Sympatric speciation under incompatibility selection

Abstract

The existing theory of sympatric speciation assumes that a local population splits into two species under one-dimensional disruptive selection, which favors both of the opposite extreme values of a quantitative trait. Here we model sympatric speciation under selection that favors high values of either of the two independently inherited traits, each required to efficiently consume one of the two available resources, but acts, because of a tradeoff, against those possessing high values of both traits. Such two-dimensional incompatibility selection is similar to that involved in allopatric speciation. Using a hypergeometric phenotypic model, we show that incompatibility selection readily leads to sympatric speciation. In contrast to disruptive selection, two distinct modes of sympatric speciation exist under incompatibility selection: under strong tradeoffs both of the new species are specialists, each consuming its own resource, but under moderate tradeoffs speciation may be asymmetric and involve the origin of a specialist and a generalist species. Also, incompatibility selection may lead to irreversible specialization: under strong tradeoffs, the population speciates if it consists mostly of unspecialized individuals, but remains undivided if most of the individuals are specialized to consume one of the resources. Incompatibility selection appears to be more realistic than disruptive selection, implying that incompatibility between individually adaptive alleles or trait states drives both allopatric and sympatric speciation.

Fig. 1.

Structure of incompatibility selection (Eq. 2). Size and agility are each controlled by eight loci, A = 2.5, B = 1.9, σ = 1.5, and D = 1.5. (A) Distribution of phenotypes before selection. (B) The expected amount of resources consumed, exp(Ax)/C_I + exp(Ay)/C_II. (C) Basic metabolism requirement, Bexp(Dxy). (D) The expected amount of consumed resources left for reproduction, R_inc(x). (E) Fitness, w_inc(x, y). (F) Distribution of phenotypes after selection.

Fig. 2.

Possible outcomes under incompatibility selection with B = 1.9 and σ = 1.5. Speciation: red, the two new species have phenotypes x = 1, y = 0 and x = 0, y = 1, i.e., they are specialists each adapted to consume one of the two resources; yellow, one of the two new species is generalist with phenotype x = 1, y = 1, and the other is specialist with phenotype x = 1, y = 0 or x = 0, y = 1. Nonspeciation: gray, all of the individuals eventually become specialists, either with x = 1, y = 0 or with x = 0, y = 1 phenotype; blue, all individuals acquire the highest value, 1, of either x or y, and remain polymorphic in the other trait; green, all individuals become generalists with x = 1 and y = 1. (A and B) Size and agility are controlled by eight loci each, mating depends on one trait (color) controlled by four loci. (C and D) Size and agility are controlled by eight loci each, mating depends on two traits (color and preference) each controlled by four loci. (E and F) Size and agility are controlled by four loci each, mating depends on two traits (color and preference) each controlled by four loci. The initial population was close to x = 0, y = 0 (A, C, and E) or x = 1, y = 0 (B, D, and F).

Fig. 3.

Typical courses of sympatric speciation under incompatibility selection. (A–C) Specialist–specialist speciation: size and agility are controlled by eight loci each, mating depends on one trait controlled by four loci, D = 1.25, B = 1.9, and σ = 1.5, and initially most individuals have phenotypes x = 0, y = 0. Selection is phased in, with A = 0 initially, and A increasing by 0.014 each generation, until it reaches its stationary value A = 2.8, in generation 200. This procedure demonstrates that even moderate genetic load (<0.75) may be sufficient for speciation. (D–F) Generalist–specialist speciation: size and agility are controlled by eight loci each, mating depends on one trait controlled by four loci, A = 4.5, D = 0.75, B = 1.9, and σ = 1.5, and initially most individuals have phenotypes x = 1, y = 0. (G–I) Specialist–specialist speciation: size and agility are controlled by four loci each, mating depends on two traits controlled by four loci each, A = 4, D = 2, B = 1.9 and σ = 1.5, and initially most individuals have phenotypes x = 0, y = 0. Dynamics of the distributions of individual traits (A, D, and G), the final state of the process (B, E, and H), and dynamics of the average values of the traits, their variances, their pairwise correlations, and parameters of selection (C, F, and I) are shown.

Fig. 3.

Typical courses of sympatric speciation under incompatibility selection. (A–C) Specialist–specialist speciation: size and agility are controlled by eight loci each, mating depends on one trait controlled by four loci, D = 1.25, B = 1.9, and σ = 1.5, and initially most individuals have phenotypes x = 0, y = 0. Selection is phased in, with A = 0 initially, and A increasing by 0.014 each generation, until it reaches its stationary value A = 2.8, in generation 200. This procedure demonstrates that even moderate genetic load (<0.75) may be sufficient for speciation. (D–F) Generalist–specialist speciation: size and agility are controlled by eight loci each, mating depends on one trait controlled by four loci, A = 4.5, D = 0.75, B = 1.9, and σ = 1.5, and initially most individuals have phenotypes x = 1, y = 0. (G–I) Specialist–specialist speciation: size and agility are controlled by four loci each, mating depends on two traits controlled by four loci each, A = 4, D = 2, B = 1.9 and σ = 1.5, and initially most individuals have phenotypes x = 0, y = 0. Dynamics of the distributions of individual traits (A, D, and G), the final state of the process (B, E, and H), and dynamics of the average values of the traits, their variances, their pairwise correlations, and parameters of selection (C, F, and I) are shown.