SEWALL WRIGHT, THE ADAPTIVE LANDSCAPE, AND WHAT WE DON'T KNOW (page 3)

Fast-forward to 2014

(For a more detailed history of the adaptive landscape I suggest reading the first chapter of this book - (edited by Calsbeek and Svensson)

The adaptive landscape concept caught on as an intuitive way of thinking about how evolution happens and as a way of describing tricky evolutionary ideas. It was co-opted to describe the mapping between phenotype and fitness both at a specific, mathematical level and at a broad, conceptual level. As we learned more about genetics, "mutational landscapes" and "fitness landscapes" emerged that were more explicit versions of Wright's genetic-factor-combination landscape. Adaptive landscapes found a place in introductory evolution textbooks, and terms like "peak-shift," "valley-crossing," and "hill-climbing" peppered the literature. But more recently, some have criticized the adaptive landscape concept for a variety of reasons, including that the idea is "meaningless in any precise sense" (Provine p. 310).

So Does the Adaptive Landscape Suck?

With all of these criticisms, we might ask whether the adaptive landscape is useful at all. I happen to think that not only is the concept useful on its own, but it is even more useful if we recognize and discuss its weaknesses.

In an excellent paper summarizing the debate about the adaptive landscape, Anya Plutynski tries to reconcile both sides of the issue by advocating for a dynamic understanding of the metaphor, in which we actively question whether parts of the analogy are correct or not. Drawing on the work of Hesse before her, Plutynski writes about neutral analogies, which are "the most important aspects of a model; these are the respects for which we do not know whether or not the model and the system under consideration are positively or negatively analogous." If we view the adaptive landscape concept and the metaphor with a physical landscape from this kind of critical perspective, we can take each point of criticism and ask whether it represents a negative analogy, a positive analogy, or - most importantly - a neutral analogy that reveals an open question in evolution. This is the perspective assumed by many biologists, each of whom "critically evaluates the foundational assumptions of the other out of which a new Adaptive Landscape is created, along with new, arguably fruitful paths of inquiry" (Skipper and Dietrich 2012).

The Criticisms

Two Silly Ones

First, I would like to identify two types of common criticisms that are not useful in this conversation. Above, I addressed the claim that Wright's main reason for inventing the landscape was to provide a non-mathematical description of his quantitative work. As Emanuele Serrelli writes, "Saying - as often happens in literature - that the adaptive landscape was a metaphor 'for complicated mathematical models of population genetics' is formally vague and misleading, and substantially wrong." (p. 70).

The second type of criticism I don't find useful is when "The Adaptive Landscape" is taken to mean specifically Wright's versions of the landscape, in which the mapping for the space of genetic combinations or allele frequencies to fitness results in many peaks. Criticism of Wright's assumptions is very useful, but making broad statements about "The Adaptive Landscape" when criticizing Wright's specific assumptions ignores the modern work by evolutionary biologists that use the general concept while defining the structure of the landscape in a way different from Wright. As Serrelli writes, "Adaptive Landscapes can thus exist with a shape different from that given by Wright. This means that the particular shape is not inherent to the landscape metaphor: the two are decoupled" (p. 59).

What's on those axes?

In his provocatively titled paper "The End of the Adaptive Landscape Metaphor?" Jonathan Kaplan touches on both of the criticisms from above, but he also makes sure to hit another common issue: Wright's multiple versions of the adaptive landscape (Kaplan 2008). In one version, the possible positions represented different combinations of allele frequencies in a population, so that a point would represent a population. In another, the possible positions represented different combinations of genetic factors, so that a point would represent an individual. Kaplan calls these adaptive landscapes and fitness landscapes, respectively, though I've seen those terms used for a different distinction, as we'll see below. In any case, there has been some disagreement about how compatible and how valuable the two versions are.

In both cases, Wright's purpose for using the concept was to make the qualitative argument that the "surface" would be rugged because of interactions. But if we compare the two versions precisely we will find, like Kaplan or Provine, that there are disturbing issues and differences. Measuring the adaptiveness of a population or the mean fitness is an interesting question in and of itself, and the idea that natural selection will even increase the mean fitness might not be true in some cases involving frequency-dependent selection. Meanwhile the other version isn't a "surface" at all, it is a discrete structure, a Hamming graph of genetic combinations. So it's not really a continuous surface like the one pictured, it doesn't have any clear units, and according to Provine, it is "meaningless in any precise sense" (p. 310).

"Meaningless in any precise sense"

This is perhaps the most revealing quote about the adaptive landscape concept that Wright presented. But rather than seeing it as a death-blow to the concept, I think it shows once again that the original adaptive landscape is not a diagram that explains well-understood work in population genetics. It is a concept that highlights not what we know, but what we don't know, what we would like to know, and what we need to know to create full-fledged and possibly predictive models of evolution. The important question is this: What is the structure of the mapping between the space of possible genetic states and fitness? Wright invented the concept to get across his guesses (he might not have called them guesses...) at the solution to this problem based on both his work in physiological genetics and animal breeding. Wright's guess was imprecise because he didn't have the mathematical tools to make it precise. Since Wright's initial work, both phenotypic and genotypic versions of the landscape have been developed that are precise models limited by strict assumptions that are often very difficult to justify. Russell Lande and Stevan Arnold led the way for phenotypic "adaptive landscapes" that rely on additive genetic variation underlying continuous phenotypic characters. Gillespie, Kauffman, and Gavrilets among others, made precise models of genotypic "fitness landscapes" based on simplifying assumptions about the mapping between genotype and fitness.

Many people are working to extend these ideas or investigate these assumptions. Many of the problems can be represented under the umbrella of understanding the genotype to phenotype to fitness mapping, an extremely difficult and complex problem in evolutionary biology. For the genetic "fitness landscape" case, each lab can only tackle a specific subspace of the problem because of the combinatorial explosion of possible genetic states. Borrowing Plutynski/Hesse's terminology, this uncertainty about the genotype-phenotype-fitness mapping is a giant neutral analogy in the landscape metaphor, and a representation of the persistent gap in knowledge that the fathers of the modern synthesis encountered in the 1930s.

So Many Dimensions

Some criticisms have focused on the difference in dimensionality on either side of the adaptive landscape metaphor: a 3-dimensional physical landscape (2 without elevation) vs. the extremely high dimensional landscape needed to represent the genetic state of an organism. This is clearly a "negative analogy," where the idea of a physical landscape is way off, and the low-dimensional visualizations of these high-dimensional spaces have been decried as "misleading in important ways" (Kaplan 2008). While Wright's correspondence with Fisher makes it clear that he was not mislead in the way Kaplan implies, it is certainly true that the low-dimensional images can be misleading. In order to combat this issue we should teach this concept with care, making sure to present the idea not as a solid mathematical surface with multiple peaks, but a complicated structure that allows us to hypothesize about the genotype-fitness or phenotype-fitness mapping.

The second important issue when thinking about the dimensionality of the "true" adaptive/fitness landscape, is that any study we do examines what is necessarily in a subspace. What this means is that if we test 5 gene combinations for fitness and find peaks separated by a valley, we have not ruled out the possibility that when we add a 6th dimension, a ridge that connects the two "peaks" will be exposed (the term for this phenomenon is one of my favorite terms in science: EXTRA-DIMENSIONAL BYPASS). Importantly, this will only be an issue if there are non-additive interactions between the subspace we are considering and elements that we aren't studying. This leads to a need to understand which genetic elements interact and at what levels. Again, this flaw in the adaptive landscape concept proves to be an effective way to illustrate an important direction for new work.

A Seascape

This criticism is simple but important to remember: the mapping between genotype or phenotype and fitness is to some degree affected by the environment. The "environment" could be abiotic factors like climate or biological factors like the abundance of predators or the density of the population in question. Even more distressingly, changes to a population due to evolution can change the environment through processes like resource depletion, so in some sense moving on the landscape can change the landscape. This realization forces us to question if these kinds of environmental change are relevant to the questions we are asking, and if so, forces us to consider the differences in the mapping in different environments. For a cool recent example of this kind of thinking, check out this paper on evolutionary rescue during environmental change (Lindsey et al. 2013).

How do things move?

This is a criticism I have seen less often, but it is a valid question, and one that leads to another pathway for further work in evolutionary biology. The question is this: after you have defined your landscape (your "space of possibilities"), how can and how do the agents move around it? We can roughly separate these two questions by saying that the first deals with "mutations" and the second deals with population genetics. Rules for what constitutes a single mutation or change (which can be called "variation operators" (Stadler et al. 2001)) define how agents can move, and rules about how they do move are defined by population genetic theories.

Focusing on the can question, we can ask what the variation operators are in genotype or phenotype space. In genotype space it is easy to give an answer, but sometimes difficult to defend it. Should we only consider genes being "on" or "off?" Or should we consider all possible DNA sequences and define a point mutation as the only variation operator? Both of these ideas have been used, but they each have issues in that other avenues for change are clearly available, even in the second case, where deletions, insertions, and inversions would really complicate our definition of genotype "space." Even so, many biologists are comfortable with making these assumptions in specific cases and for theoretical purposes. Phenotype space, on the other hand, is much more tricky. Understanding what "variation operators" are relevant requires an understanding of the genotype->phenotype map? Is it safe for us to make assumptions about this map, i.e. assuming that there is an abundant supply of mutations to alter a phenotypic character by small amounts?

These questions, while frustrating, are interesting because they 1) remind us of a string of old debates in the history of evolutionary biology about whether mutations of large effect are important, and 2) demonstrate the importance of understanding the genotype->phenotype map to understanding phenotypic evolution (which is what we really care about, right?).

Rebranding the Adaptive Landscape

At the end of his article, Kaplan says something I can agree with: "If such images are generated, the areas in which they are misleading must be very carefully evaluated and prominently featured." By recognizing these misleading areas, we more carefully define what we don't know, which is invaluable for future research. Plutynski writes, "Arguably, the very proposal of the landscape metaphor enabled some of these disanalogies to be discovered."

All of this leads me to a somewhat practical conclusion to this story. The adaptive landscape cannot be presented in college classes as a rigorous extension of population genetics, or simply as a way to depict Sewall Wright's shifting balance theory. It should be introduced as a structure that asks more questions than it answers. After all, Wright invented the adaptive landscape to describe long-term evolutionary dynamics, something we really know little about. But the great yet underutilized strength of the concept is that it reveals, clearly and intuitively, some important and open problems in evolutionary biology. With modern tools in genetics, we have a better chance now than ever to make progress on these massive, difficult questions. The adaptive landscape can help us understand why we're asking them.