Growth modelling in accordance with daily water temperature in European grayling (Thymallus thymallusL.)

Abstract

The model of von Bertalanffy has been and is still widely used to model fish growth, mainly because of its good description of annual growth over the whole life span. However, it does not take into account a seasonal variability in growth rate, an important phenomenon that appears quite well correlated with water temperature fluctuations in temperate climates. In the present study, we demonstrated that it was possible to model such variations by including daily water temperature in the von Bertalanffy growth formula owing to the correlation between the growth coefficient k and water temperature. The model we chose to describe such a correlation includes parameters with obvious biological significance and is mathematically well structured, which allowed an extensive use of our growth model. Hence, we use our new model to describe annual variability in the growth of European grayling (Thymallus thymallus L.) in a river section where water temperature could rise up to the thermal tolerance limit for this species, inducing reduced growth rates and severe mortality events. Finally, we were able to explain the growth rate variability from one year to the next by interannual water temperature fluctuations.

Population Dynamics of Grayling: Modelling Temperature and Discharge Effects

“…Biological integrity of these populations, as their persistence on the long term, can then be brought into play [14]. In previous works, we highlighted the effect of temperature on individual growth parameters [12]. We also showed in particular a significant increase in the annual average temperature (+ 1C between 1970's and 1990's) [11].…”

“…Numerical values of equation (2.5) were chosen to obtain a minimal five days survival rate in the region of 81.7% (as observed by Mallet [11]), and an inflexion point of the curve 19C or thereabouts, a temperature corresponding to the slowing down of growth [12].…”

“…As in the case of juvenile survival rate, numerical values were calibrated to obtain a minimal adult survival rate or so 84% (as observed by Mallet [11]), and an inflexion point of the logistic curve in the surroundings of 19C (point of slowing down of growth [12]). …”

Fisheries Management Under Cyclical Population Dynamics

“…3 An unpublished paper from the mathematical population dynamic literature by Castilho and Srinivasu (2005) goes over some of the same ground as Parma (1990) with respect to the implications of a time varying growth rate for optimal management. There are many population dynamic models that have growth rates that are predictable functions of identifiable factors such as environmental conditions (Mallet et al 1999). Singh et al (2006), using the Pacific Halibut fishery as an example, is one of the few papers to introduce autocorrelated error terms in a model explicitly looking at management implications.…”

Matching breeding goals with farming systems to enhance the sustainability of fish farming

“…Person-Le Ruyet et al (2004)). Therefore, the TGC formula needs to be corrected for the concave relationship between growth rate and temperature, which can be done by using a corrected temperature K as proposed by Mallet et al (1999):…”