law model, which has no upper bound, gives a significantly better fit to the mean-fitness trajectories measured in the LTEE populations than does a model with an asymptote.

Moreover, the power law predicts the trajectory of fitness evolution with much greater accuracy.  That is, if we reduce the data so that it includes only the first 20,000 generations, the power law trajectory that fits this truncated dataset accurately predicts fitness out to 50,000 generations (blue trajectory in the figure below).  By contrast, the same procedure with the asymptotic model consistently underestimates the future fitness gains (red trajectory in the figure below).

Also, a dynamical model that incorporates clonal interference (competition between different beneficial mutations) and diminishing-returns epistasis (where the marginal effect of a beneficial mutation declines with increasing fitness) produces trajectories that have the same power-law form.  That, in turn, facilitates estimation of important population-genetic parameters including the rate of beneficial mutations and the average strength of the diminishing-returns epistasis.

The figure below shows the grand-mean fitness data (symbols with error bars) over 50,000 generations of the LTEE.  It also shows the trajectories predicted by the power law (blue curve) and by a model with an asymptote (red curve) using only the first 20,000 generations of data.  The figure comes from Wiser et al., 2013, Science; it is shown here under the doctrine of fair use.

Power law prediction, 2013

6 Comments

Filed under Science

Fifty-Thousand Squared

I’ve been thinking a lot about the long-term evolution experiment (LTEE) with E. coli lately – even more than usual.  One impetus has been the paper by Mike Wiser, Noah Ribeck, and me that appeared today (14-Nov-2013) in Science (online publication in advance of print).  Another reason is that I’m working on the competitive renewal for the NSF grant that funds this experiment.

The Experiment that Keeps on Giving

Both of these have got me thinking about the long-term fate of this long-term experiment.  Should the experiment continue?  For how long should it continue?  Who will take it over when (or before) I retire?  And after that person retires, then what?  How will they sustain it?  Will they rely on the usual competitive grants?  Would an endowment be more suitable?  How does one raise an endowment?

I like to say that the LTEE is the experiment that just keeps on giving.  Between the element of time, the inventiveness of the bacteria (even in their simple, confined, little flask worlds), and the many talented students, postdocs, and collaborators who have worked on the LTEE, there seems to be no end to the insights this experiment can provide into fundamental questions about evolution.  Why shouldn’t this experiment keep on giving, even after I’m gone?

When I started the LTEE in February of 1988, I had no idea that it would continue for more than 50,000 generations.  I had previously done some other experiments that went for a few hundred generations, and I intended this one to run for at least 2,000 generations.  That would deserve the “long-term” moniker.  Although we made some fitness measurements along the way, most of the hard work comes after a milestone is reached.  That’s when one begins the intensive assays to quantify the changes that occurred.  And while we performed those assays, we continued the daily transfers.  So by the time the first paper was prepared, submitted, reviewed, revised, and published in December of 1991, the LTEE was past 5,000 generations.  And so it has gone:  new milestones, new questions, new assays, new data, new analyses, and new papers.

And the new questions keep coming based on new hypotheses of students, postdocs, and collaborators (occasionally even me), new technologies such as genome sequencing, and new observations of what the evolving bacteria have done.

Fitness Unlimited

This latest paper is an interesting one because it uses our most old-fashioned assays – the kind that was the heart of the LTEE when it started, and which also formed the core of that first paper back in 1991.  That is, the results are based on measurements of relative fitness, coupled with new models – both descriptive and dynamical.  (Although this blog post emphasizes the descriptive model, the Science paper also presents new theory showing that the descriptive model can be derived from a dynamical model of evolution that incorporates two phenomena – clonal interference and diminishing-returns epistasis – that are known to occur in the LTEE and other studies of evolving asexual populations.)

Fitness is the central phenotype in evolutionary theory; it integrates and encapsulates the effects of all mutations and their resulting phenotypic changes on reproductive success.  Fitness depends, of course, on the environment, and here we measure fitness in the same medium and other conditions as used in the LTEE.  We estimate the mean fitness of a sample from a particular population at a particular generation by competing the sample against the ancestral strain, and we distinguish them based on a neutral genetic marker.  Prior to the competition, both competitors have been stored in a deep freezer, then revived, and acclimated separately for several generations before they are mixed to start the assay proper.  Fitness is calculated as the ratio of their realized growth rates as the ancestor and its descendants compete head-to-head under the conditions that prevailed for 500 … or 5000 … or 50,000 generations.

The exciting new result is that the fitness of these evolving bacteria shows no evidence of an upper bound or asymptote.  A two-parameter power law fits the data much better than does a two-parameter hyperbolic model.  According to both models, the rate of fitness increase decelerates over time, as it clearly does.  However, the power-law model has no asymptote, whereas the hyperbolic model has an upper bound.

Even more striking and important, to my mind, is that the models differ in their predictive power.  We fit these two models to truncated datasets that included only the first 20,000 generations of data and asked how well they predicted the fitness values observed over the next 30,000 generations of data.  The unbounded power law beautifully predicts the fitness trajectory that it had not seen, whereas the asymptotic hyperbolic model underestimated later measurements.  The underestimation of the asymptotic model becomes progressively worse as the temporal data are more and more truncated; that is, the evolving bacteria consistently pass right through the “limit” predicted from previous data.  By contrast, even with only 5000 generations of data, the power-law model very nicely predicts the fitness trajectory all the way out to 50,000 generations.

A Thought-Experiment

How long can this continue?  In our paper, we present the following thought-experiment.  I’ve overseen 50,000 generations of the LTEE in my scientific life; now imagine another 49,999 generations of scientists, each one overseeing 50,000 more bacterial generations. That’s 50,000^2 generations, or 2.5 billion generations in total.  (It will take about a million years to get there.)  You’re probably thinking that the unbounded power-law model must predict some crazy high fitness that would imply a ridiculously fast growth rate.

In fact, the power law predicts that fitness relative to the ancestor will increase from ~1.7 after 50,000 generations to ~4.7 after 2,500,000,000 generations.  If the bacteria eliminate the lag time associated with the transition from starvation to growth each day (which they have already largely done), then a fitness value of 4.7 implies that the bacteria will have to reduce their doubling time from the ancestor’s ~55 minutes to ~23 minutes.  That’s very fast given that the LTEE uses a minimal medium where cells must synthesize everything from glucose, ammonium, and a few other molecules.  But it’s not so fast that it suggests the bacteria would violate some biophysical constraint.  Indeed, some bacteria can grow twice that fast, albeit in a nutrient-rich medium.

What Does the Future Hold?

I’d really like science to test this prediction!  How often does evolutionary biology make quantitative predictions that extend a million years into the future?  Maybe the LTEE won’t last that long, but I see no reason that, with some proper support, it can’t reach 250,000 generations.  That would be less than a century from now.  If the experiment gets that far, I’d like to propose that it be renamed the VLTEE – the very long-term evolution experiment.

And this prediction about the future fitness trajectory is not the only – or even the main – reason to keep the LTEE going.  Some important things in evolution simply require a lot of time.  In my presidential address to the Society for the Study of Evolution this past summer, I highlighted three findings where it proved to be important that the LTEE had continued for many years (and, if I’d had more time, I could have added more to that list).  First, it takes a very long time series to distinguish between asymptotic and non-asymptotic fitness trajectories.  Second, it took over 30,000 generations before the most dramatic phenotypic change occurred in one of the populations, which evolved the ability to use citrate – which has been present in the medium of the LTEE throughout its duration – as a second source of energy.  Third, postdoc Zachary Blount is currently studying whether the refinement of that new function is leading to changes that would qualify the citrate users as a new, or incipient, species.

What other new traits might the bacteria evolve?  Could they evolve some means of genetic exchange?  Might the within-population competitive interactions ever take a turn toward predation?  Who knows?  Only time will tell – and only if we allow time, the bacteria, and future generations of scientists to do the work of evolution and science.

Some Additional Links

27 Comments

Filed under Science

Genome Dynamics During Experimental Evolution

Jeff Barrick and I have written a review article for Nature Reviews Genetics on “Genome dynamics during experimental evolution.” Our paper recently appeared as an advanced online publication; the print version should be out in a week or so.

Jeff did a superb job illustrating the population-genetics concepts that underpin this field, as well as organizing and synthesizing the literature.  It has been such a fast-moving field that we’re both a bit embarrassed to say when the article was first proposed.  However, we think it was worth the wait for our readers, given all the exciting work that has appeared since then.

The first bacterial genome to be fully sequenced, Haemophilus influenzae, was published in 1995.  That species was likely chosen not only because it is an important pathogen, but also because it has a fairly small genome with fewer than 2-million base pairs.  I don’t know the cost of that project, but I recently heard someone say that it cost roughly a million dollars to fully sequence another important bacterial pathogen around 2002 or so.  Fast-forward just a few years and I remember being shocked – along with other members of the audience at a conference in 2005 – when Greg Velicer reported that he and colleagues had sequenced the genome of a Myxococcus xanthus strain that was part of an evolution experiment, in order to identify the mutations responsible for changes in its social behavior.  Greg did that work while he was at the Max Planck Institute, so his funding was more generous than what most of us doing experimental evolution could afford.  But it meant that genomics was becoming affordable for basic research.  In 2009, Jeff Barrick and I published two papers that analyzed the genomes, not of single clones or pairs of samples, but from multi-generational series of 7 clones and 7 whole-population samples from one of the E. coli populations in my long-term evolution experiment.  That seemed like a lot then but now, just a few years later, Lang et al. deeply sequenced 40 experimentally evolving Saccharomyces cerevisiae populations at 12 time points each!  [Note added after comment: By “deeply sequenced” I mean the authors sequenced heterogeneous population samples, and they could thus follow the trajectories of specific mutational  variants and genetic diversity over time.]  The combination of experimental evolution and genomics is no longer a novelty – it has become a powerful and affordable tool that can be used as part of almost any project on experimental evolution.

Our review paper begins by contrasting the design of two types of evolution experiments: mutation-accumulation and adaptive evolution.  In the former type, the experimenter seeks to eliminate the effects of natural selection by forcing the populations through extreme demographic bottlenecks that purge genetic variation.  (Remember: natural selection does not work in the absence of genetic variation.)  In that way, one can estimate a mutation rate directly, by minimizing the otherwise confounding effect of selection on the observable rate of genetic change.  (Of course, lethal mutations will not accumulate, although these typically represent only a small fraction of all mutations.)  Whole-genome sequencing provides dramatically increased power and precision for estimating mutation rates because one can combine and integrate data across millions of base pairs and hundreds or thousands of generations.  By contrast, older studies could detect mutations in just one or a few genes – chosen because they were known to cause specific changes in traits that could be readily scored – and they typically involved only a few generations of growth.

Adaptive evolution experiments are designed to shed light on various aspects of the process of adaptation by natural selection.  Genomic analyses of adaptive evolution experiments have allowed investigators to identify mutations responsible for interesting phenotypic changes, examine the extent of parallel evolution at the genetic level, quantify the dynamics of genetic diversity within populations, compare rates of phenotypic and genomic evolution, and address many other old and new questions.  And these adaptive evolution experiments are becoming increasingly complex as many investigators are now studying systems with multiple species, temporally or spatially varying environments, sexual reproduction or horizontal gene exchange, and so on.  Genomics will play a critical role in understanding these increasingly complex systems and scenarios.

Our review closes by drawing attention to areas of research that aren’t quite experimental evolution, as the field is usually meant, but for which similar combinations of evolutionary and genomic analyses and interpretations will become increasingly important in the years ahead.  For example, we think it won’t be too long before it becomes routine practice in genetics to sequence the entire genomes of any mutant or recombinant strain of interest and its parent, in order to be sure that the procedures employed did not inadvertently lead to other changes besides those intended.  And we point out that the combination of genomic and evolutionary analyses is extremely powerful and interesting in the context of evolution in action in microbial pathogens (see this previous post for a compelling example).

Jeff and I hope that many readers will find our Nature Reviews Genetics article a useful summary of a fast-moving field, a helpful primer at the intersection of experimental evolution and population genetics (especially for microbial populations), and a valuable lead to fascinating papers for further reading.

[The figure below is one panel from one of the figures in Barrick and Lenski, 2013, Nature Reviews Genetics; it is shown here under the doctrine of fair use.]

Image from Barrick & Lenski 2013

7 Comments

Filed under Science

Teaching Competition and Predation from a Microbiological Perspective

Life has been busy, very busy.  And life has been good!  But the busy-ness has made it hard for me to keep up with this blog.  In the next few weeks, I hope to share some of the things that have kept me so occupied this past month.

For starters, I’d like to discuss some recent teaching where I tried to emphasize the interplay between theory and experiments in ecology.

I recently taught part of our graduate-level course called “Integrative Microbial Biology.”  Some years ago this course replaced several other graduate courses (microbial ecology, microbial physiology, microbial diversity, etc.) that each had a low enrollment.  The idea is that we now offer a single, annual, intensive, team-taught course that covers all these topics, albeit more superficially but with the hope that it encourages students and faculty alike to develop a more integrated perspective of microorganisms as organisms.  More specialized courses, with a focus on reading and discussion, are offered as occasional seminar-style courses.

I teach two parts of the course – one on aspects of microbial ecology, the other on microbial evolution.   Many of the students have not had an undergraduate course in general ecology or evolutionary biology, and so I try to bring them up to speed, albeit with examples that focus on microorganisms.

So, for the ecology portion I begin with population growth and competition.  I’m a fan of resource-based competition theory, as opposed to the more familiar logistic growth and Lotka-Volterra competition models.  The key strength of resource-based competition theory is that one can predict the outcome of competition based on parameters that can be measured separately for each species or strain, without requiring that one compete them in order to understand their competition.  Of course, there are many reasons the predictions might fail, but the resource-based model (and extensions to it) provide a mechanistic framework for understanding competition.

I then present predator-prey interactions, surveying the extraordinary diversity of microbe-on-microbe predation and parasitism, and then providing again a dynamical framework for understanding those interactions.  Here, Lotka-Volterra predator-prey models do provide a reasonable starting point because one can measure key parameters that have mechanistic interpretations (e.g., attack rates, conversion efficiencies) and use them to make new predictions about the dynamics of the system as a whole.

Besides presenting the general theory, I also present empirical studies from the primary literature.  In some cases, I summarize the papers in my lectures, while in other cases the students read the papers and we then discuss them.  Here are four of the papers with summaries; I hope to blog someday in greater depth on at least the Hansen & Hubbell and Rainey & Travisano papers, which I view as “must-read” papers in the field of ecology.

Hansen, S. R., and S. P. Hubbell.  1980.  Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes.  Science 207:1491-1493.

This paper presented an early, concise, and compelling demonstration of the utility of resource-based competition theory.  By choosing three pairs of competitors that differed in various parameters, and then competing them in chemostats, the authors showed that the outcome depended on the two competitors’ relative “break-even” (equilibrium) concentrations of the growth-limiting resource.  For any student who wants more information on this approach – and every year at least some students ask for more – I recommend they read David Tilman’s outstanding book, Resource Competition and Community Structure (1982, Princeton University Press).

Rainey, P. B., and M. Travisano.  1998.  Adaptive radiation in a heterogeneous environment.  Nature 394:69-72.

This paper is a beauty.  The authors showed that the evolutionary emergence of diversity can sometimes depend on something as simple as whether a flask is shaken or not.  In the absence of shaking, an initially monotypic population of Pseudomonas fluorescens evolved into a community of three distinct ecotypes that differentially exploit the environmental gradients that arise without constant mixing; that diversity is stably maintained, as was shown by analyzing pairwise interactions.  By contrast, simply shaking the flask, with all else being equal, homogenizes the environment and the ecotypic diversity does not evolve; and if the diversity had already evolved, then it was eliminated as a single type came to dominate the well-mixed system.

Lenski, R. E., and B. R. Levin.  1985.  Constraints on the coevolution of bacteria and virulent phage: a model, some experiments, and predictions for natural communities.  American Naturalist 125:585-602.

Virulent phage infect bacteria, and they have life-cycles like those of insect parasitoids; that is, a successful infection is lethal to the host, and many phage are produced from a single infection.  In this paper, we examined the ecological and evolutionary dynamics of the interactions between E. coli and four different virulent phages.  First, the Lotka-Volterra predator-prey model – modified to include resource-based growth for the prey (bacteria) and a time-lag associated with predator reproduction (phage replicating inside bacteria) – predicted reasonably well the short-term dynamics of the interaction between E. coli and one of the phages, called T4.  Second, the model was extended to include the evolution of bacteria that are resistant to phage attack.  Resistance mutations changed the equilibrium density of the bacteria by several orders of magnitude, as the bacterial population went from top-down predator limitation to bottom-up resource limitation.  Yet despite complete resistance, the phage population persisted because there was a “cost of resistance” – in the absence of phage, the sensitive bacteria out-competed the resistant mutants.  In essence, the system becomes one of predator-mediated coexistence of sensitive and resistant prey populations.  Third, the interactions between E. coli and three other phages were examined.  Each interaction had somewhat different dynamics depending on whether resistance was costly or not, whether resistance was partial or complete, and whether the phage population produced host-range mutants that could infect the mutant bacteria that had become resistant to the progenitor phage.  [This paper built on related work that Lin Chao had done a few years earlier with Bruce Levin, and which inspired me to contact Bruce about joining his lab.]

Bohannan, B. J. M., and R. E. Lenski.  2000.  Linking genetic change to community evolution: insights from studies of bacteria and bacteriophage.  Ecology Letters 3:362-377.

This paper reviews the research that Brendan Bohannan did for his dissertation in my lab.  His work examined the same four bacteria-phage interactions studied in the Lenski and Levin paper above, but the work was extended to include some elegant new manipulations and analyses.  In particular, by changing the levels of resource available to the bacteria, the classic “paradox of enrichment” predicted by Lotka-Volterra predator-prey models was confirmed, with respect to the effects of enrichment on both equilibrium densities and the temporal fluctuations in population densities.  These experiments also provided compelling evidence for predator-prey cycles and the effects of bacterial resistance on the dynamics of the interaction between the remaining sensitive bacteria and phage populations.

8 Comments

Filed under Science