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

Abstract

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 (ΔS) of the intensity of the edges. The method is based upon known properties of vertebrate and invertebrate retinas. The mean and SD of ΔS (mΔS, sΔS) of a colour pattern can be obtained by weighting each edge class ΔS by its length, separately for chromatic and achromatic ΔS. This assumes those colour patterns, or parts of the patterns used in signalling, with larger mΔS and sΔS, 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 ΔS 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 mΔS > 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 mΔS less than expected from random contacts between all pairs of patch colour/luminance classes. The correlation between chromatic and luminance ΔS 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 mΔS values in guppies suggests an anti‐predator function because guppies are never found without predators. Moreover, mΔS 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 mΔS change with viewing angle; geometry of signalling is as important as signal geometry.

pavo 2: new tools for the spectral and spatial analysis of colour in R

“…Exciting recent advances now allow for the analysis of colour pattern geometry — that is, the spatial structure of colour patches — in conjunction with the comparatively well-developed approaches to the spectral analysis of colour out-lined above (Endler, 2012; Endler et al ., 2018; Pike, 2018; Troscianko et al ., 2017). The most significant extension of as of version 2 is the introduction of an image-based workflow to allow for the combined analysis of the spectral and spatial structure of colour patterns, currently centred on measures of overall pattern contrast (Endler & Mielke, 2005), the adjacency analysis (Endler, 2012), and its extension, the boundary strength analysis (Endler et al ., 2018). In , the various steps for such analyses are carried out through calls to , which uses k-means clustering to automatically or interactively classify image pixels into discrete colour-classes, and/or , which performs the adjacency analysis and, if appropriate colour distances are also specified, the boundary strength analysis (discussed in Endler et al ., 2018).…”

“…Finally, we use an adjacency analysis to estimate a suite of metrics describing the structure and complexity of the colour pattern geometry of model and mimic Heliconius , and by including the visually-modelled colour distances estimated above, the output will include several measures of the salience of colour patch edges as part of the boundary strength analysis (Endler, 2012; Endler et al ., 2018). We will exclude the white background since it is not relevant, simply by specifying the colour-category ID belonging to the homogeneous underlay.…”

“…colour and luminance) and spatial (i.e. the distribution of pattern elements) properties of colour patterns (Endler, 2012; Endler et al ., 2018; Kemp et al ., 2015; Renoult et al ., 2015; Troscianko et al ., 2017). The need remains, however, for tools that integrate these complex methods into clear, open, and reproducible workflows (White et al ., 2015), allowing researchers to retain focus on the exploration of interesting questions.…”

Quantitative Colour Pattern Analysis (QCPA): A Comprehensive Framework for the Analysis of Colour Patterns in Nature

“…They then 85 measured chromatic contrast (ΔS) between animal and background using point measurements 86 obtained by a spectrophotometer. While useful for many studies of animal colouration, these 87 individual analyses ignore the interaction of visual information at various perceptual stages (for 90 Spatiochromatic colour pattern analyses overcome these limitations as they are designed to 91 consider perceptual interactions between spatial, chromatic and achromatic information ( Endler et al, 2018). For example, not only is the efficiency of visual signals dependent on the presence 97 or absence of colours, but also how those colours are arranged in patterns (Endler, 1984(Endler, , 2012Endler 98 et al, 2018; Green et al, 2018;Troscianko et al, 2018).…”

Investigating Defensive Colouration in Nudibranch Molluscs using a Novel Analytical Framework for the Study of Animal Colour Patterns​​​​​​​

“…visual cortex) stages of information processing (for discussion see Gegenfurtner & Kiper, 1992;Shapley & Hawken, 2011;Stevens & Merilaita, 2011;Rowe, 2013;Endler & Mappes, 2017;Ng et al, 2018;Ruxton et al, 2018). However, recent publications continue to highlight the need to use an integrated approach to consider visual information when investigating the perception, and therefore the design, function and evolution, of complex visual signals (Endler, 1978(Endler, , 1984Rowe & Guilford, 1999;Rowe, 1999Rowe, , 2013Osorio, Smith, Vorobyev, & Buchanan-Smith, 2004;Hebets & Papaj, 2005;Shapley & Hawken, 2011;Stevens & Merilaita, 2011;Dalziell & Welbergen, 2016;Endler & Mappes, 2017;Ruxton et al, 2018;Endler, Cole, & Kranz, 2018). For example, not only is the efficiency of visual signals dependent on the presence or absence of colours, but also how those colours are arranged in patterns (e.g.…”