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The presence of the golden mussel in Brazil is a matter of great concern and causes harm to the country, particularly affecting the power generation sector. Infestation control represents a challenge, and there is a need to mathematically describe the dynamics of the problem. This work proposes to analyze a mathematical model based on differential equations that relate the populations of larvae, mussels, and algae. For this model, the critical points and stationary states are determined, seeking steady-state conditions stability, through the basic reproduction rate. In addition, it presents the sensitivity analysis of the parameters involved. The paper results are relevant as they allow mathematical interpretation of the golden mussel infestation potential through the basic reproduction rate. Furthermore, the sensitivity analysis suggests how important the parameters are for this potential. For that matter, this work can provide baseline information to guide future control strategies as it provides quantification of the species involved over time as well as a condition for infestation. • Mussel-algae interaction model. • Stability analysis of stationary solutions of the model. • Basal reproduction rate for the golden mussel model. [ABSTRACT FROM AUTHOR]

• Integral projection models (IPMs) are demonstrated as a promising approach for studying the size-structured effects of natural and anthropogenic stressors considered in ecotoxicological applications. • A fathead minnow (P. promelas) life history model is developed. Seasonal batch-spawning, over-winter growth and survival, and density dependent growth effect mechanisms are derived and built into daily time-step IPM transition kernels as a case study. • A realistic time-variable chemical exposure and associated effects are estimated using a toxicokinetic-toxicodynamic acute survival effects model and sub-lethal chronic growth effect model and linked to IPM. • IPMs are developed with consideration given to the applications and data availability constraints of ecotoxicologists and ecological risk assessors. In many ecosystems, especially aquatic ecosystems, size plays a critical role in the factors that determine an individual's ability to survive and reproduce. In aquatic ecotoxicology, size informs both realized and potential acute and chronic effects of chemical exposure. This paper demonstrates how chemical and nonchemical effects on growth, survival, and reproduction can be linked to population-level dynamics using size-structured integral projection models (IPM). The modeling approach was developed with the goals and constraints of ecological risk assessors in mind, who are tasked with estimating the effects of chemical exposures to wildlife populations in a data-limited environment. The included case study is a collection of daily time-step IPMs parameterized for the life history and annual cycle of fathead minnows (Pimephales promelas), which motivated the development of modeling techniques for seasonal, iteroparous reproduction, density dependent growth effects, and size-dependent over-winter survival. The effects of a time-variable annual chemical exposure were interpreted using a toxicokinetic-toxicodynamic model for acute survival and sub-lethal growth effects model for chronic effects and incorporated into the IPMs. This paper presents a first application of integral projection models to ecotoxicology. Our research demonstrates that size-structured IPMs provide a promising, flexible, framework for synthesizing ecotoxicologically relevant data and theory to explore the effects of chemical and nonchemical stressors and the resulting impacts on exposed populations. [ABSTRACT FROM AUTHOR]