Well, yes ... it is sort of a mix of the two. We compare the resulting spatial forms qualitatively to Hawick's clusters. But it is definitely a predator-prey model, and the oscillations match what you would expect generally from the Lotka-Volterra equations. (I say generally because of course an ABM ignores a few of the assumptions under LV. Come to think of it, I should probably look more closely at the mathematics of it. But not this week.<g>)
The interesting thing (at least, to me) is that the spatial forms emerge in our model even though we do not explicitly program the predator population to move towards each other. (In fact, they do not sense each other in any way ... their clusters form only due to indirect feedbacks.) In Hawick's model they do tend to cluster explicitly, but I think it is a much simpler mechanism than those you described (flash expansion, etc.) Thanks for the links! I will definitely check those out. I've come across Iain Couzin's site before, but I appreciate the reminder. -Ted On Tue, Mar 2, 2010 at 5:03 PM, Jochen Fromm <[email protected]> wrote: > 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 >
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