Transition probabilities.

<p>Transition probabilities for the different events appearing in the master equation (5).</p

Fixation probability profile for , , and different values of .

<p>The dots represent simulation data and the continuous lines correspond to the result of the numerical integration. The dashed line represents the (arbitrarily rescaled) average profile of an all wildtype wave.</p

The substitution rate at the front of an advancing population compared to the neutral substitution rate is described by the function , which is displayed here as a function of the selective advantage of the mutants.

<p>Notice that the axis is logarithmic. Blue, red and yellow symbols correspond to the carrying capacity , and . All curves approach in the neutral case, , in which the substitution and mutation rates are equal. Notice the rather slow increase of substitution rates with increasing selection coefficient, for small values of : even for and the highest carrying capacity, the substitution rates are merely 4 times higher than the neutral baseline, illustrating the ineffectiveness of selection at expanding fronts. For larger selection coefficients, however, the substitution rate grows roughly exponentially with .</p

Fixation probability profile for , and different values of .

<p>The dots represent simulation data and the continuous lines correspond to the result of the numerical integration. As before, the dashed line represents , arbitrarily rescaled.</p

Fixation probability as a function of the position where the mutant is introduced (for , and ).

<p>The wildtype wave profile (arbitrarily rescaled) is shown by the dashed line. The probability profile virtually vanishes in the bulk of the wave, but suddenly rises at a characteristic distance from the front, and then saturates. The shape of the function is characterized by , defined as the distance between the two points at which the curves reach half of their saturation values, by the characteristic width over which the curve rises, and by its saturation height .</p

Substitution rate divided by the deme carrying capacity as a function of for several values of the selection coefficient of the mutant.

<p>It appears quite clearly that the substitution rate increases less than linearly with , as suggested by equation (26).</p