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

1.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.

2.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.

3.BSA 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. 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 non‐random colour geometry.

4.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.

5.In species which are very convex, both chromatic and luminance mΔS change with viewing angle; geometry of signalling is as important as signal geometry.

1. 诸多物种会利用体色图案做出决策，这些决策最终会影响其达尔文适合度。体色图案由一系列几何特征与视觉属性各不相同的色块镶嵌构成。尽管传统研究中通常会分别分析图案几何特征与色块视觉属性，但这些组分大概率会作为功能整体协同发挥作用。尽管如此，关于色块视觉属性、色块几何特征以及色块边界对动物视觉系统、行为与适合度的综合效应，目前的研究仍相对匮乏。
2. 本研究介绍了边界强度分析（Boundary Strength Analysis, BSA）——一种将色块边界（不同色块类群间的分界）的几何特征，与边界强度的受体噪声估计值（ΔS）相结合的全新方法。该方法基于脊椎动物与无脊椎动物视网膜的已知特性。我们可通过按长度对每类边界的ΔS进行加权，分别计算色觉（chromatic）与消色差（achromatic）维度下体色图案的ΔS均值与标准差（记为mΔS、sΔS）。该方法的前提假设是：用于信号传递的体色图案或其组分，其mΔS与sΔS值越高，对接收者的刺激越强，因而辨识度也越高。边界强度分析可同时用于分析体色图案与视觉背景。
3. 边界强度分析已成功用于评估两种物种的体色图案变体的预估显眼程度：孔雀鱼（Poecilia reticulata）与七彩文鸟（Erythrura gouldiae），这两个物种均在色块颜色、明度与几何特征上存在多态性。对两种物种的色块边界ΔS进行三维可视化（Fort图，Fort Diagrams）的结果显示，色觉边界与消色差边界之间几乎不存在几何对应性，甚至呈负相关。所有个体在色觉与明度维度下的mΔS均大于1.5，这表明其信号传递图案内部具有预期的高对比度。但与性选择理论的预期相悖，所有孔雀鱼的mΔS值均低于所有色块颜色/明度类群随机配对时的预期值。两种物种的色觉ΔS与明度ΔS均呈负相关，但当对各物种不同色型的所有可能边界类型进行相关性分析时，相关性为零，这表明体色图案的几何结构并非随机形成。
4. 两种物种的色觉边界与消色差边界在模式上的差异，表明二者可能具备不同的功能。孔雀鱼的mΔS值低于随机预期的结果，这暗示其体色图案具备反捕食功能——因为野外环境中孔雀鱼始终伴随捕食者存在。此外，mΔS值可能随物种内部及物种间的捕食压力强度发生变化。边界强度分析可应用于任何用于种内与种间行为的体色图案研究。本研究还提出了针对体色图案的7项预测与4个研究问题。
5. 对于体型极度隆起的物种，色觉与明度维度下的mΔS均会随观察角度发生变化；这表明信号传递的几何环境与信号本身的几何特征同等重要。