The Flat Side of Evolution: Even When Multiple Evolutionary Paths Are Equally Advantageous, the Choice Among Them Is Not Random

Amazing stuff! A mathematical study of biological evolution. This work is highly theoretical and model based.

Caveat the study could have been driven by strong presumption to model the subject as a complex manifold with curved and flatter areas. So I am a little skeptical whether this study is not about reality, but a statistical modeling exercise.

"A surprising discovery by Technion researchers sheds new light on the dynamics of evolution. .. 

the study shows that when an organism has several evolutionary paths available with equal fitness, the path it follows is not necessarily chosen at random. ...

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. ...

researchers found that the choice is not random. Rather than wandering aimlessly, populations deterministically drift toward flatter regions of the evolutionary landscape, where an organism’s traits are more robust to mutations and other perturbations. In other words, when fitness is equal, evolution tends to favor directions that confer greater robustness and tolerance to change, properties that themselves provide a survival advantage. ...

The findings suggest that biological robustness and resilience to disruption can emerge spontaneously through evolutionary dynamics, even in the absence of direct selection favoring these traits. ..."

From the significance and abstract:

"Significance

Evolutionary dynamics selects more fit phenotypes over others. But fitness landscapes are complex and high dimensional, with continuous manifolds of practically identical high fitness.

Intuitively, one may imagine that evolution then proceeds to wander randomly among these degenerate states; we here show that this is generally not so.

On smooth manifolds of equal fitness, an implicit bias appears, directing evolving populations deterministically toward flatter regions.

This bias emerges from interaction between population variability and landscape geometry.

The effect has analogs in other contexts of stochastic dynamics, such as Langevin dynamics in an energy landscape and neural networks optimizing a loss function. Most importantly, it has implications on how we view evolved populations and how we interpret their observed properties.

Abstract

Degeneracy—the multiplicity of phenotypes with equal fitness—is a prevalent feature of biological systems. Such degeneracy is often associated with neutral evolution, under the assumption that adaptive dynamics on degenerate fitness manifolds is random and lacks direction.

Here we show that this is not generally the case. Using a minimal model of evolutionary dynamics on smooth degenerate fitness landscapes, we demonstrate that stochastic mutation–selection dynamics induce a directional drift on manifolds of optimal fitness toward regions of reduced curvature.

This drift arises from an interaction between population variability and landscape curvature: Curvature shapes phenotypic variation, which in turn biases evolutionary exploration even when fitness gradients vanish.

As a result evolution exhibits an implicit bias, preferentially selecting flat and robust regions of the degenerate fitness manifolds, without explicit optimization for these properties.

Interestingly, similar flatness-seeking implicit biases have been discovered in other stochastic optimization algorithms; here we reveal their different underlying mechanisms despite similar outcome, demonstrating the unique properties of evolutionary dynamics.

Our results highlight a general mechanism by which degeneracy shapes long-term evolutionary outcomes, affecting our interpretation of phenotypic variability, robustness, and neutrality in high-dimensional biological systems."

The Flat Side of Evolution: Even When Multiple Evolutionary Paths Are Equally Advantageous, the Choice Among Them Is Not Random - הטכניון-מכון טכנולוגי לישראל

Evolution on degenerate fitness landscapes is not random: Curvature drives directional drift (no public access)

Evolution on degenerate fitness landscapes is not neutral: curvature drives directional bias (preprint, open access)

Fig. 1 Evolution on degenerate landscapes is not neutral. ... 

Fig. 4 Evolutionary steady-state distributions compared to other stochastic dynamics.

(a) Evolutionary Dynamics ...

b) Gradient Langevin Dynamics ...

(c) Shift model approximating Stochastic Gradient Ascent ...