User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/05/25

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Bug fixed!

  • Wasn't taking the Jacobian of the transition terms. Fixes the unstable behavior and disagreement between simulations and theory.
  • Other note: the "hastings.c" model can trivially be obtained from the standard crowley-form metapopulation model by taking b_1 = 0.

For the crowley class of models at least, seems that while the two-step vs one-step involved different dynamics, this difference exists only in transients while equilbrium covariances agree.

hastings covarainces, b1 = 0, b2 = .6, d1 = d2 = .1, c1 = c2 =.5, K =1e4

Fig 1. Parameters: b_1 = .2, b_2 = .1, d_1 = d_2 = c = .1
Fig. 2. Parameters: b_1 = .2, b_2 = .1, d_1 = d_2 = .1, c = .15

Beetle dynamics

  • Variances aren't exactly in agreement, though much closer. Simulations with 30 replicates a piece for speed, will rerun for finer resolution on variances comparisons.
  • Wondering what parameter regimes will make most pronounced difference.