The area under the B. oleae flight curves (AUBFC) in treated and control plots was calculated by trapezoidal integration method of SAS (Campbell and Madden, 1990 ). Then, the values of AUBFC were log10 transformed and subjected to factorial analysis of variance using Statistix 9.0 (Analytical Software 2008). The same program was used to analyze mortality data. The values of average survival times obtained by the Kaplan-Meier method and compared using the log-rank test were calculated with SPSS 15.0 Software for Windows. Replicates in time, for all experiments, were analyzed as series of experiments with the model, y = treatment + experiment + treatment × experiment (Littell et al., 2006 ). Since the effect of experiment and interaction treatment × experiment was not significant, replicates from both experiments were combined in a model with only treatment as a factor (one-way ANOVA). Mortality data was transformed, , to improve normality and homogeneity of variance, both requirements for linear model analysis. Means from different treatments were compared using Tukey's test (P < 0.05). The effect of soil type and rain volume on relative percentage of M. brunneum recovered was evaluated with a generalized linear model for ordinal data (proportional odds model). This proportional odds model is the standard generalized linear model for ordinal regression (Stroup, 2012 ) and is appropriate for this experiment since we are measuring the response as ordinal data type, expressed as relative or cumulative percentage of conidia in each section of the soil column. The dependent variable or response is the four possible classes or soil sections (A, B, C, and E). This model calculates the cumulative probability or proportion of conidia at each soil section or in the sections above. i.e., P (conidia ≤ A) is the probability or proportion of conidia in section A; P (conidia ≤ B) is the probability or proportion of conidia in sections A and B; P (conidia ≤ C) is the probability or proportion of conidia in sections A, B, and C; and P (conidia ≤ E) is the probability or proportion of conidia in the effluent (E) or in any of the sections = 100%. The proportion of conidia in one specific section can be calculated then as the difference between contiguous cumulative probabilities e.g., probability or proportion of conidia in section B, P (conidia = B) = P (conidia ≤ B) − P (conidia ≤ A). The equation of the model is:
Where: Rain volume is modeled as continuous factor or covariate; k sub index refers to replicate; observations follow a multinomial distribution; and cumulative logit link function.
For the generalized linear model the estimation method was maximum likelihood with Laplace approximation. Model significance was evaluated with χ2 test and the significance of the fixed effects was evaluated with F-approximate test (α = 0.05). Estimated cumulative probabilities for soil types were compared with odds ratio test. If the confidence interval for the ratio includes 1, the two soils are not significantly different (Stroup, 2012 ).
Where: Rain volume is modeled as continuous factor or covariate; k sub index refers to replicate; observations follow a multinomial distribution; and cumulative logit link function.
For the generalized linear model the estimation method was maximum likelihood with Laplace approximation. Model significance was evaluated with χ2 test and the significance of the fixed effects was evaluated with F-approximate test (α = 0.05). Estimated cumulative probabilities for soil types were compared with odds ratio test. If the confidence interval for the ratio includes 1, the two soils are not significantly different (Stroup, 2012 ).
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