Fig 1.
Illustration of all six different linkage architectures possible along a single chromosome.
The Ak loci are given in blue and Bk in black. Red arrows show the incompatible interactions. The name of each linkage architecture is derived from the relative arrangement of the two incompatibilities and the order of the A and B loci.
Fig 2.
Fitness landscape of the 16 genotypes in the two-locus model, highlighting the effect of dominance of the incompatibility on the fitness of F1 hybrids.
For simplicity, we illustrate the case of α = β = s, where s is the selective advantage of a derived allele in the ancestral background. Note that there are only 10 genotypes represented here, as we do not distinguish the parental origins of each haplotype.
Table 1.
Classification of possible haplotypes for the “Adjacent ABAB” linkage architecture.
Fig 3.
Recombination slows down the resolution of a codominant DMI whereas it speeds DMI resolution up for a recessive one.
We represent the probability of fixation of the Ab haplotype (panels (a,b)) for different recombination rates and different dominance schemes (codominant (a,c), recessive (b,d)). In panels (c,d), we illustrate the time to resolve the genetic conflict (i.e., either allele A or B is lost). Each value is obtained from 1000 independent simulations. Note the much larger y-axis scale (x30) in panel (d). Parameters used: α = β = 0.001, ϵ = −0.2, N = 5000.
Fig 4.
Hybrid speciation probability for codominant (panels (a,c,e,g)) and recessive (panels (b,d,f,h)) DMIs.
The colored dots correspond to the probability of hybrid speciation for two DMIs situated on different chromosomes (r23 = 0.5). The recombination rate between the interacting loci is indicated below each panel (r12 = r34 = r): panels (a,b), r = 0.5; panels (c,d), r = 0.05; panels (e,f), r = 0.005; panels (g,h), r = 0.0005. The black dots correspond to the predicted hybrid speciation probability based on the resolution of a single DMI. The fast resolution of the codominant DMIs leads to a correlation between their fate, which makes hybrid speciation less likely than the independent expectation predicts. Parameters used are αi = βi = 0.001, N = 5000, ϵ = −0.2. Each dot is obtained from 1000 replicates.
Fig 5.
Hybrid speciation probability is a nonlinear function of recombination.
We consider that all four loci have the same selective advantage (αk = βj = 0.001) and are equidistant along a single chromosome. The hybrid speciation probability is plotted for different population sizes: yellow corresponds to N = 50, orange to N = 500, red to N = 5000 and purple to N = 50000. Epistasis (ϵ = −0.2) is here codominant but we obtain qualitatively similar results for recessive incompatibilities, see S10 Fig. The contribution of both parental populations is symmetric (ip = 0.5). Each panel corresponds to a different linkage architecture: (a) “Adjacent ABAB”; (b) “Crossed AABB”; (c) “Nested ABAB”; (d) “Adjacent ABBA”; (e) “Crossed ABBA”; (f) “Nested AABB”.
Fig 6.
Haplotypes produced in the F2 breakdown, assuming a single recombination event, explain how different linkage architectures leads to different outcomes for the same loci.
By identifying the relatively “epistasis-free” haplotype formed, one can infer whether hybrid speciation may be a likely outcome. In blue, we highlight these “epistasis-free” haplotypes that are important for hybrid speciation and in yellow those that are important for fixation of the parental haplotype from population 1.
Fig 7.
Probability of hybrid speciation for both recessive and codominant DMIs as a function of the recombination rate between the different loci (they are all equidistant) and the initial contribution of both parental species.
Different linkage architectures generate an unexpected pattern: for the “Adjacent ABAB” architecture, we observe a Goldilocks zone for hybrid speciation; for the “Adjacent ABBA”, the probability of hybrid speciation is no longer symmetric along the ip = 0.5 axis (white dashed line). Each panel corresponds to a given linkage architecture and a dominance scheme: (a) “Adjacent ABAB”, codominant DMIs; (b) “Adjacent ABAB”, recessive DMIs; (c) “Adjacent ABBA”, codominant DMIs; (d) “Adjacent ABBA” recessive DMIs; (e) “Nested ABAB”, codominant DMIs; (f) “Nested ABAB” recessive DMIs.