Quantifying flow–ecology relationships with functional linear models

Quantifying flow–ecology relationships across flow regime class and ecoregions in South Carolina

Analysis of hydrologic time series and fish community data across the Tennessee River Valley identified three hydrologic metrics essential to habitat suitability and food availability for insectivorous fish communities in streams of the Tennessee River Valley: constancy (flow stability or temporal invariance), frequency of moderate flooding (frequency of habitat disturbance), and rate of streamflow recession. Initial datasets included 1100 fish community sites and 300 streamgages. Reduction of these datasets to sites with coexisting data yielded 33 sites with streamflow and fish community data for analysis. Identification of critical hydrologic metrics was completed using a multivariate correlation procedure that maximizes the rank correlation between the hydrologic metrics and fish community resemblance matrices. Quantile regression was used to define thresholds of potential ranges of insectivore scores for given values of the hydrologic metrics. Increased values of constancy and insectivore scores were positively correlated. Constancy of streamflow maintains wetted perimeter, which is important for providing habitat for fish spawning and increased surface area for invertebrate colonization and reproduction. Site scores for insectivorous fish increased as the frequency of moderate flooding (3 times the median annual streamflow) decreased, suggesting that insectivorous fish communities respond positively to less frequent disturbance and a more stable habitat. Increased streamflow recession rates were associated with decreased insectivore scores. Increased streamflow recession can strand fish in pools and other areas that are disconnected from flowing water and remove invertebrates as food sources that were suspended during high‐streamflow events. Copyright © 2008 John Wiley & Sons, Ltd.

Our work focuses on the functional linear model given by \(Y=\langle\theta,X\rangle+\epsilon,\) where Y and e are real random variables, X is a zero-mean random variable valued in a Hilbert space \((\mathcal{H},\langle\cdot,\cdot\rangle)\), and \(\theta\in\mathcal{H}\) is the fixed model parameter. Using an initial sample \(\{(X_i,Y_i)\}_{i=1}^n\), a bootstrap resampling \(Y_i^{*}=\langle\hat{\theta},X_i\rangle+\hat{\epsilon}_i^{*}\), \(i=1,\ldots,n\), is proposed, where \(\hat{\theta}\) is a general pilot estimator, and \(\hat{\epsilon}_i^{*}\) is a naive or wild bootstrap error. The obtained consistency of bootstrap allows us to calibrate distributions as \(P_X\{\sqrt{n}(\langle\hat{\theta},x\rangle-\langle\theta,x\rangle)\leq y\}\) for a fixed x, where P X is the probability conditionally on \(\{X_i\}_{i=1}^n\). Different applications illustrate the usefulness of bootstrap for testing different hypotheses related with θ, and a brief simulation study is also presented.

Meta-analysis of genetic data must account for differences among studies including study designs, markers genotyped, and covariates. The effects of genetic variants may differ from population to population, i.e., heterogeneity. Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed. In this article, functional linear models are developed for meta-analyses that connect genetic data to quantitative traits, adjusting for covariates. The models can be used to analyze rare variants, common variants, or a combination of the two. Both likelihood-ratio test (LRT) and F-distributed statistics are introduced to test association between quantitative traits and multiple variants in one genetic region. Extensive simulations are performed to evaluate empirical type I error rates and power performance of the proposed tests. The proposed LRT and F-distributed statistics control the type I error very well and have higher power than the existing methods of the meta-analysis sequence kernel association test (MetaSKAT). We analyze four blood lipid levels in data from a meta-analysis of eight European studies. The proposed methods detect more significant associations than MetaSKAT and the P-values of the proposed LRT and F-distributed statistics are usually much smaller than those of MetaSKAT. The functional linear models and related test statistics can be useful in whole-genome and whole-exome association studies.

The purpose of this work was to develop and evaluate the accuracy of several predictive models of variation in tumor volume throughout the course of radiation therapy. Nineteen patients with oropharyngeal cancers were imaged daily with CT-on-rails for image-guided alignment per an institutional protocol. The daily volumes of 35 tumors in these 19 patients were determined and used to generate (1) a linear model in which tumor volume changed at a constant rate, (2) a general linear model that utilized the power fit relationship between the daily and initial tumor volumes, and (3) a functional general linear model that identified and exploited the primary modes of variation between time series describing the changing tumor volumes. Primary and nodal tumor volumes were examined separately. The accuracy of these models in predicting daily tumor volumes were compared with those of static and linear reference models using leave-one-out cross-validation. In predicting the daily volume of primary tumors, the general linear model and the functional general linear model were more accurate than the static reference model by 9.9% (range: -11.6%-23.8%) and 14.6% (range: -7.3%-27.5%), respectively, and were more accurate than the linear reference model by 14.2% (range: -6.8%-40.3%) and 13.1% (range: -1.5%-52.5%), respectively. In predicting the daily volume of nodal tumors, only the 14.4% (range: -11.1%-20.5%) improvement in accuracy of the functional general linear model compared to the static reference model was statistically significant. A general linear model and a functional general linear model trained on data from a small population of patients can predict the primary tumor volume throughout the course of radiation therapy with greater accuracy than standard reference models. These more accurate models may increase the prognostic value of information about the tumor garnered from pretreatment computed tomography images and facilitate improved treatment management.

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously estimate the bandwidths in the regression function and kernel error density by minimizing the Kullback-Leibler divergence. For estimating the regression function and error density, a series of simulation studies demonstrate that the functional partial linear model gives improved estimation and forecast accuracies compared with the functional principal component regression and functional nonparametric regression. Using a spectroscopy dataset, the functional partial linear model yields better forecast accuracy than some commonly used functional regression models. As a by-product of the Bayesian method, a pointwise prediction interval can be obtained, and marginal likelihood can be used to select the optimal semi-metric.

The 1997/1998 Mass Mortality of Corals: Effects on Fish Communities on a Tanzanian Coral Reef

This paper analyses the effects of environmental flows on water quality within a highly regulated basin, focusing on the Turia River basin in the eastern Iberian Peninsula. Through water management and water quality models, a series of simulations were conducted, introducing variations in the outflows of the Loriguilla reservoir to evaluate the effects of different environmental flow scenarios on water quality, particularly at the location of the intake for the water supply to Valencia. Three environmental flow scenarios were analyzed, alongside an alternative management scenario, considering their implications on water quality and reliability of water demand. The findings of this paper, particularly the nitrate (NO3−) concentration evolution, highlight the influence of minimum e-flow and e-flow regimes on water quality within the basin. These results suggest that while modifying the current flow regime can lead to some improvements in nitrate concentrations at the Valencia supply intake point, the primary cause of high nitrate concentrations is attributed to irrigation return flow and the pre-existing contamination of the aquifer. This analysis offers valuable insights into the complexities of water quality management in regulated basins, emphasizing the need for a multi-faceted approach to address the diverse factors influencing water quality and demand supply reliability.

The Caribbean has seen a dramatic loss of coral over the last 30 years due to direct and indirect anthropogenic factors, causing a decrease in reef three-dimensional complexity and fish abundance and diversity. Restoration practices, such as outplanting coral colonies onto degraded reefs, are increasingly used to revive reef ecosystems to preserve fisheries, tourism, and ecosystem functions, which are currently valued at $375 billion globally. However, few studies have examined whether coral restoration and the consequent addition of structural complexity can restore reef ecosystems. Thus, this study aims to better understand early fish community dynamics following restoration using Acropora cervicornis, a major reef building coral and focus species for restoration that has experienced a greater than 80% drop in cover since 1980. To examine fish dynamics after restoration, surveys of fish, environmental conditions, benthic seafloor characteristics, and rugosity were conducted on outplanted plots and control plots without outplants. Surveys were conducted off the north shore of St. Croix, USVI (17°46′15.0″N, 64°49′03.8″W) from May 30, 2016 to August 4, 2016, and on December 28, 2016, and January 4, 2017. Within a week of outplanting, fish abundance was significantly higher in experimental plots compared to controls. After outplanting, there was also an increase in fish species richness and a significant shift in fish community composition over time. These results demonstrate the early stages of fish colonization after outplanting A. cervicornis, providing insight into how restoration can cause rapid change in fish abundance, richness, and community composition.

Checking the adequacy of functional linear quantile regression model

Genome-wide association analysis is an important approach to identify genetic variants associated with complex traits. Complex traits are not only affected by single gene loci, but also by the interaction of multiple gene loci. Studies of association between gene regions and quantitative traits are of great significance in revealing the genetic mechanism of biological development. There have been a lot of studies on single-gene region association analysis, but the application of functional linear models in multi-gene region association analysis is still less. In this paper, a functional multi-gene region association analysis test method is proposed based on the functional linear model. From the three directions of common multi-gene region method, multi-gene region weighted method and multi-gene region loci weighted method, that test method is studied combined with computer simulation. The following conclusions are obtained through computer simulation: (a) The functional multi-gene region association analysis test method has higher power than the functional single gene region association analysis test method; (b) The functional multi-gene region weighted method performs better than the common functional multi-gene region method; (c) the functional multi-gene region loci weighted method is the best method for association analysis on three directions of the common multi-gene region method; (d) the performance of the Step method and Multi-gene region loci weighted Step for multi-gene regions is the best in general. Functional multi-gene region association analysis test method can theoretically provide a feasible method for the study of complex traits affected by multiple genes.

The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of ℝ and the response is scalar. The response is modelled as Y=Ψ(X)+ɛ, where Ψ is some linear continuous operator defined on the space of square integrable functions and valued in ℝ. The random input X is independent from the noise ɛ. In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of Ψ restricted to the Hilbert space generated by the random variable X. We introduce two test statistics based on the norm of the empirical cross‐covariance operator of (X,Y). The first test statistic relies on a χ2 approximation and we show the asymptotic normality of the second one under appropriate conditions on the covariance operator of X. The test procedures can be applied to check a given relationship between X and Y. The method is illustrated through a simulation study.

This paper studies how to identify in uential curves in the functional linear model in which the response is scalar and the predictor is functional and how to measure their e ects on the estimation of the model and on the forecasts, when the model is estimated by the principal components method. For that, we introduce and analyze two statistics that measure the inuence of each curve on the functional slope estimate of the model, which are generalizations of the measures proposed for the standard regression model by Cook (1977) and Pena (2005), respectively.

Point process data have become increasingly popular these days. For example, many of the data captured in electronic health records (EHR) are in the format of point process data. It is of great interest to study the association between a point process predictor and a scalar response using generalized functional linear regression models. Various generalized functional linear regression models have been developed under different settings in the past decades. However, existing methods can only deal with functional or longitudinal predictors, not point process predictors. In this article, we propose a novel generalized functional linear regression model for a point process predictor. Our proposed model is based on the joint modeling framework, where we adopt a log-Gaussian Cox process model for the point process predictor and a generalized linear regression model for the outcome. We also develop a new algorithm for fast model estimation based on the Gaussian variational approximation method. We conduct extensive simulation studies to evaluate the performance of our proposed method and compare it to competing methods. The performance of our proposed method is further demonstrated on an EHR dataset of patients admitted into the intensive care units of the Beth Israel Deaconess Medical Center between 2001 and 2008.

The Wadi El-Rayan lakes are important aquatic environments located at the border of the great North African Sahara. Quantifying the temporal changes in these lakes due to natural and/or anthropogenic stressors is critical when assessing potential impacts on aquatic ecosystem health and the sustainability of fisheries. To detect the changes in fish communities and their drivers, the landing composition of the Wadi El-Rayan lakes over the past 30 years was quantitatively analyzed. The areas of the lakes dramatically decreased from 110 km2 in 1991 to 73 km2 in 2019. The loss of the lake area was attributed to climate warming, where the evaporation rate exceeded the volume of recharge and the recharge decreased due to an increase in agriculture and aquaculture. The total landing significantly increased in the past three decades due to an increase in the fishing effort (number of licensed boats). Nile tilapia, mullet, and grass carp dominated the landings. The pelagic-to-demersal ratio indicated a shift in the fish community composition towards demersal species. This shift was attributed to an increase in the eutrophication level. The fish communities of the landing data were clustered into four distinct groups. These clusters were significantly differentiated (p < 0.001) in both a PERMANOVA test and a PCA plot. There was a gradual replacement of the dominant species among these clusters. The most recent cluster (2018–2019) was characterized by rare species dominating the community. This shift in species composition suggests that target taxa may have been overexploited. The total landing also decreased, which may have been a result of climate warming. Furthermore, the presence of alien and warm-water species significantly increased. The fish community structure and composition shift could be attributed to anthropogenic (mismanagement) and natural climatic changes (warming).