Science in Pictures: Evolution on Fitness Landscapes

Wandering Wim & Stumbling Stu

Evolution is often visualized as a search on a fitness landscape. Imagine all possible genomes as connected points in a two-dimensional plane, with the corresponding fitness value of each genome as its height (i.e., up into a third dimension). Visually, this gives rise to a mountainous landscape (or a fitness landscape), with valleys, slopes, ridges, and peaks. Evolution can now be metaphorically seen as a population (or species) wandering through such a fitness landscape, in search of the highest peaks.

In some cases, such a landscape may be very rugged, with steep slopes and many peaks of different heights. Evolution would have a difficult time in such a landscape. When climbing uphill from any given valley, a population can easily get stuck on a local peak of only low or at best average fitness. Also, because of the steep slopes, it does not take much for a population to stumble down the mountain again.

The mountains of Torres del Paine, Patagonia, Chile, could represent a very rugged fitness landscape.

In other cases, the landscape may be very smooth, with gentle slopes and only a few mountain tops of roughly similar height. In this case, evolution is relatively easy. A population can simply walk up a gentle slope, and it does not matter too much which of the mountain tops is reached, as the views are equally good. Also, the population will be able to stay at, or at least near, the top even in case of disturbances.

The Sangre de Cristo mountains near Santa Fe, NM, USA, would represent a much more smooth fitness landscape.

Many years ago, one of us (Stumbling Stu) introduced a mathematical model, known as the NK model, to investigate this notion of fitness landscapes. By varying the model parameters (N and K), landscapes of different degrees of ruggedness can be created, from a very smooth landscape with just a single hill to completely random landscapes with a large number of very steep peaks. It can then be studied how a (simulated) evolutionary process behaves on these different types of fitness landscapes.

However, species do not evolve on their own. They interact with other species in the ecosystem they are part of. And these interactions influence each of the co-evolving species’ fitness. As a variation on an often-used example from Stumbling Stu, if lizards evolve a more sticky tongue, then bugs will have to evolve more slippery feet.

A lizard that just caught its lunch in the rainforest of Singapore.

Or, in yet another variant, if herons evolve a longer beak, fish better evolve stronger fins to escape more quickly.

A heron that just caught its lunch in a city park in Vienna, Austria.

An extension of the original model, known as the NKC model, takes such fitness-changing interactions into account. In particular, if one species makes an adaptive move on its own fitness landscape, it will change the shape of another species’ fitness landscape. This other species may now suddenly find itself away from a mountain peak it previously occupied, forcing it to also make an adaptive move, which in turn changes the shape of the fitness landscape of the first species, and so on. Together, we studied such a scenario some years ago (a free pre-print is also available).

Of course in evolution there is also cooperation, next to competition. This can equally well change a species’ fitness landscape, as cooperation generally enhances the fitness of all species involved. For example, consider alpine plants growing flowers that produce a sugar-rich liquid (nectar) that attracts insects which feed on it. These insects, in turn, help in pollinating the flowers, which can then develop into tasty berries that are eaten by mountain goats. The excretions of these mountain goats help the plants distribute their seeds, and also attract insects to lay their eggs in. The next generation of insects will then again help in pollinating the flowers, and so on. All species get something out of it.

A pair of Alpine ibex (a species of mountain goat) having their lunch in the mountains near Chamonix, France.

Such a network of mutually cooperating species can be seen as an instance of an autocatalytic set, a notion that was also introduced by Stumbling Stu (already 50 years ago). Although originally formulated in the context of chemical reaction networks, together with several ecologists we have argued how this notion may also play an important role in evolution (a free pre-print is also available).

The natural world is full of wonderful beauty. And, as this short story tries to exemplify, it is a joy to both admire as well as study this natural beauty and the processes that give rise to it. We need to become more aware that our beautiful world depends delicately on the many intricate interactions between different species. Only through such an awareness will we be able (and willing) to make sure we don’t destroy it…

About the authors

Stumbling Stu has been stumbling across the scientific landscape for more than six decades. He is a prolific writer, having published numerous articles and six books. He has contributed many original ideas in the areas of evolution and origin of life, including his NK model and the notion of autocatalytic sets. Stu also stumbles back and forth between Santa Fe, NM, and Crane Island, WA, USA.

Wandering Wim is an independent scientist who has worked, lived, and traveled all over the world. He has applied his computational skills in the research areas of evolution and origin of life, among others. He is also an enthusiastic outdoor photographer. Wim is currently based in Vienna, Austria, but as soon as the situation allows it again, he will continue wandering the globe.

The authors enjoying their lunch at a restaurant in Venice, Italy. (Image credit: Colorful Kate)