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The horror and madness: Just yesterday, the Senate Confirms Climate Change Denier To Lead NASA. What $%@$%@ idiots are leading our country....
'Sen. Brian Schatz (D-Hawaii) said before Thursday's vote that it is "downright dangerous" to put someone without the appropriate expertise in charge of NASA.
"And quite frankly it is even more frightening to have a leader who has made a career out of ignoring scientific expertise," he said.'
The team leaders have confirmed that they are ready to go. Our schedule looks like this:
Monday, 4/23:
If the fluctuations are changing as temperatures rise, however, that is of interest. So we would like to know, for example, if the residuals are getting bigger as the temperature (trend) rises -- suggesting higher variability with increasing temperature, say.
I emailed Jim Cushing to tell him that we were looking at his beetles, and he replied as follows: "These days I've moved from ecology in a bottle to ecology in the field, in collaboration with Shandelle & her husband ... modeling marine bird dynamics & adaptation to climate change on Protection Island Natural Wildlife Refuge between Vancouver Island and Washington State. Not as sexy as chaotic dynamics, but complicated evolutionary dynamics nonetheless."
We're going to be working, as usual, with matrices, which represent transition between three classes:
What can we do with six parameters? Evidently make the elephant dance chaotically....
I had to look up that quote, to see who said it. I discovered that von Neumann also wrote, in 1955, that "The carbon dioxide released into the atmosphere by industry's burning of coal and oil -- more than half of it during the last generation -- may have changed the atmosphere's composition sufficiently to account for a general warming of the world by about one degree Fahrenheit."
"In fact, to evaluate the ultimate consequences of either a general cooling or a general heating would be a complex matter. Changes would affect the level of the seas, and hence the habitability of the continental coastal shelves; the evaporation of the seas, and hence general precipitation and glaciation levels; and so on. What would be harmful and what beneficial -- and to which regions of the earth -- is not immediately obvious."
(Ironically, the title of his article is Can We Survive Technology?)
But I digress...
\[ \begin{array}{ccl} {L_{n+1}}&{=}&{bA_n e^{-c_{el}L_n-c_{ea}A_n}}\cr {P_{n+1}}&{=}&{(1-\mu_l)L_n}\cr {A_{n+1}}&{=}&{P_n e^{-c_{pa}A_n}+(1-\mu_a)A_n} \end{array} \]
As I mentioned, the key to the chaotic nature of the dynamics turned out to be the assumption (or rather the incorporation) of the dynamics of cannibalism!
This turns into the following "transition matrix" (notice that the entries are no longer constant, but functions of the population values): \[ \left[ \begin{array}{ccl} {0} &{0} &{b e^{-c_{el}L_n-c_{ea}A_n}}\cr {1-\mu_l}&{0} &{0}\cr {0} &{e^{-c_{pa}A_n}}&{1-\mu_a} \end{array} \right] \] and, as you can check, we have that \[ \left[ \begin{array}{c} {L_{n+1}}\cr {P_{n+1}}\cr {A_{n+1}} \end{array} \right] = \left[ \begin{array}{ccl} {0} &{0} &{b e^{-c_{el}L_n-c_{ea}A_n}}\cr {1-\mu_l}&{0} &{0}\cr {0} &{e^{-c_{pa}A_n}}&{1-\mu_a} \end{array} \right] \left[ \begin{array}{c} {L_{n}}\cr {P_{n}}\cr {A_{n}} \end{array} \right] \] Even though this appears to be a linear system, we must realize that the transition matrix no longer has constant coefficients: so it must be updated at every step.
If the system tends to a stable equilibrium, then so does the transition matrix, however: so we may attempt to solve for an equilibrium, as we did for the wolves and moose.