We efficiently simulate range expansions of populations, by using our set of computer programs, on a laterally connected lattice in 1D, 2D (on a strip, and on a disk), and 3D (in a cylinder, and in a sphere). We employ a model with finite genome regions, each containing infinite sites, for a population of diploid individuals. Using the programs, we generate tens of simulation replicates to analyze the temporal evolution of the mean fitness of individuals on the expansion front. We explore the model over different conditions, compare normalization methods for fitness, and explore the case of radial (sphere) and axial (cylinder) expansions in 3D, which might apply in the analysis of the behavior of viruses/bacteria inside a host, in the prediction of expansions of marine species in ocean environments, and even in scenarios of interstellar space colonization. In 3D expansions, we find complex spatial fluctuations in deme-average fitness values, different from those in radial 2D expansions. In axial 3D (cylinder) expansions, we determine that the highest-valued deme-average fitness lies along the axis of the expansion. We also find the fluctuation patterns of fitness in 3D cylinder expansions, similar to those previously seen in radial expansions in 2D. In radial 2D (disk) expansions, we find that the fitness of a population undergoing multiple mutations shows a smooth combination of binary segregation pictures against each of those mutations. We confirm the accumulation of deleterious mutations -- a phenomenon known as expansion load -- in all scenarios above.Kotsar Yurii, Hikaru Matsuoka, Gen TamiyabioRxiv 2023.12.29.573608; doi: https://doi.org/10.1101/2023.12.29.573608
The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 302 methods, is shown in Figure 7. Similar to 2D strip, we have generated heatmaps that show the 303 temporal evolution of (normalised) average fitness at every deme in the habitat, at every 304 generation. This heatmap is available as an animation (see "Supporting information"). A snapshot 305 of the heatmap of deme-average fitness is given in Figure 7 (right). 306 307
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3.4 3D cylinder 308 The main goal of this study was to build a novel simulation program that can produce data for 309 range expansion in three dimensions, and analyse the evolution of mean front fitness consistently 310 with the results from 1D and 2D. In particular, we developed two programs for 3D: expansion in 311 a cylindrical habitat, and expansion in a sphere. Here, first, we describe the trial we carried out 312 using the former program. 313 In this trial, we contained a population inside of a cylinder, that is constrained by a circle 314 equation at the lateral surface and a barrier at both ends of the cylinder. This trial was roughly 315 one-directional, meaning that the individuals started in the lowermost demes of the z-axis, and we 316 measured the front as the (moving) populated highest demes in the direction of the z -axis. We ran 317 13 simulation replicates, each with a burn-in phase and an active phase of 1000 generations both; 318
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Figure 8 (left) shows the 319 evolution of mean front fitness in time, averaged over 13 simulation replicates. As before, we also 320 display the non-normalised mean front fitness for reference and the results of applying different 321 normalisation methods, in Figure 8 (left). We have also generated three-dimensional heatmaps of 322 deme-average fitness, a snapshot of which can be seen in Figure 8 (right). The animations of these 323 heatmaps are available in "Supporting information". A typical slice image of the heatmap at height 324 = 22 and generation 200 is presented in Figure 10 (left). 325 326
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3.5 3D sphere 327 Finally, we developed a simulation program for an expansion bounded by a 3D sphere of a 328 constant size. At the start, the founder individuals were put in the centre of the habitat. We have 329 performed one trial, where we likewise found the evolution of mean front fitness front in time, 330 averaged over 20 simulation replicates. This result, with different normalisation methods, is 331 shown in Figure 9. Similar to other trials, we have generated heatmaps for deme-average fitness 332 at each generation. Sample animations of these heatmaps are available in "Supporting 333 information". A snapshot of the heatmap of deme-average fitness is given in Figure 9 (right). A 334 typical slice image of the heatmap at height = 18 and generation 642 is presented in Figure 10 335 (right). bioRxiv preprint doi: ; this version posted January 13, 2024.
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