Re: [FRIAM] Question for Friamers! ... 2D vs. 3D

[Jochen Fromm]

I am not sure what you want to model,
perhaps you are mixing different models here?

* predator-prey or Lotka-Volterra equations describe
  the long-term population density over multiple generations

* boids and flocking models describe the short-term
  spatial form of animal groups on the move

In the first case you will get oscillations and
periodic population patterns, in the last case
you will get flocks and swarms.

Probably you mean defensive swarm behavior
during predatory attack: flash expansion, split,
vacuole, etc? Then maybe this link about
"Self-Organized Fish Schools" is interesting
http://www.biolbull.org/cgi/content/full/202/3/296

A National Geographic article says
"When a predator strikes a school of fish, the group is
capable of scattering in patterns that make it almost
impossible to track any individual. It might explode
in a flash, create a kind of moving bubble around the
predator, or fracture into multiple blobs, before coming
back together and swimming away
http://ngm.nationalgeographic.com/ngm/0707/feature5/text4.html

Iain Couzin's site at Princeton has also many papers
about collective motion and decision-making
http://webscript.princeton.edu/~icouzin/website/

-J.

----- Original Message ----- 
From: Ted Carmichael
To: The Friday Morning Applied Complexity Coffee Group
Sent: Tuesday, March 02, 2010 1:58 AM
Subject: Re: [FRIAM] Question for Friamers! ... 2D vs. 3D

[..]

I'm thinking about a pred-prey model (in 2D) similar to Ken Hawick's found 
here, such that the prey reproduce, forming a blob or circle.  Then the 
predators come in, and the circle degenerates into a crescent shape.  (We 
replicated these type of clusters and their movements in our model, although 
with somewhat different agents and rules.)

Since the spatial relationships matter, I assumed that a 3D model of the 
same agents would tend to form spheres rather than circles; and when the 
predators come in, they dig out a bowl shape rather than a crescent shape 
... although for the same general reasons.  But I'm just guessing here.

That covers the spatial effects.  In terms of populations, I assumed that 
either the pred or the prey would be more efficient and therefore have 
different numbers, but that these would scale up or down, and thus show the 
same general dynamics (a la the Lotka-Volterra equations).  If I had to 
guess, I would say the prey population would tend to be larger (relative to 
the pred population) than in the 2D model.  But I wouldn't really count on 
that until I ran the simulation.

Does that sound about right?  Has anyone played around with other spatial 
effects, moving from 2D to 3D?

Lee - on a side note, how familiar are you with the Lotka-Volterra dynamics? 
Particularly with more than two populations (i.e., 3 or more strictly 
defined tropic levels).  We've found some interesting results, but I don't 
yet know if they are interesting to just me, or would be to anyone.

-Ted



============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org