Musings, Explorations, and Announcements

How does overdispersion of infections affect the behavior of the multiple-infection model? I redefine the model to account for overdispersion, assuming the same overdispersion occurs in both age classes. The parameter \(k\) varies inversely with the degree of overdispersion. Again, the classes are demographically identical, and infection affects mortality but not growth: \[\begin{aligned} \frac{dJ}{dt} &= A f_A \left(1 - \frac{J+A}{K} \right) + J \left(f_J \left(1 - \frac{J+A}{K} \right) - d_J - g\right) - \alpha P_J \\ \frac{dA}{dt} &= J g - A d_A - \alpha P_A \\ \frac{dP_J}{dt} &= \lambda \frac{J}{K} (P_J + P_A) - P_J \left(d_J + \mu + g + \alpha \left(1 + \frac{(k+1)P_J}{kJ} \right) \right) \\ \frac{dP_A}{dt} &= \lambda \frac{J}{K} (P_J + P_A) + P_J g - PA \left(d_A + \mu + \alpha \left(1 + \frac{(k+1)P_A}{kA} \right) \right) \end{aligned}\]

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Here’s a little thought exercise I did that has caused me to go back and restart my Sudden Oak Death modeling in a new framework. Feedback welcome. I’m especially interested in relevant literature – I haven’t found many good examples of macroparasite/multiple infection models with age structure. Introduction Cobb et al. (2012) develop two models of forest stand demography in the face of Sudden Oak Death. The first, a statistical survival model, estimated the rates of infection and time-to-mortality as functions of density of infected trees and tree size.

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Carl Boettiger, Alan Hastings and I have a new review out on early warning signals and regime shifts. It’s about an idea that Carl and I have been kicking around for a couple of years and finally got around to writing up for a special issue of Theoretical Ecology. There has been a lot of excitement in the past six years or so about early warning signs - statistical signals that indicate that an ecosystem is near a dramatic shift, like the collapse of a fishery or a switch from grassland to desert.

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Last week at the Davis R Users’ Group Robert Hijmans gave a talk about spatial data analysis in R. Robert is a professor of biogeography at UC Davis and the author of the raster (analysis of gridded data), dismo (species distribution modeling), and geosphere (spherical trigonometry), packages. Robert’s presentation spanned topics including basic geographical data and geostatistics concepts, his raster package and its usage, and some great examples of visualization and other resources.

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In my last post I mentioned that I had improved on R’s summaryRprof() function with a custom function called proftable(). I’ve updated proftable() to take advantage of R 3.0.0’s ability to record line numbers while profiling. I’ve put it on github – you can get it there or below. proftable reads in a file generated by Rprof() and creates an easy-to read table of the most time-consuming calls in your code, ordered from most time-consuming to least.

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