- Noise in the larval class is damped by and grows proportional to its intrinsic variation and the contribution of other classes through their derivatives of
*f*_{L}, that is, as well as the sum of its intrinsic rates (essentially whichever is larger). Taking*E*dynamics to be fast we might reduce to a continous time LPA model:

and the larval fluctuations are essentially:

where β_{i} is the intrinsic noise of the age class. Hence a class *i* which propagates large noise to another class *j* has a large . If this term is a linear transition λ*X*_{i}, then the same term appears in *f*_{i} and hence damps the noise and cancels out. Hence noise must propagate into a class through nonlinear transition rates OR through an asymmetry in the transition (i.e. the c_1, c_2 large noise example in the generalized crowley).

Compare to noise in Eggs:

Adding age delay to beetle dynamics ———————————–

Current formulation has used exponential waiting times between stages. By subdividing the classes (increasing the system dimension size) and creating single jump within-state transitions, these become gamma-distributed waiting times. Adding ten steps to each phase and a little parameter fiddling introduces sustained oscillations. (Version-stable code).

beetle_pars <- c(b=5, ue= 0, ul = 0.001, up = 0.00001, ua = 0.01, ae = 1.3, al = .1, ap = 1.5, cle = .2, cap = .1, cae = 5, V=100)

Xo[1] = 100

- Implementation still needs trouble-shooting, variance dynamics don’t seem to be being computed correctly.
**done** - Adult class doesn’t need multiple stages.
**done** - Code should allow for a general k classes rather than a fixed 10 classes.
**done**

and now we have noise in oscillatory, gamma-waiting model:

- parameters as before, see version-stable code.

Misc / Code notes —————–

R-evolution parallelizes the variance dynamics calculation (perhaps the matrix multiplication step?) and is probably responsible for the openmp parallelization working.

- article on cloud computing vs grid. reminds me to include questions on cloud computing in the CSGF survey.
Should also take a closer read of the recent: Kendall BE, Wittmann ME. A stochastic model for annual reproductive success. The American naturalist. 2010;175(4):461-8. Available at: https://www.ncbi.nlm.nih.gov/pubmed/20163244.