A new growth curve model portraying the stress response regulation of fish: Illustration through particle motion and real data

Abstract

A fish has to grow in an aquatic environment with both positive and negative regulatory mechanisms under stress. Metabolic upregulation acts as a positive regulatory mechanism while metabolic downregulation acts as the negative regulation. These two mechanisms work as a response to the stress on the fish body. The Tsoularis–Wallace (TW) model can portray the two aforementioned metabolic regulations but is not applicable for fish growth under chronic stress. If the stress is chronic, then the fish body develops a metabolic depression in addition to these two aforementioned metabolic regulations. We capture stress effects through regulators similar to the regulators of population ecology in a proposed generalized model (PGM). At the same time, the chronic stress induced metabolic depression is considered in the PGM through a harvesting-like term in this study. Our PGM can capture all the conceptual phenomenon to describe the real data sets well. Like the TW model, our PGM has no analytical solution. Therefore, we propose a linearized model (PLM) from the PGM to overcome this problem. We used the mean fish body length data sets for four locations as used in Chakraborty et al. (2017). The relative growth rate (RGR) profiles of the PLM better fitted to the observed RGR values of the real data sets than the previously used models in three of the four cases. Comparing the fish body growth with the motion of a particle in Newtonian mechanics, we formulate the three broad phases (lag, log, and stationary) ending time points and the corresponding fish lengths. We also obtain the point of inflection regarding time and the corresponding length. We calculate all of these results for the real data sets. The metabolic downregulation and capacity limitation of our model cause a decreasing trend in maximum body length of the fish upon simulation. Metabolic depression rate parameter of our model is also a key control of the maximum body length of fish as per the simulation.