Re: mosaic evolution

H. M. Hubey (
27 Nov 1995 22:33:23 -0500

Alex Duncan <> writes:

>Unfortunately, I don't know how differential equations would model such
>changes. Perhaps you could provide a short explanation?

It boils down to simultaneously showing effects of things one upon
another. Here's a famous example from Lotka-volterra.

dx/dt = -x + xy

Let x be a predator population size. dx/dt represents the rate of change
(in time) of its population. I'll write it as x' from now on since that
notation is also used. So if x' is positive it means that the population
is increasing. The eqn says that the rate of increase is negatively
proportional to itself (i.e. -x) since it will die by itself and
needs the prey population y to feed on. So the xy term represents
interaction between the predator and prey, and since it's positive
it means that if there are prey around (i.e. y >0) then the population
of the predators will tend to increase (i.e. feeding on prey).

Similarly the prey population equation looks like this

y' = + y - xy

That says that the prey increases by itself (i.e. +y) since
it feeds on something else (i.e. plants) but if there are any
predators then the interaction (i.e. the -xy term) causes a reduction
in the prey population.

The trick is that these equations show instantaneous cross effects
of both species on one another. Naturally this is a simple beginning
model and does not take into consideration the many complexities of
real life.

But this is one way of modeling simultaneous effects.

>Some human traits appear to have evolved together (e.g. reduction in size
>of postcanine dentition & increase in brain size) while others don't
>appear tightly connected -- it looks as if the anatomy associated with

So isn't Ms. Morgan saying that the AAT scenario provides the ground
for simultaneous change for many/much of these?

Isn't she saying that they happened (or could have happened)
simultaneously and not serially (one after another)?


Regards, Mark