Individuality in modelling: a simplifying assumption too far?

Abstract

When developing individual-based models (IBMs) of populations of rare or cryptic species, it may not be possible to gain precise measurements of individual traits such as age or body size for example. It may be necessary to assume that an individual is a member of a discrete class, rather than a unique entity in these cases. What will be the effect on the population dynamics predicted by an IBM of using discrete classes to represent individuals, rather than modelling individuals as unique entities? An IBM was developed to answer this question. Individuals were modelled as unique organisms in the full IBM, and the resultant population dynamics compared to a series of simplified models where individuals were treated as members of discrete classes. The number of classes varied from one to 32. The full IBM generated population time series that did not go extinct, but varied around an equilibrium level with a coefficient of variation of less than 15%. When the model was simplified to the point where all individuals were found in a single class, the simulated populations were found to be less variable, the opposite result to that predicted by general IBM theory. However, between these two extreme cases of full individual variability and no individual variability, complex interactions were found between the number of classes, background mortality rate and seasonality, which did not match the results of either extreme. Mean population size in the full IBM decreased as background mortality increased, and when the amplitude of seasonal fluctuations in food availability increased. This was due to the limited reproduction rate in comparison to unlimited mortality rate assumed in the model. As with the coefficient of variation in population size, the extreme cases of the full IBM and single class differed markedly from one another in mean size, with the scenarios in between these extremes showing complex interactions. The models presented in this paper demonstrate that making simplifying assumptions about the distinctiveness of individuals can affect the predicted population dynamics dramatically. If IBMs treat individuals as members of classes, rather than as unique organisms, predictions of population size and variability may be wrong.