My
research interests lie in the intersection of population ecology,
mathematical modeling, and statistics. General topics are listed below.
Statistical methods for fitting population models to noisy time-series data
Population
dynamics data typically involve inaccurate estimates of the state of a
system undergoing stochastic dynamics. Incorporating both
measurement (or observation, or sampling) error and process noise (environmental
and/or demographic stochasticity) as well as uncertainty in model
structure has been a major challenge for
statistical methodology. I am interested in methods that fall
under the nearly synonymous labels of state-space models, hierarchical
models, mixed models, or hidden process models.
Applications of population model-fitting
I
am interested in putting new model-fitting methods to work on real
problems and in seeing those problems inspire new methods. I have
worked on fisheries and insect population dynamics. Fisheries are
particularly interesting because they represent the most common setting
where population models and statistics play a perennial role in
prediction and management. Insect population dynamics are
particularly interesting because they have important applications
in agriculture and are often amenable to independent experimental
testing.
Theoretical population dynamics
Drawing
conclusions about population dynamics by fitting biologically sensible
models to data is closely linked to understanding
theoretical dynamics of the models themselves. I am
interested in age- and stage-structured models with realistic
organismal development, species interactions, space, and stochasticity.Computational Statistics
Methods for likelihood (and related)
calculations with state-space or other hierarchical
models require numerical implementation or approximation for all but
the simplest cases. I am interested in quadrature and Monte Carlo
methods in general, including Markov chain Monte Carlo and sequential
Monte Carlo. I am also interested in the "normalizing constant"
problem. For both Bayesian
and maximum likelihood estimation of hierarchical models, an
important problem is to calculate model comparison statistics such as
Bayes Factors and normalized likelihoods. These are
mathematically related problems of estimating normalizing constants,
which are not easily available from MCMC output, for example.
Therefore additional computational steps are needed to estimate
these quantities.
Life history evolution
Natural
selection on the schedule of development, dispersal, reproduction and
mortality is intertwined with the population dynamics generated by such
demographic traits. I am interested in theoretical models that
connect evolution and population dynamics, for example to understand
the interactions between evolution of conspecific brood
parasitism and population dynamics. Here
is an errata
for typographical errors introduced in the publication process of de
Valpine (2000, PRSL-B), in which I used adaptive dynamics theory to
derive a general function of life history traits, incorporating
stage-specific density-dependence, that should be maximized by
natural selection.
Machine learning, pattern recognition, and bioinformatics
I am interested in the problem of prospective power analysis of studies
designed to discover diagnostic patterns from high-dimensional data,
such as from genomics or proteomics studies, with low sample sizes.