Figure 1.
Histograms of Gene Flow Distances.
Shown are histograms of the distances traveled, measured as simple Euclidean distance from grid cell center to grid cell center, for all chromosomes in the population within a single representative generation (step 200,000). Three typical simulations were conducted under the following selected simulation parameters: (A) movement distance δ = 1.5, outbreeding depression threshold θ = 0.6; (B) movement distance δ = 1.5, outbreeding depression disabled (θ = +∞); (C) movement distance δ = 5, outbreeding depression threshold θ = 0.6. For all graphs, target population size was 128,000, and grid size was 400×400. The movement distance parameter δ roughly defines the mean distance traveled by individuals in each of three phases within a generation (migration, mate selection, and offspring placement), so the net dispersal distance over a generation was usually greater than δ itself.
Figure 2.
Scatterplots of Genetic Distance versus Spatial Distance.
Shown are scatterplots of genetic distance versus Euclidean spatial distance between grid cell centers for 100,000 pairs of randomly selected individuals. Genetic distance was measured by comparing a randomly selected haploid from each chromosome, as described in the text. Simulation parameters were as in Figure 1 for A, B, and C. Plots 2A and 2B showed a tendency toward increasing genetic distance with increasing spatial distance, evidenced by the upward-sloping black trend line, but only the combination of isolation-by-distance and outbreeding depression (A) clearly showed multiple clusters representing distinctive genetic subpopulations. For the simulation run with large dispersal distance (C), genetic information was mixed across the landscape grid too quickly for local pockets of genetically distinct types to emerge, and the entire grid was filled with genetically similar, closely related individuals. Simple, linear regression lines are shown in (A) and (B). The regression line is not shown in (C) because the slope is not well defined by the data.
Figure 3.
Example of a Mismatch Distribution.
Shown are the frequencies of genetic distance classes between 500,000 randomly sampled pairs of haploid genomes. The multimodal distribution evident in this example indicated the existence of more than one distinctive gene pool in the population. The data here were drawn from generation 120,000 in a run where individuals contained n = 2 diploid chromosomes of l = 200 base pairs each, grid size was 400×400, population size was 128,000, maximum occupancy was 1 individual per cell, movement distance δ = 1.5, and mutation rate μ = 0.00005 per site per replication. Offspring viability dropped to 0 beyond a genetic distance of θ = 0.6. The presence of a distinct peak to the right of this threshold indicated the presence of reproductively incompatible populations. The peak to the far right never moved much beyond a genetic difference of 75%, the maximum value expected under the Jukes-Cantor mutation model [33]. The peak to the far left was also unmoving and remained centered near a genetic difference of θ0 = 0.05. This peak included all within-subpopulation comparisons. Peaks between these extremes always moved to the right; some eventually merged with the peak on the right, but most vanished first, indicating extinction of one or both subpopulations compared within the peak.
Figure 4.
Time Series of Pair Similarity Histograms.
Snapshots of frequency histograms of the genetic difference of randomly selected pairs of individuals from three runs, setting (A) low movement distance δ = 1.5 with outbreeding depression θ = 0.6, (B) low movement distance δ = 1.5 with no outbreeding depression, and (C) larger movement distance δ = 5 with θ = 0.6. Plots are shown horizontally for a sequence of four generations (100,000, 125,000, 150,000, and 175,000) within each of the conditions A, B, and C. The number of peaks does not correspond directly to the number of distinct genetic types in the population (see text for discussion of this important point). Video animations in MPEG format of the time course of the pair similarity histograms are available online in Video S1, Video S2, and Video S3. These animations are far more revealing of the fascinating time dynamics of these simulations than the small sequence of frames shown above.
Figure 5.
False-Color Depiction of Genetic Clustering on the World Grid.
Dark blue represents unoccupied cells or cells from which genomes were sampled that were not connected to any cluster. Each other color represents a set of gametes with genome sequences that are identical at more than 40% of their nucleotide sites, created according to the algorithm described in the text. Gametes colored differently have genomes that are identical at 40% or less of their nucleotide sites. Using this threshold in combination with θ = 0.6 helps identify different species with different colors. Note that (1) colors were assigned anew in each plot, so particular colors do not track the same lineage across plots, (2) the clustering algorithm is probabilistic because it is computationally expensive to compare every individual with every other individual for determination of genetic difference, and (3) some clusters are too small to discern in these plots. Plots (A1) through (A12) depict snapshots of the clustering state at 12 different generations during the simulation run with low movement distance of δ = 1.5 and outbreeding depression threshold θ = 0.6, the same simulation shown in the (A) portion of earlier figures. Also following previous figures, plots (B1) and (B2) were generated under a low movement distance of δ = 1.5 without outbreeding depression. This model shows no evidence of clustering at the difference threshold of 0.6 for two representative generations (250,000 and 500,000), nor for any other generations examined (not shown here). The (C) plots, for a simulation run with a larger movement distance of δ = 5 and outbreeding depression enabled at a threshold of θ = 0.6, presents a similar lack of clustering.
Figure 6.
Virtual Genomics and Sexual Reproduction.
Individuals are diploid hermaphrodites, in which haploid genomes consist of n = 2 chromosomes containing l = 200 nucleotide bases A, C, G, and T (only l = 8 bases per chromosome shown in this diagram). Each parent produces a haploid gamete by randomly selecting one of the chromosomes from each diploid pair (blue portions of the parent). When producing a gamete, some random point mutations may also occur with a low probability μ per site. One such mutation, from base C to base A, is depicted in red.
Figure 7.
Offspring Survival Probability S as a Function of Genetic Difference H.
For all the results presented in this paper, viability is not reduced if gametic genomes differ only by θ0 = 0.05 or less (this is an adjustable parameter in the model). If gamete genomes differ by more than 5%, offspring survival probability is reduced linearly to eventually reach 0 for a threshold amount θ of genetic difference (θ = 0.6 in this graph and in all simulations presented here).