A bivariate mixed model approach for the analysis of plant survival data

Disease resistance is often measured as plant survival, which involves taking multiple counts of plants before and after disease incidence. Often, survival data are analyzed by forming a single derived variable, namely final counts expressed as a percentage of initial counts. In this study we propose a bivariate linear mixed model approach in which the two variables are the initial and final counts. This approach is demonstrated using data from nine blackleg disease nurseries in the 2009 growing season in Australia. Replicated experiments were grown at each nursery with a mixture of commercial Australian canola cultivars and breeding lines (collectively called ‘entries’) being tested. Plant survival was determined by counting all the seedlings at emergence and then recounting the number surviving at maturity in each plot. The counts were considered as two ‘traits’, which were log transformed prior to a bivariate linear mixed model analysis. Each trait had different error variances, spatial components (both local and global) and outliers. The variance of entry effects was non-zero for both traits at all locations. The correlation of entry effects between the traits ranged from 0.218 to 0.935 across locations. Best Linear Unbiased Predictors (BLUPs) of entry effects at both sampling times provided three possible indices for selection: (log) counts at emergence, (log) counts at maturity and the difference between these two which could be exponentiated to provide percentage survival values. Thus the bivariate mixed model approach for the analysis of plant survival data provided a more detailed picture of the impact of disease resistance compared with the univariate analysis of percentage survival data. Additionally the predicted entry effects for survival were more accurate in the bivariate analysis.