274 all theoretical biology: a precise description of how canalisation takes place. However, the actual structure of the model might have only limited applicability beyond a particular stage of Drosophila development and despite its proclaimed closeness to experimental data cannot be easily linked to concrete transcriptional mechanisms. In the case of the Bicoid gradient, it even seems that after repeated rounds of modelling and experimentation, the theory currently has lost its object since it is not clear where the property responsible for scaling is to be found. In the light of these observations, the question arises whether the relation between a mathematical model and its object is fundamentally different in biology than in other areas of science. An answer to this question requires careful consideration. Are not disagreements between theoretical modelling and experimental results anyway the normal situation with which theoreticians in all fields of science are confronted? Famous examples are attempts to simulate the processes in the earth’s atmosphere from global climate changes to the local weather forecast. However, here we know very well that some of the underlying equations inherently lead to unpredictability (deterministic chaos). The impossibility of long-term predictions is mathematically understood. In other instances, this point is less clear. An impressive example is represented by the long-standing attempts to derive the properties of liquid water from computer simulations. The forces between two water molecules (the pair potential) include repulsion, electrostatic dipole interactions and hydrogen bonding. There is a surprising variety of how to formulate a pair potential based on these three contributions. Additionally, there are higher order interactions between more than two water molecules. In a comparison of simulations based on 45 different water models, Guillot summarises: ‘The fact that no model potential is able to reproduce in every detail the properties of real water despite 30 years of active research leaves a taste of incompletion.’ (Guillot 2002). From a biologist’s point of view, these simulations, however, are pretty impressive. All of them recover basic properties of water and provide accurate predictions for at least some of the measured physical constants of water. The process of approximation to the real object seems to be much smoother than in the case of biology. Indeed, Guillot can precisely localise the weaknesses in the assumption of many models and suggest very specific improvements. With slightly relaxed demands on the quantitative accuracy, another expert in the field concludes ‘…, contrary to numerous statements in the literature, I am convinced that the behaviour of water… is reasonably well understood…’ (Ben-Naim 2009). Biological pattern formation theory is a relatively young field of research. Although its object of reference is infinitely more complex than liquid water, we cannot Dev Genes Evol (2011) 221:255–279 exclude that future modelling efforts will lead to a similar degree of approximative understanding. Beyond mere material complexity, however, organisms possess features not found in the inorganic world, which are likely to complicate every mathematical approach. Proteins and mRNAs, the types of molecules which are and will be the main target of modelling are not only huge macromolecules compared to water but they also exhibit features funda- mentally different from any molecule of the inorganic world. Their sequence-based structure depends on an evolutionary process which combines adaptive (determina- tive) and non-adaptive (drift-like or stochastic) events. Evolution can target singular features (individual positions within the sequence) of these molecules. Therefore, their physical properties are to a large degree at the disposal of events buried deeply in the evolutionary past. For these events, it is not even clear whether they all have a straightforward physical grounding. As long as we are dealing with adaptive processes, physical causes have to be postulated which guide adaptive events. For example, the particular modes of early development in insects might have served as a patterning environment to which proteins (and their respective mRNAs) had to adapt if they were to be useful as morphogens in providing positional informa- tion to the embryo. For a particular morphogen, an evolutionary process can be imagined that leads to the fitting of the morphogen’s molecular characteristics to the physical environment of the embryo. This process ought to be highly complex since its goal is the fit between the physical properties of a complex molecule to a highly structured cellular environment. Nevertheless, the adaptive, ‘goal-directed’ events driving this process should in principal be physically describable. However, in particular for multicellular organisms, drift-like processes might have a significant contribution to evolutionary change (Lynch 2007). The reducing theory for such processes is probability theory (McShea and Brandon 2010). Conse- quently, some of the molecular properties of proteins and RNAs might not have a physical cause linked to the biophysics of the particular process they are involved in, but rather result from collective statistical phenomena at the population level. Thus, pattern formation theories working with function- ally and physically motivated mechanisms are, already at the level of the single molecule, likely to face unexpected complications. However, patterning processes usually re- quire coupled reactions of many components and frequently encompass several hierarchical levels (e.g. diffusion in the cytoplasm, transcription, morphogenesis). Accordingly, evolution has almost infinite possibilities to complicate and fine-tune patterning mechanisms and thus can over- come or undermine almost every physicochemical con- straint postulated by a particular theory.