Evolution’s Hidden Compass: When Fitness Is Equal, Curvature Steers the Path

One of the most enduring images in evolutionary biology is the adaptive landscape, a metaphor in which populations climb toward peaks of higher fitness, with natural selection pushing organisms uphill and mutation scattering them across the terrain. For decades, the picture has been dominated by height: where the landscape rises, selection follows, and where the terrain is flat, evolution is often assumed to wander without direction. A new study from the Technion-Israel Institute of Technology, published in the Proceedings of the National Academy of Sciences, challenges that assumption in a striking way. The researchers show that when an organism faces multiple evolutionary trajectories that all deliver the same fitness, the path it ultimately takes is not a matter of chance. Instead, populations drift deterministically toward the flattest regions of the landscape, and that hidden bias may help explain one of biology’s deepest puzzles: how living systems become robust in the first place.

The research was led by Razi Fachar Eldeen of the Faculty of Mathematics and Prof. Naama Brenner of the Wolfson Faculty of Chemical Engineering, both members of the Technion’s Network Biology Research Laboratory. Their work addresses a question that has long hovered at the edge of evolutionary theory. Fitness landscapes are frequently degenerate, meaning that many different combinations of traits, or many different sequences of mutational steps, can yield identical levels of reproductive success. In such situations, classical theory offers no obvious reason for evolution to prefer one route over another. If all directions lead to the same fitness value, one might expect the population to perform an undirected random walk, diffusing evenly across the plateau of equivalent outcomes.

That intuition, the Technion team found, is wrong. By analyzing evolution on degenerate fitness landscapes using computational simulation and mathematical modeling, they discovered that the geometry of the landscape, specifically its curvature, exerts a systematic influence even when fitness itself is identical everywhere along the available paths. Rather than drifting aimlessly, populations are drawn toward flatter regions of the landscape. In these flat zones, an organism’s traits are less sensitive to mutation and other perturbations: small changes in genotype or environment produce smaller changes in phenotype and fitness. The result is a directional bias that emerges purely from the shape of the terrain, not from any explicit reward for being robust.

The distinction between height and curvature is the conceptual heart of the finding. Fitness measures how well an organism survives and reproduces in its current environment, and selection directly rewards improvements in fitness. Curvature, by contrast, describes how fitness changes as traits are perturbed. A population sitting on a sharp peak may enjoy high fitness, but a single mutation can send it tumbling down a steep slope. A population on a broad, flat plateau may have the same measured fitness, yet its descendants remain viable across a much wider range of genetic and environmental variation. The Technion study shows that over evolutionary time, this second-order property is not invisible to the dynamics. Even without selection explicitly favoring tolerance to change, the population’s trajectory bends toward the flatter ground.

Prof. Brenner framed the question that motivated the work in terms of the classical climbing metaphor. Evolution, she noted, is commonly described as a process of climbing fitness peaks, in which organisms become better adapted to their environment and thus improve their chances of survival. However, organisms sometimes face multiple evolutionary trajectories that all yield the same level of fitness. This raises the question of how evolution selects among these paths of equivalent fitness. The answer the team arrived at is that the selection among equal-fitness paths is governed by robustness: when fitness is equal, evolution tends to favor directions that confer greater robustness and tolerance to change, properties that themselves provide a survival advantage over longer timescales.

This conclusion carries a significant implication for how scientists think about the origins of biological robustness. Robustness, the capacity of a living system to maintain its function despite genetic mutations, environmental fluctuations, and internal noise, is ubiquitous in nature. Gene regulatory networks buffer against perturbations, developmental programs produce reliable body plans despite variable conditions, and metabolic pathways continue functioning when individual components fail. Traditionally, such resilience is attributed to direct selection: lineages that survived disruptions left more descendants, so robustness was favored trait by trait. The Technion findings suggest an additional and more spontaneous route. Robustness and resilience to disruption can emerge as a byproduct of evolutionary dynamics themselves, without any explicit selection pressure favoring these properties, simply because populations on degenerate landscapes drift toward the flat, tolerant regions.

The methodological approach relied on computational simulation and modeling, allowing the researchers to explore the behavior of populations on landscapes where many trajectories lead to similar fitness levels. In the figures accompanying the study, the lighter-colored regions represent these areas of equivalent fitness. One panel depicts the classical expectation: evolution proceeding as an undirected random walk across the plateau. The other depicts what the study actually found: differences in landscape curvature driving organisms deterministically toward flatter regions, where they gain greater robustness and tolerance to change. The contrast between the two panels captures the shift in perspective that the work proposes. The flat side of the landscape, far from being an evolutionary dead zone where nothing interesting happens, turns out to be an attractor, a destination that the dynamics actively seek out.

Why should curvature produce such a systematic drift? The intuition can be sketched in terms of how populations explore the space of possible traits. On a steeply curved region of the landscape, most mutational steps away from the current state lead to large losses of fitness, and such steps are efficiently eliminated by selection. On a flat region, many mutational steps are nearly neutral, so the population can accumulate and retain far more genetic and phenotypic variation. Over time, the population effectively spends more of its history in the flat, mutation-tolerant zones, and its lineage becomes anchored there. The flat regions act as sinks in the space of evolutionary trajectories: paths leading into them are retained, while paths leading out of them are repeatedly pruned by the accumulated weight of small deleterious changes. The drift is therefore deterministic in the statistical sense, even though the individual mutations that carry it are random.

The implications extend beyond evolutionary biology into unexpected territory. The researchers point out that deep learning exhibits a strikingly parallel phenomenon. When artificial neural networks are trained, they likewise tend to converge on flat minima of their loss landscapes, and it is well established in the machine learning literature that solutions found in flat basins tend to generalize better to new data than solutions perched on sharp minima. In both domains, a system navigating a high-dimensional landscape in which many points offer equivalent performance ends up preferentially occupying the flat regions, and in both domains this preference is associated with greater stability and tolerance to perturbation. The Technion study thus builds a conceptual bridge between evolutionary dynamics and learning dynamics, suggesting that the tendency to seek flatness may reflect deep structural properties of adaptation processes in high-dimensional spaces, whether the adapting system is a population of organisms or a network of artificial neurons.

The study may ultimately help explain patterns of biological variation observed in nature, deepen understanding of the origins of robustness in living systems, and inform theoretical work across disciplines that grapple with adaptation in complex landscapes. It reframes the flat portions of fitness landscapes, long treated as the boring interludes between dramatic climbs, as regions with their own intrinsic dynamics and their own evolutionary consequences. The research was supported in part by the U.S.-Israel Binational Science Foundation, and it appeared in the Proceedings of the National Academy of Sciences under the title describing evolution on degenerate fitness landscapes as non-random, with curvature driving directional drift. What emerges from the work is a revised picture of evolution’s compass: even on ground where every direction looks equally good, the shape of the terrain quietly decides where life will go, steering it toward the places where it can best withstand whatever comes next.

Subject of Research: Directional drift of evolving populations toward flat, robust regions of degenerate fitness landscapes

Article Title: The flat side of evolution: Even when multiple evolutionary paths are equally advantageous, the choice among them is not random

Article References: The flat side of evolution: Even when multiple evolutionary paths are equally advantageous, the choice among them is not random. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: evolution, fitness landscapes, robustness, degeneracy, curvature, natural selection, Technion, computational modeling, deep learning, PNAS, mutation, adaptation