12 documents found, page 1 of 2

General population growth models with Allee effects in a random environment

Allee effects on population growth are quite common in nature, usually studied through deterministic models with a specific growth rate function. In order to seek the qualitative behaviour of populations induced by such effects, one should avoid model-specific behaviours. So, we use as a basis a general deterministic model, i.e. a model with a general growth rate function, to which we add the effect on the grow...

Encontro Nacional da Sociedade Portuguesa de Matemática 2016: livro de resumos

Weak Allee effects population growth models in a random environment

Based on a deterministic model of population growth with weak Allee e ffects, we propose a general stochastic model that incorporates environmental random fluctuations in the growth process. We study the model properties, existence and uniqueness of solution, the stationary behavior and mean and variance of the time to extinction of the population. We then consider as an example the particular case of a stochas...

XXII Jornadas de Classificação e Análise de Dados (JOCLAD 2015): Livro de Resumos

Consequences of an incorrect model specification on population growth

We consider stochastic differential equations to model the growth of a population ina randomly varying environment. These growth models are usually based on classical deterministic models, such as the logistic or the Gompertz models, taken as approximate models of the "true" (usually unknown) growth rate. We study the effect of the gap between the approximate and the "true" model on model predictions, particula...

Modelos de crescimento populacional em ambiente aleatório: efeito de incorreta ...

Allee effects in randomly varying environments

Based on a deterministic model of population growth with Allee effects, we propose a general stochastic model that incorporates environmental random fluctuations in the growth process. We study the model properties, existence and uniqueness of solution and the staionary behavior. We also obtain expressions for the first passage times, in particular, the mean and standard deviation of the extinction times for th...

Models of individual growth in a random environment: study and application of f...

We study the first-passage times for models of individual growth of animals in randomly fluctuating environments. In particular, we present results on the mean and variance of the first-passage time by a high threshold value (higher than the initial size). The models considered are stochastic differential equations of the form dY(t)=β(α−Y(t))dt+σdW(t), Y(t0) = y0, where Y(t)= g(X(t)) is a transformed size, g be...

Profit optimization for cattle growing in a randomly fluctuating environment

A class of stochastic differential equation models was applied to describe the evolution of the weight of Mertolengo cattle. We have determined the optimal mean profit obtained by selling an animal at the cattle market, using two approaches. One consists in determining the optimal selling age (independently of the weight) and the other consists in selling the animal when a fixed optimal weight is achieved for t...

Individual Growth in a Random Environment: an optimization problem

We consider a class of stochastic differential equations model to describe individual growth in a random environment. Applying these models to the weight of mertolengo cattle, we compute the mean profit obtained from selling an animal to the meat market at different ages and, in particular, determine which is the optimal selling age. Using first passage time theory we can characterize the time taken for an anim...