Re: Simulating Individual Behavior

[Mark P. Line]

Scott Christley wrote:
> 
> I am tending to notice a separation between two modelling paradigms: the
> ABMers (I was an IBMer once! ;-) and the ODEers.  Are there true
> differences between these two paradigms or is it only a perception?
> Meaning is not a Swarm program a symbolic (mathematical) description of a
> model, just not as concise as a differential equation?

I don't see it that way at all. Obviously, both an ABM and an ODE model
are abstractions of our observations of behavior on the ground. The
abstractions made in the two paradigms are different, of course.

In ABM's, the abstractions made are informed directly by observation.
There's ants, so we model ants. They cut up leaves and carry them
around, so we have leaves and pieces and leaf-cutting behavior in our
model. The more we know, the more constraints we can build into our ABM.
There is no ODE system (no matter how observationally vacuous) that
cannot be couched in terms of an ABM, unless we don't really know what
it is our model is doing (in which case its uses are limited to
crunching out trajectories).

In ODE-based and PDE-based models, the abstractions made are the ones
that are imposed by the kind of symbolic manipulation (analytic
solution) that is possible with simple ODE and very simple PDE systems.
In other words: calculus tells us the function has to be continuous, so
suddenly we are forced into an abstraction of our population of
wildebeests such that population size is a real number and population
growth is a continuous function. Biologically (or sociologically, or
whatever), we tend to remain rather unconvinced that either one of these
assumptions is particularly realistic. ODE's and PDE's were invented so
that problems could be solved analytically. But few interesting problems
that we'd model with these formalisms are soluable analytically anyway,
so there's no longer any good reason to use them, and one very good
reason not to use them: they force on us an abstraction that serves
merely a by-gone purpose and which is usually not warranted in the
biology (or sociology).

[As long as you're just doing some simple thumbnail models of biomass
and energy balances and what-not, you might be safe up to a point just
doing your ODE's, of course. I don't want to deny that.]

Now I can say what I think the answers are to the questions you pose
above. 

Are there true differences between these two paradigms? Yes, because
ABM's don't force abstractions on us that are artifacts of a method
whose day is past and which are not desired otherwise in our models.

Is a Swarm program just a less concise description of a the same thing a
differential equation describes? No, certainly not. A Swarm program does
not normally describe the effects of fractional wildebeests pairing up
and producing fractional young. It describes real, whole wildebeests
pairing up and producing real, whole young. If anything, a Swarm model
is _more_ concise. 

Swarm: "How many parents did this baby gnu have? Exactly two."

ODE: "How many parents does every baby gnu have? 1.998785622342179 +/-
5% at the instant of conception, with a first-derivative slope of
+0.73."

That's my two gnus' worth...


> It makes me wonder if the search for the fundamental laws of
> the universe have progressed from physics to the higher level sciences of
> biology, sociology, history.

I certainly hope not. I would have hoped that the experience of
physicists over the last 100 years would have taught biologists,
sociologists and historians not to look for fundamental laws of the
universe, but rather for theories that help understand the universe. :)


-- Mark

(Mark P. Line  --  Bellevue, Washington  --  <address@hidden>)



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