1 Conversation with Jennifer Williams

Had a Skype chat today with Jenn, to get back on track with this project.

1.1 Ler populations

We recalled the work I did on the Ler populations in July 2015, which showed that:

  • Variance among pots in seed production did not scale with \(1/N\), suggesting something more than simple demographic stochasticity
  • Variance in per-generation spread seemed to be iid—no consistent replicate effects or autocorrelation (but I can’t remember whether I explicitly checked the latter)
  • Among-pot heterogeneity in dispersal was required to reproduce the variance in per-generation spread
  • I had to write a rather complex model!

1.2 Evolution experiment

Jenn reminded me that the variation in spread was higher in the the control than in the evolution treatments for three of the four landscapes (there’s a figure in the appendix of the Science paper). However, that comparison was based on the CV (and that might have just been evaluated at the end of the experiment; I don’t recall whethet we looked at each generation’s spread); it might be that the patterns in total variance are different, at least in the fragmented landscape where there was a big difference in mean spread rates.

1.3 Predictions and hypotheses

I hypothesized that among-individual heterogeneity in the dispersal kernel, like variation in growth rate in the IPM, generates population level effects that don’t disapear as the population size gets large. This comes from Joe’s work in deterministic settings; the question is then, in a stochastic setting, how does the mean and variance of spread depend on individual heterogeneity?

I also wondered how iid variation in spread would translate into increasing variance among replicates over time. Is it like a random walk, with variance increasing linearly through time? This would be a “random ratchet.” It seems as though the strict non-negativity of the change shouldn’t affect the general result that the variance in total distance spread should just be the sum of the per-generation variances, so that inter-replicate variance would grow linearly with time.

The result for the evolution experiment suggests that the het created by genetic variation is increasing stochasticity of some sort, as for iid het and Poisson variation.

Central question: What are the drivers of variation in spread rate, and are they predictable?

1.4 Data

We discussed the data. There are some potentially useful observations (such as plant height in the Ler experiment) that I’ve not seen before. Jenn gave me access to all of her data on Dropbox.

We also discussed temporal variation. Plant performance is probably best in spring and autumn (the greenhouse is too hot in summer), but there were also some pathogen/pest outbreaks that were not seasonal. To the extent that the latter affected the whole greenhouse, we can just use a generation fixed effect.

I wonder if we know the season of the dispersal experiments?