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Edwards AM, Rogers LA, Holt CA. Explaining empirical dynamic modelling using verbal, graphical and mathematical approaches. Ecol Evol 2024; 14:e10903. [PMID: 38751824 PMCID: PMC11094587 DOI: 10.1002/ece3.10903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 01/14/2024] [Indexed: 05/18/2024] Open
Abstract
Empirical dynamic modelling (EDM) is becoming an increasingly popular method for understanding the dynamics of ecosystems. It has been applied to laboratory, terrestrial, freshwater and marine systems, used to forecast natural populations and has addressed fundamental ecological questions. Despite its increasing use, we have not found full explanations of EDM in the ecological literature, limiting understanding and reproducibility. Here we expand upon existing work by providing a detailed introduction to EDM. We use three progressively more complex approaches. A short verbal explanation of EDM is then explicitly demonstrated by graphically working through a simple example. We then introduce a full mathematical description of the steps involved. Conceptually, EDM translates a time series of data into a path through a multi-dimensional space, whose axes are lagged values of the time series. A time step is chosen from which to make a prediction. The state of the system at that time step corresponds to a 'focal point' in the multi-dimensional space. The set (called the library) of candidate nearest neighbours to the focal point is constructed, to determine the nearest neighbours that are then used to make the prediction. Our mathematical explanation explicitly documents which points in the multi-dimensional space should not be considered as focal points. We suggest a new option for excluding points from the library that may be useful for short-term time series that are often found in ecology. We focus on the core simplex and S-map algorithms of EDM. Our new R package, pbsEDM, enhances understanding (by outputting intermediate calculations), reproduces our results and can be applied to new data. Our work improves the clarity of the inner workings of EDM, a prerequisite for EDM to reach its full potential in ecology and have wide uptake in the provision of advice to managers of natural resources.
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Affiliation(s)
- Andrew M. Edwards
- Pacific Biological StationFisheries and Oceans CanadaNanaimoBritish ColumbiaCanada
- Department of BiologyUniversity of VictoriaVictoriaBritish ColumbiaCanada
| | - Luke A. Rogers
- Pacific Biological StationFisheries and Oceans CanadaNanaimoBritish ColumbiaCanada
| | - Carrie A. Holt
- Pacific Biological StationFisheries and Oceans CanadaNanaimoBritish ColumbiaCanada
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Cadavid Restrepo AM, Martin BM, Fuimaono S, Clements ACA, Graves PM, Lau CL. Spatial predictive risk mapping of lymphatic filariasis residual hotspots in American Samoa using demographic and environmental factors. PLoS Negl Trop Dis 2023; 17:e0010840. [PMID: 37486947 PMCID: PMC10399813 DOI: 10.1371/journal.pntd.0010840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 06/26/2023] [Indexed: 07/26/2023] Open
Abstract
BACKGROUND American Samoa successfully completed seven rounds of mass drug administration (MDA) for lymphatic filariasis (LF) from 2000-2006. The territory passed the school-based transmission assessment surveys in 2011 and 2015 but failed in 2016. One of the key challenges after the implementation of MDA is the identification of any residual hotspots of transmission. METHOD Based on data collected in a 2016 community survey in persons aged ≥8 years, Bayesian geostatistical models were developed for LF antigen (Ag), and Wb123, Bm14, Bm33 antibodies (Abs) to predict spatial variation in infection markers using demographic and environmental factors (including land cover, elevation, rainfall, distance to the coastline and distance to streams). RESULTS In the Ag model, females had a 26.8% (95% CrI: 11.0-39.8%) lower risk of being Ag-positive than males. There was a 2.4% (95% CrI: 1.8-3.0%) increase in the odds of Ag positivity for every year of age. Also, the odds of Ag-positivity increased by 0.4% (95% CrI: 0.1-0.7%) for each 1% increase in tree cover. The models for Wb123, Bm14 and Bm33 Abs showed similar significant associations as the Ag model for sex, age and tree coverage. After accounting for the effect of covariates, the radii of the clusters were larger for Bm14 and Bm33 Abs compared to Ag and Wb123 Ab. The predictive maps showed that Ab-positivity was more widespread across the territory, while Ag-positivity was more confined to villages in the north-west of the main island. CONCLUSION The findings may facilitate more specific targeting of post-MDA surveillance activities by prioritising those areas at higher risk of ongoing transmission.
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Affiliation(s)
- Angela M Cadavid Restrepo
- School of Public Health, Faculty of Medicine, The University of Queensland, Brisbane, Queensland, Australia
| | - Beatris M Martin
- School of Public Health, Faculty of Medicine, The University of Queensland, Brisbane, Queensland, Australia
| | | | - Archie C A Clements
- Curtin School of Population Health, Faculty of Health Sciences, Curtin University, Perth, Western Australia, Australia
| | - Patricia M Graves
- College of Public Health, Medical and Veterinary Sciences, James Cook University, Cairns, Queensland, Australia
| | - Colleen L Lau
- School of Public Health, Faculty of Medicine, The University of Queensland, Brisbane, Queensland, Australia
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Huang Y, Kausrud K, Hassim A, Ochai SO, van Schalkwyk OL, Dekker EH, Buyantuev A, Cloete CC, Kilian JW, Mfune JKE, Kamath PL, van Heerden H, Turner WC. Environmental drivers of biseasonal anthrax outbreak dynamics in two multihost savanna systems. ECOL MONOGR 2022. [DOI: 10.1002/ecm.1526] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Yen‐Hua Huang
- Wisconsin Cooperative Wildlife Research Unit, Department of Forest and Wildlife Ecology University of Wisconsin‐Madison Madison WI USA
| | - Kyrre Kausrud
- Norwegian Veterinary Institute, PO. box 64 Ås Norway
| | - Ayesha Hassim
- Department of Veterinary Tropical Diseases University of Pretoria Onderstepoort South Africa
| | - Sunday O. Ochai
- Department of Veterinary Tropical Diseases University of Pretoria Onderstepoort South Africa
| | - O. Louis van Schalkwyk
- Department of Veterinary Tropical Diseases University of Pretoria Onderstepoort South Africa
- Office of the State Veterinarian, Department of Agriculture, Land Reform and Rural Development Government of South Africa Skukuza South Africa
- Department of Migration Max Planck Institute of Animal Behavior Radolfzell Germany
| | - Edgar H. Dekker
- Office of the State Veterinarian, Department of Agriculture, Land Reform and Rural Development Government of South Africa Skukuza South Africa
| | - Alexander Buyantuev
- Department of Geography and Planning, University at Albany State University of New York Albany NY USA
| | - Claudine C. Cloete
- Etosha Ecological Institute, Etosha National Park, Ministry of Environment, Forestry and Tourism Namibia
| | - J. Werner Kilian
- Etosha Ecological Institute, Etosha National Park, Ministry of Environment, Forestry and Tourism Namibia
| | - John K. E. Mfune
- Department of Environmental Science University of Namibia Windhoek Namibia
| | | | - Henriette van Heerden
- Department of Veterinary Tropical Diseases University of Pretoria Onderstepoort South Africa
- Faculty of Veterinary Science, Department of Veterinary Tropical Diseases University of Pretoria Onderstepoort South Africa
| | - Wendy C. Turner
- U.S. Geological Survey, Wisconsin Cooperative Wildlife Research Unit, Department of Forest and Wildlife Ecology University of Wisconsin‐Madison Madison WI USA
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Nova N, Deyle ER, Shocket MS, MacDonald AJ, Childs ML, Rypdal M, Sugihara G, Mordecai EA. Susceptible host availability modulates climate effects on dengue dynamics. Ecol Lett 2021; 24:415-425. [PMID: 33300663 PMCID: PMC7880875 DOI: 10.1111/ele.13652] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 11/01/2020] [Indexed: 11/27/2022]
Abstract
Experiments and models suggest that climate affects mosquito-borne disease transmission. However, disease transmission involves complex nonlinear interactions between climate and population dynamics, which makes detecting climate drivers at the population level challenging. By analysing incidence data, estimated susceptible population size, and climate data with methods based on nonlinear time series analysis (collectively referred to as empirical dynamic modelling), we identified drivers and their interactive effects on dengue dynamics in San Juan, Puerto Rico. Climatic forcing arose only when susceptible availability was high: temperature and rainfall had net positive and negative effects respectively. By capturing mechanistic, nonlinear and context-dependent effects of population susceptibility, temperature and rainfall on dengue transmission empirically, our model improves forecast skill over recent, state-of-the-art models for dengue incidence. Together, these results provide empirical evidence that the interdependence of host population susceptibility and climate drives dengue dynamics in a nonlinear and complex, yet predictable way.
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Affiliation(s)
- Nicole Nova
- Department of Biology, Stanford University, Stanford, CA, USA
| | - Ethan R. Deyle
- Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA, USA
- Department of Biology, Boston University, Boston, MA, USA
| | - Marta S. Shocket
- Department of Biology, Stanford University, Stanford, CA, USA
- Department of Ecology and Evolutionary Biology, University of California Los Angeles, Los Angeles, CA, USA
| | - Andrew J. MacDonald
- Department of Biology, Stanford University, Stanford, CA, USA
- Earth Research Institute & Bren School of Environmental Science and Management, University of California Santa Barbara, Santa Barbara, CA, USA
| | - Marissa L. Childs
- Emmett Interdisciplinary Program in Environment and Resources, Stanford University, Stanford, CA, USA
| | - Martin Rypdal
- Department of Mathematics and Statistics, UiT The Arctic University of Norway, Tromsø, Norway
| | - George Sugihara
- Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA, USA
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Stern BD, Hegedus EJ, Lai YC. State dependence: Does a prior injury predict a future injury? Phys Ther Sport 2021; 49:8-14. [PMID: 33550203 DOI: 10.1016/j.ptsp.2021.01.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Revised: 01/14/2021] [Accepted: 01/19/2021] [Indexed: 12/20/2022]
Abstract
The sports medicine literature is filled with associations between injury and causal factors. However, those results have been inconsistent. We're left wondering which of our athletes might need more attention and where our efforts might be best spent. Resistance to injury is the result of interaction between many variables. These variables are interdependent with dynamic relationships which can be sometimes correlated, at times anti-correlated and from time to time show no relationship with injury risk. Relationships we may have seen yesterday do not necessarily hold true for today and we should not use those to infer what will happen. This perspective piece builds on prior works and describes how the complex interaction between injury determinants presents in other systems, why determinants are not stable and instead vary over time due to internal and external forcing and why our prediction ability remains limited even when determinants are identified. Patterns built from frequent time series data in conjunction with nonlinear dynamical methods can offer us a new approach to thinking about injury prediction.
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Affiliation(s)
- Benjamin D Stern
- Department of Outpatient Rehabilitation, HonorHealth, Scottsdale, AZ, USA.
| | - Eric J Hegedus
- Physical Therapy Program, School of Medicine, Tufts University, Boston, MA, USA
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, USA
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Barraquand F, Picoche C, Detto M, Hartig F. Inferring species interactions using Granger causality and convergent cross mapping. THEOR ECOL-NETH 2020. [DOI: 10.1007/s12080-020-00482-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Zhao N, Charland K, Carabali M, Nsoesie EO, Maheu-Giroux M, Rees E, Yuan M, Garcia Balaguera C, Jaramillo Ramirez G, Zinszer K. Machine learning and dengue forecasting: Comparing random forests and artificial neural networks for predicting dengue burden at national and sub-national scales in Colombia. PLoS Negl Trop Dis 2020; 14:e0008056. [PMID: 32970674 PMCID: PMC7537891 DOI: 10.1371/journal.pntd.0008056] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Revised: 10/06/2020] [Accepted: 08/12/2020] [Indexed: 01/05/2023] Open
Abstract
The robust estimate and forecast capability of random forests (RF) has been widely recognized, however this ensemble machine learning method has not been widely used in mosquito-borne disease forecasting. In this study, two sets of RF models were developed at the national (pooled department-level data) and department level in Colombia to predict weekly dengue cases for 12-weeks ahead. A pooled national model based on artificial neural networks (ANN) was also developed and used as a comparator to the RF models. The various predictors included historic dengue cases, satellite-derived estimates for vegetation, precipitation, and air temperature, as well as population counts, income inequality, and education. Our RF model trained on the pooled national data was more accurate for department-specific weekly dengue cases estimation compared to a local model trained only on the department's data. Additionally, the forecast errors of the national RF model were smaller to those of the national pooled ANN model and were increased with the forecast horizon increasing from one-week-ahead (mean absolute error, MAE: 9.32) to 12-weeks ahead (MAE: 24.56). There was considerable variation in the relative importance of predictors dependent on forecast horizon. The environmental and meteorological predictors were relatively important for short-term dengue forecast horizons while socio-demographic predictors were relevant for longer-term forecast horizons. This study demonstrates the potential of RF in dengue forecasting with a feasible approach of using a national pooled model to forecast at finer spatial scales. Furthermore, including sociodemographic predictors is likely to be helpful in capturing longer-term dengue trends.
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Affiliation(s)
- Naizhuo Zhao
- Department of Land Resource Management, School of Humanities and Law, Northeastern University, Shenyang, Liaoning, China
- Division of Clinical Epidemiology, McGill University Health Centre, Montreal, Quebec, Canada
| | - Katia Charland
- Centre for Public Health Research, Montreal, Quebec, Canada
| | - Mabel Carabali
- Department of Epidemiology, Biostatistics, and Occupational Health, School of Population and Global Health, McGill University, Montreal, Quebec, Canada
| | - Elaine O. Nsoesie
- Department of Global Health, Boston University, Boston, Massachusetts, United States of America
| | - Mathieu Maheu-Giroux
- Department of Epidemiology, Biostatistics, and Occupational Health, School of Population and Global Health, McGill University, Montreal, Quebec, Canada
- Quebec Population Health Research Network, Montreal, Quebec, Canada
| | - Erin Rees
- Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, Saint-Hyacinthe, Quebec, Canada
| | - Mengru Yuan
- Department of Epidemiology, Biostatistics, and Occupational Health, School of Population and Global Health, McGill University, Montreal, Quebec, Canada
| | | | | | - Kate Zinszer
- Centre for Public Health Research, Montreal, Quebec, Canada
- Quebec Population Health Research Network, Montreal, Quebec, Canada
- Department of Preventive and Social Medicine, School of Public Health, University of Montreal, Montreal, Quebec, Canada
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