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C. FERREIRA, 2002 (Terms of Use) ISBN: 9729589054

Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

The founder effect
 

In this section:


We have seen in the previous section that the evolvability of a system will depend heavily on the kind of genetic operator used to create genetic modification. And the size and kind of initial populations is closely related to this question.

In all evolutionary algorithms, an evolutionary epoch or run starts with an initial population. Initial populations, though, are generated in many different ways, and the performance and the costs (in terms of CPU time) of different algorithms depend greatly on the characteristics of initial populations. The simplest and less time consuming initial population is the totally random initial population. However, few evolutionary algorithms are able to use this kind of initial population due not only to structural constraints but also to the kind of genetic operators available to create genetic modification. The initial populations of gene expression programming are totally random and consist of the linear genomes of the individuals of the population.

In artificial evolutionary systems, the question of the initial diversity is pertinent for two main reasons. First, for some complex problems, the random generation of viable individuals (i.e., individuals with positive fitness) can be a rare event and, in those cases, it would be advantageous if the evolutionary process could get started from one or a few founder individuals; whether this is possible or not, will depend on the modification mechanisms available to the system. And, second, because of this, the kind of mechanism used to create genetic modification becomes of paramount importance. If genetic modification is created by non-homogenizing operators such as point mutation, then populations will be able to adapt and evolve. However, if genetic variation is created by homogenizing operators such as recombination, then evolution is either altogether halted when only one founder individual is available or seriously compromised when the number of founder individuals is excessively small.

The importance of the initial diversity in evolution was stressed by E. Mayr in what he called founder effect speciation (Mayr 1954, 1963). This process may be thought of as the establishment of a new population due to a founder event initiated by genetic drift and followed by natural selection. An extreme case of a founder event is the colonization of a previously uninhabited area by a single pregnant female. In nature, besides recombination, other genetic operators are used to create modification and populations that pass through a bottleneck are capable of adaptation, sometimes even originating new species.

Similarly, in artificial evolutionary systems, the capability of founder populations to evolve depends greatly on the kind of mechanism used to create genetic modification. Indeed, if homogenizing operators are the only source of genetic modification, populations will not be able to evolve efficiently or not at all in the extreme case of only one founder individual.

In this section, we will analyze the importance of the initial diversity in evolution in two different systems. The first evolves under mutation and has a non-homogenizing dynamics characteristic of an efficient adaptation. The second evolves under recombination and has a homogenizing dynamics characteristic of poorly evolving systems.

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