Modeling time-varying growth using a generalized von Bertalanffy model with application to bloater (Coregonus hoyi) growth dynamics in Lake Michigan

Abstract

A concurrent increase in lakewide abundance and decrease in size-at-age of bloater (Coregonus hoyi) in Lake Michigan have suggested density-dependent growth regulation. We investigated these temporal patterns by fitting a dynamic von Bertalanffy model and length–weight relationship with time-varying parameters to mean length- and weight-at-ages (ages 1–7) from annual surveys (1965–1999). We modeled yearling length, asymptotic size (L[Formula: see text]), and the parameters of a power relationship between mean weight and mean length (α and β) as changing slowly over time using a random walk model. The Brody growth coefficient (k) was modeled as a linear function of L[Formula: see text] with year-specific random deviations. Our results support a positive relationship between L[Formula: see text] and k, indicating that under conditions supporting larger asymptotic lengths, individuals approach the asymptote more rapidly. We explored the relationship between year-specific growth parameters and indices of lakewide bloater abundance and found evidence of density-dependent growth. However, in the most recent years, L[Formula: see text] and yearling length have remained low in Lake Michigan despite low bloater abundances, suggesting the occurrence of a fundamental shift in the food web.

Temporal trends in Mysis relicta abundance, production, and life-history characteristics in southeastern Lake Michigan

“…A dramatic suppression of Mysis abundance in Lake Michigan between the late 1970 s and late 1980 s was attributed to increasing planktivory, particularly by a resurgent population of the benthivorous bloater Coregonus hoyi (McDonald et al, 1990;Rand et al, 1995). In the mid 1990s Mysis abundance in southeast Lake Michigan apparently rebounded as bloater numbers steadily declined (Szalai et al, 2003). By 2007however, Mysis numbers declined back to 1985-1989levels (Lehman et al, 1990 despite relatively low bloater and overall planktivore biomass within Lake Michigan (Bunnell et al, 2009).…”

Morphological divergences among three sympatric populations of Silver Sharkminnow (Cyprinidae: Osteochilus hasseltii C.V.) in West Sumatra

“…At least the selective force might have contributed to the divergences those O. hasseltii was selection on ecological traits. Szalai et al (2003) observed that there were the densitydependent growth regulation generated the morphological divergence of Coregonus hoyi in lake Michigan. Hjelm et al (2003) also found that the feeding performance and the diet shift in fish species related to change in functional morphology over ontogeny.…”

Factors influencing growth of Acanthopagrus butcheri (Sparidae) in a eutrophic estuary have changed over time

“…In addition, the annual length increments produced by the model allowed us to test whether the growth of A. butcheri in the years in the 2007-14 period was related to temperature and freshwater discharge. Our modelling approach also permitted us to follow Szalai et al (2003) and He & Bence (2007) in elucidating whether growth was influenced M A N U S C R I P T…”

“…In the case of the lacustrine species Coregonus hoyi, Szalai et al (2003) described the lengths at age, using a von Bertalanffy growth curve with time-varying L ∞ and assuming a linear relationship with k, to predict the length increments of each age class in successive years and thereby accounted for inter-annual variations in growth. He & Bence (2007) later extended that model, for another lacustrine species, to allow each year-specific von Bertalanffy growth parameter to vary over time.…”