The first publication on this topic Wright introduced two different versions of fitness landscapes which Wright himself used somewhat interchangeably, laying the ground for confusion about their exact meaning, dimensionality, and justification.
In one interpretation, which is much more common but sometimes misleading, a fitness landscape is a surface in a multidimensional space that represents the mean fitness of the population as a function of gamete (or allele) frequencies. A population is represented as a point on the surface. This representation can be very illuminating because in some simple population genetic models, the population evolves in the direction of the local gradient in the mean fitness approaching a local 'peak' (i.e., maximum) in a fitness landscape. However, evolutionary dynamics of populations is a very complex process. In general, all relevant evolutionary factors (e.g., natural and sexual selection, random genetic drift, mutation, spatial structure and migration, environmental variability) and their interactions are expected to play important roles. Excluding some special cases (such as one-locus models of constant viability selection), the features and patterns of evolutionary dynamics cannot be captured or predicted on the basis of any single characteristic such as the mean fitness. Indeed, it is well known that the mean fitness of the population does not necessarily increase. Therefore, this version of fitness landscapes is not particularly useful in more realistic (e.g., multilocus) contexts.
In the second interpretation, which is a much more fundamental construction, the fitness landscape represents individual fitness as a function defined on the genotype space. The genotype space (i.e., the set of all possible genotypes) can be mathematically represented by the vertices of a (generalized) hypercube or an undirected graph. To construct a fitness landscape one assigns 'fitness' to each genotype in the genotype space. It is useful to visualize each individual as a point in this genotype space. Accordingly, a population will be a cloud of points, and different populations (or species) will be represented by different clouds. Selection, mutation, recombination, random drift, and other factors change the size, location, and structure of these clouds.
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