Fig 1.
Fitness loss per time and space under soft selection.
Trajectories of mean fitness loss for additive and recessive mutation models over time (panels A and B) and space (panels C and D) at the expanding front under soft selection show more overall fitness loss for range shifts. Vertical lines indicate when the population reaches the end of the 1x300 deme landscape and expansion is complete. Shaded regions show two standard errors calculated over ten replicate simulations. The fastest shift (v = 0.2) expands at a speed closest to the full expansion, and is compared to two slower speed shifts (v = 0.05, 0.02). The full timescale for the two slower shifts reaching the end of the landscape is shown in Supplemental S12 Fig. Analytic solutions for fitness loss over time are shown as dotted lines in panels A and B, where evolution of mean fitness is given by Eq (1) with F = K m /2, where K is the (diploid) carrying capacity of a deme. The accumulation of fixed deleterious and fixed beneficial mutations for these cases can be seen in Supplemental S1 Fig.
Fig 2.
Decomposing fitness loss per time and space.
Fitness loss measured per unit time (generations, A) and per unit distance travelled (demes, B). The non-monotonic pattern of fitness loss per distance in B is explained by the combination of mutations entering the population (C) and fixation probability (D) for a given speed of a range shift. Dashed lines indicate beneficial alleles while solid red lines indicate deleterious alleles. The product of fixation probability with number of available mutations produces the fitness change per deme shown in B in solid black. Simulations across speeds are shown in blue, where rates of fitness loss for simulations are calculated within the first 2,000 generations, before beneficial mutations begin to saturate and after generation 100 to ignore initial effects of expansion.
Fig 3.
Fitness loss per time and space under hard selection.
Trajectories of mean fitness loss for additive and recessive mutation models over time (panels A and B) and space (panels C and D) at the expanding front under hard selection during and after range expansions and range shifts. The vertical line in the top left panel indicates when the expansion has reached the end of the 1x300 deme landscape and expansion is complete. This is the only case that finished crossing the landscape during the 5,000 generation time course of simulation, with other cases going extinct or taking more time to spread. Shaded regions show two standard errors calculated over ten replicate simulations.
Fig 4.
Fitness change over varying mutational assumptions.
The assumption of fixed selection coefficients, s, and fixed dominance parameters, h, are relaxed to compare qualitative outcomes of fitness loss during expansion and fitness recovery after expansion. Shaded regions show two standard errors calculated over ten replicate simulations and the vertical line indicates when the landscape has been crossed and expansion is complete. Our original mutational parameters of fixed s and h = 0.5 (fully additive) or h = 0.0 (fully recessive) are shown in black and gray solid lines, respectively. Colored solid, dashed, and dotted lines show comparison cases of h = 0.3 with either constant or exponentially distributed s values, or an h-s trade-off along with an exponential DFE across scenarios of range expansion (A) and our fastest (B) and a slower (C) range shift scenario.