 In this video, we will present the concept of a fitness landscape as it is used to model complex adaptive systems. We will provide you with a basic description of how the model works, talk about the key parameters that affect its topology, and finally, look at the types of strategies used by agents within these different 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. 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 of 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. 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 upon 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. Now that we understand what a fitness landscape model is, 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, 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 to 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. Next, how distributed are the optimal solutions? Is there just one dominant strategy that will drastically outperform 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. 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? Is 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. Now that we have an idea of different types of topologies, we can start to think 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 of 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. This strategy is essentially just an algorithm. We will call this the explore or exploit algorithm because an agent has fundamentally just two options to either exploit their current position within the landscape or invest resources to go exploring for new solutions, that is to say looking for higher peaks. So let's start with agents on the most simple landscape by turning all our parameters fully down making it smooth, distributed, static and without any interdependencies. In this scenario, you don't even need a strategy. Like our example of trying to predict which number of fair dice will end up on, all options are equally valid. Thus your best option is to just stay exploiting your initial position. Now let's turn up the disparity between payoffs so that there is at least one optimal solution that is far superior to others, one big mountain in the middle of the landscape. Now all agents need is a simple algorithm that tells them to stay going upwards until they come to a peak and then stay there as they have now found the global optimal solution. This is called a greedy algorithm and it works well in these very simple environments. Next we will turn up the distribution of solutions. Here the topology will develop many local peaks of varying height. This landscape corresponds to a problem that involves a set of interacting variables. There are many different variables and different combinations between them giving us lots of different possible solutions. Designing a car would be an example of this. We might want it to be fast and low cost, but if we put a bigger engine in it to make it go faster, this would require a stronger chassis, which would add to the cost and there would be of course many more interacting factors involved, allowing for many different possible solutions, but some would still be better than others. Applying our greed algorithm here would result in an agent getting stuck on the first local peak it comes to, which is unlikely to be the global optimal solution. What is needed is a much greater initial investment in exploring, allowing the agent to go up and down many times, while also over a prolonged period, gradually reducing the amount of time the agent is allowed to go downhill, thus gradually closing in on a global optimal solution without getting stuck on local peaks. Next, as we turn up the volatility to the environment, peaks and valleys move up and down over time. We might think about climate change here. What was once an optimal environment for some creature may become a valley as the climate changes and the peaks move to some other part of the landscape. Take in static landscapes, where it is worth making a big investment in exploring because once you find an optimal solution, you will be able to exploit it for a long time. In these dynamic environments, this is no longer the case as the goal is changing and the agents need to stay changing with it. If we then turn up the interdependency between the actions that agents take, the environment will become more dynamic as the topology is being continuously shaped and reshaped by the actions and reactions of the agents to each other, with agents needing to be continuously adapting. In summary, we have been looking at how the model of a fitness landscape can be applied to understanding the environment within which complex adaptive systems operate, as it gives us a visual representation to the dynamics of evolution that is the primary force shaping these systems on the macro scale. We have seen how a few key parameters can fundamentally alter this topology and thus require agents to adopt very different strategies in their pursuit of optimal solutions.