相关论文: A Mathematical Model with Modified Logistic Approa…

I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…

We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…

We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in…

We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…

In 2006 (J. Differential Equ.), Lou proved that, once the intrinsic growth rate $r$ in the logistic model is proportional to the spatially heterogeneous carrying capacity $K$ ($r=K^1$), the total population under the regular diffusion…

We show that a simple nonlinear differential equation (originally studied in the physics of disordered systems) is able to mathematically describe the global population growth over the past 12000 years. Different regimes of population…

Despite the general acknowledgment of the role of niche and fitness differences in community dynamics, species abundance has been coined as a relevant feature not just regarding niche perspectives, but also according to neutral…

This chapter focuses on variable maturation delay or, more precisely, on the mathematical description of a size-structured population consuming an unstructured resource. When the resource concentration is a known function of time, we can…

We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in…

We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an…

The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…

A model for large-scale evolution recently introduced by Amaral and Meyer is studied analytically and numerically. Species are located at different trophic levels and become extinct if their prey becomes extinct. It is proved that this…

Hierarchical modeling of abundance in space or time using closed-population mark-recapture under heterogeneity (model M$_{h}$) presents two challenges: (i) finding a flexible likelihood in which abundance appears as an explicit parameter…

We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…

We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…

Production of energy (metabolism) and its distribution is vital for living organisms, both at individual level - between different functions of an organism, as well as between species of communities at different organizational levels,…

The changes on abiotic features of ecosystems have rarely been taken into account by population dynamics models, which typically focus on trophic and competitive interactions between species. However, understanding the population dynamics…

Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…

A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…

We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…