Stationary Population Research Articles

Two adjacent inversions maintain genomic differentiation between migratory and stationary ecotypes of Atlantic cod.

Atlantic cod is composed of multiple migratory and stationary populations widely distributed in the North Atlantic Ocean. The Northeast Arctic cod (NEAC) population in the Barents Sea undertakes annual spawning migrations to the northern Norwegian coast. Although spawning occurs sympatrically with the stationary Norwegian coastal cod (NCC), phenotypic and genetic differences between NEAC and NCC are maintained. In this study, we resolve the enigma by revealing the mechanisms underlying these differences. Extended linkage disequilibrium (LD) and population divergence were demonstrated in a 17.4-Mb region on linkage group 1 (LG1) based on genotypes of 494 SNPs from 192 parents of farmed families of NEAC, NCC or NEACxNCC crosses. Linkage analyses revealed two adjacent inversions within this region that repress meiotic recombination in NEACxNCC crosses. We identified a NEAC-specific haplotype consisting of 186 SNPs that was fixed in NEAC sampled from the Barents Sea, but segregating under Hardy-Weinberg equilibrium in eight NCC stocks. Comparative genomic analyses determine the NEAC configuration of the inversions to be the derived state and date it to ~1.6-2.0Mya. The haplotype block harbours 763 genes, including candidates regulating swim bladder pressure, haem synthesis and skeletal muscle organization conferring adaptation to long-distance migrations and vertical movements down to large depths. Our results suggest that the migratory ecotype experiences strong directional selection for the two adjacent inversions on LG1. Despite interbreeding between NEAC and NCC, the inversions are maintaining genetic differentiation, and we hypothesize the co-occurrence of multiple adaptive alleles forming a 'supergene' in the NEAC population.

Dynamic transition in Landau-Zener-Stückelberg interferometry of dissipative systems: The case of the flux qubit

We study Landau-Zener-Stuckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from a LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to 10 energy levels.

A Spatial Framework for Understanding Population Structure and Admixture.

Geographic patterns of genetic variation within modern populations, produced by complex histories of migration, can be difficult to infer and visually summarize. A general consequence of geographically limited dispersal is that samples from nearby locations tend to be more closely related than samples from distant locations, and so genetic covariance often recapitulates geographic proximity. We use genome-wide polymorphism data to build “geogenetic maps,” which, when applied to stationary populations, produces a map of the geographic positions of the populations, but with distances distorted to reflect historical rates of gene flow. In the underlying model, allele frequency covariance is a decreasing function of geogenetic distance, and nonlocal gene flow such as admixture can be identified as anomalously strong covariance over long distances. This admixture is explicitly co-estimated and depicted as arrows, from the source of admixture to the recipient, on the geogenetic map. We demonstrate the utility of this method on a circum-Tibetan sampling of the greenish warbler (Phylloscopus trochiloides), in which we find evidence for gene flow between the adjacent, terminal populations of the ring species. We also analyze a global sampling of human populations, for which we largely recover the geography of the sampling, with support for significant histories of admixture in many samples. This new tool for understanding and visualizing patterns of population structure is implemented in a Bayesian framework in the program SpaceMix.

Climate change and non-stationary population processes in fisheries management

AbstractThe potential influence of climate change on the future distribution and abundance of fish (and therefore commercial fisheries and food security) is increasingly recognized in the fishery management community. A changing climate will likely have differing effects on different species; some will flourish, some will flounder. Management targets for fishing mortality and spawning biomass are often calculated by assuming stationary population processes, but under climate change, this assumption may be violated. Non-stationary population processes can introduce bias into estimates of biomass from stock assessments and calculations of target fishing mortalities and biomasses. However, few accepted frameworks exist for incorporating the changing influence of the environment on exploited populations into management strategies. Identifying changes in population processes due to environmental influences is important in order to enable climate-enhanced management strategy evaluations to elucidate the potential benefits and costs of changing management targets. Cost/benefit analyses will also be useful when coincidentally caught species respond differently to environmental change.

Estimating Consumption to Biomass Ratio in Non-Stationary Harvested Fish Populations.

The food consumption to biomass ratio (C) is one of the most important population parameters in ecosystem modelling because its quantifies the interactions between predator and prey. Existing models for estimating C in fish populations are per-recruit cohort models or empirical models, valid only for stationary populations. Moreover, empirical models lack theoretical support. Here we develop a theory and derive a general modelling framework to estimate C in fish populations, based on length frequency data and the generalised von Bertalanffy growth function, in which models for stationary populations with a stable-age distributions are special cases. Estimates using our method are compared with estimates from per-recruit cohort models for C using simulated harvested fish populations of different lifespans. The models proposed here are also applied to three fish populations that are targets of commercial fisheries in southern Chile. Uncertainty in the estimation of C was evaluated using a resampling approach. Simulations showed that stationary and non-stationary population models produce different estimates for C and those differences depend on the lifespan, fishing mortality and recruitment variations. Estimates of C using the new model exhibited smoother inter-annual variation in comparison with a per-recruit model estimates and they were also smaller than C predicted by the empirical equations in all population assessed.

Transient dynamics reveal the importance of early life survival to the response of a tropical tree to harvest

Summary Exploitation of non‐timber forest products can contribute to the alleviation of poverty. However, overexploitation can also lead to species decline. Studies on the sustainability of harvest often use stationary population growth rates to assess harvesting effects. For such frequently harvested systems, transient analysis can provide new insights into the response of populations to harvest. To test the prediction that the effect of harvest differs between transient and asymptotic phases, I used four years of demographic data to compare the impact of harvesting bark and foliage on the short‐ and long‐term dynamics of African dry zone Mahogany Khaya senegalensis in West Africa. The effect of harvest was stronger in the short term than in the long term, particularly in the moist region. Patterns of transient elasticities also differed from the elasticities of long‐term growth rates to perturbation of vital rates. Survival at early life stages was more important for short‐term dynamics than for long‐term population dynamics. Synthesis and applications. This study illustrates that using the asymptotic growth rates to assess the impact of harvest may underestimate the short‐term effects of harvest. Short‐term management plans based on the elasticity analysis of long‐term growth rates will be suboptimal given the relative importance of the survival of non‐reproductive stages for population dynamics in the near term. Managers should use results from elasticity analysis of both long‐term and short‐term population dynamics to develop more realistic management plans.

Utilitarian population ethics and births timing

Births postponement is a key demographic trend of the last decades. To examine its social desirability, we study how utilitarian criteria rank histories equal on all dimensions except the age at which individuals give birth to their children. We develop a T-period dynamic overlapping generations economy with a fixed living space, where individual welfare is increasing in the available space per head, and where agents have children in one out of two fertility periods. When comparing finite histories with an equal total number of life-periods, classical, average and critical-level utilitarian criteria select the same fertility timing, i.e. the one leading to the most smoothed population path. When comparing infinite histories with stationary population sizes, utilitarian criteria may select different birth timings, depending on individual utility functions. Those results are compared with the ones obtained when agents value coexistence time with their descendants. Finally, we identify conditions under which a shift from an early births regime to a late births regime is socially desirable.

Efficient tool to calculate two-dimensional optical spectra for photoactive molecular complexes.

We combine the coherent modified Redfield theory (CMRT) with the equation of motion-phase matching approach (PMA) to calculate two-dimensional photon-echo spectra for photoactive molecular complexes with an intermediate strength of the coupling to their environment. Both techniques are highly efficient, yet they involve approximations at different levels. By explicitly comparing with the numerically exact quasiadiabatic path integral approach, we show for the Fenna-Matthews-Olson complex that the CMRT describes the decay rates in the population dynamics well, but final stationary populations and the oscillation frequencies differ slightly. In addition, we use the combined CMRT+PMA to calculate two-dimensional photon-echo spectra for a simple dimer model. We find excellent agreement with the exact path integral calculations at short waiting times where the dynamics is still coherent. For long waiting times, differences occur due to different final stationary states, specifically for strong system-bath coupling. For weak to intermediate system-bath couplings, which is most important for natural photosynthetic complexes, the combined CMRT+PMA gives reasonable results with acceptable computational efforts.

Inferring Transition Rates of Networks from Populations in Continuous-Time Markov Processes.

We are interested inferring rate processes on networks. In particular, given a network's topology, the stationary populations on its nodes, and a few global dynamical observables, can we infer all the transition rates between nodes? We draw inferences using the principle of maximum caliber (maximum path entropy). We have previously derived results for discrete-time Markov processes. Here, we treat continuous-time processes, such as dynamics among metastable states of proteins. The present work leads to a particularly important analytical result: namely, that when the network is constrained only by a mean jump rate, the rate matrix is given by a square-root dependence of the rate, kab ∝ (πb/πa)(1/2), on πa and πb, the stationary-state populations at nodes a and b. This leads to a fast way to estimate all of the microscopic rates in the system. As an illustration, we show that the method accurately predicts the nonequilibrium transition rates in an in silico gene expression network and transition probabilities among the metastable states of a small peptide at equilibrium. We note also that the method makes sensible predictions for so-called extra-thermodynamic relationships, such as those of Bronsted, Hammond, and others.

Demographic responses of piping plovers to habitat creation on the Missouri river

ABSTRACTThe piping plover (Charadrius melodus) was listed under the United States Endangered Species Act (ESA) because of habitat loss and excessive predation. The Missouri River provides important habitat for the Great Plains population of the species, some of which nest and forage on river sandbars deposited naturally during high river flows. The United States Army Corps of Engineers (USACE) operates a series of dams on the river that affect water level and the size, number, distribution, and vegetative cover of these sandbars. As a federal agency, USACE is required by the ESA to have a program to conserve the piping plover, and is prohibited from engaging in activities that jeopardize the plover's continued existence. Pursuant to these obligations, the USACE implemented a habitat creation program on the Gavins Point Reach (GVP) and Lewis and Clark Lake (LCL) on the Missouri River from 2004 to 2011. This habitat creation provided an opportunity to study the piping plover's demographic response to several habitat types, and in particular to habitat creation. The goal of this study was to assess the effects of management on plovers using the Missouri River. We studied the changes in engineered and natural habitats, and compared the effects of newly engineered habitat versus naturally created habitat on plover demography during 2005–2011. To this end, we estimated changes in nesting habitat (open or sparsely vegetated dry sand) and examined the factors affecting nest success, chick survival from hatching to fledging, survival, and movement (between and among engineered and natural sandbars) of hatch‐year and adult birds, fidelity of plovers to the study area, and immigration of plovers into engineered habitat. We used demographic estimates to determine overall and habitat‐specific reproductive output and overall population growth rate. Under the assumption that plovers are habitat limited on the Missouri River, we predicted that they would respond positively to the creation of engineered habitat, that their demographic rates would be higher at those sites than on older, natural sandbars, and that over time, the rates would resemble those on older, natural habitats. Engineered sandbars had proportionally more plover nesting habitat than natural sandbars, but the proportion of nesting habitat decreased through vegetation encroachment and erosion as the sandbars aged. Adult and hatch‐year plovers immigrated to engineered sandbars, but immigration slowed as nesting density increased. Nesting density on engineered sandbars increased soon after sandbar construction, peaked 2–3 years later, and then declined to levels similar to those on older, natural sandbars. Birds that nested on engineered sandbars had higher nest success, and those nesting on LCL had higher chick survival than those that nested on GVP sandbars. Adult survival did not differ between engineered or natural habitat, but apparent survival was lower for birds that were not known to nest, indicating higher emigration or mortality rates for non‐nesters. Adult and hatch‐year plovers had high fidelity to the study area (>60% for hatch‐year birds, >90% for adults), and hatch‐year fidelity was highest (>80%) when habitat availability increased. We estimated that given observed survival rates, the reproductive output needed for a stationary population was 1.25 chicks fledged per pair, a rate which was equaled or exceeded in 3 of 4 years on LCL, in 2 of 5 years on engineered sandbars on GVP, and in 1 of 5 years on natural sandbars on GVP. Our results support the hypothesis that piping plovers were habitat‐limited before and during the study. Although nest exclosure and predator control sometimes can improve reproductive output, we predict that these interventions will do little to increase population size unless there is additional habitat to capture enhanced productivity. Based on high fidelity rates and short distances between subsequent nesting attempts (median = 12 km for adults), we suggest that habitat construction be widely distributed within approximately 12 km of a source population to maximize the efficiency of the population‐building process. © 2015 The Wildlife Society.

The Effect of Post-Reproductive Lifespan on the Fixation Probability of Beneficial Mutations.

Post-reproductive lifespan is a common trait among mammals and is usually considered to be neutral; i.e. with no influence on population dynamics. Here, we explore the role of post-reproductive lifespan in the fixation probability of beneficial genetic variation. We compare two separate, stationary populations living in a constant environment that are equivalent except for the average time their respective members spend in the post-reproductive stage of life. Using a recently derived approximation, we show that fixation of a beneficial mutation is more likely in the population with greater post-reproductive longevity. This finding is surprising, as the population with more prolonged post-reproductive lifespan has smaller effective size and the classic population-genetic model would suggest that decreasing effective size reduces fixation chances of beneficial mutations. Yet, as we explain, in the age-structured case, when effective size gets smaller because of longer post-reproductive lifespan but census size is kept equal, a beneficial mutation has a higher likelihood to get fixed because it finds itself at higher initial frequency.

The force of mortality by life lived is the force of increment by life left in stationary populations.

BackgroundThe age distribution and remaining lifespan distribution are identical in stationary populations. The life table survival function is proportional to the age distribution in stationary populations.ObjectiveWe provide an alternative interpretation of the life table when viewed by remaining years of life.ConclusionsThe functions describing the mortality of birth cohorts over age are identical to the functions describing the growth of death cohorts as time to death decreases in stationary populations.

Modelling the Age Dynamics of Chronic Health Conditions: Life-Table-Consistent Transition Probabilities and their Application.

Surveys of chronic health conditions provide information about prevalence but not incidence and the process of change within the population. Our study shows how "age dynamics" of chronic conditions – the probabilities of contracting conditions at different ages, of moving from one chronic condition state to another, and of dying – can be inferred from prevalence data for those conditions that can be viewed as irreversible. Transition probability matrices are constructed for successive age groups, with the sequence representing the age dynamics of the health conditions for a stationary population. We simulate the life path of a cohort under the initial probabilities, and again under altered probabilities, to explore the effects of reducing the incidence or mortality rate associated with a particular condition. We show that such surveys of chronic conditions can be made even more valuable by allowing the calculation of the transition probabilities that define the chronic conditions aging process.

Evolutionary history and adaptive significance of the polymorphic Pan I in migratory and stationary populations of Atlantic cod (Gadus morhua)

The synaptophysin (SYP) family comprises integral membrane proteins involved in vesicle-trafficking events, but the physiological function of several members has been enigmatic for decades. The presynaptic SYP protein controls neurotransmitter release, while SYP-like 2 (SYPL2) contributes to maintain normal Ca2+-signaling in the skeletal muscles. The polymorphic pantophysin (Pan I) of Atlantic cod shows strong genetic divergence between stationary and migratory populations, which seem to be adapted to local environmental conditions. We have investigated the functional involvement of Pan I in the different ecotypes by analyzing the 1) phylogeny, 2) spatio-temporal gene expression, 3) structure–function relationship of the Pan IA and IB protein variants, and 4) linkage to rhodopsin (rho) recently proposed to be associated with different light sensitivities in Icelandic populations of Atlantic cod. We searched for SYP family genes in phylogenetic key species and identified a single syp-related gene in three invertebrate chordates, while four members, Syp, Sypl1, Sypl2 and synaptoporin (Synpr), were found in tetrapods, Comoran coelacanth and spotted gar. Teleost fish were shown to possess duplicated syp, sypl2 and synpr genes of which the sypl2b paralog is identical to Pan I. The ubiquitously expressed cod Pan I codes for a tetra-spanning membrane protein possessing five amino acid substitutions in the first intravesicular loop, but only minor structural differences were shown between the allelic variants. Despite sizable genomic distance (>2.5Mb) between Pan I and rho, highly significant linkage disequilibrium was found by genotyping shallow and deep water juvenile settlers predominated by the Pan IA–rhoA and Pan IB–rhoB haplotypes, respectively. However, the predicted rhodopsin protein showed no amino acid changes, while multiple polymorphic sites in the upstream region might affect the gene expression and pigment levels in stationary and migratory cod. Alternatively, other strongly linked genes might be responsible for the sharp settling stratification of juveniles and the different vertical behavior patterns of adult Atlantic cod.

Modelling production per unit of food consumed in fish populations.

The ratio of production-to-consumption (ρ) reflects how efficiently a population can transform ingested food into biomass. Usually this ratio is estimated by separately integrating cohort per-recruit production and consumption per unit of biomass. Estimates of ρ from cohort analysis differ from those that consider the whole population, because fish populations are usually composed of cohorts that differ in their relative abundance. Cohort models for ρ also assume a stable age-structure and a constant population size (stationary condition). This may preclude their application to harvested populations, in which variations in fishing mortality and recruitment will affect age-structure. In this paper, we propose a different framework for estimating (ρ) in which production and consumption are modelled simultaneously to produce a population estimator of ρ. Food consumption is inferred from the physiological concepts underpinning the generalised von Bertalanffy growth function (VBGF). This general framework allows the effects of different age-structures to be explored, with a stationary population as a special case. Three models with different complexities, depending mostly on what assumptions are made about age-structure, are explored. The full data model requires knowledge about food assimilation efficiency, parameters of the VBGF and the relative proportion of individuals at age a at time y (Py(a)). A simpler model, which requires less data, is based on the stationary assumption. Model results are compared with estimates from cohort models for ρ using simulated fish populations of different lifespans. The models proposed here were also applied to three fish populations that are targets of commercial fisheries in the south-east Pacific. Uncertainty in the estimation of ρ was evaluated using a resampling approach. Simulation showed that cohort and population models produce different estimates for ρ and those differences depend on lifespan, fishing mortality and recruitment variations. Results from the three case studies show that the population model gives similar estimates to those reported by empirical models in other fish species. This modelling framework allows ρ to be related directly to population length- or age-structure and thus has the potential to improve the biological realism of both population and ecosystem models.

On random age and remaining lifetime for populations of items

We consider items that are incepted into operation having already a random (initial) age and define the corresponding remaining lifetime. We show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we develop the population studies approach to the problem and generalize the setting in terms of stationary and stable populations of items. We obtain new stochastic comparisons for the corresponding population ages and remaining lifetimes that can be useful in applications. Copyright © 2014 John Wiley & Sons, Ltd.

Generalization of Carey's equality and a theorem on stationary population.

Carey's Equality pertaining to stationary models is well known. In this paper, we have stated and proved a fundamental theorem related to the formation of this Equality. This theorem will provide an in-depth understanding of the role of each captive subject, and their corresponding follow-up duration in a stationary population. We have demonstrated a numerical example of a captive cohort and the survival pattern of medfly populations. These results can be adopted to understand age-structure and aging process in stationary and non-stationary population models.

Purifying Selection, Drift, and Reversible Mutation with Arbitrarily High Mutation Rates

Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the resulting high diversity levels within a population (hyperdiversity) mean that standard population genetics methods are not trustworthy. We analyze a population genetics model that incorporates purifying selection, reversible mutations, and genetic drift, assuming a stationary population size. We derive analytical results for both population parameters and sample statistics and discuss their implications for studies of natural genetic and epigenetic variation. In particular, we find that (1) many more intermediate-frequency variants are expected than under standard models, even with moderately strong purifying selection, and (2) rates of evolution under purifying selection may be close to, or even exceed, neutral rates. These findings are related to empirical studies of sequence and epigenetic variation.

Inferring Microscopic Kinetic Rates from Stationary State Distributions.

We present a principled approach for estimating the matrix of microscopic transition probabilities among states of a Markov process, given only its stationary state population distribution and a single average global kinetic observable. We adapt Maximum Caliber, a variational principle in which the path entropy is maximized over the distribution of all possible trajectories, subject to basic kinetic constraints and some average dynamical observables. We illustrate the method by computing the solvation dynamics of water molecules from molecular dynamics trajectories.

Selective laser pumping of magnetic sublevels in the hyperfine structure of the cesium atom

The evolution of the populations of the magnetic sublevels of the cesium atom (133Cs isotope) in resonant laser fields with linear polarization is analyzed using the equations for the density matrix. Analytic expressions are derived for stationary populations resulting from laser-induced optical transitions on the hyperfine structure components F g = 3 ↔ F e = 2, 3 and F f = 4 ↔ F e = 3, 4 of lines D1 (62S1/2 → 62P1/2) and D2 (62S1/2 → 62P3/2) depending on the initial values of the populations. The numerical solution of the evolution equations gives the characteristic times of stabilization of the steady regime as functions of laser field intensities and detuning from optical resonance. We determine the sequences of optical transitions increasing (by more than an order of magnitude) the population of the lower sublevel 62S1/2F g = 3 M = 0 of the “clock” microwave transition F g = 3 M = 0 ↔ F f = 4 M = 0 in the cesium frequency standard, which increases the signal intensity in the recording system by the same proportion.