Boundary strength analysis: Combining colour pattern geometry and coloured patch visual properties for use in predicting behaviour and fitness

Colour patterns are used by many species to make decisions that ultimately affect their Darwinian fitness. Colour patterns consist of a mosaic of patches that differ in geometry and visual properties. Although traditionally pattern geometry and colour patch visual properties are analysed separately, these components are likely to work together as a functional unit. Despite this, the combined effect of patch visual properties, patch geometry, and the effects of the patch boundaries on animal visual systems, behaviour and fitness are relatively unexplored. Here, we describe boundary strength analysis (BSA), a novel way to combine the geometry of the edges (boundaries among the patch classes) with the receptor noise estimate (Delta S) of the intensity of the edges. The method is based upon known properties of vertebrate and invertebrate retinas. The mean and SD of Delta S (m(Delta S), s(Delta S)) of a colour pattern can be obtained by weighting each edge class Delta S by its length, separately for chromatic and achromatic Delta S. This assumes those colour patterns, or parts of the patterns used in signalling, with larger m(Delta S) and s(Delta S), are more stimulating and hence more salient to the viewers. BSA can be used to examine both colour patterns and visual backgrounds. Boundary strength analysis was successful in assessing the estimated conspicuousness of colour pattern variants in two species, guppies Poecilia reticulata and Gouldian finches Erythrura gouldiae, both polymorphic for patch colour, luminance and geometry. The 3D representations of the Delta S of patch edges (Fort Diagrams) of both species show that there is little or negative geometric correspondence between the chromatic and achromatic edges. All individuals have m(Delta S) > 1.5 for both chromatic and achromatic measures, indicating the high within-pattern contrast expected for display signals. In contrast from what one would expect from sexual selection, all guppies have m(Delta S) less than expected from random contacts between all pairs of patch colour/luminance classes. The correlation between chromatic and luminance Delta S is negative in both species but zero when correlating all possible kinds of edges between the colours of each species and morph, indicating nonrandom colour geometry. The pattern difference between chromatic and achromatic edges in both species reveals the possibility that chromatic and achromatic edges could function differently. The smaller than random expected m(Delta S) values in guppies suggests an anti-predator function because guppies are never found without predators. Moreover, m(Delta S) could vary with predation intensity within and among species. BSA can be applied to any colour pattern used in intraspecific and interspecific behaviour. Seven predictions and four questions about colour patterns are presented. In species which are very convex in cross-section, both chromatic and luminance m(Delta S) change with viewing angle; geometry of signalling is as important as signal geometry.