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.