Sumpter, 2006, Principles of Collective Animal Behaviour

Ref: Sumpter, D. J. T. (2006). Principles of collective animal behaviour. Phil. Trans. R. Soc. B, 361, 5-22.

Excellent review article about self-organization and collective behavior. The paper begins with a nice overview of collective behavior, and some extended examples: ant trails; flocks, schools, and crowds; audience applause.

Principles of self-organization.
a) More than the sum of its parts. Pretty self-explanatory, related to systems subject to positive feedback. E.g. ant pheromone trails for food source far from the nest. Small colonies will not find the trail, so the ants returning with food from there is the sum of the colony's parts. Larger colonies will be able to establish pheromone trails. Also bird flocking. Under some conditions, the transition from random to common direction is discontinuous, as for ant foraging.
b)The central limit theorem. Example: symmetrical structures such as the craters made by ants stem from the fact that many ants start with random headings from the nest, resulting in a near-perfect circle.
c) Sensitivity to initial conditions. This is such a great example. Beckers et al (1992, 1993) conducted bridge experiments with ants. In the first version, there were 2 alternative bridges at the start, one was 40% longer than the other. After 30 minutes, over 80% of the ants used the shorter bridge in 16 out of 20 experiments. This was due to the strengthening of the pheromone trails. In another experiment, they started with only the long bridge, and then introduced the short bridge when the ants has established a trail on the long one. However, the initial trail was so strong, that in 16 out of 20 trials, the ants did not switch bridges. An instance of strong positive feedback.


Individual vs. group complexity
A lot of models of self-organizing systems assume that the individuals obey simple rules. But individuals can be very complex themselves. Detailed behavioral algorithm models (ala Pratt et al, 2005) are a tool for reconciling individual and group level complexity, allowing for meaningful analysis of how each part of the algorithm contributes to overall system function.
When viewed at certain spatial and temporal scales, very complex individuals can produce very simple group level dynamics, provided they exhibit a reasonable degree of independence.
Law of small numbers: independent low frequency events in a large population follow a Poisson distribution.

Principles of Collective Behavior
In addition to the commonly known principles of positive and negative feedback and the amplification of random fluctuations, he adds a bunch of his own.

1. Integrity and variability. In all animal groups, high inter-individual variation can provide a continual supply of new solutions to the problems the group aims to solve.
   
2. Positive feedback. While individual integrity generates new group level solutions, positive feedback spreass this quickly throughout the group.
3. Negative feedback. Enables homeostasis.
4. Responsive thresholds. E.g., honeybees begin fanning to cool down the nest when the temperature exceeds a threshold, and there may be individual variation in this.
   
5. Leadership. Some individual may need to start a process - similar to sensitivity to initial conditions. Couzin et al (2005) used a SPP (self-propelled particle) model and showed that the larger the group, the smaller proportion of informed individuals required to lead it. This is consistent with Jared Diamond's analysis in Guns, Germs, and Steel that leadership becomes more centralized as population size increases.
6. Inhibition. Members of a group exhibiting one type of behavior can inhibit the behaviors of others. It can be passive or active.
   
7. Redundancy. "Insect societies never crash."
8. Synchronization. "Essentially, synchronization is an example of positive feedback in time rather than space." By being active at the same time, ants can disproportionately increase their 'output.'
9. Selfishness. Many studies have failed to detect the levels of relatedness predicted for highly cooperative insect societies (reviewed in Korb & Heinze, 2004), and helping behavior can be uncorrelated with relatedness. It could be the collective properties of the animal groups that are subject to natural selection. His bold claim here is that the other aspects of collective behavior should be understood before looking into why acting alone or cheating does not out-compete cooperation.