Statistical analyses
The three primary response variables recorded from the experiment were
diapause induction rate, development rate, and body weight. Variation in
diapause induction was tested using a generalized linear model with a
logit link function and diapause/nondiapause as the binary response
variable. Population, sex and treatment (six-level factor; see Fig. 1)
were used as explanatory variables.
Development rate was defined as 1/d , where d is the time
needed to complete a given stage of development. Three intervals were
separately analyzed: the time from hatching to the second molt (instars
1+2; this data only available for Öland and Stockholm), the time from
the second molt to the third molt (instar 3), and the time from the
third molt to pupation (instar 4). For each of these analyses a
three-way Anova was used, with treatment, sex and population as
explanatory variables. In one of the six treatments (larvae that had
been switched from long to short days in the third instar), development
rate in the fourth instar in particular was strongly bimodal according
to diapause decision (Fig. S1). For this reason, this treatment was
split by diapause decision, giving seven treatment levels instead of
six, when analyzing fourth-instar development rate.
Finally, weight was analyzed as a repeated measurement, using a mixed
linear model with individual treated as a random effect. Developmental
stage (third instar/fourth instar/pupa), treatment (six levels), sex and
population were used as fixed effects, hence testing for differences in
weights between treatments at different points in development. Because
larvae grow more or less exponentially in size, weights were
log-transformed in order to scale values across the time axis.
All analyses were carried out in R version 3.6.1 (R Development Core
Team, 2019). For each analysis, all fittable two- and three-way
interactions between the explanatory variables were tested, and
nonsignificant interactions were removed stepwise (in order of highest
p-value) so as not to sacrifice statistical power (Engqvist, 2005). The
significance of model terms (α=0.05) was evaluated using analysis of
variance (for continuous responses, i.e. weight and development rate) or
analysis of deviance (for binomial responses, i.e. diapause) with the
Anova function from the car package (Fox & Weisberg, 2019). The
final models are shown in Tables S1 and S2. Because larvae were shifted
between photoperiod regimes as they developed, the actual number of
unique conditions experienced was two, then four, then six, depending on
the stage of the experiment (Fig. 1). To address this, planned contrasts
were applied to the final models for development rate and weight, in
order to pool and compare larvae that had experienced the same
conditions up until a given point. At the start of the third instar, the
only contrast was long days vs short days. At the start of the fourth
instar, long vs short days were contrasted, and larvae that had switched
photoperiods in the previous instar were additionally contrasted with
their respective photoperiod of origin. At pupation all six treatments
were distinct, so all pairwise comparisons were made, using Tukey’s HSD
method to compensate for multiple testing. All contrasts were applied
using the emmeans package (Lenth, 2020), and were calculated
without controlling for population except where stated otherwise. All
treatment contrasts are summarized in Tables S3-S6.