Field of Science

Darwin's theory can handle the landscape

ResearchBlogging.orgCue the fitness landscape. A multi-dimensional function for organism fitness (ability to reproduce) as a function of the genotype*. A population moves "uphill" when it can to maximize fitness, akin to physical systems, which always moves to minimize its energy.

If the population (average) sits on the red dot in this fitness landscape (where fitness is on the ordinate (y-axis) and genotype is on the abscissa (x-axis)), then it will move up to the top of the peak (green dot), by spawning and acquiring beneficial mutations in a straight-forward manner.

Imagine, then, a landscape with many hills and valleys. Specifically, many peaks (local fitness optima) which, once 'inhabited', the population can only move away from by decreasing its fitness (moving from the green to the purple dot in the figure above). The individuals who do move away from the peak will have lower fitness, and thus won't have as many offspring (on average) as those who stay on the peak. Two or more genotypic mutations are required before the organisms can escape that local peak and ascend the adjacent higher one. When this happens, those individuals who stay behind will be outcompeted by the mutational emigrants.

But, since finding a new higher peak then requires that the organisms first decrease in fitness, then the question begs if this ever happens. It sounds like a very unlikely event, and, indeed, Darwin expressed concern about the matter:
"If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down."
I am aware that Darwin most likely wasn't talking about decreasing fitness, but other have since taken it to mean that every genotypic change must be advantageous.

But there is now plenty of evidence that evolution doesn't (can't) always proceed by small steps that increase fitness, so...

I'd really like to present just one of the papers that model valley-crossing dynamics: The rate at which asexual populations cross fitness valleys, by Weissman et al. (2009). Gotta love the title. As they say in the discussion,
the conventional assumption is that adaptation is far more likely to occur by single mutations which each increase the fitness, since double mutations or more complex processes are far less probable.

These two figures here of one-dimensional fitness landscapes illustrate this point. In figure a and b above, the population sits on a peak and needs two and three mutations to higher fitness, respectively. It is obviously easier to go straight up a hill, increasing fitness by every mutation, than these two situations, where the first one or two mutations will still not increase fitness, but a second or third mutation will. The question is how likely it is valleys like these can be crossed, and which parameters make it more likely.

This is answered by calculating the waiting times for a beneficial mutation (increasing fitness) to go to fixation (i.e. being present in all individuals, which, for asexuals populations, means that the individual that first acquired the mutation is an ancestor of all individuals at a later time). This time is denoted by τ:

The crosses are results from their simulations, and the lines are the analytically derived results (and they agree very well, don't you think?). The effect we see is that the larger the population size, the higher the mutation rate and the lower the fitness cost of the intermediate, deleterious mutations are, the less time it takes a population to cross a fitness-valley. This is not surprising: the larger the population is, the more mutations is tried per time, since more individuals means more offspring, and that offspring can mutate when the parent DNA is copied. And, of course, the higher the rate of mutation is, the more mutations. Lastly, the shallower the fitness-valley that must be crossed is, the more likely it is that the one- or two-mutant genotypes will produce offspring (which is required to generate a second/third mutant).

The phenomenon that gives rise to multiple peaks in the fitness-landscape is called epistasis: interaction between genes or between mutations. The first mutation alone decreases fitness. The second mutation alone (i.e. without the first one happening) is also deleterious. But together they are beneficial. This is termed positive epistasis, when the fitness of the two mutations together is higher than the sum (or product) of the fitness of the two mutations independently of each other.

Darwin's worries were unfounded. Yes, it's comfortable to imagine that evolution proceeds by ever so many slightly beneficial steps, but the fact that it doesn't always do that does not mean that Darwin's theory breaks down. At least not the way the Theory of Evolution is understood in this century.

* The fitness landscape really should be fitness as a function of the phenotype (all the physical characteristics of the organism), but in many computational models of evolutionary processes, the genotype (the genetic make-up) maps uniquely onto the phenotype, so there's no distinction.

Weissman DB, Desai MM, Fisher DS, & Feldman MW (2009). The rate at which asexual populations cross fitness valleys. Theoretical population biology, 75 (4), 286-300 PMID: 19285994

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