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The dawn of a golden age in mathematical insect sociobiology

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23 pages; It is bold. It is also arguably overly grand and it may be illusory. History alone will judge if this is the dawn of a golden age in mathematical sociobiology. To be sure, mathematical biology has already seen a number of false dawns. It may appear, for example, that both catastrophe theory and chaos theory each have enjoyed almost all of their 15 minutes of fame. However, it is right and proper that a wave of initial excitement, or indeed, hyperbole, is followed by slower and steadier progress as a field matures. So what justifies our unbridled optimism? The first answer is demonstrable progress. Self-organization theory and complex systems theory coupled with pioneering experiments have already revolutionized our understanding of organizational aspects of insect societies and even our own societies. Such is the gathering excitement, predictive power, and massing evidence that this endeavor has earned a new epithet: "Sociophysics" or "the physics of society" (Ball 2004; Strogatz 2004). Why sociophysics? Because the philosophy and even some of the principles of statistical mechanics are now being applied in sociobiology to great effect. The central issue in social biology to which mathematical biology is being applied is the question of how societies are organized. In shorthand, how do superorganisms work? The second answer is that necessity is the mother of invention. The requirement for a mathematical sociobiology was not only predicted by Wilson (1971) but he gave a clear directive that results would come from considering mass action and stochastic effects...