Networks Unit
IMT School
for Advanced Studies
Lucca (Italy)


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Mathematical modelling

In biology, the word "model" is often used to indicate a biological object that is amenable to experimental manipulation, and which is expected to exhibit properties analogous to those of other biological systems: the squid giant axon, the gill withdrawal reflex of aplysia, the lactose operon of Escherichia coli. In this acceptance of the meaning, living systems are "models" of living systems. The advantage is that they preserve all the complexity of real biological systems, with the multiple interactions and regulations on which we are not directly focusing our attention, but are nevertheless essential to maintain the living system functional and alive.
A different class of models are mathematical models. Historically, these models have been produced and analysed in biology in particular in the context of genetics (from the inheritance laws proposed by Gregor Mendel to the more recent genomic analysis techniques). By themselves, these models can give probabilities for a certain phenotype to be observed, but do not explain directly the process of biological self-organization occurring in-between.
A third, more recent, class of models are Mathematical models of self-organization, that is, descriptions of biological systems that select some properties of the system, and derive predictions about different properties of the same system. These models are what we usually refer to when we talk about models in the field of collective animal behaviour.

Modelling collective behaviour

All objects of biological relevance are "collective", in the sense that they are composed of multiple units in interaction: molecules interact within the cell, cells interact to form tissues and organs, organisms interact with each other within ecosystems.
Models of collective systems provide a link between individual interactions and collective behaviour. Depending on the specificities of the system, different modelling approaches can be more or less appropriate, including partial differential equations, agent based models, stochastic models etc.
When a model successfully reproduces different aspects of a collective pattern we have an indication that the implemented rules are sufficient to account for the pattern. It does not prove that the rules are also necessary. It does provide us with consistent theories of how a potential behaviour emerges, as well as suggestions for experiments that can be used to determine which model provides the most accurate description of a biological system.

Related scientific publications

  • Sumpter et al. "The modeling cycle for collective animal behaviour". Interface Focus (2012) [Web]
  • Mann et al. "Multi-scale inference of interaction rules in animal groups using Bayesian model selection". Plos Computational Biology (2013) [Web]