Characterizing amplifiers of natural selection and their optimization

Selection of new genetic mutations that are beneficial puts some organisms within a population at an advantage compared to others. In some populations, the same beneficial mutation is more likely to take over than in other populations. The population structures that increase the likelihood of the successful takeover are known as "amplifiers of selection," because they enhance the effect of natural selection.

However, there is a trade-off for how well these population structures can amplify natural selection. The trade-off is the relationship between the probability that a mutation will become fixed in the whole population and the time until it does. The paper, by a team at the mathematics department of Harvard University, Aarhus University in Denmark, and the Institute of Science and Technology in Austria, appears in Nature Communications, June 29.

Over the past 15 years, the authors state, "extensive research has produced remarkable structures called strong amplifiers, which guarantee that every beneficial mutation fixates with high probability." The amplification, however, has the drawback of delaying the fixation and often slowing the overall rate of evolution in the population. 

The researchers aimed to characterize how much strong amplifiers delay the fixation event.

Current Science Daily asked Josef Tkadlec, the lead author of the paper, to discuss the team's work. Tkadlec is a member of the mathematics department at Harvard.

The role of population structures

Tkadlec described amplifiers of natural selection as "population structures that increase the fixation probability of beneficial mutants, when compared to the baseline `well-mixed' structure where every two individuals compete directly."

"A population structure is a network, as in a social network, where there are sites that each host one individual," Tkadlec said. "Some sites are connected and some are not. In a single step, the mutation can spread only along the `edges' of the network, that is, from an individual only to a connected individual."

"When a single individual in a large population acquires a beneficial mutation, it might produce a lineage of offspring that eventually takes over the whole population, an event called fixation," he added.  

Alternatively, he said, "the mutation could also disappear due to `bad luck,' even though it was beneficial."

The probability that fixation occurs depends mostly on two factors, Tkadlec noted, saying these are "how much the mutation increases the fitness of the individual," and "what the underlying population structure is. That is, how easy it is for the offspring to migrate to other parts of the population."

But the fixation probability of a new mutation is only half the story. The other half is the time until fixation.

Asked about the tradeoff between the two, Tkadlec said because amplifiers can delay the fixation event so much, they can be "outperformed" in terms of the overall speed of evolution, by a well-mixed population. 

"To speed up the evolution, ideally you would like a population structure that amplifies the fixation probability and also shortens the fixation time of each mutation," he said. "The current amplifiers are perfect in the first regard, but so bad in the second one that, all in all, they are often not that great."

He summarized the researchers findings in quantifying the process. 

"We prove that, sadly, there are no strong amplifiers that are as fast as the well-mixed populations (or even faster)," he said. "Every strong amplifier must incur some slowdown, as compared to a well-mixed population of the same size."

The natural follow-up question is, "What is the smallest possible slowdown for which strong amplification is possible?" Tkadlec said. "Surprisingly, we show that the slowdown can be arbitrarily small. For an arbitrarily small (super constant) slowdown, we describe strong amplifiers that suffer only that slowdown and not more! It is a little bit like a strict inequality with numbers: There is no smallest number larger than 2.5--you can have 2.51, 2.5001, ... "

By studying this trade-off, Tkadlec’s group provides a higher resolution picture for probability and time in the overall speed of evolution. This also has led to a new class of fast strong amplifiers: selection reactors. The authors write: “A key component of this resolution is a new class of fast and strong amplifiers, which we call selection reactors. The selection reactor is a population structure with four parameters defining the sizes of its two components (hub and periphery) and the migration rates between them.”

The importance of the research

Asked how the new research moved the field forward, Tkadlec said: "Before this work, the experimental scientists we talked to viewed amplifiers more like a curiosity."

"In the lab, the first naive approach to speeding up evolution would be to increase the mutation rate (for example, by radiation)" he said. "The trouble is that once you do that, the known amplifiers cease to do better than the well-mixed population, because they are so much slower than the well-mixed population."

"In contrast," Tkadlec said, "since the new amplifiers are fast, they should be able to withstand an increased mutation rate and still do well. Another good sign is that the new amplifiers have a remarkably simple structure—the individuals can be thought of as living in two large chambers, and occasionally migrating from one chamber to the other one."

As for future research, Tkadlec said "there are many fundamental questions that are still left unanswered."

"Our focus in this work was on structures that allow something--a mutation--to spread much better than it would otherwise," he said. "As one example there is the complementary question of finding structures that are good at preventing something from spreading. One does not have to think too hard to see that this could be useful in epidemiology, for example, to help curb a future pandemic."