Wright–Fisher model

A translator learns a language not from a dictionary but from living conversations: they hear fragments of phrases, street noise, different accents. Out of that chaos they assemble rules that are written in no book.

Two runners start a race on a course with changing incline. One starts earlier, the other later, and the judge measures their speeds without knowing about the staggered starts. So it is with virus variants: data arrive with delays, and if those delays are unequal, estimates of competitive advantage can be badly wrong.

Chemotherapy hits cancer like a powerful spray on a dirty plate: the stream washes away almost everything, but crumbs remain in the cracks. Old models said that if you make the pressure strong enough, the plate becomes perfectly clean. New work shows this isn't so.

Rare species in a large community are like thin branches on a tree: a random gust can easily snap them. Even if conditions are stable, a small population simply lacks enough individuals to survive a bad season. In a new study, scientists added this factor to an ecosystem model and watched the community clean itself out.

A superfluid gas is like a crowd of people marching in step: each atom knows where to go and doesn't fall out of the common rhythm. But this crowd has three 'valleys'—three different directions it can take. In a new experiment, physicists made one valley slightly more 'favorable' than the others and watched how the crowd darted between them.

A mosquito swarm resembles a living cloud — hundreds of bodies circle together, but no one lines up or mimics a neighbor's movements like starlings or fish. For a long time, it was unclear what held such unity together. The authors of a new study suggested that the insects communicate by sound.

An optical trap holds an atom almost motionless, like a ball on a soft spring. But as soon as acceleration appears, say gravity, the equilibrium shifts. The atom moves within the standing light wave, and this changes the rate at which it exchanges energy with the field. The frequency of this exchange becomes a direct indicator of acceleration.

It is commonly believed that a black hole is a merciless cosmic vacuum cleaner, sucking in everything indiscriminately. But new research flips the picture: right at the horizon, curvature transforms from a trap into a trampoline.

Imagine a cookbook that gets rewritten from generation to generation. One day, the borscht recipe receives a secret ingredient from a pastry chef, and from that moment, the taste remembers not only ancestors but also a neighbor. In the Standard Model of evolution, genes behave the same way.

For a long time, biologists argued: if a herd of animals stably maintains a mix of aggressive and peaceful individuals, does each one alternately change behavior, or do some always fight while others always yield? In classical equations, these options are indistinguishable.

In the web of life, predators and prey exchange carbon and water, and each act of eating slightly increases the universe's disorder. But the intrusion of disease turns this system into a giant seesaw. When a mid-level predator gets sick, its hunting abilities decline, and it becomes easy prey.

Ecosystems are not chaos but a complex dance where every species plays its part. Scientists modeled such a dance: two prey compete for carbon and water (the building blocks of cells), while a predator eats both. Sixteen scenarios emerged — from predator extinction to a steady rhythm for all three species.

A family tree becomes a tangle if you account for adopted children and remarriages. Evolution often resembles such a tangle: although the Standard Model, the traditional view of divergent evolution where species branch like a tree, paints a neat tree of species, in reality genes travel not only by inheritance but also directly between unrelated organisms — a process…

Evolution flows like water. In a wide river, changes are smooth and slow, while a mountain stream churns with every stone. Population size and mutation rate set the channel: broad and calm, or narrow and rapid-filled.

Molecules float in a pot of broth. Some copy themselves, others help their neighbors, and still others just get in the way. This isn't soup: it's a model of early life: a replicator system. Usually, we assume the rules of the game are fixed once and for all: whoever reproduces fastest wins. But the authors of this study proposed something different — the rules can change too, just very slowly.

Two dead suns circle in an eternal dance. Their orbit is a perfect metronome, keeping time with the accuracy of atomic clocks. But even dead stars can tremble.

A candle flame in a draft dances: now it flares up, now it almost goes out. Quasars behave much the same way — supermassive black holes in the centers of distant galaxies, surrounded by a scorching disk of infalling matter. Only they flicker not over seconds, but over months and years.

Engineers improving neural networks act like breeders: they try a variant, check the result, and keep the best. They collected 935 such trials from 161 papers and measured how often a code tweak turns out beneficial, harmful, or neutral. The picture is familiar to any biologist: 68% of changes degrade performance, 19% do nothing, and only 13% yield a gain.

The atmosphere is a chaotic system, and a detailed global forecast requires monstrous computing power. StretchCast sidesteps this by working like the human eye: it creates 'sharp vision' over a selected region with an ultra-fine grid, while seeing the rest of the world blurry, but sharp enough to capture global connections.

An epidemic is like a fire in a dry forest: a spark flares up, the flames leap from tree to tree, and within a week the whole area is burning. A hundred years ago, scientists devised a simple mathematical model for such a fire: they divided people into those who had not yet fallen ill, those who were ill, and those who had already recovered.

A hawk soars over a field, its wings tracing an intricate dance. Each flap, each tilt is not random but a combination of simple motions that can be broken down into components. Collective behavior in the air may seem intuitive, but behind it lies strict mechanics. Scientists recorded the hawks' movements using cameras that track the position of every point on the wing and tail.

A brain tumor is like a traveler trudging through a dense forest: trees and bushes are the different types of brain tissue, some easier to traverse than others. Glioma cells don't move in a straight line; they constantly loop around, bumping into obstacles and going around them.

Light trapped in a tiny cavity is like a pendulum that gets pushed harder and harder. At first, it swings smoothly and predictably, like an ordinary clock. But if you push it hard enough, the motion becomes strange: the pendulum seems to be in two extreme positions at once.

A fisherman in Queensland notices that in some years snapper are harder to catch, even though the nets and boat are the same. The reason hides not in the catch itself but in the water temperature several months earlier, when the fry were just hatching. A warm current arrived not for the whole year but only for a few weeks, and that short episode decided the fate of an entire fish generation.