Fitness Landscapes

A fitness landscape – also called an adaptive landscape – is a model that comes from biology where it is used to describe the “fitness” of a creature, or more specifically genotypes within a particular environment.1 The better suited the creature to that environment the higher its elevation on this fitness landscape will be. As such it visually represents the dynamics of evolution as a search over a set of possible solutions to a given environmental condition in order to find the optimal strategy which will have the highest elevation on this landscape and receive the highest payoff.
As evolution is a fundamental process that plays out across many different types of systems, natural, social and engineered, this model has been abstracted and applied to many different areas in particular within computer science, business management, and economics; but is equally applicable to all complex adaptive systems. Within this more generic model, a location on the landscape is a solution to a given problem. The elevation captures how functional that solution is, and solutions that are similar in nature are typically placed close to each other.2

Basic Model

For example, the challenge might be commuting to work in the morning. There are many different strategies we could take from flying to possibly swimming to driving our car or taking the bus. We could then create a fitness landscape to represent this, where each one of these solutions would be given a fitness value based on how well it performs against some measurement of success, such as time or cost. The result being swimming or flying will likely end up at a low elevation relative to taking our car or the bus. We might also note that our car or bus strategy would be located in proximity to each other because they have many similarities while swimming or flying would be placed at very different locations on this landscape.
There are two main things we need to consider. Firstly, the type of landscape we are dealing with and secondly, the types of strategies we might use given these different landscapes. Firstly, to talk about the types of landscapes, what we will call their topology, there are a number of different parameters that will define the overall topology.3 Starting with how different are the payoffs on the landscape? The lower the range between the height of the peaks the more equal the payoffs between strategies. An example of an even topology might be a scenario where I roll a fair dice and ask you to try and predict the number it will land on. Each number is equally likely to turn up and thus each one of your strategies is an equally viable solution. As we turn up this parameter to the unevenness of the topology, there will come to be a greater disparity to the functionality of the different strategies and their payoffs.

Distribution Of Solutions

A key consideration is how distributed are the optimal solutions on the landscape? Is there just one dominant strategy that will drastically out-perform all others or are there many different viable solutions? For example, in terms of intercontinental passenger transportation, air travel drastically outperforms all other methods with respect to time. If we create a fitness landscape of the different methods, we would see one dominant mountain in the center with lots of other much smaller peaks around it.4 Thirdly, how dynamic is the environment? Are we dealing with some ecology where environmental conditions may remain relatively stable for prolonged periods of time, or are we dealing with say some emerging market where the context is changing rapidly, resulting in the peaks and valleys to the landscape moving up and down as the whole landscape dances around? Lastly, how interdependent are events? Does what one agent chooses to do affect the landscape or other agents? A fitness landscape of say a market is created by all the companies, consumers and regulators within that market. Every time one of these players moves it affects the whole landscape, and thus we have a dynamic landscape that will be defined by these sets of interdependencies.

Complexity Of Landscapes

The adaptive landscape represents the different types of environments that agents are operating within and these different environments can span from the very simple to the very complex. On the simple end of the spectrum, we are dealing with a context that is static in nature and with limited interdependencies. On the complex end of the spectrum, we are dealing with environments that are dynamic in nature, consisting of many interdependent interacting parts.  

Linear Environments

The most simple environments are static in nature and consist of the least amount of interacting variables, as an example we might think about an absolute monarch or absolute dictatorship where all social, economic and cultural institutions are controlled and held constant through the political hierarchy, within such an environment everything is in relation to one political institution, simply succeeding within that single organization can achieve global success. Or as another example, we might think about some homogeneous cultural system that defines clearly what is considered right and wrong and from this the one correct way to live one’s life. These are examples of linear socio-cultural environments that would give the landscape a single dominant peak, one optimal solution that is well-defined, and because of this the agent needs only to follow some linear optimization algorithm.

Interconnected Environments

If we now increase the complexity by turning up the number of equally viable solutions we will get a landscape that has many different peaks and agents now have to invest a certain amount of time searching for the optimal position. As an example of this we might think about a young person having completed high school choosing which university to go to. They will be trying to optimize for a number of different variables, cost of tuition, location, facilities, college ranking etc. and thus there will be a number of different viable solutions, giving the landscape a number of different peaks, a roughed landscape.5 But in this situation the variables are not changing over time thus the student could invest quite a bit of time and resources in researching all of the factors involved to find whatever they consider the optimal. Although this environment may represent complicated problems in that there are a number of interacting variables that require a significant amount of computation, it is still a relatively simple environment.

Adaptive Environment

If we now allow for the different interacting variables to adapt and change over time, we then have a complex environment.6 We now have a landscape where agents are acting and reacting to each other’s behavior constantly adapting and it is out of this interdependence and adaptation that we get a landscape where the peaks and valleys are moving up and down over time. An example of this might be the current international political environment as we move into an increasingly multipolar world, with the rise of China and the other emerging economies we are now no longer in an international environment dominated by the homogeneous Western ideology of the Bretton Woods institutions, but increasingly have many more actors, both public and private, each with their own strategies and interest that are constantly acting and reacting to each other. This means the end target is constantly changing, any solution that may be effective now, may cease to be effective when others adapt to it which once again alters the payoffs on the landscape as it moves up and down over time.

Open Environments

lastly, this whole complex adaptive system of agents acting and reacting is receiving some set of input values from external sources, whether this is the natural environment or the technology infrastructure of a society. A major change in these input values can cause the whole landscape to transform, in such circumstances we are no longer talking about the agents acting and reacting to each other, but instead, we are talking about the whole topology to the landscape transforming.
This is similar to a paradigm shift within science or culture where the whole landscape gets changed. We can think about the paradigm shift in our culture as we moved into the modern era, everything got recontextualized, through a scientific and materialistic context. With this cultural paradigm shift virtually every single social and cultural institution within the entire landscape had to reinvent itself within this new context. Education, governance, work, etc. everything got redefined and those that were not have slowly lost relevance, this is a long-term systemic change where we are no longer talking about adaptation but instead evolution.

Strategies

Knowing the different types of topologies, our attention then turns to thinking about the different types of strategies that agents might use, as the degree of functionality to any solution will alter drastically depending upon the type of landscape it is operating on. Agents within complex adaptive systems can typically only respond to local level information. Whether we are talking about a trader in a financial market or a herd of deer looking for pasture, these agents do not have complete information about their environment. They can only access and thus respond to a limited amount of typically local level information, and they need to have a strategy for processing this information and generating an optimal response.

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2018-06-23T08:31:02+00:00