A river flows downhill, but some of its water slips into a side channel. Evolution works the same way: selection pushes a beneficial gene toward fixation, while chance can drag it toward extinction. For a long time, scientists watched only the main channel, tracking how a gene's frequency rises. The side channel, where the gene is lost, was dismissed as unimportant. That mistake was a big one: when calculating the spread of frequency, it reached 100%.
The new method keeps an eye on both channels. It splits a gene's history into two paths: fixation and loss. Each path gets its own trajectory, and then they are combined with probabilities taken into account. This makes it possible to predict precisely the mean frequency of a gene and its spread at any moment. For example, with selection strength R=50 and an initial frequency of 0.001, the error in the mean drops from 10.6% to 3.2%, and the error in the spread falls from 12.6% to 4.9%.
Now researchers can see both channels of the river. The method helps analyze data from evolution experiments on viruses, bacteria, and artificial selection. It estimates selection strength more accurately and predicts whether a beneficial gene will fix in a small population. The river of evolution has become clearer.
Even under strong selection, when the deterministic force is large, the variance of the allele frequency can be almost entirely determined by random fluctuations for a long time. For example, at R=50 and initial frequency y=0.001, the deterministic contribution to the variance is essentially zero up to time τ≈5, whereas the fluctuation contribution accurately describes the actual variance.