Age at maturity
We estimated age at maturity (A50, age at 50%
probability of the individuals have reached maturation age) for each
cohort (year-class) with sufficient data in the time series for perch in
both Lake Vaggatem (ncohorts= 12) and Lake Skrukkebukta
(ncohorts= 4) (Appendix Fig. S13) using logistic
regression. We related the estimated cohort-specific A50to the estimated total cohort-specific length increment (age 1 to age 4
year old) using linear regression. We estimated cohort-specific\(A_{50}\) to address how environmental variables (water temperature and
relative density) indirectly affected age at maturity mediated through
individual juvenile growth. In addition, we estimated maturation age
separately for males and females to explore if it differed between the
sexes and if the proportion of males and females changed over time
(Appendix 8, Fig. S11 & S12).
Age at maturation is assumed to be plastic and depending on a
probabilistic maturation reaction norm (PMRN) describing the length- and
age-specific probabilities of maturation (Heino et al. 2002). To
illustrate how age at maturity changes with differing individual growth
rates and to highlight the population response to altered individual
growth rates, we calculated the PMRN from the long-term data on perch in
the Pasvik watercourse (See details on PMRN estimation routine in the
Supplementary Information, Appendix 8).
To investigate causal relationship between environmental variables and
age at maturation (A50) we used structural equation
modelling (SEM) with the “piecewiseSEM” package in R. We constructed
the SEM to assess direct and indirect effects of summer water
temperature and relative density on age at maturation
(A50) mediated through mean length increment
(mm·year-1) from age 1 to age 4 year old perch. Summer
water temperature and relative density of perch were modelled as
exogenous random variables, influencing other variables, but not
themselves being influenced by other variables. The biotic variable
length increment (from age 1 to age 4, mm·year-1) was
included as endogenous variable influenced by others and itself also
influencing other variables. Finally, age at maturity
(A50) was set as a response endogenous variable,
influenced by all other variables, but not influencing other variables.
All variables were standardized prior to the analysis. Figures and maps
were created by using the ggplot-package in R or BioRender.com, and
tables were made using the Sjplot-package in R.