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Experimental evolution of bet hedging

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Guest blogger: Will Ratcliff

This week's paper, "Experimental evolution of bet hedging" by Hubertus Beaumont, Jenna Gallie, Christian Kost, Gayle Ferguson and Paul Rainey, published in Nature, shows that a trait that initially evolves for non bet hedging purposes can be maintained in the population through bet hedging.

The theory of bet hedging was first mathematically developed by Daniel Bernoulli (yes, the Bernoulli we all learned about in high school physics) in 1738. Because the basic idea is so simple - uncertain future conditions make conservative strategies beneficial - it is likely that folk wisdom advising bet hedging long predates Bernoulli's maths. The phrase "Don't put all your eggs in one basket" is one example of a widespread but anachronistic reminder to spread risk. Before we dive into this week's paper, I want to briefly cover the theory of bet hedging.

Like investing in the stock market, evolution is a multiplicative process, not an additive one. Steve Stearns (2000) illustrates this well....

"If a genotype has reproductive success that is twice the [population's] average in this generation and three times the average in the next, then its fitness [measured, as usual, relative to the population average] over those two generations is six times (2 × 3), not five times (2 + 3). If each of two children has three grandchildren, then there are six, not five, grandchildren."

This means that the correct way to measure average returns is the geometric mean, not the arithmetic mean. The geometric mean is fairly easy to find: just multiply a genotype's fitness in generations 1 through n, and then take the nth root of that number. For example, the geometric mean of 3, 2, and 4 is the cube root of 24 (3x2x4), or about 2.88. Key properties of the geometric mean are:

1) It is always lower than the arithmetic mean. For example, the arithmetic mean of 3, 2, and 4 is 3, which is greater than 2.88. The amount that it is lower depends on how variable fitness is during the period in which it is measured. The more variable fitness is, the lower the geometric mean is relative to the arithmetic mean.

2) Genotypes with the highest geometric mean fitness will dominate the population over the long-term. Natural selection thus optimizes the geometric mean, not the arithmetic mean (though in the short-term this is not always true: see this recent paper that I really should blog about).

So, what does this all have to do with bet hedging? Qualitatively, bet hedging is defined as a trait that spreads risk, trading-off some potential short-term benefit for a long-term benefit. "Trading off" implies that a bet hedging trait is one that reduces arithmetic mean fitness but increases geometric mean fitness. Let me illustrate with an example: assume that for an annual plant, March 23rd is the single best day for its seeds to germinate. However, there is a small risk that there will be a severe frost that kills 95% of the seedlings that germinated that day. This event is rare enough to have little effect on the arithmetic mean, but it has a big effect on the geometric mean. A plant genotype that produces seeds which all germinate on March 23rd will have the highest fitness in the population until the year that early frost hits, but then that lineage will decrease drastically. If a plant were to leave seeds that germinate from March 15-30th, it is giving up some potential arithmetic mean fitness because many of its seeds are germinating at suboptimal dates, but by spreading risk it reduces variation in fitness and increases geometric mean fitness. This would be bet hedging.

Thus we arrive at the central problem with empirical bet hedging research: how do we know if a putative bet hedging trait evolved for the purposes of bet hedging? Simply observing that a trait is unexpectedly variable provides no evidence for bet hedging. One needs to show that the trait decreases arithmetic mean fitness, but increases geometric mean fitness. As stated by Andrew Simons (2009, see Ford's blog post on this paper) "It is because of difficulties in characterizing the fitness effects of environmental variance over appropriate time scales that so little empirical work on bet hedging exists." A more subtle variation on the above question has to do with evolutionary dynamics: might a trait evolve for reasons other than bet hedging, then be maintained as a bet hedging strategy when conditions change?
If only we had the complete history of an organism's evolution of bet hedging! Then we could actually answer the questions above...

Enter this week's blog post. Paul Rainey's group works with the bacterium Pseudomonas fluorescens, which is well-known for experimental evolutionary studies on adaptive radiation. A new niche for these bacteria can be created simply by letting a flask of nutrient media sit still on a bench. Mutants capable of making a surface biofilm (and getting access to oxygen, a limiting nutrient when the flask is still) have a large fitness advantage and quickly invade. Shaking the flask removes this niche and the biofilm formers are quickly outcompeted by non-biofilm formers.

The authors created an environment that fluctuated frequently by transferring bacteria from static to shaking flasks. Further, they waited to make the transfer until a new genotype evolved in the flask with a different colony shape, transferring only this rare genotype to the next flask (Figure 1). This transfer strategy sets the fitness of the common genotype to 0. In order to maximize geometric mean fitness (or even have it greater than 0 after two transfers), a single genotype must produce variation in colony morphology faster than a different genotype with novel colony morphology can arise through mutation and selection.
Thumbnail image for bet-hedge.jpg
Figure 1- Pseudomonas transfer regime

Beaumont et al. found that in 2 out of 12 replicate selection lines, a single genotype evolved that stochastically switched the expression of a gene that encapsulated the bacteria on and off. As a result, this single genotype formed two distinct colonies, depending on whether or not the cell that founded the colony was encapsulated or not. Unlike all the other non-switching genotypes, this genotype was able to persist in the selection experiment through many transfers.

So is this bet hedging? In the context of our definition of bet hedging above, the genotype that generates new colony morphologies at a high rate (thereby increasing geometric mean fitness) must come at a cost to growth rate within a single flask, relative to a non-switching genotype (thereby reducing arithmetic mean fitness). This is not what happened.
The mutation leading to switching was totally beneficial relative to the immediate ancestor. Within a single flask, it actually grew faster than the immediate ancestor, possessing a relative fitness of ~1.18. As a result, this mutation increased both arithmetic and geometric mean fitness, so did not originally evolve because of bet-hedging.

Although the initial evolution of this trait doesn't meet our definition of bet hedging, the persistence of this genotype in the experiment can be attributed to bet hedging. No non-switching genotypes were able to invade the population, and thus be passed on to new flasks, because the switching genotype generated variation in colony morphology so quickly. This illustrates that the switching genotype had the highest geometric mean fitness of any strain tested. But further experiments showed that the switching genotype did not always possess the highest arithmetic mean fitness.

When the switching genotype was used to found a population that was then transferred in bulk from flask to flask (without choosing a single colony to found the next flask), new mutants were eventually able to invade the population. Some of these invaders had lost the ability to switch phenotypes. These new genotypes thus possessed higher growth rates, and if the environment did not change, would have both higher arithmetic and geometric mean fitness. But under the original rules of the selection experiment (Figure 1), these non-switching genotypes would not be transferred to the next flask and would thus possess a geometric mean fitness of 0, which is lower than the switching strain. The switching strain thus trades growth rate in a constant environment (and reduced arithmetic mean fitness) for growth rate in a fluctuating environment (and increased geometric mean fitness). We can conclude that the persistence of the switching genotype in the environment was thus due to bet hedging.

This work provides a beautiful view of the evolutionary dynamics of bet-hedging. While it does not change our theoretical understanding of how natural selection maximizes fitness in a fluctuating world, it does demonstrate that bet-hedging can evolve through co-option of a trait that originally evolved for non-bet hedging reasons.

Beaumont H. J. E., J. Gallie, C. Kost, G. C. Ferguson, and P. B. Rainey. 2009. Experimental evolution of bet hedging. Nature 462:.
Simons A. M. 2009. Fluctuating natural selection accounts for the evolution of diversification bet hedging. Proceedings of the Royal Society B: Biological Sciences 276:1987-1992.
Stearns S. 2000. Daniel Bernoulli (1738): evolution and economics under risk. Journal of Biosciences 25:221-228.


Hedging bets - very sexy - but when are Darwinians going to stop using human metaphors based on human intelligent behavior to describe non-human biological behavior?

Evolutionists do not want to say mutations are purposeful but then proceed to treat them as deliberate strategy.

You are all sounding more and more ridiculous by the minute!

But when I write about "linkage disequilibrium in semelparous species evolving in sympatry", people ask for plain English!

I agree that using terms like "strategy" to describe behavior of species without brains could give some people the wrong idea: that we are implying conscious decision-making. I once had a fellow scientist object to my discussing bacterial strategies, five minutes after he had referred to "host recognition" by a plant parasite -- recognition without cognition? (Why hasn't the "Lord of hosts" done something about all those parasites?)

If a chess-playing computer has a strategy coded in its "memory chips" -- do you write letters to computer manufacturers objecting to their metaphorical use of "memory"? -- why can't a brainless bacterium have a strategy coded in its DNA? But go ahead and substitute "seemingly strategic behavior", if it makes you feel better.

Without brains, individual bacterial cells have little or no ability to change strategies when they don't work. At the population level, however, when one of many random mutants happens to have a better DNA-coded strategy, its descendants displace those with inferior strategies, as the research described in this paper shows in molecular detail.

Just a quick note to say that I greatly enjoyed your explanation of this paper, which I normally would not have read because I didn't understand the title. I thought you explained it quite well.

I greatly enjoy this blog. Keep up the good work!!

In your illustration you refer to a devastating frost occurring in March as an "early" frost. I think you meant a late frost. Early frost of course is what we experience in the fall.

Aside from that I have to agree with Gerry... nicely done!

Gerry and Clem, thanks for the support! Knowing that people get something out of these posts makes all the difference. @Clem- You are right, late frost would be better than early frost.

Hey Will, I enjoyed the post. I stumbled upon it while I was looking for this paper in particular. Hope things are well. -Matt (from the GRC)

Ahh the benefits of a high Google search rank. It's great to hear from you Matt! Hope everything is well in Houston, I'll see you at the next conference (Portland 2010?).

Ford: As it stands when people ask for plain English they get in return Dawkinesque metaphors i.e. non-human amoral biological behavior described in human value/moral judgment form.

I would not argue with computer terminology because when we say "memory" we literally mean electronic memory in terms of both function and design.

When you say "strategy" you don't literally mean a deliberate device used to meet enviromental contingencies.

But the pure fact may be that all biological systems do have the ability to recognize imperatives and devise strategies to respond these imperatives.

Darwinian Theory doesn't allow for such purposeful behavior so it is left flailing around with no resort other than to describe biological behavior in the very terms they seek to deny i.e. very, very, very intelligent design.

I am an atheist IDer. I seek to understand the nature of this 'intelligence' inherent in all biological systems. I am yet to meet a Dawinist who is even willing to contemplate such a heresy.

Contemplation of scientific topics is enhanced by data. Is there a recent journal article, containing data directly relevant to your claims, which you would like me to discuss?

If not, try the Troll Refuge.

One claim I am making is this: It might be a fact that all biological systems have the ability to recognize imperatives and devise strategies to respond these imperatives.

[ What kind of data would test, i.e., have the potential to disprove if wrong, such a vague claim? -- Ford ]

Ratcliff WC, Hawthorne P, Travisano M, Denison RF (2009) When Stress Predicts a Shrinking Gene Pool, Trading Early Reproduction for Longevity Can Increase Fitness, Even with Lower Fecundity. PLoS ONE 4(6): e6055. doi:10.1371/journal.pone.0006055

[ What part of the word "data" do you not understand? If you'd even skimmed the paper, which I've already discussed on this blog, you'd see that it contains mathematical models, not data, so it couldn't be used to test your claim, even if your claim were explicit enough to be testable. The model predictions could be tested experimentally, however, and we hope to do so. If any of those predictions turn out to be wrong, then we will have to recheck our math and the assumptions upon which the model is based. -- Ford ]

[ Additional ranting deleted, but feel free to post it to the Troll Refuge. ]

I didn't realize that bet hedging has it's roots back in 18th century. Thanks for the enlightenment

Interesting experiment - one question - how long does the trait persist if it isn't used? (i.e. if the bet-hedging isn't required?) I think this is especially important when you look at species with longer lives and reproductive cycles.

I'd like to do an experiment to answer this question in some experimentally tractable species. A trait can become less common in a few generations if it's harmful under current conditions and if mutations eliminating it arise frequently.

This is quite interesting. I would say that hedging could be safer. Plants that germinate on the best day could run into trouble based on that 5% chance of severe frost. But it is not always good to spread risk. If the chance of frost is little enough, germinating on the best day would be best to enjoy best of health.

Fascinating! My logic tells me that if a particular trait is not utilized on a regular basis, it will be lost but what are your thoughts about that? Would it take years, decades, generations?

Hi Ida,

This is a great question precisely because there is no simple answer. The persistence of an unused trait in a population depends on any costs associated with that trait when it is not in use (high cost results in rapid selection against it) and generation time (shorter generations result in more opportunity for selection per year). If there is no cost at all to the unused trait, it can be lost from the population by genetic drift. The rate of this process (per generation) is inversely proportional to population size. A great figure illustrating this can be found on Wikipedia (http://en.wikipedia.org/wiki/File:Random_genetic_drift_chart.png).

Often, traits that are protective in stressful but rare environments will carry a cost in the 'average' environment. Because bet-hedging maximizes long-term fitness, bet-hedging genotypes are susceptible to invasion by non bet-hedgers during a series of 'average' years. However, when the stressful year occurs, bet-hedging genotypes that have evolved optimal long-term traits should be able to outcompete non-bet hedging genotypes. There are interesting complications to this interaction, however. For more on this subject I recommend the recent paper by Sebastian Gourbieere "Adaptive dynamics of dormancy duration variability: evolutionary trade-off and priority effect lead to suboptimal adaptation".

Amazing! Our judgement tells me that in case a unique mark is just not applied to a regular basis, will probably be misplaced although precisely what are your ideas with that? Will it acquire many years, many years, a long time?
This is fascinating. I'd personally claim that securing may be less risky. Plants this germinate for the best evening may possibly run across trouble dependant on that 5% chance of significant frost. However it is not at all times very good to help pass on danger. If the prospect of frost is no plenty of, germinating for the very best morning work best to experience best of health.

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