EVOLUTION OF MULTIGENE FAMILIES BY GENE DUPLICATION - A HAPLOID MODEL

Evolution of multigene families by gene duplication and subsequent div ersification is analyzed assuming a haploid model without interchromos omal crossing over. Chromosomes with more differ ent genes are assumed to have higher fitness. Advantageous and deleterious mutations and du plication/deletion also affect the evolution, as in previous studies. In addition, negative selection on the total number of genes (copy num ber selection) is incorporated in the model. First, a Markov chain app roximation is used to obtain formulas for die average numbers of diffe rent alleles, genes without pseudogene mutations, and pseudogenes assu ming that mutation rates and duplication/deletion rates are all very s mall. Computer simulation shows that the approximation works well if t he products of population size with mutation and duplication/deletion rates are all small compared to 1. However, as they become large, the approximation underestimates gene numbers, especially the number of ps eudogenes. Based on the approximation, the following was found: (1) Ge ne redundancy measured by the average number of redundant genes decrea ses as advantageous selection becomes stronger. (2) The number of diff erent genes can be approximately described by a linear pure-birth proc ess and thus has a coefficient of variation around 1. (3) The birth ra te is an increasing function of population size without copy number se lection, but not necessarily so otherwise. (4) Copy number selection d rastically decreases the number of pseudogenes. Available data of muta tion rates and duplication/deletion rates suggest much faster increase s of gene numbers than those observed in the evolution of currently ex isting multigene families. Various explanations for this discrepancy a re discussed based on our approximate analysis.