A classical nonlinear system, the “Brusselator”, was used to illustrate the modeling and simulation of oscillating chemical systems using stability analysis techniques with modern software tools such as Comsol Multiphysics, Matlab, and Excel. A systematic approach is proposed in order to establish a regime of parametric conditions that lead to oscillations in chemical systems. A Matlab script that symbolically finds the equilibrium points of the system, and the Jacobian of the assembly matrix at equilibrium was written. The Matlab script also calculates the trace, determinant and discriminant of the Jacobian and finds the critical points for which the trace and determinant are zero. An emphasis on finding the bifurcation points is made in the simulations and on the conditions for the onset of limit cycles, which are of most interest in biological systems.
In tropical species, the study of parental care and the description of the intraspecific variation of parental care remain relatively understudied, especially when compared to the vast works dedicated to species from the Northern Hemisphere. In Colombia, the saffron finch Sicalis flaveola, is a species with a wide geographical distribution, and despite its abundance in open habitats and urban environments, little is known about its reproductive ecology. As a small-bodied, short-lived passerine, we postulated that the saffron finch should behave according to the 'reproductive value hypothesis', investing in the current brood at the expense of future survival. Consequently, we predicted: 1) that parental investment would be associated with brood size and 2) parental investment would be positively associated with nestling growth rate and reproductive success (defined as the number of nestlings which reached fledging age). In 2018, two reproductive peaks of S. flaveola flaveola were documented in the Meléndez campus of Universidad del Valle, Cali. Direct observations and video cameras (> 1700 h of recording) were used to monitor the nests from 38 different breeding pairs. We found that feeding visits and the number of regurgitation events were positively related to brood size. In an experiment of simulated nest predation, 85% of breeding pairs responded to the stimulus and parents who exhibited highly responsive behaviours (50%) raised nestlings with a higher growth rate. We also found that egg surface area positively affected the number of incubation bouts per hour. Whilst no relationship was found between overall parental investment and reproductive success, our results appear to show that the intensity of parental investment during reproduction was modulated by brood size. Our findings suggest that there are multiple ecological factors that influence reproductive success in the saffron finch, and reinforce the need for longer term studies of tropical passerines.
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