Systematic changes and random variations: Understanding lake trout (Salvelinus namaycush) growth dynamics in US waters of Lake Huron

Abstract

Changes in fish length-at-age can be modeled by adding the age, year-class, and year effects together, or tracking cohort-specific growth with time-dependent parameters. We implemented both approaches to better understand lake trout (Salvelinus namaycush) length-at-age variations in US waters of Lake Huron, 1977–2019. We directly compared length-at-age over time using our linear-mixed model, where the expected length-at-age on logscale was represented by the sum of a fixed age effect, a fixed year-class effect (same for all ages of a cohort), and a random year effect (same for all ages within a year). The age, year-class, and year effects together indicated a general decline in length-at-age between the two time-periods of 1977–1997 and 1998–2019. The random year effect had local temporal trends that differed between the two time-periods, while the pattern of decreases in the fixed year-class effect appeared to reflect changes in growth conditions that were represented eventually by the largest prey-biomass decline during 1995–1996 and the final alewife collapse in 2003. We also predicted annual averages of length-at-age by tracking cohort-specific growth histories. We modified the Ford-Walford plot to illustrate how the growth processes are both cohort-specific and time-dependent. The estimates of year-specific asymptotic length indicated the decline in lake trout growth potential between the two time-periods specified above. Our two models differed fundamentally in their statistical assumptions, but they both fitted the data well and explained the growth decline between the two time-periods, which was also consistent with our understanding of the trophic shift in the ecosystem.