Correlation Analysis of Fitness Landscapes

Brandt, H. (2001). Correlation Analysis of Fitness Landscapes. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-01-058

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Abstract

The notion of a fitness landscape has permeated the analysis of evolutionary processes for more than 60 years. Introduced by Sewall Wright for discussing biological evolution and speciation, the concept has recently been transferred to the study of abstract genotypes of various evolutionary algorithms. The features of high-dimentional fitness landscapes can vary to a high degree, and the question by which means they can be described has turned out to be a challenging problem. Even though some statistics have been suggested for this purpose and are already well-analyzed, presently discussed statistics do not seem appropriate for obtaining sufficiently accurate predictions of evolutionary dynamics at the level of fitness.

In this study, an analysis of three different types of fitness landscapes is presented. I introduce a new correlation measure, and show by comparing the actual evolutionary waiting times to those predicted when only taking into account the correlation statistics, that these statistics seem to capture salient information of the underlying fitness landscapes.

Based on one-dimensional correlation statistics, very accurate predictions of evolutionary waiting times are achieved for the fitness landscape of the Travelling Salesman Problem and NKp landscapes with low degree of neutrality. Both for the NKp landscapes with high neutrality and RSF landscapes, which in a similar way involve large-scale neutrality, high-dimensional correlation statistics provide enough information to estimate evolutionary waiting times. Finally I present an approach towards analytic descriptions of evolutionary dynamics for the analyzed fitness of low neutrality.

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