An Asymmetric Model of Heterozygote Advantage at Major Histocompatibility Complex Genes: Degenerate Pathogen Recognition and Intersection Advantage

Rick J. Stoffels^*^,^,1 and Hamish G. Spencer^*

^* Allan Wilson Centre for Molecular Ecology and Evolution, Department of Zoology, University of Otago, Dunedin 9054, New Zealand and The Murray-Darling Freshwater Research Centre, CSIRO Land and Water, Wodonga, Victoria 3689, Australia

^¹ Corresponding author: The Murray-Darling Freshwater Research Centre, CSIRO Land and Water, P.O. Box 991, Wodonga, VIC 3689, Australia.
E-mail: rick.stoffels{at}csiro.au

We characterize the function of MHC molecules by the sets ofpathogens that they recognize, which we call their "recognitionsets." Two features of the MHC–pathogen interaction maybe important to the theory of polymorphism construction at MHCloci: First, there may be a large degree of overlap, or degeneracy,among the recognition sets of MHC molecules. Second, when infectedwith a pathogen, an MHC genotype may have a higher fitness ifthat pathogen belongs to the overlapping portion, or intersection,of the two recognition sets of the host, when compared witha genotype that contains that pathogen in only one of its recognitionsets. We call this benefit "intersection advantage," ${gamma}$ , and incorporateit, as well as the degree of recognition degeneracy, m, intoa model of heterozygote advantage that utilizes a set-theoreticdefinition of fitness. Counterintuitively, we show that levelsof polymorphism are positively related to m and that a highlevel of recognition degeneracy is necessary for polymorphismat MHC loci under heterozygote advantage. Increasing ${gamma}$ reduceslevels of polymorphism considerably. Hence, if intersectionadvantage is significant for MHC genotypes, then heterozygoteadvantage may not explain the very high levels of polymorphismobserved at MHC genes.