SUPER-INDIVIDUALS A SIMPLE SOLUTION FOR MODELING LARGE POPULATIONS ON AN INDIVIDUAL BASIS

Modelling populations on an individual-by-individual basis has proven to be a fruitful approach. Many complex patterns that are observed on the population level have been shown to arise from simple interactions between individuals. However, a major problem with these models is that the typically large number of individuals needed requires impractically large computation times. The common solution, reduction of the number of individuals in the model, can lead to loss of variation, irregular dynamics, and large sensitivity to the value of random generator seeds. As a solution to these problems, we propose to add an extra variable feature to each model individual, namely the number of real individuals it actually represents. This approach allows zooming from a real individual-by-individual model to a cohort representation or ultimately an all-animals-are-equal view without changing the model formulation. Therefore, the super-individual concept offers easy possibilities to check whether the observed behaviour is an artifact of following a limited number of individuals or of lumping individuals, and also to verify whether individual variability is indeed an essential ingredient for the observed behaviour. In addition the approach offers arbitrarily large computational advantages. As an example the super-individual approach is applied to a generic model of the dynamics of a size-distributed consumer cohort as well as to an elaborate applied simulation model of the recruitment of striped bass.