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.