User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/02/03

{| width="800"
 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Stochastic Population Dynamics
 * style="background-color: #F2F2F2" align="center"|  |Main project page
 * style="background-color: #F2F2F2" align="center"|  |Main project page


 * colspan="2"|
 * colspan="2"|

Hastings Meeting

 * Meeting with Dr. Alan Hastings soon to discuss progress on this project. We'll also see what he thinks of the open lab notebook.  There's a lot I want to cover in this meeting.

Warning Signals

 * Tomorrow I'm leading a discussion in seminar on regime shift literature, so I need to review major ideas of the paper with Alan. Particularly need to be clear on the role of dimensionality and if/when the population dynamics lack an appropriate Hamiltonian and whether that's an important part of the argument.

Beetle Dynamics

 * Summary of where we are / what I've done and the primary goals for the project. I'm hoping the intro to the lab notebook will help facilitate this.
 * Finish discussion of Denis et al Eco Monographs (2001) paper. Discuss alternate approaches that use model comparison.
 * Dealing with the age classes in continuous time when rates are time dependent remains a source of frustration. There are several possible approaches here, so might be good to compare how each performs against the data:
 * 1) assume constant rates of transition between age classes, restoring temporal homogeneity.
 * 2) add an energy function that explicitly models energy uptake and make transition rates between age classes dependent upon this
 * 3) see how far I can get with the straight-forward / correct approach of integrating directly.  Certainly fine for the ODE but less familiar with the theory for temporally heterogeneous stochastic process, since it loses the Markov property (rate depends on how long you've been in a state).

Post Meeting Eval

 * Goals for next time: Feb 10th
 * 1) Implement the analytic energy-based model for transitions between states, solve for fluctuation dynamics
 * 2) Review integral projection models of Steve Ellner as an approach to handling age / stage structure
 * 3) Experiment with adding individual heterogeneity and environmental variation to the continuous time simulation
 * 4) Explore implementation strategies for likelihood evaluation of the various models to simulated and real data
 * 5) Continue background reading


 * }