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Natural mortality rates (M) are poorly quantified and commonly identified as a key source of uncertainty in fish stock assessments. Increasingly, stock assessments account for size- and age-dependence in M instead of using a constant M for all sizes and ages, as has traditionally been the default assumption. Empirical studies show that M is approximately inversely proportional to body length in fish populations, and this generalization has been used together with a von Bertalanffy growth curve to derive an age-dependent M. Here we extend this approach to the three commonly used growth functions of the Richards family (i.e., Logistic, von Bertalanffy, and Gompertz growth models). These models allow flexible production of various growth curves with a sigmoid shape and an upper asymptote, making them useful for displaying diverse growth curves for various long-lived fishes. The influences of growth parameters on predicted M were investigated, and the outcomes were compared among the three growth models. Age-dependent M for blue sharks (Prionace glauca) were estimated as an example. [ABSTRACT FROM AUTHOR]

The problem of biological invasion is an issue of increasing significance in conservation ecology. Fisher equation is one of the traditional methods to describe biological invasion. In ecosystems, however, species usually live in patchy environments. In this study, a modified Fisher equation is derived, where the recently developed "swapping migration" is applied and the relation between invasion velocity and patch capacity is discussed. [ABSTRACT FROM AUTHOR]

We study a food-web model which is known to exhibit a parity law: the behavior of stationary state differs by whether the species number is odd or even. Here we deal with the same ecosystem in patchy environment, where the capacities of patches are different. The migration between patches is permitted, only when there are empty cells in the destination. From reaction-migration equations, we find that the patch capacities largely affect the dynamics and phase transition. The previous parity law is paradoxically modified. Moreover, we find a new parity law originated in the difference of patch capacities. [ABSTRACT FROM AUTHOR]

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This paper investigates a class of viral infection models with a nonlinear infection rate and two discrete delays, one of which represents an intracellular latent period for the contacted target cell with virus to begin producing virions, the other of which represents the time needed in cytotoxic T cells (CTLs) response before immune becomes effective after a novel pathogen invades. Since immune system is a complex network of cells and signals that have evolved to respond to the presence of pathogens, we further assume two situations for immune activation delay. When both delays are ignored, the global stability for the ordinary differential equations model are established. While both delays are included, the positivity and boundedness of all solutions of the delay differential equations model are proved. Utilizing Lyapunov functionals and LaSalle invariance principle, the global dynamical properties are also studied. In particular, stability switch is shown to occur as immune delay increasing by bifurcation theory. Our results exhibit that the intracellular delay does not affect the stability of equilibria. However, the immune activation delay is able to destabilize the interior equilibrium and brings periodic solutions. Numerical simulations are performed to verify the theoretical results and display the different impacts of two type delays in two cases. Those analysis give us some useful suggestions on new drugs to fight against viral infection such that it is effective for the drugs to prolong the latent period, and/or to reduce the activation delay of CTLs immune response and/or to inhibit infection. [ABSTRACT FROM AUTHOR]