Animals display extensive diversity in motifs adorning their coat, yet these patterns have reproducible orientation and periodicity within species or groups. Morphological variation has been traditionally used to dissect the genetic basis of evolutionary change, while pattern conservation and stability in both mathematical and organismal models has served to identify core developmental events. Two patterning theories, namely instruction and self-organisation, emerged from this work. Combined, they provide an appealing explanation for how natural patterns form and evolve, but in vivo factors underlying these mechanisms remain elusive. By bridging developmental biology and mathematics, novel frameworks recently allowed breakthroughs in our understanding of pattern establishment, unveiling how patterning strategies combine in space and time, or the importance of tissue morphogenesis in generating positional information. Adding results from surveys of natural variation to these empirical-modelling dialogues improves model inference, analysis, and in vivo testing. In this evo-devo-numerical synthesis, mathematical models have to reproduce not only given stable patterns but also the dynamics of their emergence, and the extent of inter-species variation in these dynamics through minimal parameter change. This integrative approach can help in disentangling molecular, cellular and mechanical interaction during pattern establishment.

中文翻译：

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用于识别图案形成因素的“数字Evo-Devo”合成。

动物的外衣装饰图案表现出广泛的多样性，但这些图案在物种或群体内具有可复制的方向和周期性。传统上，形态学变异被用来剖析进化变化的遗传基础，而数学和机体模型中的模式守恒和稳定性则有助于确定核心发展事件。这项工作产生了两种模式理论，即指导和自我组织。结合起来，它们提供了关于自然模式如何形成和进化的吸引人的解释，但是这些机制背后的体内因素仍然难以捉摸。通过将发展生物学和数学联系在一起，新颖的框架最近使我们对模式建立的理解有了突破，揭示了模式策略如何在时空上结合在一起，或组织形态发生在生成位置信息中的重要性。将自然变异调查的结果添加到这些经验建模对话中，可以改善模型推断，分析和体内测试。在这种evo-devo-数值合成中，数学模型不仅必须复制给定的稳定模式，还必须复制它们出现的动力学，以及通过最小的参数变化来改变这些动力学中物种间变化的程度。这种整合方法可以帮助在模式建立过程中解开分子，细胞和机械相互作用。数学模型不仅必须重现给定的稳定模式，还必须重现它们出现的动力学，以及通过最小的参数变化来改变这些动力学中物种间变化的程度。这种整合方法可以帮助在模式建立过程中解开分子，细胞和机械相互作用。数学模型不仅必须重现给定的稳定模式，还必须重现它们出现的动力学，以及通过最小的参数变化来改变这些动力学中物种间变化的程度。这种整合方法可以帮助在模式建立过程中解开分子，细胞和机械相互作用。