Data analysis

Data analysis was done in RStudio (RStudio, Inc. Boston, MA, United States, 2016) using the R software version 4.1.2. through different fitted models and controlled for the overdispersion.

To analyse some of the data from the dose–response experiment, Generalized Linear Mixed Models (GLMM) under the package lme4⁷⁴ were used with the relevant family after the model overdispersion verification⁷⁵. Thus, adult emergence and insemination rate from the experiment 3 were analysed using this model with binomial family, where the irradiators nested in the radiation type and doses were considered as the fixed effect and the replications as random effect. The same model was used with Poisson family to analyse the effect of irradiators and doses on the number of aborted eggs. To analyse spermathecae fill a GLMM with gaussian family was used after Tukey’s Ladder of Powers transformation of data.

To analyse the effect of gamma- and X-ray irradiators on male sterility/residual fertility, the dose response model with “drm” function was used under the Dose–Response Curves (drc) package⁷⁶. The best model was selected with the “mselect” function based on the log likelihood value, Akaike's Information Criterion (AIC), known as the estimated residual standard error or the p-value from a lack-of-fit test as criteria.

The best model for the fecundity data was the Weibull three-parameters type 1 model (W1.3) given by the expression y(x) = 0 + (d−0) exp(− exp(b(log(x) − e))), while the induced sterility fitted with the Weibull model with two parameters (W2.2) expressed by y(x) = exp(− exp(b(log(x) − e))). The first model assumes that the lower limit is 0 (fecundity tended to zero at high doses), and d represents the upper limit of the fecundity, while b assigns the slope, e denotes the median effective irradiation dose (ED₅₀) and x is the absorbed radiation dose (Gy). In the second model, the lower limit was fixed at 0, and the upper limit d is fixed at 1, being the full sterility of 100%. The curves parameters were then compared between the irradiators using the compParm function. The estimated effective doses that reduce 50, 95 and 99% of the fertility and induce the same levels of sterility for the three irradiators were determined with the ED function and then compared using the Kruskal–Wallis test.

To analyse the survival time, the Cox Mixed Effects Models (“survival” package, “coxme” function) fit by maximum likelihood was used. In this analysis, the survival time served as the response variable, and the treatments (irradiation with three different irradiators as well as a non-irradiated control group) and doses were included as fixed effects and the replications as random effect. Multiple comparisons were done using the estimated marginal means (“emmeans” function in package “emmeans”) with the Tukey p-value adjustment method. The survival graphs were constructed using “ggsurvplot” with “survimer”, “ggplot2,” and “ggpubr” packages.

For the flight quality control and the mating performance, the data were analysed using GLMM with binomial family and the overdispersion test. Adult emergence rate and flight propensity were modelled considering the treatments (irradiated with three irradiators and non-irradiated) and doses as fixed effects and replications as random effect. Male survival was analysed using the Cox Mixed Effects Model fit by maximum likelihood as in the dose response section.

The mating latency, duration and the spermathecae fill data were analysed using a Generalized Linear Model with gaussian family after Tukey’s Ladder of Powers transformation of data. The effect of the treatments as irradiated and non-irradiated and doses on the mating index was analysed with a Poisson family. During the data analysis, multiple comparisons were done using the estimated marginal means where a significant difference was found at the global level.