Field of Science

Crossing valleys in fitness landscapes

ResearchBlogging.orgWith his "holey adaptive landscapes", Sergey Gavrilets (e.g. 1997) solved the problem of crossing valleys of low fitness in the fitness landscape* by positing that for high-dimensional landscapes (which is realistic - typically the genotype consists of thousands of genes and many more DNA nucleotides) there is always a ridge between fitness "peaks" (which are then not really peaks). The only rationale for that idea is that the more neighbors a genotype has, the higher the chance that the fitness of one of them is about the same. However, there are indications that this is generally not true. Gavrilets himself says that if all the high fitness genotypes are over in one "corner" of the fitness landscapes, then there could not always be ridges. One way to formulate this is Kauffman's Massif Central hypothesis, which just says that the chance of finding a fitness peak of high fitness is higher closer to another high peak; peaks cluster in genotype space, and there is a correlation between peak fitness of neighbors. This has already been shown to be true in Kauffman's NK landscape (Østman et al., 2010), and is under investigation in other models as well. Stay tuned.

Ridges are irrelevant
That is not to say that it couldn't be true that there are ridges in real biological fitness landscapes of extremely high dimensionality. After all, the numerical landscapes investigated have few genes/loci in comparison. But, looking at real biological fitness landscapes empirically, there is every reason to believe that they are rugged, containing many peaks varying in height/fitness. I could state it like this: no one (that I have heard of) have shown that there is always a path of about constant fitness between any two genotypes. In other words, there are generally (at least) not any accessible paths between genotypes separated by more than one mutation that does not vary enough in fitness that selection can distinguish between them**. However, even if there is, it doesn't matter! If there were always paths of neutral fitness - ridges - between any two genotypes, it would be extremely unlikely that the population would find them. The ridges, supposedly, appear in fitness landscapes of very high dimensionality, meaning that the number of neighboring genotypes is going to be huge, so when increasing dimensionality and the first ridge appears, there are already a fantastic number of mutational neighbors, making it very improbable that the ridge will be discovered by stochastic processes (as evolutionary processes inherently are).

Fitness landscapes are not static
Not only has it been shown that valleys can be crossed when the mutation rate is not prohibitively low (Østman et al., 2012), as in the strong-selection weak-mutation regime (SSWM), where each new mutation is lost or goes to fixation alone, so no two mutations segregate in the population at the same time. But Gavrilets assumed that fitness landscapes are static in both space and time. Static in space means that they are the same in different geographical locations (wet vs. dry conditions, for example). Static in time means that for one location it stays constant and fitness does not change from one point in time to another. And I really should not have to explain how not true this is, right? I mean, not only is it obvious that a genotype adapted to a wet environment will not have the same fitness in a dry environment, it should also make immediate sense that the environment at one location can change over time, for example from a wet climate to a dry one. Fitness landscapes are clearly not static functions (references, you lazy bastard!).

The fitness landscape changes when 1) environmental conditions change and 2) when the population changes. Changes in population size can reduce the strength of selection; the larger the population is, the better able selection is to distinguish small fitness effects. When the population size is low, stochastic effects dominate, and genetic drift rules. In this case, valleys may be crossed in small populations just because the decrease in fitness while crossing the valley matters less (but see Weissman et al., 2009).

The effect of changing the environment is to change the fitness landscape. This could result in peaks shifting position in genotype-space, peaks appearing and disappearing, and deep valleys becoming shallow or vice versa. In two dimensions, instead of thinking of a rigid landscape, think of a seascape of water (e.g., Mustonen and Lässig, 2009). In this case, where fitness as a function of genotype is forever changing, evolutionary dynamics (i.e., moving around in the fitness landscape, crossing valleys, and locating new peaks) may be reduced to moving only uphill, rather than having to actually tolerate deleterious mutations at all. Some landscapes may indeed be rather static over longer periods of time, and then the dynamics of populations crossing valleys may be relevant. But it is totally possible that all the important evolutionary changes occur when the fitness landscape changes, rendering theories of valley-crossing somewhat immaterial.

* There are these two terms in use among researchers: adaptive landscapes and fitness landscapes. The only thing the former term has going for it is that Sewall Wright (1931) - accredited as the inventor of the idea - called it "adaptive landscapes". However, most people actually call it "fitness landscapes", but in addition to that important fact, it also makes a lot more sense. A fitness landscape is a function where fitness is given by genotype or phenotype values (rather than frequencies - incidentally, Gavrilets and I agree that fitness as a function of population allele frequencies makes no sense), so it makes a lot more sense to call it that. On top of that, fitness as a function of genotype/phenotype does not have to have anything to do with adaptation. The fitness landscapes can be flat, in which case there will be no adaptation going on. To my exasperation I just discovered a new book here at the Evolution 2012 conference in Ottawa by the title of The Adaptive Landscape in Evolutionary Biology (Oxford University Press). Nearly all the chapters, written by more or less famous people in the field, have 'adaptive landscape' in the title. Piss me off, it does.

 ** If two genotypes differ in fitness by a small amount, it may be too small for selection to distinguish between them. Since evolution is an inherently stochastic process, in which genetic drift is always present, and selection only chooses who gets to reproduce based on probabilities (fitness can be thought of as this probability), having higher fitness than your neighbor does not guarantee that you will have more offspring; it only makes it so on average. Generally, selection can distinguish fitness effects that are greater than one divided by the population size (s>1/N). If the selection coefficient (the measure of the fitness effect of a mutation, s=w'/w-1, where w' is the fitness with mutation, and w without) is less than one over the population size, then that mutation/genotype will drift, and selection makes no difference. The smaller the population is, the larger a mutation's fitness effect has to be for selection to see it, and therefore selection is weaker in small populations. This is the basis of Sewall Wright's Shifting Balance Theory (Wright, 1982), which explains how crossing valleys in a rugged fitness landscape can be done by breaking the population up into smaller groups (demes), which are then able to drift across the valleys, because selection is now weaker.

Gavrilets S and Gravner J (1997). Percolation on the fitness hypercube and the evolution of reproductive isolation. Journal of theoretical biology, 184 (1), 51-64 PMID: 9039400

Mustonen V and Lässig M (2009). From fitness landscapes to seascapes: non-equilibrium dynamics of selection and adaptation. Trends in genetics : TIG, 25 (3), 111-9 PMID: 19232770

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

Wright S (1931). Evolution in Mendelian populations Genetics (16), pp. 97–159

Wright S (1982). The shifting balance theory and macroevolution. Annual review of genetics, 16, 1-19 PMID: 6760797

Østman B, Hintze A, and Adami C (2010). Critical properties of complex fitness landscapes Proc. 12th Intern. Conf. on Artificial Life, H. Fellerman et al., eds. (MIT Press, 2010), pp. 126-132 arXiv: 1006.2908v1

Østman B, Hintze A, and Adami C (2012). Impact of epistasis and pleiotropy on evolutionary adaptation. Proceedings. Biological sciences / The Royal Society, 279 (1727), 247-56 PMID: 21697174

ALife 13 at Michigan State

The 13th conference on Artificial Life is going on right now at Michigan State University. Follow tweets at #alife13, and see program here. Being hosted by BEACON, it's got lots of evolution in action.

12 reasons why there is something

Why is there something rather than nothing? Pick your favorite reason among Michael Shermer's picks in Nothing is Negligible: Why There is Something Rather than Nothing. 

In the meantime, while scientists sort out the science to answer the question Why is there something instead of nothing?, in addition to reviewing these dozen answers it is also okay to say “I don’t know” and keep searching. There is no need to turn to supernatural answers just to fulfill an emotional need for explanation. Like nature, the mind abhors a vacuum, but sometimes it is better to admit ignorance than feign certainty about which one knows not. If there is one lesson that the history of science has taught us it is that it is arrogant to think that we now know enough to know that we cannot know. Science is young. Let us have the courage to admit our ignorance and to keep searching for answers to these deepest questions.

Defining life foolishly

Some like to define living organisms as that which

1) reproduces,
2) has inheritance, and
3) has variation.

In other words, living things would be those which evolve by natural selection. Rosie Redfield (blog) espoused this view in a recent and otherwise really goo talk at the Evolution 2012 conference in Ottawa (#evol2012 Twitter feed). Jerry Joyce (lab page) did the same at the 74th symposium of Quantitative Biology at Cold Spring Harbor Labs in 2009.

But this is folly.

First of all, I can easily give an hypothetical example of something that must clearly be alive, but which does not evolve. I'll defer that to the end of this post.

But I can also give an example of something that most people will not agree is alive, namely languages. Metaphorically, I can accept that languages are alive. "Danish is such a beautiful language, alive with raunchy adjectives and verbs that sing." Or something. But not actually alive in a literal sense. It is spoken by beings that are alive, but is no more alive than thoughts or books, even if it does evolve (note that languages evolution really isn't of the Darwinian kind, either, just like memes aren't).

We can of course define for our own purposes life (or living things) as anything we want. Doing that sensibly, however, is key, since science is all about communication. I could define life as anything that grows, anything that moves, anything that catalyzes chemical reactions, etc. Those are all things that most things we would call life do in some way or other. But it would not be sensible, because there are things that are not alive that do those things, too. Fires grow, the wind moves, earth catalyzes. Defining something sensibly means that it should conform to daily use of the term, or in the cases where it does not, it should make sense to refine the vernacular.

So in defining life as something that evolves by natural selection, we would both include things that clearly are not alive in the sense that most people understand it (language), and we would also exclude some things that are clearly alive, but does not evolve.

This latter thing that is alive but does not evolve - what is it, then? It's true that no living organisms that we know of do not evolve, right?

Well, both true and false. First of all, individual organisms do not evolve at all. Populations evolve. Lineages evolve. Individuals develop - from a single cell to an adult human, for example. Organisms are collections of cells, and does not evolve. Does that mean I am not alive? Clearly I am. This definition does not work. It is true that all living things descend* with modification from ancestors that were different from themselves. But what if we one day discovered an organism, looking quite like any other, but which does not die and does not reproduce? Would it not be alive?

Suppose we go to another planet and find one being there, looking exactly like a human being. Everything we can measure about this being confirms that it is just as much alive as you and me. It eats, moves, heals, replenishes, communicates, feels, defecates. Learning more about this being, though, we find that it has no ancestors, and that it does not age. It does not reproduce, and it is the only such being on the planet. Thus, there is no lineage of descent and no population that can evolve. So this being is then not alive? Of course it is. This definition does not work.

For those of you who would object that this example is irrelevant, because no such being that is alive but does not evolve has ever been found: definitions must encompass such thought experiments, or they are useless. If our definitions can not guide us when we are in doubt - in situations where something new is encountered, them they are useless. In that case we might as well just define life as the things that we already know are alive, which just amounts to bookkeeping.

Lastly, see what I did there? I demolished something without providing a solution. Tough luck! I am not required to put forth another definition that I think is better than this one. Just as well as I am not required to come up with some alternative to religion just because I am an atheist.

Is R2-D2 alive? Is it evolving?

* Actually, I prefer to say 'ascend', like the twigs on a tree grows up, and not down. Idiosyncrasies.

Blogger poutine

Here we are a group of bloggers in Quebec just across the border from Ottawa having poutine. Jerry Coyne, Rosie Redfield (blue hair), T. Ryan Gregory, Steve Watson, and Seanna Watson. Picture is taken by Larry Moran.

Tweets from Evolution 2012 in Ottawa

Lots of people are tweeting from the Evolution 2012 conference in Ottawa. It's the biggest evolution conference ever - first joint North American and European. Sad for those who are missing it, but at least you can follow it on Twitter.

Carnival of Evolution #49 at Mousetrap

CoE #49 is up at the Mousetrap. This is Joachim Dagg's blog, and he really likes mousetraps. I suppose this may be inspired by Michael Behe, but I cannot be sure. Here's one of my favorites:


 As he says, notice the trap to the right. There are other interesting things to notice here.

 Next edition - the 50th - will be at Teaching Biology.

On independence

[Repost from July 4th, 2009.]

On this 4th of July allow me to quote that famous sentence from the Declaration of Independence:

"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."

I personally disagree and agree with everything said in that sentence at the same time. Those truths are not self-evident. They must be arrived at. They aren't truths to me, and yet they are all goals worth pursuing. All men (humans?) are not created equal, but some are born into slavery, poverty, or born with mental or physical disabilities. However, they should be treated with equal respect and compassion. Since there is no Creator to endow us with anything, nor to uphold any rules (the latter, at least, is evidently true), then rights are something that we humans instill by law, and nothing else. A "right" to life doesn't even make any sense, but that we afford, by law and compassion, everyone with the help they may need to live, that would be a worthwhile effort (hopefully we'll get there eventually). Liberty is a human concept, thus we decide what we want of it. And it is safe to say that nearly everyone living in this country (that's the USA) agrees to uphold the law, and thereby forego some of that very liberty. Freedom is good, but only partially so*. Same for pursuing happiness, granted you don't diminish anyone else's, I would say.

In summary, those words can be interpreted with good meaning, but are so horribly written that they allow themselves to be used with favor by anyone anywhere on the political spectrum.

In regards to independence, I value it as much as - equate it to, even - Life, Liberty and the pursuit of Happiness. I say on to ye, let these proud nations be free to govern themselves. Free Tibet, if that's what they really want (by majority). Let Taiwan go. Let the measure of China be whether nations want to be part of them. If not, take it up for consideration, and change in ways that will entice others to join you. Why is larger better, anyway? Greenland ceased to be a Danish colony in 1953. If they want independence, I say let them have it. Iceland got their independence from Denmark in 1944. Good for them. The Faroe Islands, like Greenland, is a part of the Danish Kingdom, and has been stirring with thoughts of independence. If they can ever make a decision, let them them go too, if that's what they decide. Then get a proper football team.

*Who said "Free as a bird. The next best thing to be."?