A synthesis is presented of recent work by the authors and others on the formation of localised patterns, isolated spots, or sharp fronts in models of natural processes governed by reaction–diffusion equations. Contrasting with the well-known Turing mechanism of periodic pattern formation, a general picture is presented in one spatial dimension for models on long domains that exhibit sub-critical Turing instabilities. Localised patterns naturally emerge in generalised Schnakenberg models within the pinning region formed by bistability between the patterned state and the background. A further long-wavelength transition creates parameter regimes of isolated spots which can be described by semi-strong asymptotic analysis. In the species-conservation limit, another form of wave pinning leads to sharp fronts. Such fronts can also arise given only one active species and a weak spatial parameter gradient. Several important applications of this theory within natural systems are presented, at different lengthscales: cellular polarity formation in developmental biology, including root-hair formation, leaf pavement cells, keratocyte locomotion; and the transitions between vegetation states on continental scales. Philosophical remarks are offered on the connections between different pattern formation mechanisms and on the benefit of subcritical instabilities in the natural world.

综述了作者和其他人在由反应扩散方程控制的自然过程模型中局部模式，孤立斑点或锋利锋线形成方面的最新工作。与众所周知的周期性图灵形成图灵机制相反，对于呈现亚临界的长域模型，在一个空间维度上展示了一张普通图片图灵不稳定。局部模式自然出现在钉扎区域内的广义Schnakenberg模型中，该区域由构图状态与背景之间的双稳性形成。进一步的长波长跃迁创建了孤立点的参数范围，可以通过半强渐近分析来描述。在物种保护极限内，另一种形式的波浪钉扎导致锋利的锋面。如果仅提供一种活性物种且空间参数梯度较弱，也会出现此类前沿。本文介绍了该理论在自然系统中在不同长度尺度上的几个重要应用：发育生物学中的细胞极性形成，包括根毛形成，叶面细胞，角膜细胞运动；以及大陆尺度上植被状态之间的过渡。