Field record of E(K) and V(K) across diverse taxa.

The paradox of genetic drift when the population size (N) changes.

(a) In the laboratory cell culture, nearly all cells proliferate when N is very small (interpreted in the next panel). (b) The simulation of Haldane model shows little genetic drift in the exponential phase. As in (a), drift may increase due to the heightened competition as the population grows. (c) Simulation by the WF model shows a pattern of drift opposite of the Haldane model. (d) The patterns of drift at the low and high N are analyzed in the framework of the logistic growth model. (e-f) Measurements of genetic drift in laboratory yeast populations at low and high density as defined in (d). The progeny number of each cell, K, is counted over 4 or 5 intervals as shown by the dots, the sizes of which reflect the cell number. E(K) and V(K) are presented as well. In panel (f), the change of offspring number overtime, denoted as V(ΔK), is shown above the braces. (g) The variance of offspring number V(K) increases, observed in (e) and (f), as population size increases.

The meaning of population size (N) changes in ecology vs. in population genetics.

(a) In ecology, changing N would generally mean a population approaching or departing the carrying capacity. (b) In population genetics, a population of size N is assumed to be at the carrying capacity, Ck. Thus, changes in N would mean an evolving Ck, likely the consequence of environmental changes. The arrows indicate the disparity in time scale between the two scenarios.

Genetic drift as a function of population size in the DDH model.

For all panels, the carrying capacity is Ck = 10,000 and the intrinsic growth rate is r = 2. (a) When N increases, E(K) decreases as modeled in Eq. (5). The z value of Eq. (5) (0.1, 1.5 and 3) determines the strength of N regulation, indicated by the slope of E(K) near Ck = 10,000. (b) Depending on the strength of N regulation near Ck, genetic drift can indeed decrease, increase or stay nearly constant as the population size increases. Thus, the conventional view of Ne being positively dependent on N is true only when the regulation of N is weak (the green line). At an intermediate strength (the red line), Ne is nearly independent of N. When the regulation becomes even stronger at z = 3, Ne becomes negatively dependent on N. (c-e) V(K)/E(K) of Eq. (6)) is shown as a function of N. The results of panel (b) are based on a constant V(K)/E(K) shown in panel (c). Interestingly, the results of panel (b) would not be perceptibly changed when V(K)/E(K) varies, as shown in panel (d) and (e).

Estimation of Vm/Vf in chimpanzee and bonobo.

Fixation probability of a new advantageous mutation in the Haldane model.

The fixation probabilities of a new advantageous mutation with the selective advantage of s = 0.1 are calculated based on approximate solution from Eq. (9) (i.e., 2s/V(K)) as well as numerical solution from Eq. (10). The numerical solution from Eq. (10) has been confirmed accurate by simulations (Supplementary Fig. 4). (a-b) When N < 50, the approximate fixation probability (the gray line) is lower than the simulated values (the color lines) due to population extinction. (c-d) By the Haldane model, the expected fixation probability of Eq. (9) is accurate when N reaches 100, as in most natural populations.