Mathematical modelling is widely recognized as a powerful and convenient theoretical tool for investigating various aspects of biological evolution and explaining the existing genetic complexity of the real world. It is increasingly apparent that understanding the key mechanisms involved in the processes of species biodiversity, natural selection and inheritance, patterns of animal behaviour and coevolution of species in complex ecological systems is simply impossible by means of laboratory experiments and field observations alone. Mathematical models are so important because they provide wide-ranging exploration of the problem without a need for experiments with biological systems—which are usually expensive, often require long time and can be potentially dangerous. However, as the number of theoretical works on modelling biological evolution is constantly accelerating each year as different mathematical frameworks and various aspects of evolutionary problems are considered, it is often hard to avoid getting lost in such an immense flux of publications. The aim of this issue of Interface Focus is to provide a useful guide to important recent findings in some key areas in modelling biological evolution, to refine the existing challenges and to outline possible future directions. In particular, the following topics are addressed here by world-leading experts in the modelling of evolution: (i) the origins of biodiversity observed in ecosystems and communities; (ii) evolution of decision-making by animals and the optimal strategy of populations; (iii) links between evolutionary and ecological processes across different time scales; (iv) quantification of biological information in evolutionary models; and (v) linking theoretical models with empirical data. Most of the works presented here are in fact contributed papers from the international conference ‘Modelling Biological Evolution’ (MBE 2013), which took place in Leicester, UK, in May 2013 and brought together theoreticians and empirical evolutionary biologists with the main aim of creating debates and productive discussions between them. Finally, we should emphasize that the individual papers in this issue are not limited to only one of the topics mentioned above, but often lie at the interface of them.
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