Another Way to Calculate Fitness from Life History Variables: Solution of the Age-Structured Logistic Equation

On infinitesimally short time interval various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann (1986)). This is one of the cornerstones for differential equations modeling in general. Complicated models for processes interacting in a complex manner may be built up, and not only in population dynamics. The principle holds as long as the various contributions are taken into account exactl...

Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations governed by the discrete stochastic logistic equation at equilibrium. It is well known that the population dynamics of deterministic logistic models are dependent on the range of intrinsic growth rate. In this paper, we identify the same fea...

Mutualistic communities have an internal structure that makes them resilient to external per- turbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons of the system robustness. Much less attention has been invested in analyzing the systems dynamics. The main population models in use are modifi- cations of the logistic equation with additional terms to account for the benefits produced by ...

W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full non-linear demographic model for mutation accumulation of Evans et al. (2007), we find surprising differences. Non-linear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine pr...

The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied. This failure becomes severe in situations where the direction of selection switches sign. Here we employ the WKB (large-deviations) method, which requires only th...

We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical properties of this model with its continuous counterpart. We give sufficient conditions for competitive exclusion and the existence of periodic solutions related to the classical logistic, Beverton-Holt and Ricker models.

The logistic equation has been extensively used to model biological phenomena across a variety of disciplines and has provided valuable insight into how our universe operates. Incorporating time-dependent parameters into the logistic equation allows the modeling of more complex behavior than its autonomous analog, such as a tumor's varying growth rate under treatment, or the expansion of bacterial colonies under varying resource conditions. Some of the most commonly used nume...

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting fea...

We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time and the individual's nourishment history. A food-limited environment induces intraspecific competition and henceforth the carrying capacity of the medium may be finite, often emulating the qualitative features of logistic growth. Inherently n...

There is currently no consensus on how the global population will evolve in the next decades and in the next century. The reason for this uncertainty is the absence of reliable population dynamic models. In this paper, we remedy to this situation by reporting on a population dynamic model, a single nonlinear differential equation adapted from the physics of disordered systems, which is able to mathematically describe all the various regimes encountered in the global populatio...