Here I summarize my recent research projects:
Community Ecology and the Neutral Theory of Biodiversity
My early work on stochastic community models (Alonso and Sole 1999, McKane et al 2000)
and metapopulation models (Alonso and McKane 2002) establishes a
stochastic mathematical framework to analyze and model complex
ecological interactions (Alonso 2004a). My approach emphasizes
the discrete nature of individuals and their
inherent random interactions. However, my most relevant
contributions in community ecology are rather recent. In
collaboration with Rampal Etienne at the University of Groningen,
we have developed a new sampling theory which takes into account the
sampling, ecological and evolutionary processes that
ultimately determine the number and relative frequencies of the
species (or strains) arising in a typical sample from a given
community (Etienne et al 2007). In particular, in the context of the
neutral theory of biodiversity, we have shown
that samples from any local community can be seen as a result of
a dispersal-limited sampling from a larger biogeographical area
(Alonso and McKane 2004, Etienne and Alonso 2005, Alonso et al 2006). This new
formulation of sampling has applications both to community
ecology and population genetics and provides a
unifying theoretical framework where other factors beyond
neutrality can be easily considered (Etienne et al 2007).
Dynamics
of Infectious Diseases
Recently,
I have developed stochastic models to analyze time series data of
infectious diseases (Alonso and Pascual 2005). This type of data can
potentially register the signal of environmental and climate
change. The main goal of this ongoing research is to quantify the
relative importance of stochasticity, seasonal or climatic
forcing on the nonlinear dynamics of infectious diseases, with
applications to dynamics of malaria. In addition, in
collaboration with Alan McKane from the University of Manchester
and Mercedes Pascual at the University of Michigan, I have been
working on the effect of demographic stochasticity on the
non-linear dynamics of infectious diseases. Our recent
theoretical work “Stochastic Amplification in Epidemics”
(Alonso et al 2007) provides a novel quantitative description of
stochastic fluctuations in epidemics. There is evidence that
childhood diseases are clustered on specific regions of the
parameter space. Due to inherent instabilities
within these parameter domains, these infectious diseases appear
to be prone to produce huge outbreaks. These fluctuations
challenge control strategies. Our work is the first accurate
quantitative characterization of strong coherent oscillations
through endogenous stochastic resonance in real
epidemiological systems. This phenomenon is also relevant to
population oscillations in ecological systems in general.
Ecology and Evolutionary Biology,
University of Michigan
830 North University Av,
Ann Arbor, MI-48109-1048, USA
Phone: (+1) 734 623 5008
Fax:
(+1) 734 763 0544
dalonso@umich.edu
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