Cyclic data and planar ordinary differential equations: statistical modeling and inference

点击翻译按钮获取中文摘要

The present program is on solving a broad question, which is to estimate parameters of solutions to ODEs (ordinary differential equations) that occur in biostatistical applications and have cyclic solutions. We start with ecology, and the emphasis is on predator-prey interactions; in practice, many animal populations exhibit oscillatory behaviour. Therefore, in their models, ecologists are considering systems that admit limit cycles or spiral to an equilibrium. In our proposal we introduce a simple method for estimating elements that are put forward by the qualitative analysis of the ODE system, like isoclines, e.g. The method works whenever periodicity is present. Once the estimation is performed, one can test various models as well. The originality of the present program is to work in the phase plane, and the methodology is an extension of the one developed in Froda & Colavita (2005) and Froda & Nkurunziza (2006).From the applied point of view, various  areas of ecological research are concerned by this proposal. At first, we consider the choice of an appropriate predator-prey model at one geographical site. Later,  we should be able to extend our methodology and fit predator-prey models in metapopulations, i.e. when the habitat is fragmented (e.g. after habitat destruction). Understanding the impact of habitat destruction on animal behaviour is extremely important in conservation biology.It is to be noted that our method allows to discriminate among alternative models, a problem which is debated among ecologists, and is central to the field.Finally, in the long run, other fields of application  can be considered, like the study of epidemic models.