Christian M. Erikson and Jens M. Turowski of the GFZ Helmholtz Centre for Geosciences in Potsdam, Germany, publish their analysis in the journal Earth Surface Dynamics as a highlight letter. Their central claim is that step-pool spacing occupies a continuum between regularity and randomness, with the full range of possible configurations realized in nature and no single formation mechanism dominating. The finding, drawn from a compilation of 131 step-pool sequences spanning field sites, laboratory flume experiments, and numerical simulations, resolves a long-standing tension between competing models that had produced contradictory expectations about what a healthy mountain stream should look like.

The stakes are considerable. Mountain streams account for an estimated 60 to 80 percent of total global river length, and the transport of floodwaters and sediment through them is a costly natural hazard in populated mountainous regions. Step-pools are prominent in rivers with slopes exceeding roughly 3 percent, and their ability to provide flow resistance makes them a favored tool in hazard management. They are also used as a benchmark of channel recovery in river restoration, particularly in the growing number of dam-removal projects worldwide. Without a clear, mechanism-independent expectation for step spacing, practitioners have had no reliable target: one scientific camp predicted regular spacing tied to channel hydraulics, another predicted random spacing tied to the size and location of large boulders, and restoration designs inherited the confusion.

The roots of the dispute run deep. Mechanisms linked to hydraulics, such as the antidune mechanism, associate steps with regular spacing. Antidunes are bedforms that organize under rapidly flowing water into roughly periodic crests, and the idea, first proposed from flume experiments in 1982, was that these precursory bedforms act as nucleation points for developing steps. The pool-scour mechanism offers another hydraulic route to regularity: high-energy flow over a step scours a pool downstream, and the excavated material builds the next step, propagating a rhythmically spaced sequence. In contrast, mechanisms tied to channel properties and particle interactions predict randomness. In particle jamming, grains chain together across the channel, often in narrow sections; in keystone clustering, sediment accumulates around large immobile boulders. Because the underlying boulders and rough patches are themselves randomly distributed, the resulting steps inherit that randomness.

The scientific literature has swung back and forth between these camps, and the antidune mechanism is the emblematic case. Once a commonly invoked explanation, it fell from prominence as random-interaction models gained ground, was at one point called on to be abandoned entirely, and has recently been resurrected and again put forward as the dominant mechanism. Erikson and Turowski argue that this vacillation reflects a structural problem: without a comparative framework transferable across mechanisms, interpretations of step spacing have been constrained by prior assumptions about the formative process. A researcher who assumes antidunes will find regularity; one who assumes jamming will find randomness. Both may be partly right, and neither can settle the debate alone.

To break the deadlock, the researchers built a diagnostic framework from two statistical measures of spacing variability that can be calculated from readily obtainable measurements. The first is the coefficient of variation, the standard deviation of step spacing divided by the mean spacing, a standard measure of scatter. The second is a new metric they call the relative minimum: the smallest observed gap between steps divided by the mean spacing. The relative minimum exists to capture the effect of exclusion zones, the stretches of channel immediately downstream of a step where the hydraulic influence of that step prevents a new one from forming. The longer the exclusion zone, the less room remains for new steps, and the lower the maximum achievable coefficient of variation. Because no general method exists to measure exclusion-zone length directly, the minimum spacing serves as a practical proxy.

With these two metrics defining a two-axis plotting space, the team established two reference lines using Monte Carlo simulations repeated 100,000 times. A regular reference line was generated by taking a perfectly regular step sequence, adding Gaussian noise to the spacing, and adjusting positions until all steps respected the minimum-spacing constraint. A random reference line came from a modified Poisson process, in which spacings were drawn from an exponential distribution and any spacing below the minimum constraint was rejected, mimicking the way an exclusion zone limits pure randomness. A range-normalized coefficient of variation then places any real sequence between the two lines: values below 0.5 indicate a sequence closer to regular, values above 0.5 closer to random.

The compiled dataset of 131 sequences, drawn from channels with slopes spanning an order of magnitude from about 3 to 35 percent, revealed that natural step-pool sequences span nearly the full range of possible relative minimum spacing, from 0.07 to 0.84 against a possible range of 0 to 1. The observed coefficients of variation fell almost entirely within the bounds set by the two reference lines, with only three exceptions. Crucially, most sequences sat somewhere between the lines rather than clustering near either one. Of 27 averaged data sources, 18 were closer to the random reference line and 9 closer to the regular line, but the dominant impression was of a continuum fully occupied rather than two distinct populations. Sequences explicitly tied to roughness, keystone, and jamming mechanisms plotted nearest the random line, as expected, while pool-scour sequences and true antidunes plotted nearest the regular line. Channel slope showed no strong correlation with spacing variability.

The framework also produced surprises that cut against cherished assumptions. The flume experiments of Whittaker and Jaeggi, from which the antidune mechanism was first proposed, plotted closer to the random reference line than to the regular one, in an opposite corner of the diagram from genuine antidunes, suggesting that a roughness-based mechanism better explains their observations. The three outliers beyond the random reference line proved diagnostic in their own right: wood-constructed steps in the Vogelbach in Switzerland and Shatford Creek in Canada, and newly developed steps in Charles Brown Brook in the United States after a dam removal, where steps clustered around rough patches with large gaps between clusters. Artificially close spacing or isolated clustering can push a sequence past what pure randomness allows, turning the random reference line into a practical tool for spotting reaches where spacing has been forced by wood, engineering, or disturbance.

The implications reach directly into stream management. Because irreducible natural variability prevents full regularity and hydraulic exclusion zones prevent full randomness, any isolated set of observations will fail to match a truly regular or truly random ideal, meaning that restoration designs built on either assumption are fundamentally misguided. The authors suggest that channel equilibrium, a central concept in restoration, may need redefinition away from a static spacing target toward objectives that accommodate a range of configurations and multiple simultaneous processes. Moreover, because the random reference line is explicitly tied to channel hydraulics, it offers a testable prediction for how spacing evolves in channels that are not in equilibrium, potentially serving as an indicator of river adjustment. In the context of accelerating dam removals, where recovery is currently gauged by metrics tied to assumptions of regularity, such a mechanism-independent yardstick could eventually define concrete, physically grounded targets for restoring the staircases of the world’s mountain streams.

Subject of Research: Spacing regularity and randomness of step-pool sequences in steep mountain streams

Article Title: From regular to random: a unifying framework for step-pool spacing

Article References: Erikson, C. M., & Turowski, J. M. (2026). From regular to random: a unifying framework for step-pool spacing. Earth Surface Dynamics, 14(4), 653-659. https://doi.org/10.5194/esurf-14-653-2026

Image Credits: AI Generated

DOI: 10.5194/esurf-14-653-2026

Keywords: step-pools, mountain streams, geomorphology, fluvial processes, stream restoration, hydraulics, antidunes, particle jamming, sediment transport, dam removal, channel equilibrium, Earth Surface Dynamics

The scale of the problem the study confronts is difficult to overstate. Over the past century, streams and lakes across the country have deteriorated under mounting human pressure. More than 150,000 dams now fragment river networks, severing the upstream and downstream connections that countless species depend on for migration, spawning and genetic exchange. Beyond the barriers themselves, changes to the landscape, from agriculture to urbanization, and the extraction of groundwater have altered how and where water flows through entire watersheds. Flow regimes that evolved over millennia have been reshaped within a few human generations, and the consequences are visible in the biological record. Many freshwater species are now in rapid decline, a trend that researchers warn is being exacerbated by the impacts of a changing climate, which shifts temperature and precipitation patterns faster than aquatic organisms can disperse or adapt.

To confront this crisis systematically, The Nature Conservancy assembled a collaboration of 66 freshwater conservationists and set out to map freshwater networks across the contiguous United States and evaluate how resilient each one is to degradation. The approach was deliberately multidimensional. Each watershed received scores based on four criteria: its connectivity, meaning how well its aquatic habitats link together into functioning networks; its condition, reflecting the ecological integrity of the stream or river; its water availability; and the naturalness of its flow, a measure of how closely the timing and magnitude of water movement still resemble historical patterns. These scores were then checked against local surveys of freshwater biodiversity, grounding the resilience assessment in observed biological reality rather than purely physical or chemical proxies.

The result of this effort is a spatial blueprint the researchers call the Freshwater Resilient and Connected Network. This patchwork of rivers and streams covers 35 percent of the lower 48 states, yet the analysis indicates it could preserve the nation’s freshwater biodiversity if conserved and, where necessary, restored. The logic behind such a network is rooted in conservation biology: rather than spreading limited resources thinly across every waterway, concentrating protection on the places where ecosystems are most intact, most connected and most likely to withstand climatic disruption offers a disproportionate return on investment. Resilient, connected networks give species room to move, access to diverse habitat types and the ecological redundancy needed to absorb disturbances such as droughts, floods and warming waters.

Realizing that vision, however, will be a formidable challenge, and the study is candid about the gap between ambition and current reality. Of the 35 percent of waterways identified in the network, only 6 percent of the area is both protected and resilient today. A further 14 percent needs both protection and restoration before it can fulfill its role in the network. In other words, the vast majority of the lands and waters that underpin the nation’s freshwater future currently lack formal safeguards, and many have already been degraded enough to require active intervention. The numbers underscore that identifying priority areas is only the first step; the harder work of securing durable protection and reversing damage on the ground remains ahead.

The broader statistical picture the analysis paints of the contiguous United States is equally revealing. Of the 5.2 million miles of rivers and streams in the lower 48 states, 33 percent rated as above average for resilience. Rivers in this category should continue to support similar patterns of biodiversity in the future, making them strong candidates for protection. The researchers note an important nuance, however: rivers that score just above average may still require restoration to maintain their ecological function, meaning that even some of the better-performing waterways cannot simply be left alone. The geography of resilience is uneven as well. The strongest networks are concentrated along the Pacific Coast, in the Northern Rocky Mountains, around the Great Lake areas of Wisconsin and Minnesota, in northern Maine, and along the coastal regions of the southeastern United States and the Gulf of Mexico, areas where relatively intact landscapes and healthier flow regimes persist.

At the other end of the spectrum, vulnerable or below-average river networks made up 15 percent of the nation’s river and stream miles, and their distribution tells a story about the cumulative weight of human land use and arid climates. These stressed networks cluster in the Southwest deserts, in lower New England, across the shortgrass prairie east of the Rocky Mountains, and throughout the agricultural lands of the midwestern states. In these regions, decades of water diversion, damming, row-crop cultivation and development have eroded the connectivity and natural flow patterns that freshwater communities need. The identification of these hotspots of vulnerability is not merely descriptive; it signals where restoration investment is most urgent if the country hopes to prevent further local extinctions and the loss of aquatic ecosystem services.

The practical value of the new maps is already being demonstrated, according to the research team. The analysis has been used to identify dams for removal, a critical step in reestablishing longitudinal connectivity in fragmented river systems. It has also guided the prioritization of land protection in key headwaters, where safeguarding the upper reaches of watersheds protects water quality and flow for everything downstream. In addition, the framework is being applied to improve conditions in river systems that need restoration, directing effort toward reaches where interventions are most likely to succeed. The authors acknowledge one important limitation: the maps do not take into account human needs, such as water supply, recreation and economic uses of rivers. They note, however, that data representing human dimensions could be combined with this analysis to identify where conservation goals and human priorities intersect or conflict.

The researchers emphasize that resilience to climate change adds essential context to biodiversity conservation that static protection alone cannot provide. A reserve that protects a species’ current habitat may fail within decades if warming, altered precipitation or shifting flow regimes render that habitat unsuitable. By scoring watersheds for the physical features that confer long-term resilience, such as connectedness, water availability and natural flow, the framework aims to identify places where biodiversity can persist not just today but across a range of future climate scenarios. The authors state the hope directly: resilience to climate changes adds important context to efforts to conserve freshwater biodiversity, and they hope the study will help state, federal, Tribal and other conservation partners make investments where they have the greatest chance to succeed into the future.

The study, authored by Mark G. Anderson, Arlene P. Olivero, Analie R. Barnett, Melissa L. Khoury and Erika H. Martin of The Nature Conservancy, was funded by an anonymous donor, the Volgenau Foundation, Kia America and the Enterprise Mobility Fund, none of which played a role in study design, data collection and analysis, decision to publish or manuscript preparation. The authors report no known competing interests. As an observational, nationwide assessment published in PLOS One, it offers conservation planners a rigorous, data-driven foundation for sustaining freshwater life across the United States, and a clear-eyed picture of the challenges ahead: a third of the nation’s waters hold the key, but most of that territory still awaits the protection and restoration it will need to do its job.

Subject of Research: Mapping resilient and connected freshwater networks to conserve biodiversity in United States rivers and streams under climate change

Article Title: Conserving just 35% of nation’s waterways could sustain freshwater biodiversity

Article References: Conserving just 35% of nation’s waterways could sustain freshwater biodiversity. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: freshwater biodiversity, river conservation, climate resilience, PLOS One, The Nature Conservancy, watershed connectivity, dam removal, stream restoration, United States rivers, habitat protection, flow regime, conservation planning