This thesis explores the geometric description of animal colour vision. It examines the relationship of colour spaces to behavior and to physiology. I provide a derivation of, and explore the limits of, geometric spaces derived from the notion of risk and uncertainty aversion as well as the geometric objects that enumerate the variety of achievable colours. Using these principles I go on to explore evolutionary questions concerning colourfulness, such as aposematism, mimicry and the idea of aesthetic preference.

Cephalopods first appeared around 500 million years ago. Since then they have developed from the external shelled ammonites, belemnites and nautiloid's to the soft bodied organisms we find today. By becoming soft bodied, protection which would have been provided by the shell was lost and a different approach to predator avoidance was adopted. Modern day cephalopods such as octopus, squid and cuttlefish frequently use camouflage techniques to avoid detection. In addition to countershading, which is an often used camouflage technique by aquatic species, the presence of chromatophores allow a versatile and rapid response in relation to stimuli. Cuttlefish expression of these chromatic responses can be categorised into chromatic components. It is the intensity and combination of the expression which makes them an interesting organism to study, when looking at how the environment influences camouflage decisions. In this thesis, I present six experiments looking at how external environmental factors influence camouflage in Sepia officinalis. The first experimental chapter looks at how 3D objects and proximity play a role in not only camouflage, but behavioural responses. The first set of experiments discuss how factors such as contrast and size of an object may elicit different responses both behaviourally and chromatically. The proximity of the cuttlefish to the object was then investigated to determine if visual input was a possible cause for the differences. Size of the object, proximity and contrast produced a differing response to that of a cuttlefish on a uniform background. The two subsequent chapters look at differing light information and whether cuttlefish treat these differences similar to that of low contrast. Reaction to turbid and low light levels show similar responses in camouflage, suggesting that similar mechanisms are employed when there is reduced light and high scatter information. In respect to luminance versus reflectance, cuttlefish seem to be able to differentiate between a projected and reflected image where they appear to treat projected images like a lower contrast value. The last experimental chapter investigates motion camouflage in respect to predation. Prey and distance had a large effect on behaviour and how camouflage was expressed. Over greater distances behavioural variance reduced. Darkening of the head region and arm waving was also present over a greater distance. Camouflage varied in relation to background with a more uniform background producing reduced expression when moving. Stationary predation therefore elicits a different response than that of motion camouflage in cuttlefish.

Introduction – Insect societies are well known for cooperation. However, there is a high potential for conflict both over resources (intercolonial) and over reproduction (intracolonial). Here I present the key results of my thesis in these two areas. 1. – In our first study we show that T. angustula possesses two types of entrance guards, hovering and standing guards, and that they have different tasks. Standing guards, however, can switch to hovering if needed. 2. – Honey bee, A. m. mellifera, guards recognise allospecific intruders via “different odours” not “harmful intruder odours”. 3. – Following up on project 1 we demonstrated a relatively clear division of labour in guarding of T. angustula where guards either act as standing or hovering guards. This study also adds descriptive data on the natural history at the nest entrances of T. angustula. 4. – In our fourth project we found that worker policing in the honey bee (A. m. mellifera and A. m. carnica) has a low cost because few recognition errors are made, 9.6% and 4.1% of eggs in male and female cells were removed in error, and because these errors are easily rectified. 5. – Virgin queens of M. quadrifasciata were only elected in queenless colonies and generally only shortly after the removal of the resident queen. The virgin queens' behaviour did affect their survival or their life time, respectively. Finally, we described the election process of virgin queens by their colony. Conclusion – Mainly the finding of two different entrance guards in T. angustula generated a series of new questions. In addition, this thesis helped clarifying how social insects recognise each other, it provided the first study that did not measure the benefit but the cost of worker policing, and it shed some light on the bizarre behaviour of queen replacement and execution in Melipona.

In this thesis we investigate a model for biological pattern formation during growth development. The pattern formation phenomenon is described by a reaction-diffusion system on a time-dependent domain. We prove the global existence of solutions to reaction-diffusion systems on time-dependent domains. We extend global existence results for a class of reaction-diffusion systems on fixed domains to the same systems posed on spatially linear isotropically evolving domains. We demonstrate that the analysis is applicable to many systems that commonly arise in the theory of pattern formation. Our results give a mathematical justification to the widespread use of computer simulations of reaction-diffusion systems on evolving domains. We propose a finite element method to approximate the solutions to reaction-diffusion systems on time-dependent domains. We prove optimal convergence rates for the error in the method and we derive a computable error estimator that provides an upper bound for the error in the semidiscrete (space) scheme. We have implemented the method in the C programming language and we verify our theoretical results with benchmark computations. The method is a robust tool for the study of biological pattern formation, as it is applicable to domains with irregular geometries and nonuniform evolution. This versatility is illustrated with extensive computer simulations of reaction-diffusion systems on evolving domains. We observe varied pattern transitions induced by domain evolution, such as stripe to spot transitions, spotsplitting, spot-merging and spot-annihilation. We also illustrate the striking effects of spatially nonuniform domain evolution on the position, orientation and symmetry of patterns generated by reaction-diffusion systems. To improve the efficiency of the method, we have implemented a space-time adaptive algorithm where spatial adaptivity is driven by an error estimator and temporal adaptivity is driven by an error indicator. We illustrate with numerical simulations the dramatic improvements in accuracy and efficiency that are achieved via adaptivity. To demonstrate the applicability and generality of our methodology, we examine the process of parr mark pattern formation during the early development of the Amago trout. By assuming the existence of chemical concentrations residing on the surface of the Amago fish which react and diffuse during surface evolution, we model the pattern formation process with reactiondiffusion systems posed on evolving surfaces. An important generalisation of our study is the experimentally driven modelling of the fish's developing body surface. Our results add weight to the feasibility of reaction-diffusion system models of fish skin patterning, by illustrating that a reaction-diffusion system posed on an evolving surface generates transient patterns consistent with those experimentally observed on the developing Amago trout. Furthermore, we conclude that the surface evolution profile, the surface geometry and the curvature are key factors which play a pivotal role in pattern formation via reaction-diffusion systems.