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.