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 Victor MacGill
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Phase Space or State
Space
and the Fitness Landscape The phase space is a mathematical space where each point on the surface of the space represents a possible configuration of the system. The result is called the fitness landscape because it looks like a landscape with hills and valleys where each point indicates the level of fitness of a system as indicated by the height or depth of that point. A hill on the landscape represents an effective state, while a low valley indicates a less effective state. For example, if we could create a fitness landscape for the ability of a group of people to co-operate at particular tasks. Those parts of the landscape that mapped states of the group dynamics in which they cooperate well with others would be raised up compared to the rest of the landscape and those points which map to poor levels of co-operation.  It takes energy to
roll a ball uphill and similarly energy is required for a person to
move their operating level to a higher place on the fitness landscape.
We need to gain extra skills and abilities to communicate better and
take us to the top of the hill near us. The other side of this,
however, is that it is easy to roll into a valley that becomes
difficult to escape from. Just as energy is required to climb a hill,
energy is required to climb out of a hole. Effort is required to break
old, entrenched habits.Most usually the hill we have been able to climb is not the highest hill available on the whole landscape. There are usually points on the fitness landscape that are more effective than the hill we are on. In order to reach that even higher hill, we must first come down off the hill we are on and climb all the way up the other hill. We become accustomed to being on the hill we are on and leaving the state to which we have become accustomed often leaves us feeling uncomfortable or even distressed. Leaving the known state involves some risk and uncertainty. The local hill, which is the highest in the local area is known as a local maximum. Sometimes we become entrenched in certain habit patterns, such as a person who is caught in an addiction. If their addiction is alcohol, for example, their use of alcohol becomes dug in as a canal on the fitness landscape and we talk of canalisation. When an alcoholic encounters a stressful situation, or feels a craving for alcohol, their position on the fitness landscape means they are likely to quickly run back into the canal of their habituated behaviour. The more addicted to the alcohol they are, the more quickly they enter the canal. The deeper the canal the harder it is to escape back to a more effective point on the fitness landscape. Falling into a valley or a canal on the fitness landscape can also be understood as falling under the influence of a negative attractor so a "ball" on the fitness landscape would roll to the lowest point, and would only be brought out of that place by a concerted effort. The landscape is not fixed, but all the points on the fitness landscape move around as the system and the environment respond to the interactions between the various influences. The hills and valleys are changing over time. An alcoholic can change their life so as to reduce or perhaps even eliminate the canalisation that has occurred. On the other hand, new addictions might appear or the canalization etches an even deeper groove on the fitness landscape. There will sometimes be two basins near each other. When that happens there will be a “saddle” between the two basins. If the small ball rolls along this saddle it could just as easily fall to either side. This means the system can suddenly change state and move into one particular attractor, but which one can not be determined before it happened. This is called bifurcation since the system “selects” one of two possible states. |
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