Bigger backcross bang for the buck
--Ed Weck
In a backcross population, as in any breeding population, individuals have a fixed genomic composition. In order to speed backcross conversions using molecular markers, we must measure the number of recurrent parent alleles of each individual. One constraint of molecular marker analysis, however, is the high cost.
There are two ways to reduce total analysis costs; either reduce the cost per analysis or reduce the total number of analyses. As technical breakthroughs occur, the cost per analysis will decrease. Reduction of total analysis costs should maintain the same selection intensity while analyzing only a subgroup of the population. I present a stepwise procedure, like a taxonomic key for species identification or the qualitative analysis of inorganic chemicals, for reducing the total number of data points required in marker-assisted backcross conversions.
The binomial distribution explains the behavior of populations in which there are only two classes of information, such as molecular marker data from a backcross population. Backcross population data from 4 unlinked markers are binomially distributed in 5 classes (0, 1, 2, 3 and 4 recurrent parent alleles) just as backcross data from 40 unlinked markers are binomially distributed in 41 classes (0, 1, 2 . . . 40 recurrent parent alleles). After an initial analysis with 4, 6 or 8 markers, what progress can be made by selecting the individuals with the highest percentage recurrent parent? A theoretical population of 250 individuals was analyzed with 4, 6 and 8 binomially distributed (unlinked) markers. The results of a 40 marker analysis, after initial selections with 4, 6, and 8 markers, are shown in Figure 1. The best individuals (greater than 50% recurrent parent) selected after analysis with 4, 6, or 8 markers and further analysis with 36, 34, or 32 markers produced the black, stippled or lined curves in Figure 1A, 1B and 1C. The populations of individuals selected after 4, 6, or 8 markers are all skewed toward higher number of recurrent parent alleles of a 40 probe distribution. Selection after this limited analysis eliminated the worst members (lowest percentage recurrent parent) of the population and pushed the distribution (slightly) toward the higher percentage recurrent parent. It seemed amazing that selection after only 4 markers could decrease the number of individuals analyzed and still provide a majority of the best (highest percentage recurrent parent) individuals after a total of 40 analyses.
Based on the previous result, it seemed possible to analyze a backcross population incrementally and select the majority of the best individuals, without being required to analyze every individual with all 40 markers. Consecutive selections in 5, 10, and 15 marker increments are shown in Figure 2. The best individuals (from a 250 plant binomial distribution) were selected at 3/5, 4/5, and 5/5 recurrent parent alleles and analyzed with an additional 5 markers. This distribution is shown in Figure 2A as the black bars. Individuals from the 6/10, 7/10, 8/10, 9/10, and 10/10 recurrent parent classes were selected and analyzed with an additional 5 markers. The result of this binomial analysis is shown in Figure 2B as the black bars. Individuals from the 9/15, 10/15, 11/15, 12/15, 13/15, 14/15, and 15/15 classes were selected and an additional 5 marker binomial was run. The predictions for these selections are shown in Figure 2C. This procedure identifies more than 80% of the individuals with >13/20 recurrent parent alleles but requires only half of the analysis.
The attainable progress in a backcross conversion is dependent on the number of plants in the population. Once the number of plants has been selected, theoretical progress is fixed and success is predicated on an accurate measurement of recurrent parent percentage. If a major goal in plant breeding is to eliminate the "losers," this stepwise procedure does that rapidly.
The use of the stepwise selection procedure presented here can reduce the cost of marker-assisted backcross conversions. The total number of individuals analyzed is reduced by sequential selection of the best individuals (2575 vs. 5000 analyses in this example). Additional selection steps can be incorporated if a higher percentage of the "best" individuals is required. This molecular analysis of backcross conversions is better suited to RAPDs (Tingey/McClelland) than to RFLPs because of the ability to set up each PCR experiment individually (no reusable nylon membrane required).
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