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). For model comparison, the difference in AIC between each model and the lowest AIC model (Δi ) and Akaike weights (ωi ) were calculated.
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).
The survival curves for mothers in each treatment group were estimated using Kaplan-Meier survival analysis. We analysed the effect of nutritional stress and delayed mating on the survival of females in the experiment using a Cox proportional hazards model and estimated the hazard function by treatment using a kernel-based method with a bandwidth grid of 30 components (Moore 2016). For each treatment we also tested whether the risk of death increased with age by comparing exponential and Weibull parametric survival model fits to the data. For these analyses, we used the R packages ‘survival’, ‘survminer’ and ‘muhaz’ (Hess & Gentleman n.d.; Therneau & Grambsch 2000; Kassambara & Kosinski 2018).
For the probability of abortion, offspring wet weight, probability of offspring emergence and duration of offspring survival, 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 of the models described below, we first assessed the influence of repeated measures from individual mothers by comparing: i) a full model including all explanatory variables, random intercept and slope: ii) a full model with random intercept; and iii) a full model with no random effects (Zuur et al. 2009). In each model, maternal age in days was incorporated as a continuous variable.
Logistic regression was used to quantify the effect of maternal age on the probability of larval abortion for each treatment. After comparing models with and without a random effect of individual mother, we compared a model including maternal age with that of the null model.
The effect of maternal age on pupal wet weight was quantified using linear mixed effects models, with the full model including a cubic effect of mother age on offspring wet weight and assuming wet weight was normally distributed. Models including mother age as a cubic, quadratic or linear effect were compared with each other and the null model.
We hypothesised that the effect of maternal age on the probability of emergence and the subsequent survival time would be determined largely by energy reserves, as indirectly measured by offspring wet weight. Heavier offspring would have more reserves and therefore would be more likely to emerge and then survive longer before starvation. Maternal age could also, however, affect offspring survival directly. The effect of mother age and offspring wet weight on the probability of emergence was therefore quantified using logistic regression. We assessed the effect of repeated measures from the same mothers, including a quadratic effect of mother age in the full model.
For the survival data, there was no censoring and the data were approximately normally distributed (S3 Fig.). The relationship between offspring wet weight, sex, mother age and survival time was therefore modelled using linear mixed effects models for each treatment. We included mother age, as a quadratic or linear effect, and compared model fits with sex to the fit of models including only wet weight and the fit of the null model. To visualise our results, we used fitted models to predict the effect of maternal age on emergence and survival for each wet weight quartile.