Statistical analyses
Measuring fertility which is a long-term adult trait when individuals
are heated during different life-stages introduces significant temporal
biases. We decided to measure fertility from the earliest possible
time-point post-stress, and continue to measure over time. This allowed
us to capture any visible loss/regain of fertility. Flies do not breed
as pupae, so fertility cannot be measured immediately following
heat-stress during this stage. Therefore, in order to understand how
these responses change depending on life-stage, we measured fertility
over a substantial period of time after stress for both pupae and
adults. Due to the inherent differences this introduced, we analysed
pupal and adult heat-stress separately, so comparisons of responses
between stages can only be qualitative.
Data were analysed using variations on linear models. We assessed model
fit by plotting patterns in residuals against fits and against
predictors. All statistical analyses were completed in R (version
3.5.0), using the packages: binom (Dorai-Raj 2014), car (Fox 2011),
“ggplot2” (Wickham 2016) and “survival” (Therneau 2015). We did
model selection using Wald Chi-squared likelihood ratio-tests, removing
non-significant interactions. We retained all main effects and reported
statistics of these from type II likelihood ratio tests using the
‘Anova’ function from the ‘car’ package (Fox 2011).
1a) Pupal survival after heat-stress
We chose 36°C as our single experimental ‘hardening’ temperature since
it is the highest temperature that does not reduce fertility when males
experience it for 4h (Walsh et al. 2020; Parratt et al.2021). We analysed pupal survival after heat stress using a logistic
regression with survival as a Bernoulli response variable. Stress
temperature, hardening treatment (non-hardened or hardened at 36°C), and
their interaction were fitted as explanatory variables. To determine
whether the hardening temperature altered its protective effect, we
analysed pupal survival of all flies hardened at 34, 35, and 36°C prior
to heat stress at the key stress temperature of 40°C where protection is
observed. We performed a logistic regression with survival as a
Bernoulli response variable. We used hardening temperature as the
explanatory variable. Note that the 34 and 35°C hardening temperatures
were not measured at 37 and 38°C temperature stress at this preliminary
stage, as these temperatures are non-lethal after a 4h stress (Walshet al. 2020).
1b) Adult survival after heat-stress
As every fly stressed at control temperatures (23°C) survived, we
analysed adult survival at the chosen stress temperature (38°C) only,
using a logistic regression with survival as a Bernoulli response
variable and sex (male or female), hardening treatment (non-hardened or
hardened), and their interaction as explanatory variables.
2a) Pupal fertility over time
We analysed the effect of heat stress on fertility over time with
inverse Cox proportional hazard survival analyses (using the
“survival” package (Therneau 2015)). This allowed us to model the time
in days post-eclosion until focal individuals become fertile. We fit the
time point at which fertility (scored as the presence of larvae) was
observed as our response variable with heat treatment (benign or
stress), hardening treatment (non-hardened or hardened) and their
interaction as independent variables.
2b) Adult fertility over time
We examined whether there was an immediate effect of heat stress on
fertility, and whether hardening affects this response. We used a
logistic regression with day 1 fertility as a Bernoulli response
variable and stress (benign or stressed), hardening treatment
(non-hardened or hardened), and their interaction as explanatory
variables.
Adult fertility over time was analysed using two separate approaches due
to the observed delayed sterility and how the experimental design was
constructed around it. This allowed us to pull apart different
hypotheses and test them. We first tested whether heat-stress reduced
fertility from day 7 onwards compared to benign temperature controls,
due to delays in adult sterility. To do this we used a mixed effect
logistic regression on non-hardened flies, with fertility as a Bernoulli
response variable and stress, time, and their interaction as explanatory
variables. Fly ID was used as a random effect to account for
non-independence in the data.
We then tested whether hardening can improve fertility over time in
stressed males. We used a mixed effect logistic regression on stressed
flies, with fertility as a Bernoulli response variable and hardening,
time, and their interaction as explanatory variables. Fly ID was used as
a random effect to account for repeated measures in the data.