Аннотация: How evolution computes life within a multidimensional fractal landscape - a perspective on nature devoid of the customary two-dimensional imagery (English version)
Evolution as a Flow in a Multidimensional Landscape
How evolution computes life within a multidimensional fractal landscape - a perspective on nature devoid of the customary two-dimensional imagery.
When we attempt to visualise evolution, the image of an "adaptive landscape" often springs to mind - a surface of hills and valleys where populations "climb" towards peaks of fitness. This imagery is convenient, yet it severely constrains our understanding. It suggests that evolution is a journey across a three-dimensional surface that can be sketched or, at the very least, imagined. However, real evolution occurs within a space far more complex than our familiar geometry allows.
Let us consider a different image. Suppose evolution is not a climber scaling a summit, but a flow of liquid moving across a surface. In this representation, depressions become stable states where the water accumulates; watersheds become stretches through which the flow cannot pass; and "mountains" are zones of low fitness that are impossible to traverse. Liquid does not leap over barriers or spill over high ridges. It flows where the topography permits and becomes trapped wherever a local depression forms. Evolution behaves in a similar fashion: populations move towards more stable combinations of traits but cannot jump across regions where fitness drops sharply.
This image becomes particularly potent if we abandon habitual three-dimensionality. Genetic space is not a surface with two coordinates and a height. It is a space of immense dimensionality, where each coordinate corresponds to a parameter affecting the organism: mutations, gene expression levels, interactions between genes, regulatory mechanisms, and developmental nuances. These parameters do not number in the dozens or hundreds - they are in the thousands and millions. In such a space, it is impossible to "see" the landscape, but one can comprehend its structure.
In a multidimensional space, conventional intuitions cease to function. "Mountains" and "valleys" transform into complex manifolds, while "flows" become trajectories passing through narrow channels, bypassing barriers, and occasionally stalling in local troughs. Evolution cannot pass through a region of low fitness, even if a more advantageous state lies on the other side. To reach it, the population would have to cross a "dry spot" - a region where survival rates plummet. Consequently, certain evolutionary paths remain closed, even if they are theoretically possible.
However, multidimensionality is only part of the story. In real biology, parameters are not independent of one another. Genes interact, expression depends on context, and regulatory networks operate non-linearly. This means that the effective dimensionality of the space changes from point to point. In one region, it may behave as though almost two-dimensional - where multiple parameters are rigidly linked. In another, it may act as a ten-dimensional space. In a third, as a space with hundreds of degrees of freedom. This variable dimensionality renders the landscape fractal: its structure changes depending on the scale and local context.
Here, a curious implication arises. Evolution in such a landscape behaves as a process of computation. Not in the sense that nature "calculates" or "solves problems", but in the sense that the very dynamics of the system resemble a computational algorithm. The flow of populations updates its state step by step, reacting to local fitness gradients. Mutations, recombinations, and expression noise act as input data; selection serves as a non-linear function; and the distribution of genetic variants within a population represents the current state. At every step, the system "computes" a new position in the multidimensional space, and this calculation occurs continuously, without any external controlling centre.
Such a perspective allows us to view many phenomena anew. It explains why evolution often arrives at local rather than global solutions; why certain life forms emerge repeatedly while others never do; why complex organs appear gradually rather than by a sudden leap; and why some evolutionary paths remain barred. Most importantly, it demonstrates that evolution does not move along a preordained route. It flows as the structure of the space permits, and this structure itself is the result of millions of interactions.
The model of a flow in a multidimensional fractal landscape does not claim to replace all other metaphors. But it helps us see evolution not as a progression across a picture - from an amoeba to an office worker with a laptop - but as dynamics within a complex system where a multitude of factors are intertwined, and trajectories are determined not only by mutations but by the topology of the space of possibilities itself. This space cannot be drawn, but it can be understood - if one abandons familiar two-dimensional images and permits oneself to think in terms of structures, flows, and constraints.