19 7 June 2017

19.1 Taking stock

Here’s what we “knew” on May 1:

  • In the single-plant pots, average home seed production is consistent across generations 2-5, but is high in gen 1 and low in gen 6.
  • In the single-plant pots, the variance in home seed production seems lowest in gens 1, 3, and 6, and highest in gen 2 (this is based on looking at the IQR from the boxplots; I haven’t actually calculated the variances yet).
  • In the population runs, the density-dependent pattern of seed production looks, in expectation, the same across all generations except 6, which runs low. I can’t actually measure the density-dependent curve in gen 1, but the observations at \(N=50\) are consistent with the curves from gens 2-5. I have not looked at whether the residual variance differs among generations.

Note that these were based on “unclean” data, but reanalysis with clean data led to the same conclusions (May 19).

Further observations:

  • The number of home-pot seedlings in Ler B-3p declines linearly with time (19 May; looking at sqrt(seedlings) as the response). It’s not clear whether this is a pattern of declining seed production or one of increasing dispersal efficacy.
  • When looking at density dependence (log(Seedlings/Adults) ~ log(Adults), using 3p landscapes in both B and C), there appears to be a quadratic effect of generation, but this is largely driven by generation 6 (19 May)
  • Per-generation spread rates in the continuous runways (C-0p) were a quadratic function of time, had negative autocorrelation (\(\rho = -0.33\)), and weak evidence for differences among runways (\(P = 0.075\)) (24 May).
  • Per-generation spread rates in all fragmented runways were indedpendent of generation and replicate, and had no autocorrelation (24 May).
  • Analysis of cumulative spread (24 May) showed that the linear approximation to mean spread is pretty good, although we see a dip in generation 6, as expected from the reduced seed production, and even without gen 6, the continuous runways seem to be decelerating. The ranking between landscapes makes sense. The variances are rather more over the map, although we don’t have confidence intervals on them. But exept for 1-pot gaps, we can squint and imagine that the variances are linear in time. Note, however, that with only 6 generations we’re not going to easily detect nonlinearities. I don’t know that the CVs tell us much.
  • Per-generation spread in the evolution experiment (24 May) are a bit of a mixed bag:
    • For evolution YES, we have:
      • Autocorrelation in gaps 0, 2, 3
      • Gen effects in gap 2
    • For evolution NO, we have:
      • Autocorrelation in gaps 1
      • Gen effects in gaps 0, 1
  • Cumulative spread in the evolution experiment (24 May) shows more-or-less linear growth in the mean (though perhaps some decelleration in 2p); but the variance seems to level out in the evolution treatments showing autocorrelated spread. We need confidence intervals on these, however.
  • In treatment B, seedling production is effectively independent of silique number! (2 June) This is found both by looking at home pot seedlings in gappy landscapes and at total seedlings in the runway of the first generation of the continuous landscape.
  • Looking at home-pot seedling production in Ler B & C, 1p and 2p (which should be mostly locally produced, but colonizes multiple pots allowing us to look at runway effects), there are:
    • Density dependence (log-log model)
    • Variance among generations
    • Variance among runways within a generation
    • Variance among pots within a runway that goes to zero in the limit of large N, suggesting that it is just demographic stochascitiy (as previously seen, however, this demographic stochasticity is large)

So far I’ve addressed 2, 3, 10, and 11 in the May 1 “remaining empirical questions.”

19.2 Strategy for a paper

Here’s what I think we want to lay out for the motivation of a paper:

  • We know there are lots of sources of stochasticity in spreading populations
  • This could lead to “unpredictability” in spread rates
  • Replicated lab populations have empirically demonstrated this unpredictability
  • However, we don’t know how various sources of stochasticity and heterogeneity contribute to spread rate unpredictability
    • This could be important if some of those sources can themselves be predicted
    • Need to double-check what Melbourne & Hastings did; there are some other experimental spread experiments (without evolution, or without evolutionary controls) to check.
  • In this paper, we do three things:
    • Develop a simple model of stochastic spread
    • Demonstrate how different sources of stochasticity contribute to spread variability in a monotypic plant population
    • Demonstrate how evolution in a spreading population might make spread more or less predictable.