Published on December 16th, 2013 | by Emily Corbett0
By Jesse Sharp, Queensland University of Technology
This student took part in the 2012/13 AMSI Vacation Research Scholarship program. For more information on this years program please click here
Since cells are the building blocks of all living things, and we are in fact living; an interest in the way that cells interact and develop as a population is to be expected. To this avail, a great deal of research has been done (both empirical/experimental and theoretical) in the area of population dynamics.
One such result of this research is the logistic differential equation, or “mean field” assumption. The mean field assumption is very commonly used to model population dynamics; however it seems that it is commonly applied when it perhaps should not be.
The “mean field” makes the assumption that the individuals in a population are spread out evenly. This is suitable sometimes, however when you look around in nature, you can see that this is not always the case. If you look at a forest of trees or a flock of birds you can immediately see that the individuals are not evenly spread out. Instead, they form clustering patters. The same can be said about certain cells, based on experimental data.
We used discrete simulation techniques to investigate the population dynamics of cells. We then explored the impact of clustering behaviour on the effectiveness of the “mean field” assumption. For certain combinations of parameter values we observe clustering in the discrete simulations, and we show that in some cases the logistic equation (or mean field) description fails to predict the simulated behaviour.
Based on these cases in which the mean field was ineffective, we sought to characterise the types of clusters and distribution of clusters which lead to the breakdown of the “mean field”. While further exploration needs to be conducted, the preliminary findings indicate that the “mean field” is a fairly robust predictor in the presence of smaller clusters (such as pairs or triplets of cells), however it suffers when medium to large clusters are present.