It has been shown theoretically that sympatric speciation can occur if intraspecific competition is strong enough to induce disruptive selection. However, the plausibility of the involved processes is under debate, and many questions on the conditions for speciation remain unresolved. For instance, is strong disruptive selection sufficient for speciation? Which roles do genetic architecture and initial composition of the population play? How strong must assortative mating be before a population can split in two? These are some of the issues we address here. We investigate a diploid multilocus model of a quantitative trait that is under frequency-dependent selection caused by a balance of intraspecific competition and frequency-independent stabilizing selection. This trait also acts as mating character for assortment. It has been established previously that speciation can occur only if competition is strong enough to induce disruptive selection. We find that speciation becomes more difficult for very strong competition, because then extremely strong assortment is required. Thus, speciation is most likely for intermediate strengths of competition, where it requires strong, but not extremely strong, assortment. For this range of parameters, however, it is not obvious how assortment can evolve from low to high levels, because with moderately strong assortment less genetic variation is maintained than under weak or strong assortment-sometimes none at all. In addition to the strength of frequency-dependent competition and assortative mating, the roles of the number of loci, the distribution of allelic effects, the initial conditions, costs to being choosy, the strength of stabilizing selection, and the particular choice of the fitness function are explored. A multitude of possible evolutionary outcomes is observed, including loss of all genetic variation, splitting in two to five species, as well as very short and extremely long stable limit cycles. On the methodological side, we propose quantitative measures for deciding whether a given distribution reflects two (or more) reproductively isolated clusters.
The evolution of genotypic mutation rates has been investigated in numerous theoretical and experimental studies. Mutations, however, occur not only when copying DNA, but also when building the phenotype, especially when translating and transcribing DNA to RNA and protein. Here we study the effect of such phenotypic mutations. We find a maximum phenotypic mutation rate, u max , that is compatible with maintaining a certain function of the organism. This may be called a phenotypic error threshold. In particular, we find a minimum phenotypic mutation rate, u min , with the property that there is (nearly) no selection pressure to reduce the rate of phenotypic mutations below this value. If there is a cost for lowering the phenotypic mutation rate, then u min is close to the optimum phenotypic mutation rate that maximizes the fitness of the organism. In our model, there is selective pressure to decrease the rate of genotypic mutations to zero, but to decrease the rate of phenotypic mutations only to a positive value. Despite its simplicity, our model can explain part of the huge difference between genotypic and phenotypic mutation rates that is observed in nature. The relevant data are summarized.
Molecular dynamics simulations were used to compute the frequency-dependent dielectric susceptibility of aqueous solutions of alanine and alanine dipeptide. We studied four alanine solutions, ranging in concentration from 0.13-0.55 mol/liter, and two solutions of alanine dipeptide (0.13 and 0.27 mol/liter). In accord with experiment we find a strong dielectric increment for both solutes, whose molecular origin is shown to be the zwitterionic nature of the solutes. The dynamic properties were analyzed based on a dielectric component analysis into solute, a first hydration shell, and all remaining (bulk) waters. The results of this three component decomposition were interpreted directly, as well as by uniting the solute and hydration shell component to a "suprasolute" component. In both approaches three contributions to the frequency-dependent dielectric properties can be discerned. The quantitatively largest and fastest component arises from bulk water [i.e., water not influenced by the solute(s)]. The interaction between waters surrounding the solute(s) (the hydration shell) and bulk water molecules leads to a relaxation process occurring on an intermediate time scale. The slowest relaxation process originates from the solute(s) and the interaction of the solute(s) with the first hydration shell and bulk water. The primary importance of the hydration shell is the exchange of shell and bulk waters; the self-contribution from bound water molecules is comparatively small. While in the alanine solutions the solute-water cross-terms are more important than the solute self-term, the solute contribution is larger in the dipeptide solutions. In the latter systems a much clearer separation of time scales between water and alanine dipeptide related properties is observed. The similarities and differences of the dielectric properties of the amino acid/peptide solutions studied in this work and of solutions of mono- and disaccharides and of the protein ubiquitin are discussed.
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