**2. Related work**

Prior to the introduction of quantitative genetics to the EC community, research along similar lines was already being conducted. Most notable among these was the discovery that parent-offspring fitness correlation is a good predictor of an algorithm's ability to converge on highly fit solutions [18].

Mühlenbein and Altenberg began to introduce elements of biology theory to EC at roughly the same time. Mühlenbein's work has focused mainly on adapting the equation for the response to selection (also known as the breeder's equation) for use with evolutionary algorithms [19] Initial work involved the development several improved EAs and reproductive operators [21, 23, 24], and progressed to the development of Estimation of Distribution Algorithms (EDAs) [20, 22].

Altenberg's work used Price's Theorem [27] as a foundation for his EC theory. One of his goals was to measure the ability of certain EA reproductive operators to produce high quality individuals, and identify what qualities were important in achieving this [1]. He referred to this as evolvability, and the equations he developed looked similar in some regards to the response to selection equation. In particular he provided a theoretics foundation for why the relationship between parent and offspring fitness (i.e. heritability of fitness) was important.

Another aspect of Altenberg's work involved going beyond a simple aggregation of the relationships between parent and offspring fitness. He focused on the idea that the upper-tail of the distribution was a key element. After all, creating a few offspring that are more fit than their parents can be much more important than creating all offspring with the same fitness as their parents. This is why his equation really became a measure of variance instead of mean, which is what Price's Theorem typically measures. As an indication that his theories were in some sense fundamental to how EAs work, he was able to use them to re-derive the schema theorem [2].

Langdon [14] developed tools based on quantitative genetics for analyzing EA performance. He used both Price's Theorem and Fisher's Fundamental Theorem [26] to model GP gene frequencies, and how they change in the population over time.

Work by Potter et al. [25] also used Price's Theorem as a basis for EA analysis. They also recognized the importance of variance, and developed some approaches to visualizing the distributions during the evolutionary process [5, 6].

The work of Prügel-Bennett & Shapiro [29] [28] is based on statistical mechanics, but it has some important similarities to the methods used in quantitative genetics. Here, populations are also modeled as probability distributions, but the approach taken is more predictive than diagnostic. This means that detailed information about the fitness landscape and reproductive operators is needed in order to analyze an EA. Still, this approach has some interesting capabilities. For example, up to six higher-order cumulants are used to describe the distributions, allowing it to move beyond assumptions of normality, and thus providing much more accurate descriptions of the actual distributions.

Radcliffe [30] developed a theoretical framework that, while not directly related to quantitative genetics, has certain similarities. His formae theory is a more general extension of the schema theorem, and can be applicable at a phenotypic level.
