Stability of Equilibrium Prices in a Dynamic Duopoly Bertrand Game with Asymmetric Information and Cluster Spillovers

Bounded rationality, asymmetric information and spillover effects are widespread in the economic market, and had been studied extensively in oligopoly games, but few references discussed incomplete information in a duopoly market with rationality expectations. Considering the positive externalities brought by the spillover effect between enterprises in a cluster, a duopoly Bertrand game with bounded rationality and asymmetric information is proposed in this paper. In our model, a firm with private information, high or low marginal cost, is introduced. Interestingly, our theoretical analysis reveals that: (1) In a dynamic duopoly Bertrand game with perfect rationality and asymmetric information, the equilibrium price is positively correlated with product substitution rate and the probability of a high marginal cost, while it is negatively correlated with the cluster spillover. (2) In a dynamic duopoly Bertrand game with asymmetric information and adaptive expectation adopted by both firms, the Nash equilibrium prices are always asymptotically stable. (3) In a dynamic duopoly Bertrand game with heterogenous expectation and asymmetric information, where two firms use adaptive expectation and boundedly rational expectation respectively, the Nash equilibrium prices are locally stable under certain conditions. Furthermore, results indicate that, high product substitution rate or large probability of high marginal cost for firm 2 with private information may make the market price unstable, bifurcating or even falling into chaos, while high technology spillover is conducive to stabilize the market by contrast. It is also shown that the chaos can be controlled by a hybrid control strategy with the state variables feedback and parameter variation. Our research has an important theoretical and practical significance to the price competition in oligopoly markets.

Dynamic Patterns of Sex Chromosome Evolution in Neognath Birds: Many Independent Barriers to Recombination at the ATP5F1A Locus

Avian sex chromosomes evolved after the divergence birds and crocodilians from their common ancestor, so they are much younger than the better-studied chromosomes of mammals. It has long been recognized that there may have been several stages to the evolution of avian sex chromosomes. For example, the CHD1 undergoes recombination in paleognaths but not neognaths. Genome assemblies have suggested there may be variation in the timing of barriers to recombination among Neognathae, but there remains little understanding of the extent of this variability. Here, we look at partial sequences of ATP5F1A, which is on the avian Z and W chromosomes. It is known that recombination of this gene has independently ceased in Galliformes, Anseriformes, and at least five neoavian orders, but whether there are other independent cessations of recombination among Neoaves is not understood. We used a combination of data extracted from published chromosomal-level genomes with data collected using PCR and cloning to identify Z and W copies in 22 orders. Our results suggest there may be at least 19 independent cessations of recombination within Neognathae, and 3 clades that may still be undergoing recombination (or have only recently ceased recombination). Analyses of ATP5F1A protein sequences revealed an increased amino acid substitution rate for W chromosome gametologs, suggesting relaxed purifying selection on the W chromosome. Supporting this hypothesis, we found that the increased substitution rate was particularly pronounced for buried residues, which are expected to be more strongly constrained by purifying selection. This highlights the dynamic nature of avian sex chromosomes, and that this level of variation among clades means they should be a good system to understand sex chromosome evolution.

KaKs_Calculator 3.0: calculating selective pressure on coding and non-coding sequences

KaKs_Calculator 3.0 is an updated toolkit that is capable for calculating selective pressure on both coding and non-coding sequences. Similar to the nonsynonymous/synonymous substitution rate ratio for coding sequences, selection on non-coding sequences can be quantified as non-coding nucleotide substitution rate normalized by synonymous substitution rate of adjacent coding sequences. As testified on empirical data, it shows effectiveness to detect the strength and mode of selection operated on molecular sequences, accordingly demonstrating its great potential to achieve genome-wide scan of natural selection on diverse sequences and identification of potentially functional elements at whole genome scale. The package of KaKs_Calculator 3.0 is freely available for academic use only at https://ngdc.cncb.ac.cn/biocode/tools/BT000001.

Coupled Effects of Reduced Chemical Fertilization and Biochar Supplementation on Availability and Transformations of Nitrogen and Phosphorus in Vegetable Farmland Soil: An In Situ Study in Southern China

Reduced fertilization technology is an eco-friendly strategy to minimize nitrogen (N) and phosphorus (P) surpluses and losses in vegetable production. However, little is known about the performance of chemical fertilizer reduction when supplemented with palm silk biochar (PSB) in subtropical acid soils. A short-term (60 d) field investigation under conditions of in situ incubation was conducted in vegetable farmland in southern China. The treatments included no fertilization (Control), 100% conventional fertilization (CF100), 90% conventional fertilization plus 10% PSB-based fertilization (CF90B10), 85% conventional fertilization plus 15% PSB-based fertilization (CF85B15), and 80% conventional fertilization plus 20% PSB-based fertilization (CF80B20). The CF90B10, CF85B15, and CF80B20 treatments had the same inputs of total N and P as the CF100 treatment. Reduced chemical fertilization generally decreased the soil NH4+-N regardless of the PSB substitution rate (10%, 15%, or 20%), incubation condition (top-covered or top-open: preventing or allowing the leaching process, respectively), and sampling time (1 day or 60 days). Conversely, compared with the CF100 treatment, both the CF85B15 and CF80B20 treatments did not lead to a significant decrease in the NO3−-N concentration in soil under top-open incubation conditions, but significantly (p < 0.05) increased soil NO3−-N under top-covered incubation conditions. The CF80B20 treatment significantly (p < 0.05) decreased soil Olsen-P in comparison with the CF100 treatment, regardless of the incubation condition and sampling time. After applying chemical fertilizer in combination with PSB, soil net ammonification and N mineralization tended to be reduced considerably, with substantial reductions of 39–76% and 24–45%, respectively; reversely, soil net nitrification was stimulated by an increased PSB substitution rate. As the rate of chemical fertilization decreased, the trends in NH4+-N and NO3−-N losses from the soil were similar to the trends observed in soil net ammonification and net nitrification, respectively. Additionally, there were no significant differences in the soil net P mineralization and Olsen-P loss between chemical fertilization alone and in combination with PSB application. Generally, the partial substitution of chemical fertilizer with PSB at a low application rate may not substantially reduce plant-available NO3−-N and Olsen-P. It can also contribute to the sustainable availability of N and P in vegetable farmland soil via a variety of transformation processes, such as mineralization, immobilization, and loss.

Effect of Sulphur-Containing Tailings Content and Curing Temperature on the Properties of M32.5 Cement Mortar

The effect of the dosage of sulphur-containing tailings (STs) and curing temperature on the properties of M32.5 cement mortar was studied in this work. An experimental study was conducted to evaluate the effects of STs with different substitution ratios (0, 10%, 20%, 30%, 40%) on the compressive strength experiment, fluidity, expansion ratio, and pore structure of M32.5 cement mortar. The results showed that the addition of STs reduced the fluidity of mortar, and the fluidity decreased with the increase of the STs dosage. The compressive strength of mortars increased at a lower substitution rate (0~20%) but decreased at a higher substitution rate (>20%). Ettringite peaks and new sulfate peaks were found by X-ray diffraction (XRD) analysis. Scanning electron microscope (SEM) observation of the microstructure showed that a large number of hydrated products, such as ettringite, formed and filled in the interstitial space, which was conducive to the development of strength. The optimal STs replacement ratio of river sand was 10%. Then, the performance of mortar at curing temperatures of 23 ± 1, 40, 60, and 80 °C was further investigated under the optimal STs replacement ratio. Under high-temperature curing conditions, the early strength of M32.5 cement mortar with STs increased greatly, but the late strength decreased gradually with the increase in curing temperature. The early strength development of the mortar mainly depended on the high speed of hydration reaction, and the late strength variation was mainly affected by hydration products and the pore size distribution. After comprehensive consideration, the optimal curing temperature of M32.5 cement mortar with STs was 40 °C.

Genetic Characterizations and Molecular Evolution of the Measles Virus Genotype B3’s Hemagglutinin (H) Gene in the Elimination Era

Measles virus (MeV) genotype B3 is one globally significant circulating genotype. Here, we present a systematic description of long-term evolutionary characterizations of the MeV genotype B3’s hemagglutinin (H) gene in the elimination era. Our results show that the B3 H gene can be divided into two main sub-genotypes, and the highest intra-genotypic diversity was observed in 2004. MeV genotype B3’s H gene diverged in 1976; its overall nucleotide substitution rate is estimated to be 5.697 × 10−4 substitutions/site/year, and is slowing down. The amino acid substitution rate of genotype B3’s H gene is also decreasing, and the mean effective population size has been in a downward trend since 2000. Selection pressure analysis only recognized a few sites under positive selection, and the number of positive selection sites is getting smaller. All of these observations may reveal that genotype B3’s H gene is not under strong selection pressure, and is becoming increasingly conservative. MeV H-gene or whole-genome sequencing should be routine, so as to better elucidate the molecular epidemiology of MeV in the future.

Genetic barriers to gene flow separate divergent substitution rates across a butterfly hybrid zone

Substitution rate defines the fundamental timescale of molecular evolution which often varies in a species-specific manner. However, it is unknown under what conditions lineage-specific rates can be preserved between natural populations with frequent hybridization. Here, we show in a hybrid zone between two butterflies, Papilio syfanius and Papilio maackii, that genome-wide barriers to gene flow can effectively separate different rates of molecular evolution in linked regions. The increased substitution rate in the lowland lineage can be largely explained by temperature-induced changes to the spontaneous mutation rate. A novel method based on entropy is developed to test for the existence of barrier loci using a minimal number of samples from the hybrid zone, a robust framework when system complexity far exceeds sample information. Overall, our results suggest that during the process of speciation, the separation of substitution rates can occur locally in the genome in parallel to the separation of gene pools.

Frequent lineage-specific substitution rate changes support an episodic model for protein evolution

Since the inception of the molecular clock model for sequence evolution, the investigation of protein divergence has revolved around the question of a more or less constant change of amino acid sequences, with specific overall rates for each family. Although anomalies in clock-like divergence are well known, the assumption of a constant decay rate for a given protein family is usually taken as the null model for protein evolution. However, systematic tests of this null model at a genome-wide scale have lagged behind, despite the databases’ enormous growth. We focus here on divergence rate comparisons between very closely related lineages since this allows clear orthology assignments by synteny and reliable alignments, which are crucial for determining substitution rate changes. We generated a high-confidence dataset of syntenic orthologs from four ape species, including humans. We find that despite the appearance of an overall clock-like substitution pattern, several hundred protein families show lineage-specific acceleration and deceleration in divergence rates, or combinations of both in different lineages. Hence, our analysis uncovers a rather dynamic history of substitution rate changes, even between these closely related lineages, implying that one should expect that a large fraction of proteins will have had a history of episodic rate changes in deeper phylogenies. Furthermore, each of the lineages has a separate set of particularly fast diverging proteins. The genes with the highest percentage of branch-specific substitutions are ADCYAP1 in the human lineage (9.7%), CALU in chimpanzees (7.1%), SLC39A14 in the internal branch leading to humans and chimpanzees (4.1%), RNF128 in gorillas (9%), and S100Z in gibbons (15.2%). The mutational pattern in ADCYAP1 suggests a biased mutation process, possibly through asymmetric gene conversion effects. We conclude that a null model of constant change can be problematic for predicting the evolutionary trajectories of individual proteins.

Viruses Without Borders: Global Analysis of the Population Structure, Haplotype Distribution, and Evolutionary Pattern of Iris Yellow Spot Orthotospovirus (Family Tospoviridae, Genus Orthotospovirus)

Iris yellow spot, caused by Iris yellow spot orthotospovirus (IYSV) (Genus: Orthotospovirus, Family: Tospoviridae), is an important disease of Allium spp. The complete N gene sequences of 142 IYSV isolates of curated sequence data from GenBank were used to determine the genetic diversity and evolutionary pattern. In silico restriction fragment length polymorphism (RFLP) analysis, codon-based maximum likelihood studies, genetic differentiation and gene flow within the populations of IYSV genotypes were investigated. Bayesian phylogenetic analysis was carried out to estimate the evolutionary rate. In silico RFLP analysis of N gene sequences categorized IYSV isolates into two major genotypes viz., IYSV Netherlands (IYSVNL; 55.63%), IYSV Brazil (IYSVBR; 38.73%) and the rest fell in neither group [IYSV other (IYSVother; 5.63%)]. Phylogenetic tree largely corroborated the results of RFLP analysis and the IYSV genotypes clustered into IYSVNL and IYSVBR genotypes. Genetic diversity test revealed IYSVother to be more diverse than IYSVNL and IYSVBR. IYSVNL and IYSVBR genotypes are under purifying selection and population expansion, whereas IYSVother showed decreasing population size and hence appear to be under balancing selection. IYSVBR is least differentiated from IYSVother compared to IYSVNL genotype based on nucleotide diversity. Three putative recombinant events were found in the N gene of IYSV isolates based on RDP analysis, however, RAT substantiated two among them. The marginal likelihood mean substitution rate was 5.08 × 10–5 subs/site/year and 95% highest posterior density (HPD) substitution rate between 5.11 × 10–5 and 5.06 × 10–5. Findings suggest that IYSV continues to evolve using population expansion strategies. The substitution rates identified are similar to other plant RNA viruses.