The statistical treatment for hypothesis testing using real-time PCR data is a challenge for quantification of gene expression. One has to consider two key factors in precise statistical analysis of real-time PCR data: a well-defined statistical model and the integration of amplification efficiency (AE) into the model. Previous publications in real-time PCR data analysis often fall short in integrating the AE into the model. Novel, user-friendly, and universal AE-integrated statistical methods were developed for real-time PCR data analysis with four goals. First, we addressed the definition of AE, introduced the concept of efficiency-adjusted Delta Delta Ct, and developed a general mathematical method for its calculation. Second, we developed several linear combination approaches for the estimation of efficiency adjusted Delta Delta Ct and statistical significance for hypothesis testing based on different mathematical formulae and experimental designs. Statistical methods were also adopted to estimate the AE and its equivalence among the samples. A weighted Delta Delta Ct method was introduced to analyze the data with multiple internal controls. Third, we implemented the linear models with SAS programs and analyzed a set of data for each model. In order to allow other researchers to use and compare different approaches, SAS programs are included in the Supporting Information. Fourth, the results from analysis of different statistical models were compared and discussed. Our results underline the differences between the efficiency adjusted Delta Delta Ct methods and previously published methods, thereby better identifying and controlling the source of errors introduced by real-time PCR data analysis.
Many hosts preferentially associate with or reward better symbionts, but how these symbiont preference traits evolve is an open question. Legumes often form more nodules with or provide more resources to rhizobia that fix more nitrogen (N), but they also acquire N from soil via root foraging. It is unclear whether root responses to abiotically and symbiotically derived N evolve independently. Here, we measured root foraging and both preferential allocation of root resources to and preferential association with an effective vs an ineffective N-fixing Ensifer meliloti strain in 35 inbred lines of the model legume Medicago truncatula. We found that M. truncatula is an efficient root forager and forms more nodules with the effective rhizobium; root biomass increases with the number of effective, but not ineffective, nodules, indicating preferential allocation to roots harbouring effective rhizobia; root foraging is not genetically correlated with either preferential allocation or association; and selection favours plant genotypes that form more effective nodules. Root foraging and symbiont preference traits appear to be genetically uncoupled in M. truncatula. Rather than evolving to exclude ineffective partners, our results suggest that preference traits probably evolve to take better advantage of effective symbionts.
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