Equilibrium Expectations Research Articles

Heterozygote deficits in cyst plant-parasitic nematodes: possible causes and consequences.

Deviations of genotypic frequencies from Hardy-Weinberg equilibrium (HWE) expectations could reveal important aspects of the biology of populations. Deviations from HWE due to heterozygote deficits have been recorded for three plant-parasitic nematode species. However, it has never been determined whether the observed deficits were due (i) to the presence of null alleles, (ii) to a high level of consanguinity and/or (iii) to a Wahlund effect. The aim of the present work was, while taking into the possible confounding effect of null alleles, to disentangle consanguinity and Wahlund effect in natural populations of those three economically important cyst nematodes using microsatellite markers: Globodera pallida, G.tabacum and Heterodera schachtii, pests of potato, tobacco and sugar beet, respectively. The results show a consistent pattern of heterozygote deficiency in the three nematode species sampled at the spatial scale of the host plant. We demonstrate that the prevalence of null alleles is weak and that heterozygote deficits do not have a single origin. Our results suggested that it is restricted dispersal that leads to heterozygote deficits through both consanguinity and substructure, which effects can be linked to soil movement, cyst density, and the number of generations per year. We discuss potential implications for the durability of plant resistances that are used to protect crops against parasites in which mating between relatives occur. While consanguineous mating leads to homozygosity at all loci, including loci governing avirulence/virulence, which favours the expression of virulence when recessive, the Wahlund effect is expected to have no particular effect on the adaptation of nematodes to resistances.

Relaxing Rational Expectations

The assumption of rational expectations is potentially a serious source of misspecification in DSGE models. Many recent theories of expectations formation have relaxed rational expectations and improved the predictive properties of benchmark macroeconomic models. Problematically, the space of possible theoretical deviations from rational expectations is very large, especially since the aggregate consequences of deviations from rational expectations in equilibrium may not be directly measurable using existing surveys of expectations. This paper provides evidence on which small reduced-form state-contingent deviations from rational expectations yield the most improvement in replicating features of macroeconomic time series, and which aspects of model misspecification are and are not ameliorated by these small deviations from rational expectations. The findings: a) The data favor deviations from rational expectations among firms in which they over-estimate the persistence of inflation. b) Relaxing rational expectations in a New Keynesian model partially substitutes for the additional structural mechanisms in the larger Smets Wouters (2007) model. Relaxing rational expectations within the Smets Wouters (2007) model improves that model’s ability to reproduce some of the spectral coherencies between output growth, investment growth, and labor supply. The mechanism is a combination of shocks to beliefs themselves and the role that deviations from rational expectations have in changing the propagation of other shocks.

Information Aggregation in a Dynamic Stochastic General Equilibrium Model

We introduce the information microstructure of a canonical noisy rational expectations model (Hellwig 1980) into the framework of a conventional real businesscycle model. Each household receives a private signal about future productivity. In equilibrium, the stock price serves to aggregate and transmit this information. We find that dispersed information about future productivity affects the quantitative properties of our real businesscycle model in three dimensions. First, households’ ability to learn about the future affects their consumptionsavings decision. The equity premium falls and the riskfree interest rate rises when the stock price perfectly reveals innovations to future productivity. Second, when noise trader demand shocks limit the stock market’s capacity to aggregate information, households hold heterogeneous expectations in equilibrium. However, for a reasonable size of noise trader demand shocks the model cannot generate the kind of disagreement observed in the data. Third, even moderate heterogeneity in the equilibrium expectations held by households has a sizable effect on the level of all economic aggregates and on the correlations and standard deviations produced by the model. For example, the correlation between consumption and investment growth is 0.29 when households have no information about the future, but 0.41 when information is dispersed.

Abstracts

Abstracts

Thomas Park: ESA President's Address, 1960

Thomas Park: ESA President's Address, 1960

Exact estimation for Markov chain equilibrium expectations

We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functionals defined on a Markov chain. We provide easily implemented algorithms for the class of positive Harris recurrent Markov chains, and for chains that are contracting on average. We further argue that exact estimation in the Markov chain setting provides a significant theoretical relaxation relative to exact simulation methods.

Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain

The steady state after a quantum quench from the Néel state to the anisotropic Heisenberg model for spin chains is investigated. Two methods that aim to describe the postquench non-thermal equilibrium, the generalized Gibbs ensemble and the quench action approach, are discussed and contrasted. Using the recent implementation of the quench action approach for this Néel-to-XXZ quench, we obtain an exact description of the steady state in terms of Bethe root densities, for which we give explicit analytical expressions.Furthermore, by developing a systematic small-quench expansion around the antiferromagnetic Ising limit, we analytically investigate the differences between the predictions of the two methods in terms of densities and postquench equilibrium expectation values of local physical observables. Finally, we discuss the details of the quench action solution for the quench to the isotropic Heisenberg spin chain. For this case we validate the underlying assumptions of the quench action approach by studying the large-system-size behavior of the overlaps between Bethe states and the Néel state.

Exact estimation for Markov chain equilibrium expectations

We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functionals defined on a Markov chain. We provide easily implemented algorithms for the class of positive Harris recurrent Markov chains, and for chains that are contracting on average. We further argue that exact estimation in the Markov chain setting provides a significant theoretical relaxation relative to exact simulation methods.

XTRAM: Estimating Equilibrium Expectations from Time-Correlated Simulation Data at Multiple Thermodynamic States

Computing the equilibrium properties of complex systems, such as free energy differences, is often hampered by rare events in the dynamics. Enhanced sampling methods may be used in order to speed up sampling by, for example, using high temperatures, as in parallel tempering, or simulating with a biasing potential such as in the case of umbrella sampling. The equilibrium properties of the thermodynamic state of interest (e.g., lowest temperature or unbiased potential) can be computed using reweighting estimators such as the weighted histogram analysis method or the multistate Bennett acceptance ratio (MBAR). weighted histogram analysis method and MBAR produce unbiased estimates, the simulation samples from the global equilibria at their respective thermodynamic state--a requirement that can be prohibitively expensive for some simulations such as a large parallel tempering ensemble of an explicitly solvated biomolecule. Here, we introduce the transition-based reweighting analysis method (TRAM)--a class of estimators that exploit ideas from Markov modeling and only require the simulation data to be in local equilibrium within subsets of the configuration space. We formulate the expanded TRAM (xTRAM) estimator that is shown to be asymptotically unbiased and a generalization of MBAR. Using four exemplary systems of varying complexity, we demonstrate the improved convergence (ranging from a twofold improvement to several orders of magnitude) of xTRAM in comparison to a direct counting estimator and MBAR, with respect to the invested simulation effort. Lastly, we introduce a random-swapping simulation protocol that can be used with xTRAM, gaining orders-of-magnitude advantages over simulation protocols that require the constraint of sampling from a global equilibrium.

Development and characterization of microsatellite markers for blackfin tuna (Thunnus atlanticus) with the use of Illumina paired-end sequencing

Twenty homologous microsatellite markers, or simple sequence repeats (SSRs), were developed for blackfin tuna (Thunnus atlanticus) through the use of a direct Seq-to-SSR approach. The number of alleles per locus ranged between 5 and 26, and the expected heterozygosity ranged between 0.640 and 0.969. Three loci displayed significant departure from Hardy-Weinberg equilibrium expectations, likely reflecting occurrence of null alleles. Another locus showed consecutive alleles that differed by one base pair only. Consequently, this locus may be prone to elevated rates of scoring errors. The remaining 16 loci will be valuable for studies in conservation genetics of blackfin tuna.

Typical Pure States and Nonequilibrium Processes in Quantum Many-Body Systems

We show that it is possible to calculate equilibrium expectation values of many-body correlated quantities such as the characteristic functions and probability distributions with the use of only a single typical pure state. It also means that we can apply the pure state approach to Heisenberg operators and their spectral fluctuation, and hence to nonequilibrium processes starting from equilibrium. In particular, we can accurately analyze the full statistics of entropy production in nonequilibrium mesoscopic systems. In this way, we can access the full information on higher-order fluctuations in the large deviation regime far from equilibrium.

Quenching the anisotropic heisenberg chain: exact solution and generalized Gibbs ensemble predictions.

We study quenches in integrable spin-1/2 chains in which we evolve the ground state of the antiferromagnetic Ising model with the anisotropic Heisenberg Hamiltonian. For this nontrivially interacting situation, an application of the first-principles-based quench-action method allows us to give an exact description of the postquench steady state in the thermodynamic limit. We show that a generalized Gibbs ensemble, implemented using all known local conserved charges, fails to reproduce the exact quench-action steady state and to correctly predict postquench equilibrium expectation values of physical observables. This is supported by numerical linked-cluster calculations within the diagonal ensemble in the thermodynamic limit.

Allele frequencies for 15 autosomal STR loci and haplotype data for 17 Y-STR loci in a population from Belize.

Allele frequencies for 15 autosomal STR loci (N = 290) and haplotype data for 17 Y-STR loci (N = 157) were determined for an admixed population from Belize. There were no detectable departures from Hardy-Weinberg equilibrium expectations at any autosomal STR loci except for the D8S1179 locus (p = 0.002). The combined power of discrimination (PD) and combined power of exclusion (PE) were greater than 0.99999999 and 0.99999951, respectively. In addition, a total of 144 distinct Y-STR haplotypes were observed with 133 Y-STR haplotypes observed only once. The most common Y-STR haplotype was observed three times for two separate haplotypes. The various analyses of these forensically relevant STR loci showed that these markers are informative in the Belize population for forensic and parentage testing applications.

Effects of mitochondrial DNA rate variation on reconstruction of Pleistocene demographic history in a social avian species, Pomatostomus superciliosus.

Mitochondrial sequence data is often used to reconstruct the demographic history of Pleistocene populations in an effort to understand how species have responded to past climate change events. However, departures from neutral equilibrium conditions can confound evolutionary inference in species with structured populations or those that have experienced periods of population expansion or decline. Selection can affect patterns of mitochondrial DNA variation and variable mutation rates among mitochondrial genes can compromise inferences drawn from single markers. We investigated the contribution of these factors to patterns of mitochondrial variation and estimates of time to most recent common ancestor (TMRCA) for two clades in a co-operatively breeding avian species, the white-browed babbler Pomatostomus superciliosus. Both the protein-coding ND3 gene and hypervariable domain I control region sequences showed departures from neutral expectations within the superciliosus clade, and a two-fold difference in TMRCA estimates. Bayesian phylogenetic analysis provided evidence of departure from a strict clock model of molecular evolution in domain I, leading to an over-estimation of TMRCA for the superciliosus clade at this marker. Our results suggest mitochondrial studies that attempt to reconstruct Pleistocene demographic histories should rigorously evaluate data for departures from neutral equilibrium expectations, including variation in evolutionary rates across multiple markers. Failure to do so can lead to serious errors in the estimation of evolutionary parameters and subsequent demographic inferences concerning the role of climate as a driver of evolutionary change. These effects may be especially pronounced in species with complex social structures occupying heterogeneous environments. We propose that environmentally driven differences in social structure may explain observed differences in evolutionary rate of domain I sequences, resulting from longer than expected retention times for matriarchal lineages in the superciliosus clade.

Isolation and characterization of microsatellite loci for the blackstripe topminnow Fundulus notatus and their variability in two closely related species.

A total of 17 polymorphic microsatellite loci were isolated from the blackstripe topminnow Fundulus notatus. In a sample of 29 individuals, these loci were found to possess two to 19 alleles with expected heterozygosity values ranging from 0.212 to 0.919 and all but one of the loci conformed to Hardy-Weinberg equilibrium expectations. Many of these loci were polymorphic in the closely related species Fundulus olivaceus and Fundulus euryzonus providing a set of markers that should prove useful in future ecological and evolutionary studies of members of this species complex.

Probability of stochastic depletion: an easily interpreted diagnostic for stock assessment modelling and fisheries management

Abstract Marine fish populations have high variation in cohort strength, and the production of juveniles (recruitment) may have persistent positive or negative residuals (autocorrelation) after accounting for spawning biomass. Autocorrelated recruitment will occur whenever average recruitment levels change between oceanographic regimes or due to predator release, but may also indicate persistent environmental and biological effects on shorter time-scales. Here, we use estimates of recruitment variability and autocorrelation to simulate the stationary distribution of spawning biomass for 100 real-world stocks when unfished, fished at FMSY, or fished following a harvest control rule where fishing mortality decreases as a function of spawning biomass. Results show that unfished stocks have spawning biomass (SB) below its deterministic equilibrium value (SB0) 58% of the time, and below 0.5SB0 5% of the time on average across all stocks. Similarly, stocks fished at the level producing deterministic maximum sustainable yield (FMSY) are below its deterministic prediction of spawning biomass (SBMSY) 60% of the time and below 0.5SBMSY 8% of the time. These probabilities are greater for stocks with high recruitment variability, positive autocorrelation, and high natural mortality—traits that are particularly associated with clupeids and scombrids. An elevated probability of stochastic depletion, i.e. biomass below the deterministic equilibrium expectation, implies that management actions required when biomass drops below a threshold may be triggered more frequently than expected. Therefore, we conclude by suggesting that fisheries scientists routinely calculate these probabilities during stock assessments as a decision support tool for fisheries managers.

DECIPHERING THE ATMOSPHERIC COMPOSITION OF WASP-12b: A COMPREHENSIVE ANALYSIS OF ITS DAYSIDE EMISSION

WASP-12b was the first planet reported to have a carbon-to-oxygen ratio (C/O) greater than one in its dayside atmosphere. However, recent work to further characterize its atmosphere and confirm its composition has led to incompatible measurements and divergent conclusions. Additionally, the recent discovery of stellar binary companions ~1" from WASP-12 further complicates the analyses and subsequent interpretations. We present a uniform analysis of all available Hubble and Spitzer Space Telescope secondary-eclipse data, including previously-unpublished Spitzer measurements at 3.6 and 4.5 microns. The primary controversy in the literature has centered on the value and interpretation of the eclipse depth at 4.5 microns. Our new measurements and analyses confirm the shallow eclipse depth in this channel, as first reported by Campo and collaborators and used by Madhusudhan and collaborators to infer a carbon-rich composition. To explain WASP-12b's observed dayside emission spectrum, we implemented several recent retrieval approaches. We find that when we exclude absorption due to C2H2 and HCN, which are not universally considered in the literature, our models require implausibly large atmospheric CO2 abundances, regardless of the C/O. By including C2H2 and HCN in our models, we find that a physically-plausible carbon-rich solution achieves the best fit to the available photometric and spectroscopic data. In comparison, the best-fit oxygen-rich models have abundances that are inconsistent with the chemical equilibrium expectations for hydrogen-dominated atmospheres and are 670 times less probable. Our best-fit solution is also 7.3*10^{6} times more probable than an isothermal blackbody model.

Development of microsatellite markers for the near threatened eagles Harpia harpyja and Morphnus guianensis using next-generation sequencing

We isolated and characterized 11 microsatellite loci for Harpia harpyja using the IonTorrent PGM. The loci were validated in 22 Harpia harpyja and 16 Morphnus guianensis individuals. Ten of the loci were variable in H. harpyja, ranging from two to six alleles per locus. Seven of the loci were variable in M. guianensis ranging from two to six alleles per locus. Genotypes did not deviate from Hardy–Weinberg equilibrium expectation, and no linkage disequilibrium was observed. These markers have a promise to provide an important resource for genetic population studies, conservation and monitoring of these two near threatened accipitrid species.

Exploring the diversity of Jupiter-class planets.

Of the 900+ confirmed exoplanets discovered since 1995 for which we have constraints on their mass (i.e. not including Kepler candidates), 75% have masses larger than Saturn (0.3 MJ), 53% are more massive than Jupiter and 67% are within 1 AU of their host stars. When Kepler candidates are included, Neptune-sized giant planets could form the majority of the planetary population. And yet the term 'hot Jupiter' fails to account for the incredible diversity of this class of astrophysical object, which exists on a continuum of giant planets from the cool jovians of our own Solar System to the highly irradiated, tidally locked hot roasters. We review theoretical expectations for the temperatures, molecular composition and cloud properties of hydrogen-dominated Jupiter-class objects under a variety of different conditions. We discuss the classification schemes for these Jupiter-class planets proposed to date, including the implications for our own Solar System giant planets and the pitfalls associated with compositional classification at this early stage of exoplanetary spectroscopy. We discuss the range of planetary types described by previous authors, accounting for (i) thermochemical equilibrium expectations for cloud condensation and favoured chemical stability fields; (ii) the metallicity and formation mechanism for these giant planets; (iii) the importance of optical absorbers for energy partitioning and the generation of a temperature inversion; (iv) the favoured photochemical pathways and expectations for minor species (e.g. saturated hydrocarbons and nitriles); (v) the unexpected presence of molecules owing to vertical mixing of species above their quench levels; and (vi) methods for energy and material redistribution throughout the atmosphere (e.g. away from the highly irradiated daysides of close-in giants). Finally, we discuss the benefits and potential flaws of retrieval techniques for establishing a family of atmospheric solutions that reproduce the available data, and the requirements for future spectroscopic characterization of a set of Jupiter-class objects to test our physical and chemical understanding of these planets.

Information Aggregation in a DSGE Model

We introduce the information microstructure of a canonical noisy rational expectations model (Hellwig, 1980) into the framework of a conventional real business cycle model. Each household receives a private signal about future productivity. In equilibrium, the stock price serves to aggregate and transmit this information. We find that dispersed information about future productivity affects the quantitative properties of our real business cycle model in three dimensions. First, households' ability to learn about the future affects their consumption-savings decision. The equity premium falls and the risk-free interest rate rises when the stock price perfectly reveals innovations to future productivity. Second, when noise trader demand shocks limit the stock market's capacity to aggregate information, households hold heterogeneous expectations in equilibrium. However, for a reasonable size of noise trader demand shocks the model cannot generate the kind of disagreement observed in the data. Third, even moderate heterogeneity in the equilibrium expectations held by households has a sizable effect on the level of all economic aggregates and on the correlations and standard deviations produced by the model. For example, the correlation between consumption and investment growth is 0.29 when households have no information about the future, but 0.41 when information is dispersed.