Time to fixation in changing environments

Although many experimental and theoretical studies on natural selection have been carried out in a constant environment, as natural environments typically vary in time, it is important to ask if and how the results of these investigations are affected by a changing environment. Here, we study the properties of the conditional fixation time defined as the time to fixation of a new mutant that is destined to fix in a finite, randomly mating diploid population with intermediate dominance that is evolving in a periodically changing environment. It is known that in a static environment, the conditional mean fixation time of a co-dominant beneficial mutant is equal to that of a deleterious mutant with the same magnitude of selection coefficient. We find that this symmetry is not preserved, even when the environment is changing slowly. More generally, we find that the conditional mean fixation time of an initially beneficial mutant in a slowly changing environment depends weakly on the dominance coefficient and remains close to the corresponding result in the static environment. However, for an initially deleterious mutant under moderate and slowly varying selection, the fixation time differs substantially from that in a constant environment when the mutant is recessive. As fixation times are intimately related to the levels and patterns of genetic diversity, our results suggest that for beneficial sweeps, these quantities are only mildly affected by temporal variation in environment. In contrast, environmental change is likely to impact the patterns due to recessive deleterious sweeps strongly.

Fixation and effective size in a haploid-diploid population with asexual reproduction

The majority of population genetic theory assumes fully haploid or diploid organisms with obligate sexuality, despite complex life cycles with alternating generations being commonly observed. To reveal how natural selection and genetic drift shape the evolution of haploid-diploid populations, we analyze a stochastic genetic model for populations that consist of a mixture of haploid and diploid individuals, allowing for asexual reproduction and niche separation between haploid and diploid stages. Applying a diffusion approximation, we derive the fixation probability and describe its dependence on the reproductive values of haploid and diploid stages, which depend strongly on the extent of asexual reproduction in each phase and on the ecological differences between them.

Mapping of QTLs Detected in a Broccoli Double Diploid Population for Plant Height and Leaf Characteristics

Background The planting density of broccoli can directly affect the yield and overall health of plants. So there is necessary to reveal the regulatory genes of planting density in broccoli by QTL mapping. In this study, the important planting density-dependent factors of broccoli, plant height (PH), maximum outer petiole length (PL) and leaf width (LW), were investigated during 2017 and 2018. The mapping of QTLs for PH, PL and LW were performed, and the interaction between QTLs and the environment was also analyzed by a DH population constructed with 176 genotypes derived from F1 obtained by crossing the broccoli inbred lines 86101 (P1) and 90196 (P2).Results A linkage group including a total of 438 SSR markers were constructed covering a length of 1168.26 cM using QTL IciMapping 4.0 software. Finally, there were mainly four QTLs (phc1, phc2, phc4-1, phc4-2), one QTL (plc6), and two QTLs (lwc1, lwc3) corresponding for PH, PL and LW recurred during the two years. In three environments, inclusive composite interval mapping (ICIM) analysis showed that there was a major QTL for PH at 7.20 cM on chromosome 1 between molecular markers 8C024 and sf4482 with a high explanatory contribution rate of 20.05%. The QTL at the 11.10 cM position of chromosome 6 was located for the PL with a high explanatory contribution rate of 20.02% between the molecular markers sc2170 and sf43960. The QTL at the 147.00 cM position of chromosome 3 was located on LW with a high explanatory contribution rate of 19.97% between molecular markers of Sc52751 and RA2-E12.Conclusions According to the QTL results of planting density in broccoli by a DH population, the possible positions of candidate genes were screened to provide a basis for further locating and cloning genes for plant height, maximum outer petiole and leaf width.

Dominance patterns in dynamic environments

Natural environments are seldom static and therefore it is important to ask how a population adapts in a changing environment. We consider a finite, diploid population with intermediate dominance evolving in a periodically changing environment and study how the fixation probability of a rare mutant depends on its dominance coefficient and the rate of environmental change. We find that in slowly changing environments, the dominance patterns are the same as in the static environment, that is, if a mutant is beneficial (deleterious) when it arrives, it is more (less) likely to fix if it is dominant. But in fast changing environments, these patterns depend on the mutant’s fitness on arrival as well as that in the time-averaged environment. We find that in a rapidly varying environment that is neutral or deleterious on-average, an initially beneficial (deleterious) mutant that arises while selection is decreasing (increasing) has a fixation probability lower (higher) than that for a neutral mutant leading to a reversal in the standard dominance patterns. We also find that recurrent mutations decrease the phase lag between the environment and the allele frequency, irrespective of the level of dominance.

The effect of offspring number on the adaptation speed of a polygenic trait

There is increasing evidence that rapid phenotypic adaptation of quantitative traits is not uncommon in nature. However, the circumstances under which rapid adaptation of polygenic traits occurs are not yet understood. Building on previous concepts of soft selection, i.e. frequency and density dependent selection, I developed and tested the hypothesis that adaptation speed of a polygenic trait depends on the number of offspring per breeding pair in a randomly mating diploid population. Using individual based modelling on a range of offspring per parent (2-200) in populations of various size (100-10000 individuals), I could show that the by far largest proportion of variance (42%) was explained by the offspring number, regardless of genetic trait architecture (10-50 loci, different locus contribution distributions). In addition, it was possible to identify the majority of the responsible loci and account for even more of the observed phenotypic change with a moderate population size. The simulation results suggest that offspring numbers may a crucial factor for the adaptation speed of quantitative loci. Moreover, as large offspring numbers translates to a large phenotypic variance in the offspring of each parental pair, this genetic bet hedging strategy increases the chance to contribute to the next generation in unpredictable environments.