<q>
When Behe was cross-examined during the Kitzmiller v. Dover trial in
October 2005, he was asked if he still believed that the scientific
literature had no answers on the origin of the immune system. He said
that he did. Then, in a Perry Mason-like flourish, the plaintiffs'
attorney piled fifty-eight peer-reviewed articles and a stack of books
about the origin of the immune system on the witness stand in front of
Behe. When asked, Behe said that he had not read most of them, but
dismissed the pile with a wave of his hand. As the cell biologist
Kenneth Miller, who testified for the plantiffs in the trial, put it
later, "Aint' nothing going to convince this guy."
</q>
Eugenie C. Scott and Glenn Branch, _Not in Our Classrooms_, Beacon Press
Books, 2006.
The link to the transcript is here:
http://earthfusion.org/faqs/dover/day12pm.html
Behe may still be convinced that the scientific literature has no answers
on the origins of the immune system. But the plantiffs' attorney wasn't
trying to convince Behe, he was trying to convince a judge (and Behe was,
too). Behe found out --- as you're finding out --- that "you're
bluffing!" starts to lose its effectiveness as the peer-review articles
start piling up.
I doubt you'd recognize a PDE if you saw one let me give you a more
verbose cite:
<q>
The variance of the change of gene frequency due to random drift is x(1 −
x)/(2N) and (x, t|p0) can be obtained by solving the following partial
differential equation (PDE),
$$
\frac{\partial\phi(x,t\vert p_0)}{\partial t}
=
\frac{1}{4N}
\frac{\partial^2\(x(1-x)\phi (x,t\vert p_0))}{\partial x^2}
-
\frac{\partial (sx(1-x)\phi(x,t\vert p_0))}{\partial x}
$$
with boundaries x = 0 and x = 1, where N is the Wright-Fisher population
size. Kimura solved this PDE by using the separation-of-variables method
(Kimura 1955b, 1957, 1964).
</q>
Ying Wang and Bruce Rannala, "A Novel Solution for the Time-Dependent
Probability of Gene Fixation or Loss Under Natural Selection", Genetics,
168(2):1081-1084, 2004. 10.1534/genetics.104.027797
Am I bluffing? Would you like to check my transcription of the text?
Here's the link I used:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1448842/
It's equation #2.
Want another one?
"This paper shows how biological population dynamic models in the form of
partial differential equations can be applied to heterogeneous
landscapes. The systems of coupled partial differential equations
presented combine dispersal, growth, competition and genetic
interactions. The equations belong to the class of reaction diffusion
equations and are strongly non-linear. Realistic biological dispersal
behaviour is introduced by density dependent diffusion coefficients and
chemotaxis terms, which model the active movement along gradients of
environmental variables. The resulting non-linear initial boundary value
problems are solved for geometries of heterogeneous landscapes, which
determine model parameters such as diffusion coefficients, habitat
suitability and land use. Geometry models are imported from a
geographical information system into a general purpose finite element
solver for systems of coupled PDEs. The importance of spatial
heterogeneity is demonstrated for management of biological control by
sterile males and for risk management of GMO crops."
Otto Richter, "Modelling dispersal of populations and genetic information
by finite element methods", Environmental Modelling Software, 23:2,
206-14, 2008.
Would you now kindly pick up Durretts, Ewens, or either of these papers
and explain to me what they're doing wrong?