Self‐organized pattern formation is widespread and functionally significant. Scale‐dependent feedback in space (short‐distance positive feedback coupled with long‐distance negative feedback) has been embraced as an arguably universal mechanism of ecological self‐organization. Recently, intraspecific territorial competition has been proposed as a complementary mechanism contributing to spatial self‐organization in ecology. In geomorphology, regular patterning is also widespread and has often been attributed to competition among geomorphic features. This mechanism has never been integrated into the framework of ecological pattern formation. Using the regularly patterned landscape of Big Cypress National Preserve in South Florida as a case study, we formalize a third mechanism of spatial self‐organization: competition among pattern elements of finite amplitude stabilized by scale‐dependent feedback in time. Depressions first accelerate their expansion rate via the positive feedback between depression volume and weathering rate. Later negative feedbacks become stronger, and eventually stabilize the size of depressions. While scale‐dependent feedback in time provides a mechanism to stabilize individual depressions, it is the competition among depressions that induces spatial regularity. A relatively smaller depression could have a greater expansion rate than larger ones in its development. Higher weathering rate on the side of a divide toward the smaller depression causes migration of the divide to the larger depression. Consequently, the smaller depression expands its catchment area while the catchment area of the neighboring larger depression contracts, resulting in depressions achieving similar size and distance from each other. The diversity of regular patterns dictates the need to integrate perspectives from multiple disciplines.

中文翻译：

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石灰岩洼地之间的竞争导致在平坦的景观上自组织规则的图案

自组织模式的形成是广泛的，并且在功能上很重要。空间尺度反馈（短距离正反馈与长距离负反馈）被认为是生态自组织的普遍机制。最近，种内领土竞争已被提出作为一种补充机制，有助于生态学中的空间自组织。在地貌学中，规则的图案化也很普遍，通常归因于地貌特征之间的竞争。这种机制从未被整合到生态格局形成的框架中。以南佛罗里达大柏树国家自然保护区的规律性格局景观为例，我们确定了空间自组织的第三种机制：有限幅度的格局要素之间的竞争通过及时的比例依赖性反馈得以稳定。抑郁首先通过抑郁量和风化率之间的正反馈来加速其膨胀率。后来，负面反馈变得更加强烈，并最终稳定了萧条的规模。尽管时间尺度依赖的反馈提供了稳定单个凹陷的机制，但正是凹陷之间的竞争才引发了空间规律性。相对较小的萧条在发展过程中可能比较大的萧条具有更大的扩张率。隔板朝向较小凹陷的一侧较高的风化率会导致隔板向较大凹陷的迁移。因此，较小的凹陷扩大了其捕获面积，而相邻的较大凹陷的捕获面积缩小了，从而导致凹陷彼此之间的大小和距离相似。