Systems with multiple time scales, often referred to as `slow–fast systems’, have been a focus of research for about three decades. Such systems show a variety of interesting, sometimes counter-intuitive dynamical behaviors and are believed to, in many cases, provide a more realistic description of ecological dynamics. In particular, the presence of slow–fast time scales is known to be one of the main mechanisms resulting in long transients—dynamical behavior that mimics a system’s asymptotic regime but only lasts for a finite (albeit very long) time. A prey–predator system where the prey growth rate is much larger than that of the predator is a paradigmatic example of slow–fast systems. In this paper, we provide detailed investigation of a more advanced variant of prey–predator system that has been overlooked in previous studies, that is, where the predator response is ratio-dependent and the predator mortality is nonlinear. We perform a comprehensive analytical study of this system to reveal a sequence of bifurcations that are responsible for the change in the system dynamics from a simple steady state and/or a limit cycle to canards and relaxation oscillations. We then consider how those changes in the system dynamics affect the properties of long transient dynamics. We conclude with a discussion of the ecological implications of our findings, in particular to argue that the changes in the system dynamics in response to an increase of the time scale ratio are counter-intuitive or even paradoxical.

Pigmentation abnormalities, ranging from hypo- to hyperpigmentation, can serve as biomarkers of developmental disruption in fish exposed to environmental contaminants. However, the mechanistic pathways underlying these alterations remain poorly understood. Studies have shown that pattern formation in fish development requires specific pigment cell interactions. Motivated by experimental observations of pigmentation alterations following contaminant exposure, we investigate how pollutants influence pigment cell self-organization using a continuum reaction–diffusion–advection framework. The model incorporates non-local Morse-type kernels to describe short- and long-range interactions among melanophores and xanthophores. Our results show that perturbations to the strengths of adhesion or repulsion can drive transitions between stripes, spots and mixed patterns, reproducing phenotypes characteristic of fish pigmentation mutants. In particular, homotypic interactions are sensitive to contamination, leading to pronounced changes in melanophore density and resulting pigmentation patterns. Time-dependent simulations indicate that pigment changes from early short-term contaminant exposure may be recoverable, whereas prolonged exposure can lead to sustained pigment loss. In a growing fish, contaminant-induced changes in cell–cell interactions directly influence stripe formation rate, stripe number and pigmentation levels. Overall, our study provides insight into the mechanistic link between experimentally observed pigmentation alterations and the changes in spatial patterns of adult fish.