Re: ABM/I(C?)BM

[Steve Emsley]

Perhaps I'm tagging this onto the wrong thread but Doug Donalson refers to a
reference that I had in mind as I brought up the ODE / ABM dichotomy.

Chapter 3 of DeAngelis' book on IBM (referred to by Doug)  on IBM is by 
Caswell & Meredith John. In this they differentiate between the i-state 
configuration model (individual-based with individual differences), the
p-state (a model of the population as a mean of the i-state configuration)
and the i-state distribution ( a simplification of the p-state arising when
all individual's experience the same environment).

ODE's are justifiably used to model the p-state (including the special case of
the i-state distribution). However, the authors suggest that the i-state
configuration is important with "complicated i-states, small
populations and local interactions". In addition, the p-state is derivable 
from the i-state whereas the i-state not derivable from the p-state. As a
parting thought they suggest that "i-state configuration models may be useful 
... 
to drive maximum likelihood parameter values [of i-state distribution
models]".

Personally, I view this distinction as having more mileage than an argument
on the relative merits of ODE/PDE vrs. ABM(IBM) models. The latter being a set
of tools to understand/describe/model the former.

One posting suggested that ODEs are attractive due to the possibility
of their analytical solution. IMHO if you have an ODE-based ecology
capable of analytical solution (rather than numerical simulation) you are
dealing with a mathematical abstraction (ecology as an excitable medium) NOT a
system that propagates through time based on local interactions and
continually varying stochastic or adaptive parameters i.e. a real ecosystem.

It is not unusual for ODE/PDE models to be "tuned" to actual data though
modifying the closure terms. Better, in my opinion, to turn one's back on
parsimony and computational efficiency in order to model the i-state. If 
there's no significant difference between the i-state configuration (IBM) 
model and the p-state (ODE/PDE) model then efficiency favours the latter. 

In my field the ergonomics and economics of sampling skew the available
data towards coarse resolution. To fit a multi-parameter mean-field model
to such data could, unsympathetically I admit, be called tautologous. By
my, naive, appraisal of current 'scientific method' I see modelling
driving observation - a reversal of the traditional paradigm. To assume 
a mean-field solution from the onset establishes a priori length scales 
and time scales to the system under investigation which, a posteriori, can
establish observational criteria. I suppose that the impact of IBMs on
conventional mean-field modelling may be analogous to the impact of Kepler's 
First Law on the aesthetic bias of the Platonic circular orbit - as
observations become more exact then no system of epicycles (or parameters)
will exactly fit the facts.

Regards
-- 

--
Steve Emsley
address@hidden


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