Dynamic Factor Analysis Model Research Articles

Joint analysis of multivariate longitudinal, imaging, and time-to-event data

Abstract Alzheimer’s (AD) is a progressive neurodegenerative disease frequently associated with memory deficits and cognitive decline. Despite its irreversible once onset, some discoveries revealed the existence of a certain percentage of people who are non-susceptible to AD. This study proposes a joint analysis of multivariate longitudinal data, survival data with a non-susceptible fraction, and ultrahigh-dimensional imaging data. The proposed model comprises three major components. The first component is a mixture proportional hazards cure model with images to examine the potential predictors of the non-susceptible probability and hazards of interest. The second component is a dynamic factor analysis model with images to characterize group-specific latent factors through multiple observed variables. The last component is a semiparametric trajectory model to reveal the change patterns of the dynamic latent factors in the ‘non-susceptible’ and ‘susceptible’ groups. A two-stage approach is developed for statistical inference. The first stage manages the imaging data through high-dimensional functional principal component analysis. The second stage develops a Bayesian approach coupled with penalized splines, data augmentation, and Markov chain Monte Carlo techniques to perform estimation. The application to the Alzheimer’s Disease Neuroimaging Initiative dataset sheds new insight into the pathology of AD.

Spatiotemporal patterns in the ecological community of the nearshore Mid-Atlantic Bight

Recognition of the need for a more holistic, ecosystem approach to the assessment and management of living marine resources has renewed interest in quantitative community ecology and fueled efforts to develop ecosystem metrics to gain insight into system status. This investigation utilized 12 years (2008 to 2019) of fisheries-independent bottom trawl survey data to quantify and synthesize the spatiotemporal patterns of species assemblages inhabiting the nearshore Mid-Atlantic Bight (MAB). Assemblages were delineated by ecomorphotype (EMT), and all species collected by the survey were allocated among 9 EMTs: demersal fishes; pelagic fishes; flatfishes; skates; rays; dogfishes; other sharks; cephalopods; and benthic arthropods. Annual time series and seasonal spatial distributions of relative aggregate biomass were quantified for each EMT using delta-generalized additive models. Dynamic factor analysis (DFA) revealed that the information content of the 9 annual time series was effectively summarized by 3 common trends, and DFA model fits to each EMT time series represented a new suite of ecosystem indicators for this system. Mean sea surface temperature during winter in the MAB was included in the selected DFA model, suggesting that winter environmental conditions influence the structure of this system at an annual scale. Principal component analysis uncovered a north-to-south gradient in the seasonal spatial distributions of these EMTs and identified a distinct area of elevated biomass for several assemblages along the south shore of Long Island, NY. Taken together, these results characterize the community structure of the nearshore MAB and yield requisite information to support ongoing ecosystem-scale assessment and management activities for this region.

Bayesian semiparametric approach to quantile nonlinear dynamic factor analysis models with mixed ordered and nonignorable missing data

In classical nonlinear dynamic factor analysis models (NDFAMs), we assume manifest variables follow the normal distribution. However, in some applications, the normality assumption may be unreasonable or questionable. This paper proposes a quantile NDFAM in which manifest variables may be observed or unobserved but associated with the observed ordinal indicators or subject to missingness, and develops a Bayesian semiparametric method to estimate unknown parameters and latent variables by utilizing the Dirichlet process prior to approximate unknown distribution of random effects. Logistic and probit models are adopted to specify propensity scores for missing manifests and covariates, respectively. An exponential family distribution is assumed for missing covariates. Bayesian local influence is presented to assess the effect of minor perturbations to data, priors, and sampling distributions. Several simulation studies and a real example are illustrated by the proposed methodologies.

Synchronization and cyclicality of social spending in economic crises

This paper expands the analysis of the cyclical characteristics of social spending by providing information on its joint behaviour across OECD countries. With this aim we propose the use of dynamic factor analysis and recursive models to estimate synchronization and cyclicality of social policies within a broad perspective. By considering the synchronization of social spending it is possible to assess the short-run characteristics of the joint response to changes in the economic cycle. We find that synchronization of social spending was only possible for advanced economies, achieving the highest countercyclical stabilization effect during the Global Financial Crisis. Emerging market economies are not able to join the synchronized response, maintaining independent and, in most cases, procyclical stances in the behaviour of their social policies.

Predicting year class strength for climate-stressed gadid stocks in the Gulf of Alaska

Climate change makes fish stocks more vulnerable to recruitment failure, and early detection of these events is important for an effective management response. Here, we evaluate the value of larval and juvenile surveys, and a thermal spawning habitat index, for predicting recruitment in two economically important gadids, walleye pollock (Gadus chalcogrammus) and Pacific cod (G. macrocephalus), in the Gulf of Alaska. These stocks have been exposed to rapid human-induced ocean warming since 2014, which has apparently contributed to anomalies in age structure, size at age, and other population variables (for pollock) and stock collapse (for cod). We found that warming results in recruitment that falls short of predictions from historical spawner-recruit relationships for both stocks, highlighting that climate change makes recruitment expectations based on historical experience less reliable. However, we also found that recruitment could be successfully predicted with surveys of early-life stages. Using Bayesian regression, we found that juvenile trawl survey data for pollock predicts recruitment to age-1 (as estimated by a stock assessment model), while prediction from larval surveys was less successful. Beach seine estimates of juvenile abundance also predicted pollock recruitment, a surprising result for a species that is typically sampled in offshore habitats. The spawning habitat index and beach seine survey both predicted cod recruitment to age-3 as estimated by the stock assessment model. We did not find a predictive relationship between cod larval abundance and recruitment. However, residuals from the larval model showed low-frequency variability, suggesting nonstationarity (time-dependence) in the predictive relationship. Dynamic Factor Analysis (DFA) models summarizing information across multiple data sets showed reasonable predictive value for both species (Bayesian R2 ≈ 0.4 for log recruitment), and they also allowed recruitment prediction for years with missing observations in some data sets. We conclude that surveying multiple early life stages may be the most useful approach for predicting gadid recruitment.

A joint model for multivariate longitudinal and survival data to discover the conversion to Alzheimer's disease.

Alzheimer's disease (AD) is an incurable and progressive disease that starts from mild cognitive impairment and deteriorates over time. Examining the effects of patients' longitudinal cognitive decline on time to conversion to AD and obtaining a reliable diagnostic model are therefore critical to the evaluation of AD prognosis and early treatment. Previous studies either assess patients' cognitive impairment through a single cognitive test or assume it changes linearly across time, thereby leading to an incomplete measure of cognitive decline or overlooking the subtle trajectory pattern of patients' cognitive impairment. This study develops a new joint model to address these shortcomings. First, a dynamic factor analysis model is adopted to characterize cognitive impairment through multiple cognitive measures in a comprehensive manner. Second, a spline-based random coefficient model is proposed to reveal possibly nonlinear trajectories of patients' cognitive decline. Finally, a proportional hazard model is considered to examine the effects of time-invariant markers and time-variant cognitive impairment on AD hazards. A Bayesian approach coupled with spline approximation techniques and MCMC methods is developed to conduct statistical inference. The application of the proposed method to the Alzheimer's Disease Neuroimaging Initiative study provides new insights into the prevention of AD and shows a high prediction capacity of the proposed method.

Shifting baselines and cross‐scale drivers of lake water clarity: Applications for lake assessment

AbstractTemporal Secchi depth trends are used in lake assessment to evaluate lake condition and possible shifts in trophic state. For accurate lake assessments, it is important to differentiate regional trends from lake‐specific trends, but this can be confounded by interacting factors. We present a divergent trend analysis which uses temporal patterns of Secchi depth water clarity from 1999 to 2018 for five different types of reference lakes from minimally disturbed watersheds to create dynamic baselines against which we evaluate Secchi depth trends from nonreference lakes in Maine, USA. We used mixed‐effect generalized additive models to generate smoothed curves of the expected baseline Secchi depth for each reference lake type to account for the nonlinear dynamics of lake condition through time. The majority of nonreference lakes (74%) showed no difference between measured trend (actual Secchi depth data) and divergent trend (residual Secchi depth from baseline trends). The most common difference in lakes with inconsistent trend test results showed stability in measured trends but apparent declining trends in divergent Secchi depth clarity. We used a Dynamic Factor Analysis (DFA) model to help interpret the variation and shifts observed in baseline reference lake trends. The best DFA model identified two common trends in water clarity among lake types and precipitation during the primary stratification season as the most informative covariable. Because precipitation amount and intensity are expected to increase according to predictive climate models for the Northeast US, our results suggest that baseline lake clarity in Maine will decrease with climate change.

An assessment of the larval fish diversity within a coastal marine reserve: Larval fish diversity within a marine reserve

Knowledge of ichthyoplankton diversity and distribution is important in the management of a fishery for increased productivity and to ensure sustainability. In the Discovery Bay Special Fishery Conservation Area (DBSFCA) and other marine protected areas in Jamaica, there is a paucity of information on larval fish communities and the factors affecting their diversity and distribution. Therefore, we compared the efficiencies of light traps and plankton nets to assess the richness and composition of ichthyoplankton species in Jamaica’s oldest fish sanctuary, the DBSFCA. Min/Max Auto-correlation Factor Analysis (MAFA) and the Dynamic Factor Analysis (DFA) were then used to compare biotic and abiotic factors that influenced larval fish diversity and distribution. A total of 41 species belonging to 39 families of predominantly reef-associated species were identified during the sampling period of February to November 2014. The plankton net proved to be more efficient, catching 2202 individuals from 36 species, while light traps caught 590 individuals from 15 larval fish species. The plankton nets and light traps collected 27 and seven mutually exclusive species, respectively. From February to July, Clupeidae and Pomacentridae dominated the larvae community and throughout the study period Clupeidae was the most abundant family in the light traps. Blennidae, Gobiidae, Labridae, Labrisomidae, Pomacentridae and Sparidae frequently accounted for less than 50% of the relative abundance. Commercially important families such as Lutjanidae and Haemulidae were rarely caught with both gears. Additionally, temporal changes in the abundance and richness of fish larvae, indicating peak abundance during July and August, were detected with both DFA and MAFA. A DFA model with two common trends and three explanatory variables (mean day-length, mean zooplankton richness and mean monthly sea temperature) was the optimal model for characterizing ichthyoplankton abundance. The study highlights the importance of incorporating ichthyoplankton surveys in marine reserves especially with the threat of climate change and overfishing.

Evaluating ecosystem change as Gulf of Alaska temperature exceeds the limits of preindustrial variability

The Gulf of Alaska experienced extreme temperatures during 2014–2019, including the four warmest years ever observed. The goal of this study is to evaluate the ecological consequences of that warming event, across multiple trophic levels and taxa. We tested for evidence that observed sea surface temperature (SST) anomalies were outside the envelope of natural climate variability in order to evaluate the risk of novel ecosystem configurations. We also tested for state changes in shared trends of climate (n = 11) and biology (n = 48) time series, using a Bayesian implementation of Dynamic Factor Analysis (DFA). And we tested for evidence of novel ecological relationships during 2014–2019. We found that 3-year running mean SST anomalies during 2014–2019 were outside the range of anomalies from preindustrial simulations in CMIP5 models, indicating that the combined magnitude and duration of the warming event was outside the range of natural variability. A DFA model of climate variability also returned a shared trend in climate time series that was at unprecedented levels during 2014–2019. However, DFA models fit to biology data did not show shared trends of variability at unprecedented levels, and Hidden Markov Models fit to shared trends from the climate and biology models failed to find evidence of shifts to a new ecosystem state during 2014–2019. Conversely, we did find preliminary indications that community responses to SST variability strengthened during 2014–2019 after decades of a mostly neutral relationship. Tests for nonstationary patterns of shared variability suggest that covariance between SST and other ecologically-important climate variables remained weaker than during the 1970s Pacific Decadal Oscillation shift, suggesting the potential for muted ecological responses to the 2014–2019 event. Finally, we found that recent patterns of community variability appear to be highly dissimilar to those associated with the 1970s event, suggesting the potential for novel community states with continued warming. In summary, we find no evidence for wholesale ecosystem reorganization during 2014–2019, though nonstationary relationships among climate and community variables suggest the ongoing possibility of novel patterns of ecosystem functioning with continued warming.

Use of Composites in Analysis of Individual Time Series: Implications for Person-Specific Dynamic Parameters

Psychology has seen an increase in the study of intra-individual processes through time series. Although timely and relevant, modeling variance from unique sources in time series may lead to model non-convergence, making it tempting to reduce the number of parameters in the model. The purpose of this paper was to investigate use of composite scores in analysis of individual time series. To meet this goal, we compared the dynamic factor analysis (DFA) model using multiple indicators with the autoregressive (AR) and autoregressive + white noise (AR + WN) models using composites. We conducted a Monte Carlo study in which a DFA(1,1) model was used to generate the data with varying conditions of size of factor loadings, number of indicators, size of AR parameters, and time series length. We also conducted analysis of empirical data from six individuals’ daily self-reports of mood. Findings indicated that the DFA(1,1) and AR(1) + WN models performed comparably in their recovery of AR parameters, while the AR(1) model underestimated the parameter under nearly all conditions. However, variability of estimates may make the AR(1) + WN model less viable for researchers conducting individual-level analyses when the true data-generating mechanism is the DFA(1, 1) model.

The Shifting Role of mRUE for Regulating Ecosystem Production

To create a comprehensive view of ecosystem resource use, we integrated parallel resource use efficiency observations into a multiple-resource use efficiency (mRUE) framework using a dynamic factor analysis model. Results from 56 site-years of eddy covariance data and mRUE factors for a site in the US Midwest show temporal dynamics and coherence (using Pearson’s R) among resources are associated with interannual variation in precipitation. Loading factors are derived from mRUE observations and quantify how strongly data are connected to the underlying ecosystem state. Water and light resource use loading factors are coherent at annual timescales (Pearson’s R of 0.86), whereas declining patterns of carbon use efficiency loading factors highlight the ecosystem’s trade-off between carbon uptake and respiration during the growing season. At annual and monthly timescales, influence decreases from ~ 85 to ~ 65% for loading factors for carbon use, while influence of light use loading factors peaks to ~ 60% at growing season timescales. Quantifying variation in ecosystem function provides novel insights into the temporal dynamics of changing importance of multiple resources to ecosystem function.

Using a coupled dynamic factor - random forest analysis (DFRFA) to reveal drivers of spatiotemporal heterogeneity in the semi-arid regions of southern Africa.

Understanding the drivers of large-scale vegetation change is critical to managing landscapes and key to predicting how projected climate and land use changes will affect regional vegetation patterns. This study aimed to improve our understanding of the role, magnitude, and spatial distribution of the key environmental and socioeconomic factors driving vegetation change in a southern African savanna. This research was conducted across the Kwando, Okavango and Zambezi catchments of southern Africa (Angola, Namibia, Botswana and Zambia) and explored vegetation cover change across the region from 2001–2010. A novel coupled analysis was applied to model the dynamic biophysical factors then to determine the discrete / social drivers of spatial heterogeneity on vegetation. Previous research applied Dynamic Factor Analysis (DFA), a multivariate times series dimension reduction technique, to ten years of monthly remotely sensed vegetation data (MODIS-derived normalized difference vegetation index, NDVI), and a suite of time-series (monthly) environmental covariates: precipitation, mean, minimum and maximum air temperature, soil moisture, relative humidity, fire and potential evapotranspiration. This initial research was performed at a regional scale to develop meso-scale models explaining mean regional NDVI patterns. The regional DFA predictions were compared to the fine-scale MODIS time series using Kendall’s Tau and Sen’s Slope to identify pixels where the DFA model we had developed, under or over predicted NDVI. Once identified, a Random Forest (RF) analysis using a series of static social and physical variables was applied to explain these remaining areas of under- and over- prediction to fully explore the drivers of heterogeneity in this savanna system. The RF analysis revealed the importance of protected areas, elevation, soil type, locations of higher population, roads, and settlements, in explaining fine scale differences in vegetation biomass. While the previously applied DFA generated a model of environmental variables driving NDVI, the RF work developed here highlighted human influences dominating that signal. The combined DFRFA model approach explains almost 90% of the variance in NDVI across this landscape from 2001–2010. Our methodology presents a unique coupling of dynamic and static factor analyses, yielding novel insights into savanna heterogeneity, and providing a tool of great potential for researchers and managers alike.

Changes in abundance and biomass of the bivalve Macoma calcarea in the northern Bering Sea and the southeastern Chukchi Sea from 1998 to 2014, tracked through dynamic factor analysis models

We used dynamic factor analysis (DFA) to track underlying trends in the abundance (number m−2) and biomass (g C m−2) of a common bivalve, Macoma calcarea, at eleven stations in the northern Bering and Chukchi Seas, as part of the Distributed Biological Observatory (DBO) sampling effort. Five of the stations are located in the northern Bering Sea (DBO1 - SLIP stations) and the other six stations are located in the southeastern Chukchi Sea (DBO3 - UTN stations). M. calcarea abundance and biomass were analyzed from 1998 to 2014 as part of a 25+ year benthic community dataset. Results from the DFA indicate that there are two abundance trends (one increasing and one decreasing, depending on station location) for M. calcarea in the DBO1 region. Biomass data for M. calcarea in this region also indicates simultaneous increasing and decreasing trends, depending on location. In the DBO3 region, there are also both increasing and decreasing abundance trends for M. calcarea depending on location. Furthermore, DFA of biomass data in the DBO3 region indicates that M. calcarea biomass has three underlying trends among stations (one increasing, a second trend that decreases and then increases, and third that is relatively stable through time). Model results indicate that certain surface sediment characteristics (chlorophyll-a inventories, total organic carbon, and percent ≥5 phi grain size) as well as bottom water temperature are correlated with abundance and biomass of M. calcarea in these two regions. Overall, we conclude that M. calcarea abundance and biomass declined in the DBO1 region, with some spatial complexities, which is apparent principally as a northward shift of M. calcarea abundance. Since this area is a critical winter foraging habitat for the world population of a threatened diving sea duck, the spectacled eider (Somarteria fischeri), the decline and northward shift in prey is potentially significant for management of the species. By comparison, abundance of M. calcarea in the DBO3 region exhibited a southward shift in abundance away from station UTN5 and towards UTN2, suggesting that hydrographic influences on sediment composition and food supply may be key drivers for this species.

The Influence of Population Aging on Technological Innovation: Based on Innovation Evaluation Using Dynamic Factor Analysis and Dynamic GMM Model

In the double background of population aging and China’s economy increasingly driven by technological innovation, the investigation into the effect of population aging on technological innovation is of great importance. This paper evaluates three influence mechanisms of population aging on technological innovation, namely human capital mechanism”, labor productivity mechanism” and the elderly burden mechanism”. Using dynamic factor analysis model, we choose multiple indicators in five aspects-innovation input, innovation output, innovation efficiency, synergy innovation and innovation environment. Then we get a new comprehensive index of technological innovation concerning 29 provinces from 1990 to 2014 and use it as a new indicator of innovation capacity. Using dynamic GMM model, we prove that population aging has two opposite effects on technological innovation: on one hand, population aging has positive effect on technological innovation by improving researchers’ labor efficiency, having the positive labor productivity effect”; on the other hand, population aging has negative effect on technological innovation by reducing the level of human capital, aggravating the pension burden and squeezing out innovation input, having negative human capital” and elderly burden” effects. Our work contributes to the present research by creating a new innovation indicator and analyzing the effect of population aging on technological innovation, and has policy implications for dealing with the challenge of population aging.

Container Throughput Forecasting Using Dynamic Factor Analysis and ARIMAX Model

The paper examines the impact of integration of macroeconomic indicators on the accuracy of container throughput time series forecasting model. For this purpose, a Dynamic factor analysis and AutoRegressive Integrated Moving-Average model with eXogenous inputs (ARIMAX) are used. Both methodologies are integrated into a novel four-stage heuristic procedure. Firstly, dynamic factors are extracted from external macroeconomic indicators influencing the observed throughput. Secondly, the family of ARIMAX models of different orders is generated based on the derived factors. In the third stage, the diagnostic and goodness-of-fit testing is applied, which includes statistical criteria such as fit performance, information criteria, and parsimony. Finally, the best model is heuristically selected and tested on the real data of the Port of Koper. The results show that by applying macroeconomic indicators into the forecasting model, more accurate future throughput forecasts can be achieved. The model is also used to produce future forecasts for the next four years indicating a more oscillatory behaviour in (2018-2020). Hence, care must be taken concerning any bigger investment decisions initiated from the management side. It is believed that the proposed model might be a useful reinforcement of the existing forecasting module in the observed port.

Accounting for spatiotemporal variation and fisher targeting when estimating abundance from multispecies fishery data

Estimating trends in abundance from fishery catch rates is one of the oldest endeavors in fisheries science. However, many jurisdictions do not analyze fishery catch rates due to concerns that these data confound changes in fishing behavior (adjustments in fishing location or gear operation) with trends in abundance. In response, we developed a spatial dynamic factor analysis (SDFA) model that decomposes covariation in multispecies catch rates into components representing spatial variation and fishing behavior. SDFA estimates spatiotemporal variation in fish density for multiple species and accounts for fisher behavior at large spatial scales (i.e., choice of fishing location) while controlling for fisher behavior at fine spatial scales (e.g., daily timing of fishing activity). We first use a multispecies simulation experiment to show that SDFA decreases bias in abundance indices relative to ignoring spatial adjustments and fishing tactics. We then present results for a case study involving petrale sole (Eopsetta jordani) in the California Current, for which SDFA estimates initially stable and then increasing abundance for the period 1986–2003, in accordance with fishery-independent survey and stock assessment estimates.

Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness.

Many psychological concepts are unobserved and usually represented as latent factors apprehended through multiple observed indicators. When multiple-subject multivariate time series data are available, dynamic factor analysis models with random effects offer one way of modeling patterns of within- and between-person variations by combining factor analysis and time series analysis at the factor level. Using the Dirichlet process (DP) as a nonparametric prior for individual-specific time series parameters further allows the distributional forms of these parameters to deviate from commonly imposed (e.g., normal or other symmetric) functional forms, arising as a result of these parameters' restricted ranges. Given the complexity of such models, a thorough sensitivity analysis is critical but computationally prohibitive. We propose a Bayesian local influence method that allows for simultaneous sensitivity analysis of multiple modeling components within a single fitting of the model of choice. Five illustrations and an empirical example are provided to demonstrate the utility of the proposed approach in facilitating the detection of outlying cases and common sources of misspecification in dynamic factor analysis models, as well as identification of modeling components that are sensitive to changes in the DP prior specification.

Within-lake habitat heterogeneity mediates community response to warming trends.

Climate change is rapidly altering many aquatic systems, and life history traits and physiological diversity create differences in organism responses. In addition, habitat diversity may be expressed on small spatial scales, and it is therefore necessary to account for variation among both species and locations when evaluating climate impacts on biological communities. Here, we investigated the effects of temperature and spatial heterogeneity on long-term community composition in a large boreal lake. We used a five-decade time series of water temperature and relative abundance of fish species captured in the littoral zone throughout the summer at 10 discrete locations around the lake. We applied a spatial dynamic factor analysis (SDFA) model to this time series, which estimates the sensitivity of each species to changing water temperature while accounting for spatiotemporal variation. This analysis described the trend in community composition at each sampling location in the lake, given their different trends in temperature over time. The SDFA indicated different magnitude and direction of species responses to temperature; some species increased while others decreased in abundance. The model also identified five unique trends in species abundance across sites and time, indicating residual dynamics in abundance after accounting for temperature effects. Thus, different regions in the lake have experienced different trajectories in community change associated with different rates of temperature change. These results highlight the importance of considering habitat heterogeneity in explaining and predicting future species abundances, and our model provides a means of visualizing spatially-explicit temporal variation in species' dynamics.

Ambient Precursor Gaseous Pollutants and Meteorological Conditions Controlling Variations of Particulate Matter Concentrations

In many areas of China, rapid industrialization, urbanization, and transportation development have resulted in PM2.5 concentrations higher than the WHO‐recommended level. The precursor gaseous pollutants, which will be finally transformed to PM2.5, should be identified and controlled in the early stage. Dynamic factor analysis (DFA) was performed to investigate how precursor gaseous pollutants and meteorological factors associate with the temporal dynamics of fine particulate matter (PM2.5) in Wuhan in 2013. The optimal DFA model satisfactorily accounted for the fluctuations in PM2.5 (coefficient of efficiency was 0.88). The results showed that the temporal dynamics of PM2.5 in Wuhan were primarily associated with sulfur oxides, nitrogen oxides (NOx), carbon monoxide (CO), relative humidity, temperature, and wind speed. PM2.5 concentrations were also slightly affected by three common trends mainly representing soil dust and urbanization process. Temperature contributed more to the long‐term dynamics of PM2.5 than wind speed and relative humidity did. High temperature favors the formation of PM2.5. However, relative humidity was negatively contributed to PM2.5. NO2 and CO were the two major precursor gaseous pollutants contributing to the compositions of PM2.5. In Wuhan, NO2 and CO mainly emitted from motor vehicles and industrial processes should be restricted, because these precursor emissions will finally format particulate matter.

Preliminary recovery of coastal sharks in the south‐east United States

AbstractRelative abundance of many shark species in the Atlantic is assessed by compiling data from several independently conducted, but somewhat spatially limited surveys. Although these localized surveys annually sample the same populations, resulting trends in yearly indices often conflict with one another, thereby hindering interpretation of abundance patterns at broad spatial scales. We used delta‐lognormal generalized linear models (GLMs) to generate indices of abundance for seven Atlantic coastal shark species from six fishery‐independent surveys along the US east coast and Gulf of Mexico from 1975 to 2014. These indices were further analysed using dynamic factor analysis (DFA) to produce simplified, broad‐scale common trends in relative abundance over the entire sampled distribution. Effects of drivers including the North Atlantic Oscillation index, the Atlantic Multidecadal Oscillation index, annually averaged sea surface temperature and species landings were evaluated within the DFA model. The two decadal oscillations and species landings were shown to affect shark distribution along south‐east US coast. Estimated common trends of relative abundance for all large coastal shark species showed similar decreasing patterns into the early 1990s, periods of sustained low index values thereafter and recent indications of recovery. Small coastal shark species exhibited more regional variability in their estimated common trends, such that two common trends were required to adequately describe patterns in relative abundance throughout the Gulf of Mexico and Atlantic. Overall, all species’ (except the Gulf of Mexico blacknose shark) time series concluded with an increasing trend, suggestive of initial recovery from past exploitation.