Main topics

Populations dynamics in space

Problems related to dispersal/diffusion of populations in space over time, employing reaction-diffusion equations or integro-difference equations. I also work on metapopulations and metacommunities, which seek to understand the influence of space in fragmented landscapes. +info: presentation of one of my earliest works.

© Fabiana Arantes @fabi.r.a

Dynamics of age- or stage-structured populations

Species whose individual's stage of life drastically alter their dynamics (e.g. larval and adult stages in insects) are challenging to model: the full equations are hard to deal with, but it is, in general, possible to reduce them to systems of delay differential equations. Questions involving this kind of system are specially important to study the impact of climate change on populations. +info: see this presentation (in portuguese).

© Fabiana Arantes @fabi.r.a

Rapid evolution of phenotypic traits

The so-called eco-evolutive dynamics couple fast evolution (in few generations) of phenotypic traits to population fluctuations due to ecological processes, in such a way the one drives the other. I have been interested in analysing the evolution of trait distributions of whole communities (particularly planktonic), looking for ways to reduce model complexity. +info: see this presentation or this (in portuguese).

Others

Fitting of models to noisy data

In ecology and epidemiology, models usually cannot fit the data very well, both because the data are very noisy, and because the models don't contain all, or even most, processes involved. I have been working with methods of fitting that build on stochastic versions of the starting (deterministic) model—called partially observed markov process (POMP)—which allow not only the fitting, but also a measure of the model uncertainty at each step.

Causality in time series

Correlation does not imply causation—and therefore, more sophisticated methods are required to infer causality. Convergent cross-mapping (CCM) is a recently-developed technique that applies methods from dynamical systems (attractor reconstruction) to infer causality between two variables from their time series data. +info: see here (in portuguese).

Analysis and projection of the water in the Cantareira reservoir

Started from simple ideas about the dynamics of this system at the time of the São Paulo water crisis, it evolved to a major project involving statistical indicators of the water reservoir levels. The website Águas Futuras (in Portuguese), with projections of this level for the next month, is still up-to-date.

Publications

Here is a full listing (with pdfs), or see my Lattes CV or Google Scholar.