The more complex the world gets, the more we need models to simplify it. One of the models I return to often is fitness landscapes, which can help solve problems, design better experiences, and explain the world around us.
Imagine you and a group of friends are on a team playing a game.
The game takes place on a huge playing field with rough, mountainous terrain, like the Himalayas or Alps. The only goal is to increase your team’s average altitude. This seems easy enough, but there are a few catches: (1) any player can only see a few feet ahead of them, (2) the terrain slowly changes over time, and (3) if a player drops below a certain altitude for long enough, they’re eliminated. Given these rules, what strategies would your team use to find the highest peaks?
This is a metaphor for the “game” that species must play to survive in an ecosystem.
The terrain is a fitness landscape representing a library or design space of every possible variation of organism, spread out over a nearly infinite surface. The closer together on the surface, the more similar the genotype. This means single species would be clustered together. Dogs would be near wolves, far from fish, and even farther from fungi.
Altitude indicates the fitness of the organism — or how likely it is to survive in a particular environment. The higher it is on the landscape, the better the design and more fit the organism. Below a certain threshold, organisms can’t survive and species go extinct.
As a model, landscapes can help show us visually and mathematically how to find the best designs. The original concept was developed by evolutionary theorist Sewell Wright in 1931, and focused only on biological entities. But a design space could represent almost any set of possibilities — as long as it has building blocks or variables that combine into many variations, each with a value (or fitness level) that can be assigned. This means it could apply to design spaces of problems, equations, technologies, strategies, memes, or even sets of LEGOs.
Features of landscapes
A vast majority of the variations on a typical landscape are bad designs. These are oceans of low fitness, below the surface of which organisms are incapable of survival or reproduction.
But certain regions — springing out of the oceans like islands or continents — are full of a range of potential variations, all with some usable level of fitness. The basic features of these regions of terrain are:
- Local peaks or plateaus — A point or area of high fitness where all surrounding paths go down.
- Global peak — The highest peak in the region. The fittest entity in the area. The best design of all similar variations.
- Valleys — Flatter areas of low fitness adjacent to hills and mountain ranges.
- Pits or Crevasses — Deep holes of low fitness below the “sea-level” of survival.
Peaks are good. Pits are bad. And crossing valleys is very risky: you could find higher fitness, but likely not.
The unconscious process of evolution drives genotypes uphill over time, finding and settling on peaks of fitness until the landscape shifts or some other factor forces a move. More on this later.
Ruggedness of terrain
The distribution of fitness values in a region determines its topology, or how rugged the terrain is. It can be anywhere from smooth to maximally rugged:
- Smooth — Also known as a “Mt. Fuji” landscape. The easiest terrain to navigate: just go up!
- Rough — Fitness values are roughly correlated between neighboring points. The terrain is more like the Alps or the Rockies, but with more pits and flat spots.
- Maximally Rugged — Fitness values are completely uncorrelated. The fitness of one point has no relation to nearby points, making the terrain completely random. Understandably hard to navigate and find global peaks on.
Most of the real-world evolutionary fitness landscape is in the middle somewhere, or “roughly” correlated. Studies of landscapes in other interactively-complex areas like business models or technologies show that they also tend to be roughly-correlated.
Some landscapes, like solutions to complex math problems or designs of LEGO blocks, are static: fitness and terrain don’t change. The evolutionary landscape is dynamic — it’s constantly changing.
Shifts in fitness values can result from changes in the physical environment, such as climate change or a natural disaster. Most often shifts are caused by the existence and movement of the entities (organisms) themselves. As an entity evolves and moves across the landscape, it changes the fitness of others that interact with it. A new species may lower the fitness of others, for example, by competing with them for the same resources.
Terrain can change at different rates, depending on how linked the entities on the landscape are with their surrounding environment. Some parts of the landscape change very slowly, reacting mildly to outside changes. Some are in a constant state of upheaval: a high peak today may not exist tomorrow.
Strategies for navigating
The landscape model isn’t just about what the terrain looks like and the location of each entity. It’s about how entities move across the landscape and the best strategies or “moves” for finding high peaks of value. These moves are essentially algorithms — a set of repeatable rules for searching the landscape. Here’s the most common examples:
- Hill climbing (gradient heuristic) — The “safe” strategy of starting at a point and continually moving uphill until you can’t go any higher.
- Random jumps — Somewhat randomly “jumping” around the nearby landscape.
- Evolution — A combination of mostly hill climbing through small, iterative changes, and the occasional random jump.
The best algo depends on the topology of the terrain. For smooth landscapes, hill climbing is enough to find a good peak. On rugged landscapes, hill climbing alone may lead to a local peak but no further — you’d be stuck there until the terrain changed.
Evolution, it turns out, is the best at finding high peaks of value in rough-correlated landscapes. This can be evolution via natural selection, or a process of conscious adaptation.
“Adaptive evolution is a search process — driven by mutation, recombination, and selection — on fixed or deforming fitness landscapes.” — Stuart Kauffman
Evolution naturally experiments by diversifying populations, successfully spreading across the landscape, exploring it in search of high peaks of fitness. When a group of genotypes have moved far enough from their original starting point, we call it a new species.
Let’s return to the game mentioned in the intro, and how our team would find the highest peaks. By mimicking evolution, our strategy would look something like this:
Players in the team start relatively close to one another. Each would try hill climbing by moving up their steepest immediate path. Most (but not all) would follow anyone who found the most promising steep, ascending path that will eventually lead to a peak. A few members of the team would jump or run in a random direction for a random distance — but not so far they can’t still communicate their altitude with the team.
These players may end up in a hole or crevasse and be eliminated. If they get lucky and don’t, they can hill climb from their new starting point and see how high they get. Remember — the terrain is slowly changing over the game. So if we played it safe and had everyone hill climb, we may either end up on a small local peak or have our peak shift lower over time.
This combination of strategies helps find a good balance between exploitation (focus on climbing up the hill you’re currently on) and exploration (finding new, higher peaks).
Applying the model
There is no single “right” way to model a landscape. Landscapes can be defined however you need to best model or explore the problem at hand. The major inputs are:
- Design space or library — The space of possibilities the landscape represents can be chosen at any level of abstraction. Amazon.com could fit on a landscape of e-commerce companies, tech companies, or all companies. These levels could share some of the same features (peaks, valleys, etc.) but the terrain would still be different.
- Focus on specific variables or components — Modeling a landscape in 3 dimensions means you’re only focusing on 2 variables at a time. More can be modeled of course but it becomes harder conceptually to visualize. Choosing which variables or building blocks to focus on becomes very important to the model.
- Fitness function — What defines fitness of the entities? This is similar to the question of what the ultimate “goal” is. It could be an objective/quantitative metric like frequency of genotype, financial profits, or investment return. It could also be more subjective like value-creation potential or customer satisfaction. If the equation can be precisely defined, it would look like:
Fitness = f(x, y)where x and y are the variables chosen.
So the same way evolution finds good designs or peaks of fitness, one could use strategies to navigate the landscapes of:
- Designs of a tool or product — What are the building blocks that define the tool? Is fitness based on utility or some other measure of usefulness? What are the areas of the landscape that aren’t possible due to physical limitations or lack of understanding?
- Potential future outcomes — What does the terrain of potential outcomes look like? Is there one clear global peak? How objective is the fitness function? Does progress toward a peak have to be incremental — slowly crossing valleys and moving uphill — or is the path clear enough that you can “jump” to the peak?
- Many more…
There’s a lot more depth we can go into about applying the fitness landscape model, some of which I’ll try to tackle in future essays.
When you understand fitness landscapes, you start seeing them everywhere. The simplicity of the landscape metaphor can not only help explain the world but help us better navigate it as well.
What actually determines how rugged the fitness values are in a region? The more an entity’s building blocks (genes, in this case) interact with one another, the more rugged the landscape becomes. Interdependence → ruggedness. This is proven mathematically, but is also intuitive. If fitness of an entity is a function of all its individual building blocks, and all those blocks can interact with each other, then changing 1 of them even a bit would cause overall fitness to change dramatically. This means variations close together on the landscape would have very different fitness values, resulting in maximal ruggedness. Evolution eventually finds a balance been the “chaos” of maximal ruggedness and the simplicity of a non-robust Mt. Fuji-type terrain.↩︎
We can use wolves as an example. All variations of wolves (with slightly different fur colors, body types, features, etc.) would be clustered together as a species on the landscape. Most mutations in genome are minor, moving individuals and their offspring to nearby points representing different genotypes. Natural evolution has no foresight and can’t “see” the whole landscape, so clusters of individuals can only flow blindly across it over time. If the cluster has moved far enough away from its original population, we would call it a new species. In the case of wolves, humans created a nearby peak of high fitness and a small group moved toward it over time. Eventually this population was far enough away that it became the species we know as dogs, and continued to diversify into breeds over time.↩︎
- The best high-level overview of fitness landscapes in all their forms can be found in the book The Origin of Wealth (2007), by Eric Beinhocker, along with a lot of other useful models. Beinhocker discusses design spaces of many varieties including organisms, business models, technologies, and LEGOs.
- Stuart Kauffman’s The Origins of Order (1993) has a much more technical look at the nature of fitness landscapes. If you’re interested in the advanced math that goes behind footnote #1 this is the place to go.
- Michael Mauboussin’s book More Than You Know (2013) also has a great chapter in it on fitness landscapes and how they can be used to think about business models.