Formatted for GENETICS Modeling Population Genetic Data in Autotetraploid Species

Allozyme and PCR-based molecular markers have been widely used to investigate genetic diversity and population genetic structure in autotetraploid species. However, an empirical but inaccurate approach was often used to infer marker genotype from the pattern and intensity of gel bands. Obviously, this introduces serious errors in prediction of the marker genotypes and severely biases the data analysis. This paper developed a theoretical model to characterize genetic segregation of alleles at genetic marker loci, in autotetraploid populations and a novel likelihood-based method to estimate the model parameters. The model properly accounts for segregation complexities due to multiple alleles and double reduction at autotetrasomic loci in natural populations, and the method takes appropriate account for incomplete marker phenotype information with respect to genotype due to multiple dosage allele segregation at marker loci in tetraploids. The theoretical analyses were validated by making use of a computer simulation study and their utility is demonstrated by analyzing microsatellite marker data collected from two populations of sycamore maple (Acer pseudoplatanus L.), an economically important autotetraploid tree species. Numerical analyses based on simulation data indicate that the model parameters can be adequately estimated and double reduction is detected with good power using reasonable sample size. INTRODUCTION Polyploidy has played an important role in the evolutionary diversification of up to 80% of angiosperm species (Lewis 1980; Grant 1971; Otto and Whitton 2000; Soltis and Soltis 2000). Two types of polyploids can be distinguished according to their genome origin. Allopolyploids are the product of an interspecific hybridization event and subsequent chromosome doubling, while autopolyploids originate from the whole genome doubling, likely by fusion of unreduced conspecific gametes. Because bivalents are always formed between pairs of chromosomes with the same origin at meiosis, allopolyploids display disomic inheritance. In contrast, autopolyploids have more than two sets of homologous chromosomes, show multivalent chromosome pairing at meiosis and display polysomic inheritance. The complexities in modeling polysomic inheritance lie in two major aspects: segregation of multiple dosage alleles at individual loci and the occurrence of double reduction, the phenomenon by which sister chromatids enter into the same gamete (Mather 1936). Another distinct feature in the population genetics of polyploids is the formation of partial heterozygotes. For example, when two alleles (A1 and A2) segregate at a locus in an autotetraploid population, there are three types of partial heterozygotes: A1A1A1A2, A1A1A2A2, A1A2A2A2. For their significance in evolutionary biology and agriculture, autopolyploids have attracted increasing research efforts at both theoretical and experimental scales (Ronfort et al. 1998; Luo et al. 2000, 2001, 2004; Mahy et al. 2000; Lopez-Pujol et al. 2004). Furthermore, rapid advances in the techniques of molecular biology and computer technology have made the genetical analysis of autopolyploids more tractable than ever before (De Winton and Haldane 1931; Fisher 1947). Allozyme and DNA-based microsatellite markers have been used to investigate the divergent heterozygosity between autotetraploids and their parental diploids (Mahy et al. 2000; Hardy and Vekemans 2001), to infer the genetic mode of autopolyploidy (Lopez-Pujol et al. 2004) and to assess population structure and gene flow in autotetraploid species (Ronfort et al. 1998). Trall and Young (2000) developed a computer program, AUTOTET, for calculating allele frequencies of genetic markers in autotetraploid populations. However, it must be pointed out that to use the program, one has to empirically infer genotypes of the markers from inspecting the pattern and intensity of electrophoretic gel bands (for example, Lopez-Pujol et al. 2004). Obviously, diagnosing the intensity of gel bands could be unreliable or impossible for the marker data generated, for example, from DNA sequencers. In this paper, we develop a likelihood-based method for calculating allele frequencies of genetic markers in a random mating autotetraploid population. The method accounts properly for the problem of missing information of marker phenotype in regard to the corresponding genotype and for the presence of double reduction. It can be used to analyze the genetic structure of autotetraploid populations by making use of allozyme and PCR-based molecular markers. The method is demonstrated by analyzing a dataset consisting of five microsatellite markers scored on two populations of Acer pseudoplatanus L., an autotetraploid tree species.