Response to Wang and Luo

See correspondence article http://www.biomedcentral.com/1741-7007/10/30 webcite and the original research article http://www.biomedcentral.com/1741-7007/9/24 webcite.As stated in Matzke et al. [1], '[c]haracterizing the ways in which polyploid genomes evolve is essential for an understanding of plant and vertebrate evolution'. In our recent study [2], we investigated whether polyploidy has an influence on the frequency of meiotic recombination. In a seed fluorescence assay we observed increased meiotic recombination frequencies (MRFs) between two transgenic marker loci in autotetraploids, when compared to diploids. Results from newly synthesized allotetraploids corroborated our findings, indicating that the observed increase of MRF in tetraploids is independent of the formation of multivalents [2]. Wang and Luo argue in their correspondence that the analysis of our marker data needs to be formulated on the basis of disomic and tetrasomic inheritance models and apply a previously developed method [3].Wang and Luo argue that our calculation 'did not use full information of the data. For example, the individuals with yellow seeds were not taken into consideration when counting for recombination events.' The solution of r that we used in the selfing case is the one root in [0,1] of the equation 2r - r2 = 2(n2 + n3)/n (in Wang and Luo's notation), namely r ^ = 1 - 1 - 2 ( n 2 + n 3 ) / n which is indeed in general not the maximum likelihood solution but the simple formula from [4]. Nevertheless, the resulting estimates are nearly identical to Wang and Luo's estimates (see below). Furthermore, the formula we used in the backcross cases, r ^ = ( n 2 + n 3 ) / n , is a maximum likelihood solution (that of the equation system n1 = n(1 - r)/2, n2 = nr/2, n3 = nr/2, n4 = n(1 - r)/2; details not shown).Wang and Luo state that the green marker 'is nearer to the centromere than the red marker locus'. However, it is the red marker that