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Behavioral Simulation

Computational problems constructed from differentiable functions and constraints can theoretically be solved analytically, even in dimensional spaces far beyond human comprehension (it doesn’t take much). Linear optimization problems with thousands of variables can be solved in a few hours of modern day workstation CPU time. On the other hand, chaotic three or four dimensional domains involving transcendental functions can easily be so sensitive to initial conditions that analytical approaches aren't readily discernible. Alternative approaches for these cases include: simulation, step-wise refinement, and evolutionary optimization. Simulation is particularly valuable for discovering tipping points in the emergent behavior of simulated systems. The dojo scene from The Matrix (1999) illustrates the quest for a tipping point in the combatants’ relative skills, though in the real world, we’re much more likely to be simulating larger populations of less complex agents in our quest to discover tipping points, attractor states, and emergent behaviors.

Temporarily hampered by server configuration issues, we’re unable to present live simulations, so we’re including a screenshot from a run of a muskox herd simulation in NetLogo augmented by R. As is always the case in systems modeling, more nuanced behavior is an ever present opportunity for improvement though this model does incorporate realistic reproductive behavior, a local dominance approach to herding, gender specific mortality tables, and competition for resources that directly impacts survival. In general, the muskox population is sustainable with grass_Recovery=21 days, muskox_VisionRadius=7, and FoodVsHerd=0.13. Increasing FoodVsHerd makes them want to move toward muskoxen with greater weight (for safety), while lower values make them more independent foragers. Although there are no predators in the model, the downside of increased proximity to the herd is a greater likelihood of being on the same patch with another individual, thereby dividing the available nutrition between those present, which can easily result in insufficient energy gain, ultimately leading to starvation.

Although increased independence makes them more likely to obtain adequate nutrition, increased independence also tends to inject more space between individuals, thereby reducing the likelihood of reproduction during mating season. muskox_VisionRadius is the distance within which they will consider the lushness of the food supply and location of other members of the herd. Males take five years to reach sexual maturity; females mature in two years. No individual can ever develop more than a fourteen day energy reserve, based on a daily energy requirement of six calories per pound. At present, movement doesn't cost energy, though daily growth does.

The size of the icons represent each individual's weight relative to the gender average. Newborns follow their mother for sixty days, then become fully independent. Reproduction occurs when a sexually mature gender pair meet on the same patch during mating season (a two month window). Females give birth thirty-four weeks after conception. During mating season, males with seven days energy reserve or more prioritize their movement on the location of nearby sexually mature non-pregnant females to the exclusion of food, but below that energy level, they focus on food supply and herd proximity.

Death can occur due to starvation and other causes. Starvation results from staying on a patch that has been eaten down and hasn't had time to regrow. Virgin patches can supply as much as twice the daily energy requirement of a high weight male. Other causes of death are summarized by an actuarial table rescaled from that of humans in the United Kingdom - males and females having independent risks of dying, in windows of age two years wide, based on human age windows that are generally ten years wide. The color of the patches represents the lushness of the grass on the patch; yellow representing a standard deviation on either side of the caloric requirement of a high weight male; green above that; and brown below. Males are blue, females are magenta, dead oxen are black.

Opportunities for improvement include: adding a cost for movement so food at the edge of vision is more costly to obtain than that underfoot; too low odds of dying above age twenty-two (easily remedied by adding a twelfth age bracket in the 'other causes' mortality tables); unconstrained geometric weight gain (logistic or asymptotic would be better); use of bona fide age specific mortality rates for muskoxen (presently unavailable); and constraints on herd size (currently unconstrained), thereby better modeling real-life herds which typically include no more than twenty individuals, after which adolescent males get forced out.

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