A new model of group interaction draws from lessons learned in reproducing global population and natural resource consumption by proposing that the result of two groups interacting depends on potential changes in three variables: available resources, population, and the available resources per person.
People in each group attempt to maximize those variables by choosing among three possible interactions: remaining isolated, taking over the other group's resources (domination), or combining the two groups and sharing all resources. Whether resources are appropriated or shared, people can choose to maintain the same resources per person by changing the group's population, or to divide the resources equally among them. Each group's success in pursuing these options depends on its population: the more people it has, the more successful it will be.
The net result is the generation of a new, integrated group that is a mix of all the possibilities based on their probabilities (likelihood of success) and another group of "lost" people and resources. Just as some energy becomes useless when two gases mix, the losses are the equivalent of "waste" as far as the original two groups are concerned. The integrated group still has some differentiation into subgroups, with five subgroups (corresponding to interactions) for each of the original groups. These subgroups can now interact to generate another version of the integrated group; this second generation also results in losses of people and resources to join the waste from the first generation.
Barring interaction between the integrated group and one or more new groups, further generations will change the integrated group until there is no one left (every person has been converted into waste). If a new group is encountered, then the new group's people and resources will interact with the integrated group to generate a larger integrated group, while also expelling more waste.
This model needs to be tested, a process that should yield some interesting insights. For example, a first attempt at using it to describe humanity's relationship with the rest of the biosphere has shown that our population and the equivalent population of other species will be equal at 7.9 billion members, which is also the peak value of population before per-capita ecological resource consumption is forced to drop in the backcast model of population and consumption (with no global warming). Unless we find a new biosphere, keeping humanity's population constant will require reducing the biosphere's population and resources over several more generations which each take much less actual time than the many millennia in the first generation.