Dynamical Systems, Development and Evolution
Peter T Saunders
Institute of Science in Society
and
King’s College, London
Three aspects of stability in development (Waddington):
Homeorhesis (similar flow; cf homeostasis): describes a
system which after a perturbation returns to its trajectory
rather than to the point at which it was perturbed.
Chreod (necessary path): a trajectory which is stable in the above sense.
Canalisation: development can proceed to one of a restricted
number of final states, not a continuous spectrum.
“Systems are stable”.
This is almost a tautology, because if something isn’t stable
-- in some sense -- we don’t call it a system.
But we can say something more:
“Complex nonlinear systems, and this includes developing
organisms, have a kind of stability that gives them a number of
important properties, including those Waddington identified
and portrayed in the epigenetic landscape.”
"I know from my experience that I can develop
a plum half an inch long or one two and a half
inches long, with every possible length in
between, but I am willing to admit that it is
hopeless to try to get a plum the size of a small
pea or one as big as a grapefruit.”
Luther Burbank
What the fossil record should look like if evolution is continuous
What the fossil record should look like if evolution is continuous
but a lot of the fossils have not been found
What the fossil record actually looks like
Darwin (1859): Natura non facit saltum
Dawkins (1985):
Gradualism is of the essence. In the context of
the fight against creationism, gradualism is
more or less synonymous with evolution itself.
If you throw out gradualism you throw out the
very thing that makes evolution more plausible
than creation
How an abrupt change could occur
X
U
V
X
Vc
V
Flounder
It’s obviously an advantage for a bottom dwelling fish to have both
eyes on the upper side of its head, but how did they get there?
X
Vc
V
Multiple speciation
In two dimensions, a trajectory can have at most two neighbours,
but in three (or more) it can have many. So when a trajectory
is in an unstable region, the system may have more than two
trajectories to move to.
Mitchell KJ (2007) The Genetics of Brain Wiring: From Molecule to Mind. PLoS Biol 5(4): e113 doi:10.1371/journal.pbio.0050113