# Noisy beetles

Fig 1: Noise in lavae dominate

Fig: 2 lower mortality, higher noise

• Success! My first full implementation of the four stage (EPLA) beetle model, so far without any adaptation, and the noise of the larval class dominates (Fig 1). Without the time delays the stationary dynamics are stable nodes, at least in this part of parameter space, with a large adult class clamping tightly down on the other classes. Despite adults being the most numerous, the larval class is the most variable, just as observed.
• Standard parameter set, figure produced by this version of the beetles.R code.
• The level of noise depends closely on mortality estimate for this larva class. For instance, cutting the mortality rate of larva from 0.001 to 0.0001 results in much larger noise, Fig 2.

### Modifications to implementation

• Updated code to accurately take account of the two-step process. (Will add notes on the mathematics later, meanwhile is implemented in the noise_approx.R (version stable link) code.
• User now specifies the birth and death rates separately, rather than the first and second jump moments (b and f). User also specifies the two-step jumps and (as before) the Jacobian of b(x)-d(x).
• Added cannibalism of adults on pupae, who previously had no mortality terms. Without this their noise level will rise indefinitely.
• Separated the code for the linear noise approximation from the code for the crowley and beetles models.

### Git log

commit 0b6ce3ea1210284b71f3ab270b1ad6532ee0f31b Author: Carl Boettiger Date: Tue May 18 23:54:45 2010 -0700

   added adult cannibalism on pupa

commit 22c42eb726ddc6216932906953eea18dc165185f Author: Carl Boettiger Date: Tue May 18 15:59:51 2010 -0700

   getting second-order transitions implmented

commit 2cb4215b1028619e96ec809875c693fb84fdc185 Author: Carl Boettiger Date: Tue May 18 15:22:24 2010 -0700

   replaced f and g with birth and death

commit c9bc00fbf7dcd3eabd1935d1df96adb7dd54480d Author: Carl Boettiger Date: Tue May 18 14:13:25 2010 -0700

   seperated examples from noise approx code