Statistical analyses
For each analysis described below, models were compared using Akaike’s information criterion (AIC). If the ratio of the sample size to the number of model parameters was <40, we used AIC corrected for small sample size (AICc) (Burnham & Anderson 2002). Figures were produced using the model with the lowest AIC. For model comparison, the difference in AIC between each model and the lowest AIC model (Δi ) and Akaike weights (ωi ) were calculated. Akaike weights sum to one and provide a relative indication for the weight of evidence for any one model as the best approximating model (Burnham & Anderson 2002). We analysed the data using R version 3.6 (R Core Team 2014). The data and R scripts to produce the results can be accessed at (https://github.com/jenniesuz/tsetse_senescence.git).
For the probability of abortion, offspring wet weight, and starvation tolerance, we carried out statistical analyses for each treatment separately using linear and generalised linear mixed effects models implemented with the ‘lme4’ and ‘nlme’ R packages (Bates et al.2015; Pinheiro et al. 2018). For each analysis described below, maternal age in days was incorporated as a continuous variable. All models with and without random effects were fitted and simultaneously compared using maximum likelihood estimation, assuming that the bias in the variance components would be relatively small (n /(n -p ): 1.009 for the probability of abortion; 1.049 for offspring wet weight; and 1.095 for offspring survival, largest values across treatments reported). Models with and without a random intercept were compared to assess evidence for variation among individual mothers in the probability of abortion, offspring wet weight and offspring starvation tolerance. We also compared models with and without a random slope for maternal age, to assess evidence for variation in senescence patterns among individual mothers.
The effect of maternal age on probability of abortion, offspring wet weight and offspring starvation tolerance were compared between treatments using fitted coefficients and 95% confidence intervals from the model with the lowest AIC. We took this approach to analysis rather than including treatment as a factor in models as it is simpler and does not require the assumption of equal variance between treatments.
Logistic regression was used to quantify the effect of maternal age on the probability of abortion for each treatment, assuming a linear relationship between maternal age and the log odds of abortion. For the effect of maternal age on offspring wet weight and starvation tolerance, models including maternal age as a cubic, quadratic, logistic or linear effect were compared. For wet weight, we also compared the most parsimonious model with a model fit using generalised additive modelling (GAM). Cubic regression splines were fitted for each treatment, with maternal age as the explanatory variable and accounting for multiple offspring from individual mothers, using the mgcv R package (Wood 2017). Generalised additive model fits with knots – locations where the slope changes – ranging from 3 to 10 were compared using AICc. The correlation between offspring wet weight and fat was summarised using Pearson’s correlation coefficient.
For offspring starvation tolerance, there was no censoring and the data were approximately normally distributed (S4 Fig.). The relationship between offspring wet weight, sex, maternal age and number of days to starvation was therefore modelled using linear mixed effects models for each treatment. Maternal age was included in models as described for offspring wet weight. In addition to maternal age and wet weight, we also included offspring sex as females are larger than males on emergence (Hargrove et al. 2019).
We repeated the above analyses for the nutritional stress treatment, excluding females that had died, to ensure our results were not affected by the possibility that females who died allocated more to their offspring. For the other two treatments this was not done as >90% of mothers were still alive by the end of the experiment. Lastly, an analysis of maternal survival is provided in S5 File.