# A PERSONAL INTRODUCTION TO THE ADAPTIVE LANDSCAPE

**how systems with many interacting parts change over time**- systems like life, businesses, public policy, sets of beliefs, and more. This is not the textbook definition (if there is one) of the adaptive landscape concept - if you're looking for that I'd suggest checking out Wikipedia or an actual textbook. Because I'm taking the long way. Here, I will be building up my view of the concept theoretically from the ground up, sometimes using my own terms and occasionally borrowing and butchering some work that is well established in math, computer science, and evolutionary biology (where I can, I'll try to leave references to more in depth descriptions of these concepts). I'm doing it this way because it's fun and working through it logically helps me (and hopefully you!) understand the concept. OK, here goes:

## Part 1: "Spaces" of Possibility, Some Toy Examples

### A Continuous Multidimensional Whiskey Drink

Are you surprised I started with whiskey? I certainly hope so. Moving on...

Let's start with the simplest drink: whiskey neat, no ice.

Here is the question: How can we

*think of*

**all of the possibilities for your drink**? Well, we could do it abstractly, with symbols like this: { x | 0 ≤ x < ∞ }. But let's decide that we want to think of it spatially. So for the neat whiskey we can think of all the possibilities as lying along a line extending out from point 0, with the distance along the line representing the fingers of whiskey (or should we measure in liters?). This line is what I'm going to call a

**space of possibility**(elsewhere it might be called a combinatorial space or a phase space, but I've decided to go about things from scratch, so I'll stick with my term).

*dimension*, or

*ingredient*, or

*trait*.

### Discrete Light Switches

*discrete*.

Off

On

Now I'll add more lights to the room: one over in the corner, to light up my favorite reading chair, and one that casts a soft, blue light over the ceiling. So now we have three lights and three switches. The sharp reader might guess from the whiskey example that we are once again moving into a familiar three-dimensional space. This time we define each possible state as a point in space where if the first light is on, x=1 (if not x=0), if the second is on, y=1 (if not y=0), and if the third is on, z=1 (if not z=0). We put all the possible states in this space and voila, they're the corners of a cube!

### Putting on the High-Dimensional Goggles

From down the hallway, a mathematician chimes in, "Well... just add more dimensions."

And we answer, "More than three? Where will we add them?"

The mathematician replies, "Just in a direction orthogonal to all the other axes."

"Oh, of course..." and we walk away quietly as if we understood.

So how dire is our situation? Should we be worried? Certainly, if we add a fourth ingredient for the drink recipe or more and more lights in our little room, we will struggle to plot our possibilities in three-dimensional space. But I like to think that a clever mathematician would ease our minds by having us imagine we lived in a two-dimensional world for a moment. From our 2D world, our 3D space representing the whiskey-cola-water recipe would be as difficult to imagine as a 4D space is to those of us still in this familiar world. But is the 3D space of possibilities wrong? The resounding answer should be no. It's just difficult to imagine and impossible to picture. So although we realize that real-world systems are more complicated than our toy examples, and are in fact very high-dimensional,

**we don't need to be disturbed by the fact that we struggle to imagine what they look like**.

What

**is**important is to understand is that adding new dimensions means exponentially increasing the number of possibilities and opening up new paths between states. In simple terms this means that getting from x=0 to x=1 can happen along new paths if we open up the space of possibilities to include the y dimension as well. In special cases (which I will discuss later), we call this new path a high-dimensional or extra-dimensional bypass. EXTRA-DIMENSIONAL BYPASS! This is perhaps my favorite term in all of science, and it is what the Tortoise discovers in order to move from one peak to another in the dialogue.

### Back to Biology: Sequence Space / Genotype Space

*sequence*is our

*state*. Let's start by imagining a DNA sequence with only one nucleotide. It has four possible states (bases), and we define the variation operator as a change of a base at a position (there is only one to chose from). Here's how I might lay out these possibilities in space:

*A quick note:*

The term

The term

*genotype space*is often used to refer to the space of possibilities for the whole genome, basically all the DNA sequences for one organism. However, the term is also sometimes used in place of sequence space for a particular gene sequence because the sequence space is a part of the larger genotype space (I might use the term "subspace", but I'm not sure what the mathematicians would think of that).### Phenotype Space

*phenotype*, we are talking about your entire collection of

*observable traits*, from the shape of the molecules within your cells to your height. These traits are usually described by

*continuous*variables, so the space we construct will be more like the whiskey drink spaces than the light switch spaces. This is probably the most common type of space presented in introductions to the adaptive landscape metaphor, because it involves things we can readily see. Here is another toy example:

If you're wondering how we would define distance in this space of possibilities, you're onto something - we'll look into it more in Part 3. For now, on to Part 2: The Mapping.