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Hay EM, McGee MD, White CR, Chown SL. Body size shapes song in honeyeaters. Proc Biol Sci 2024; 291:20240339. [PMID: 38654649 PMCID: PMC11040244 DOI: 10.1098/rspb.2024.0339] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Accepted: 03/22/2024] [Indexed: 04/26/2024] Open
Abstract
Birdsongs are among the most distinctive animal signals. Their evolution is thought to be shaped simultaneously by habitat structure and by the constraints of morphology. Habitat structure affects song transmission and detectability, thus influencing song (the acoustic adaptation hypothesis), while body size and beak size and shape necessarily constrain song characteristics (the morphological constraint hypothesis). Yet, support for the acoustic adaptation and morphological constraint hypotheses remains equivocal, and their simultaneous examination is infrequent. Using a phenotypically diverse Australasian bird clade, the honeyeaters (Aves: Meliphagidae), we compile a dataset consisting of song, environmental, and morphological variables for 163 species and jointly examine predictions of these two hypotheses. Overall, we find that body size constrains song frequency and pace in honeyeaters. Although habitat type and environmental temperature influence aspects of song, that influence is indirect, likely via effects of environmental variation on body size, with some evidence that elevation constrains the evolution of song peak frequency. Our results demonstrate that morphology has an overwhelming influence on birdsong, in support of the morphological constraint hypothesis, with the environment playing a secondary role generally via body size rather than habitat structure. These results suggest that changing body size (a consequence of both global effects such as climate change and local effects such as habitat transformation) will substantially influence the nature of birdsong.
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Affiliation(s)
- Eleanor M. Hay
- School of Biological Sciences, Monash University, Melbourne, Victoria 3800, Australia
| | - Matthew D. McGee
- School of Biological Sciences, Monash University, Melbourne, Victoria 3800, Australia
| | - Craig R. White
- School of Biological Sciences, Monash University, Melbourne, Victoria 3800, Australia
| | - Steven L. Chown
- School of Biological Sciences, Monash University, Melbourne, Victoria 3800, Australia
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Loguercio S, Calverley BC, Wang C, Shak D, Zhao P, Sun S, Budinger GS, Balch WE. Understanding the host-pathogen evolutionary balance through Gaussian process modeling of SARS-CoV-2. Patterns (N Y) 2023; 4:100800. [PMID: 37602209 PMCID: PMC10436005 DOI: 10.1016/j.patter.2023.100800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 02/22/2023] [Accepted: 06/22/2023] [Indexed: 08/22/2023]
Abstract
We have developed a machine learning (ML) approach using Gaussian process (GP)-based spatial covariance (SCV) to track the impact of spatial-temporal mutational events driving host-pathogen balance in biology. We show how SCV can be applied to understanding the response of evolving covariant relationships linking the variant pattern of virus spread to pathology for the entire SARS-CoV-2 genome on a daily basis. We show that GP-based SCV relationships in conjunction with genome-wide co-occurrence analysis provides an early warning anomaly detection (EWAD) system for the emergence of variants of concern (VOCs). EWAD can anticipate changes in the pattern of performance of spread and pathology weeks in advance, identifying signatures destined to become VOCs. GP-based analyses of variation across entire viral genomes can be used to monitor micro and macro features responsible for host-pathogen balance. The versatility of GP-based SCV defines starting point for understanding nature's evolutionary path to complexity through natural selection.
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Affiliation(s)
| | - Ben C. Calverley
- Department of Molecular Medicine, Scripps Research, La Jolla, CA, USA
| | - Chao Wang
- Department of Molecular Medicine, Scripps Research, La Jolla, CA, USA
| | - Daniel Shak
- Department of Molecular Medicine, Scripps Research, La Jolla, CA, USA
| | - Pei Zhao
- Department of Molecular Medicine, Scripps Research, La Jolla, CA, USA
| | - Shuhong Sun
- Department of Molecular Medicine, Scripps Research, La Jolla, CA, USA
| | - G.R. Scott Budinger
- Division of Pulmonary and Critical Care Medicine, Northwestern University, Chicago, IL, USA
| | - William E. Balch
- Department of Molecular Medicine, Scripps Research, La Jolla, CA, USA
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Ali R, Mitcham T, Brickson L, Hu W, Doyley M, Rubens D, Ignjatovic Z, Duric N, Dahl J. Separation of mainlobe and sidelobe contributions to B-mode ultrasound images based on the aperture spectrum. J Med Imaging (Bellingham) 2022; 9:067001. [PMID: 36337381 PMCID: PMC9626368 DOI: 10.1117/1.jmi.9.6.067001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 10/12/2022] [Indexed: 03/06/2023] Open
Abstract
Purpose Isolating the mainlobe and sidelobe contribution to the ultrasound image can improve imaging contrast by removing off-axis clutter. Previous work achieves this separation of mainlobe and sidelobe contributions based on the covariance of received signals. However, the formation of a covariance matrix at each imaging point can be computationally burdensome and memory intensive for real-time applications. Our work demonstrates that the mainlobe and sidelobe contributions to the ultrasound image can be isolated based on the receive aperture spectrum, greatly reducing computational and memory requirements. Approach The separation of mainlobe and sidelobe contributions to the ultrasound image is shown in simulation, in vitro, and in vivo using the aperture spectrum method and multicovariate imaging of subresolution targets (MIST). Contrast, contrast-to-noise-ratio (CNR), and speckle signal-to-noise-ratio are used to compare the aperture spectrum approach with MIST and conventional delay-and-sum (DAS) beamforming. Results The aperture spectrum approach improves contrast by 1.9 to 6.4 dB beyond MIST and 8.9 to 13.5 dB beyond conventional DAS B-mode imaging. However, the aperture spectrum approach yields speckle texture similar to DAS. As a result, the aperture spectrum-based approach has less CNR than MIST but greater CNR than conventional DAS. The CPU implementation of the aperture spectrum-based approach is shown to reduce computation time by a factor of 9 and memory consumption by a factor of 128 for a 128-element transducer. Conclusions The mainlobe contribution to the ultrasound image can be isolated based on the receive aperture spectrum, which greatly reduces the computational cost and memory requirement of this approach as compared with MIST.
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Affiliation(s)
- Rehman Ali
- University of Rochester Medical Center, Department of Imaging Sciences, Rochester, New York, United States
- Stanford University School of Medicine, Department of Radiology, Palo Alto, California, United States
| | - Trevor Mitcham
- University of Rochester Medical Center, Department of Imaging Sciences, Rochester, New York, United States
| | - Leandra Brickson
- Stanford University School of Medicine, Department of Radiology, Palo Alto, California, United States
| | - Wentao Hu
- University of Rochester, Department of Electrical and Computer Engineering, Rochester, New York, United States
| | - Marvin Doyley
- University of Rochester, Department of Electrical and Computer Engineering, Rochester, New York, United States
| | - Deborah Rubens
- University of Rochester Medical Center, Department of Imaging Sciences, Rochester, New York, United States
| | - Zeljko Ignjatovic
- University of Rochester, Department of Electrical and Computer Engineering, Rochester, New York, United States
| | - Nebojsa Duric
- University of Rochester Medical Center, Department of Imaging Sciences, Rochester, New York, United States
- University of Rochester, Department of Electrical and Computer Engineering, Rochester, New York, United States
| | - Jeremy Dahl
- Stanford University School of Medicine, Department of Radiology, Palo Alto, California, United States
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Colloby SJ, Nathan PJ, Bakker G, Lawson RA, Yarnall AJ, Burn DJ, O'Brien JT, Taylor JP. Spatial Covariance of Cholinergic Muscarinic M 1 /M 4 Receptors in Parkinson's Disease. Mov Disord 2021; 36:1879-1888. [PMID: 33973693 DOI: 10.1002/mds.28564] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 03/01/2021] [Indexed: 01/07/2023] Open
Abstract
BACKGROUND Parkinson's disease (PD) is associated with cholinergic dysfunction, although the role of M1 and M4 receptors remains unclear. OBJECTIVE To investigate spatial covariance patterns of cholinergic muscarinic M1 /M4 receptors in PD and their relationship with cognition and motor symptoms. METHODS Some 19 PD and 24 older adult controls underwent 123 I-iodo-quinuclidinyl-benzilate (QNB) (M1 /M4 receptor) and 99m Tc-exametazime (perfusion) single-photon emission computed tomography (SPECT) scanning. We implemented voxel principal components analysis, producing a series of images representing patterns of intercorrelated voxels across individuals. Linear regression analyses derived specific M1 /M4 spatial covariance patterns associated with PD. RESULTS A cholinergic M1 /M4 pattern that converged onto key hubs of the default, auditory-visual, salience, and sensorimotor networks fully discriminated PD patients from controls (F1,41 = 135.4, P < 0.001). In PD, we derived M1 /M4 patterns that correlated with global cognition (r = -0.62, P = 0.008) and motor severity (r = 0.53, P = 0.02). Both patterns emerged with a shared topography implicating the basal forebrain as well as visual, frontal executive, and salience circuits. Further, we found a M1 /M4 pattern that predicted global cognitive decline (r = 0.46, P = 0.04) comprising relative decreased binding within default and frontal executive networks. CONCLUSIONS Cholinergic muscarinic M1 /M4 modulation within key brain networks were apparent in PD. Cognition and motor severity were associated with a similar topography, inferring both phenotypes possibly rely on related cholinergic mechanisms. Relative decreased M1 /M4 binding within default and frontal executive networks could be an indicator of future cognitive decline. © 2021 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.
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Affiliation(s)
- Sean J Colloby
- Translational and Clinical Research Institute, Faculty of Medical Sciences, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne, United Kingdom
| | - Pradeep J Nathan
- Department of Psychiatry, University of Cambridge, Herschel Smith Building for Brain & Mind Sciences, Cambridge, United Kingdom
| | - Geor Bakker
- Experimental Medicine, Sosei Heptares, Cambridge, United Kingdom
| | - Rachael A Lawson
- Translational and Clinical Research Institute, Faculty of Medical Sciences, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne, United Kingdom
| | - Alison J Yarnall
- Translational and Clinical Research Institute, Faculty of Medical Sciences, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne, United Kingdom
| | - David J Burn
- Population Health Science Institute, Faculty of Medical Sciences, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne, United Kingdom
| | - John T O'Brien
- Department of Psychiatry, University of Cambridge, Herschel Smith Building for Brain & Mind Sciences, Cambridge, United Kingdom
| | - John-Paul Taylor
- Translational and Clinical Research Institute, Faculty of Medical Sciences, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne, United Kingdom
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Morgan MR, Trahey GE, Walker WF. Intrinsic Tradeoffs in Multi-Covariate Imaging of Sub-Resolution Targets. IEEE Trans Ultrason Ferroelectr Freq Control 2020; 67:1980-1992. [PMID: 32396077 PMCID: PMC7565283 DOI: 10.1109/tuffc.2020.2993241] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Multi-covariate Imaging of Sub-resolution Targets (MIST) is an estimation-based method of imaging the statistics of diffuse scattering targets. MIST estimates the contributions of a set of covariance models to the echo data covariance matrix. Models are defined based on a spatial decomposition of the theoretical transmit intensity distribution into ON-axis and OFF-axis contributions, delineated by a user-specified spatial cutoff. We define this cutoff as the region of interest width (ROI width). In our previous work, we selected the ROI width as the first zero crossing separating the mainlobe from the sidelobe regions. This article explores the effects of varying two key parameters on MIST image quality: 1) ROI width and 2) the degree of spatial averaging of the measured echo data covariance matrix. These results demonstrate a fundamental tradeoff between resolution and speckle texture. We characterize MIST imaging performance across these tunable parameters in a number of simulated, phantom, and in vivo liver applications. We consider performance in noise, fidelity to native contrast, resolution, and speckle texture. MIST is also compared with varying levels of spatial and frequency compounding, demonstrating quantitative improvements in image quality at comparable levels of speckle reduction. In an in vivo example, optimized MIST images demonstrated 20.2% and 13.4% improvements in contrast-to-noise ratio over optimized spatial and frequency compounding images, respectively. These results present a framework for selecting MIST parameters to maximize speckle signal-to-noise ratio without an appreciable loss in resolution.
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Morgan MR, Bottenus N, Trahey GE, Walker WF. Synthetic Aperture Focusing for Multi-Covariate Imaging of Sub-Resolution Targets. IEEE Trans Ultrason Ferroelectr Freq Control 2020; 67:1166-1177. [PMID: 31940530 PMCID: PMC7337595 DOI: 10.1109/tuffc.2020.2966116] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Coherence-based imaging methods suffer from reduced image quality outside the depth of field for focused ultrasound transmissions. Synthetic aperture methods can extend the depth of field by coherently compounding time-delayed echo data from multiple transmit events. Recently, our group has presented the Multi-covariate Imaging of Sub-resolution Targets (MIST), an estimation-based method to image the statistical properties of diffuse targets. MIST has demonstrated improved image quality over conventional delay-and-sum, but like many coherence-based imaging methods, suffers from limited depth of field artifacts. This article applies synthetic aperture focusing to MIST, which is evaluated using focused, plane-wave, and diverging-wave transmit geometries. Synthetic aperture MIST is evaluated in simulation, phantom, and in vivo applications, demonstrating consistent improvements in contrast-to-noise ratio (CNR) over conventional dynamic receive MIST outside the transmit depth of field, with approximately equivalent results between synthetic transmit geometries. In vivo synthetic aperture MIST images demonstrated 16.8 dB and 16.6% improvements in contrast and CNR, respectively, over dynamic receive MIST images, as well as 17.4 dB and 32.3% improvements over synthetic aperture B-Mode. MIST performance is characterized in the space of plane-wave imaging, where the total plane-wave count is reduced through coarse angular sampling or total angular span. Simulation and experimental results indicate wide applicability of MIST to synthetic aperture imaging methods.
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Wang C, Balch WE. Bridging Genomics to Phenomics at Atomic Resolution through Variation Spatial Profiling. Cell Rep 2020; 24:2013-2028.e6. [PMID: 30134164 PMCID: PMC6261431 DOI: 10.1016/j.celrep.2018.07.059] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2018] [Revised: 06/25/2018] [Accepted: 07/16/2018] [Indexed: 01/04/2023] Open
Abstract
To understand the impact of genome sequence variation (the genotype) responsible for biological diversity and human health (the phenotype) including cystic fibrosis and Alzheimer's disease, we developed a Gaussian-process-based machine learning (ML) approach, variation spatial profiling (VSP). VSP uses a sparse collection of known variants found in the population that perturb the protein fold to define unknown variant function based on the emergent general principle of spatial covariance (SCV). SCV quantitatively captures the role of proximity in genotype-to-phenotype spatial-temporal relationships. Phenotype landscapes generated through SCV provide a platform that can be used to describe the functional properties that drive sequence-to-function-to-structure design of the polypeptide fold at atomic resolution. We provide proof of principle that SCV can enable the use of population-based genomic platforms to define the origins and mechanism of action of genotype-to-phenotype transformations contributing to the health and disease of an individual.
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Affiliation(s)
- Chao Wang
- Department of Molecular Medicine, The Scripps Research Institute (TSRI), La Jolla, CA 92037, USA
| | - William E Balch
- Department of Molecular Medicine, The Scripps Research Institute (TSRI), La Jolla, CA 92037, USA; The Skaggs Institute for Chemical Biology, The Scripps Research Institute (TSRI), La Jolla, CA 92037, USA.
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Wang C, Zhao P, Sun S, Teckman J, Balch WE. Leveraging Population Genomics for Individualized Correction of the Hallmarks of Alpha-1 Antitrypsin Deficiency. Chronic Obstr Pulm Dis 2020; 7:224-246. [PMID: 32726074 DOI: 10.15326/jcopdf.7.3.2019.0167] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Deep medicine is rapidly moving towards a high-definition approach for therapeutic management of the patient as an individual given the rapid progress of genome sequencing technologies and machine learning algorithms. While considered a monogenic disease, alpha-1 antitrypsin (AAT) deficiency (AATD) patients present with complex and variable phenotypes we refer to as the "hallmarks of AATD" that involve distinct molecular mechanisms in the liver, plasma and lung tissues, likely due to both coding and non-coding variation as well as genetic and environmental modifiers in different individuals. Herein, we briefly review the current therapeutic strategies for the management of AATD. To embrace genetic diversity in the management of AATD, we provide an overview of the disease phenotypes of AATD patients harboring different AAT variants. Linking genotypic diversity to phenotypic diversity illustrates the potential for sequence-specific regions of AAT protein fold design to play very different roles during nascent synthesis in the liver and/or function in post-liver plasma and lung environments. We illustrate how to manage diversity with recently developed machine learning (ML) approaches that bridge sequence-to-function-to-structure knowledge gaps based on the principle of spatial covariance (SCV). SCV relationships provide a deep understanding of the genotype to phenotype transformation initiated by AAT variation in the population to address the role of genetic and environmental modifiers in the individual. Embracing the complexity of AATD in the population is critical for risk management and therapeutic intervention to generate a high definition medicine approach for the patient.
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Affiliation(s)
- Chao Wang
- Department of Molecular Medicine, Scripps Research, La Jolla, California
| | - Pei Zhao
- Department of Molecular Medicine, Scripps Research, La Jolla, California
| | - Shuhong Sun
- Department of Molecular Medicine, Scripps Research, La Jolla, California
| | - Jeffrey Teckman
- Pediatrics and Biochemistry, Saint Louis University, and Cardinal Glennon Children's Medical Center, St. Louis, Missouri
| | - William E Balch
- Department of Molecular Medicine, Scripps Research, La Jolla, California
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Colloby SJ, Taylor JP, Davison CM, Lloyd JJ, Firbank MJ, McKeith IG, O'Brien JT. Multivariate spatial covariance analysis of 99mTc-exametazime SPECT images in dementia with Lewy bodies and Alzheimer's disease: utility in differential diagnosis. J Cereb Blood Flow Metab 2013; 33:612-8. [PMID: 23361395 DOI: 10.1038/jcbfm.2013.2] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
We examined (99m)Tc-exametazime brain blood flow single-photon emission computed tomography (SPECT) images using a spatial covariance analysis (SCA) approach to assess its diagnostic value in distinguishing dementia with Lewy bodies (DLB) from Alzheimer's disease (AD). Voxel SCA was simultaneously applied to a set of preprocessed images (AD, n=40; DLB, n=26), generating a series of eigenimages representing common intercorrelated voxels in AD and DLB. Linear regression derived a spatial covariance pattern (SCP) that discriminated DLB from AD. To investigate the diagnostic value of the model SCP, the SCP was validated by applying it to a second, independent, AD and DLB cohort (AD, n=34; DLB, n=29). Mean SCP expressions differed between AD and DLB (F(1,64)=36.2, P<0.001) with good diagnostic accuracy (receiver operating characteristic (ROC) curve area 0.87, sensitivity 81%, specificity 88%). Forward application of the model SCP to the independent cohort revealed similar differences between groups (F(1,61)=38.4, P<0.001), also with good diagnostic accuracy (ROC 0.86, sensitivity 80%, specificity 80%). Multivariate analysis of blood flow SPECT data appears to be robust and shows good diagnostic accuracy in two independent cohorts for distinguishing DLB from AD.
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Abstract
We demonstrate a novel imaging technique, named short-lag spatial coherence (SLSC) imaging, which uses short distance (or lag) values of the coherence function of backscattered ultrasound to create images. Simulations using Field II are used to demonstrate the detection of lesions of varying sizes and contrasts with and without acoustical clutter in the backscattered data. B-mode and SLSC imaging are shown to be nearly equivalent in lesion detection, based on the contrast-to-noise ratio (CNR) of the lesion, in noise-free conditions. The CNR of the SLSC image, however, can be adjusted to achieve an optimal value at the expense of image smoothness and resolution. In the presence of acoustic clutter, SLSC imaging yields significantly higher CNR than B-mode imaging and maintains higher image quality than B-mode with increasing noise. Compression of SLSC images is shown to be required under high-noise conditions but is unnecessary under no- and low-noise conditions. SLSC imaging is applied to in vivo imaging of the carotid sheath and demonstrates significant gains in CNR as well as visualization of arterioles in the carotid sheath. SLSC imaging has a potential application to clutter rejection in ultrasonic imaging.
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Affiliation(s)
- Jeremy J Dahl
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA.
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Abstract
Spectral methods are powerful tools to study and model the dependency structure of spatial temporal processes. However, standard spectral approaches as well as geostatistical methods assume separability and stationarity of the covariance function; these can be very unrealistic assumptions in many settings. In this work, we introduce a general and flexible parametric class of spatial temporal covariance models, that allows for lack of stationarity and separability by using a spectral representation of the process. This new class of covariance models has a unique parameter that indicates the strength of the interaction between the spatial and temporal components; it has the separable covariance model as a particular case. We introduce an application with ambient ozone air pollution data provided by the U.S. Environmental Protection Agency (U.S. EPA).
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Affiliation(s)
- Montserrat Fuentes
- Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, U.S.A
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Abstract
1. Theoretical models predict that spatial synchrony should be enhanced in cyclic populations due to nonlinear phase-locking. 2. This is supported by Rohani et al.'s (1999) comparison of spatial synchrony of epidemics in two childhood diseases prior to and during the vaccination era. Measles is both more synchronous and more cyclic before vaccination. Whooping cough, in contrast, is more synchronous during the vaccination era, during which multiannual fluctuations are also more conspicuous. 3. Steen et al. (1990) analysed historic records of cyclic rodents, to show that cyclicity was lost during the early part of the 20th century. I reanalyse the data, and find that the loss of cyclicity is associated with loss of regional synchrony. 4. I use a coupled map lattice model to show that imperfect phase-locking provides an alternative explanation for regionwide synchrony of cyclic populations.
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Affiliation(s)
- Ottar N Bjørnstad
- National Center for Ecological Analysis and Synthesis, 735 State St., Suite 300, Santa Barbara, California 93101-3351 USA
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