Back-calculated length at age and length increment
The back-calculated length increment was estimated for a sub-sample of
perch from Lake Vaggatem and Lake Skrukkebukta. On the opercular bones
of individual perch, we measured the width of annual growth increments
as the distance between the opaque zones. We used these measurements in
addition to the total opercular length and the body length of the
individual perch to estimate length-at-age with the nonlinear
body-proportional hypothesis method. This method is commonly used for
perch (Thoresson 1996) and assumes that the deviation in body size from
the expected body size given by the operculum size does not change
through life (Thoresson 1996),
\(L_{a}=L_{A}({\frac{O_{a}}{O_{A}})}^{\beta_{1}}\),
where \(L_{a}\) is the back-calculated length-at-age a, \(O_{a}\) the
measured operculum radius at age a, \(O_{A}\) the observed operculum
size at time of capture, and \(L_{A}\) the observed fish length at time
of capture. \(\beta_{1}\) is the linear regression slope coefficient
estimated from the log-log relationship between the body length and
operculum length at capture. A total of 1646 perch were used in the
back-calculation procedure. We back-calculated length increment
(mm·year-1) for juvenile fish in the age group of 1-4
years with individual perch ranging from age 2 to 10 years, giving us
length increment data from year 1995 to year 2018. We did not asses
growth during the sampling year, because those estimates would be
dependent on sampling time within the year, which was not exactly the
same every year. A comparison between back-calculated length at final
winter before capture and length at capture revealed a good fit of the
back-calculation model (p<0.001, F= 2501 on 1 and 1644 df,
adj-R2=0.94) (Appendix Fig. S6 & Table S9).
Back-calculated length increment (mm·year-1) for 1, 2,
3 and 4 year old perch were related to summer water temperature and
relative density in a Linear Mixed Effect model (LME) with sampling year
and age at capture as random effects, with the nlme-package in R. In
addition, we estimated cohort-mean (year class) length increment from
age 1 to 4, which was related to mean summer water temperature (°C) and
mean relative density (CPUE) for the same time period (three-year
moving-average) with linear regression.